ExtraNodesetGenerator

nodes

C++ Type:std::vector<unsigned int>

Controllable:No

Description:The nodes you want to be in the nodeset (Either this parameter or "coord" must be supplied).

(modules/solid_mechanics/test/tests/finite_strain_elastic_anisotropy/3d_bar_orthotropic_full_rotation_ad.i)

[Mesh]
  [generated_mesh]
    type = GeneratedMeshGenerator
    dim = 3
    xmin = 0
    xmax = 2
    ymin = 0
    ymax = 10
    zmin = 0
    zmax = 2
    nx = 1
    ny = 1
    nz = 1
    elem_type = HEX8
  []
  [corner]
    type = ExtraNodesetGenerator
    new_boundary = 101
    coord = '0 0 0'
    input = generated_mesh
  []
  [side]
    type = ExtraNodesetGenerator
    new_boundary = 102
    coord = '2 0 0'
    input = corner
  []
[]

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = FINITE
    add_variables = true
    use_finite_deform_jacobian = true
    volumetric_locking_correction = false
    generate_output = 'stress_xx stress_yy stress_zz stress_xy stress_xz'
    use_automatic_differentiation = true
  []
[]

[Materials]
  [stress]
    type = ADComputeFiniteStrainElasticStress
  []
  [elasticity_tensor]
    type = ADComputeElasticityTensor
    fill_method = orthotropic
    C_ijkl = '2.0e3 2.0e5 2.0e3 0.71428571e3 0.71428571e3 0.71428571e3 0.4 0.2 0.004 0.004 0.2 0.4'
  []
[]

[BCs]
  [fix_z]
    type = ADDirichletBC
    variable = disp_z
    boundary = bottom
    value = 0
  []

  [rot_y]
    type = DisplacementAboutAxis
    boundary = bottom
    function = t
    angle_units = degrees
    axis_origin = '0. 0. 0.'
    axis_direction = '0. 0. 1.'
    component = 1
    variable = disp_y
  []
  #
  [rot_x]
    type = DisplacementAboutAxis
    boundary = bottom
    function = t
    angle_units = degrees
    axis_origin = '0. 0. 0.'
    axis_direction = '0. 0. 1.'
    component = 0
    variable = disp_x
  []

  [rot_y90]
    type = DisplacementAboutAxis
    boundary = bottom
    function = 360
    angle_units = degrees
    axis_origin = '0. 0. 0.'
    axis_direction = '0. 0. 1.'
    component = 1
    variable = disp_y
  []
  #
  [rot_x90]
    type = DisplacementAboutAxis
    boundary = bottom
    function = 360
    angle_units = degrees
    axis_origin = '0. 0. 0.'
    axis_direction = '0. 0. 1.'
    component = 0
    variable = disp_x
  []

  [press]
    boundary = top
    function = '-1.0*(t-360)*10.0'
    use_displaced_mesh = true
    displacements = 'disp_x disp_y disp_z'
    type = Pressure
    variable = disp_y
  []

[]

[Controls]
  [c1]
    type = TimePeriod
    enable_objects = 'BCs::rot_x BCs::rot_y'
    disable_objects = 'BCs::rot_x90 BCs::rot_y90 BCs::press'
    start_time = '0'
    end_time = '360'
  []
  [c190plus]
    type = TimePeriod
    enable_objects = 'BCs::rot_x90 BCs::rot_y90 BCs::press'
    disable_objects = 'BCs::rot_x BCs::rot_y '
    start_time = '360'
    end_time = '660'
  []
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-ksp_gmres_restart'
  petsc_options_value = '101'

  line_search = 'none'

  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-08
  nl_max_its = 50

  l_tol = 1e-4
  l_max_its = 50
  start_time = 0.0

  dt = 5
  dtmin = 5

  num_steps = 132
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Outputs]
  exodus = true
[]

(modules/combined/test/tests/optimization/compliance_sensitivity/2d_mmb_2material_cost.i)

vol_frac = 0.5

power = 3

E0 = 1.0e-6
E1 = 0.3
E2 = 1.0

rho0 = 1.0e-6
rho1 = 0.3
rho2 = 1.0

C0 = 1.0e-6
C1 = 0.5
C2 = 1.0

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  [MeshGenerator]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 150
    ny = 50
    xmin = 0
    xmax = 30
    ymin = 0
    ymax = 10
  []
  [node]
    type = ExtraNodesetGenerator
    input = MeshGenerator
    new_boundary = hold
    nodes = 0
  []
  [push]
    type = ExtraNodesetGenerator
    input = node
    new_boundary = push
    coord = '30 10 0'
  []
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
[]

[AuxVariables]
  [Dc]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = -1.0
  []
  [mat_den]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = ${vol_frac}
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = SMALL
    add_variables = true
    incremental = false
  []
[]

[BCs]
  [no_x]
    type = DirichletBC
    variable = disp_y
    boundary = hold
    value = 0.0
  []
  [no_y]
    type = DirichletBC
    variable = disp_x
    boundary = right
    value = 0.0
  []

[]
[NodalKernels]
  [push]
    type = NodalGravity
    variable = disp_y
    boundary = push
    gravity_value = -1
    mass = 1
  []
[]
[Materials]
  [elasticity_tensor]
    type = ComputeVariableIsotropicElasticityTensor
    youngs_modulus = E_phys
    poissons_ratio = poissons_ratio
    args = 'mat_den'
  []
  [E_phys]
    type = DerivativeParsedMaterial
    # ordered multimaterial simp
    expression = "A1:=(${E0}-${E1})/(${rho0}^${power}-${rho1}^${power}); "
                 "B1:=${E0}-A1*${rho0}^${power}; E1:=A1*mat_den^${power}+B1; "
                 "A2:=(${E1}-${E2})/(${rho1}^${power}-${rho2}^${power}); "
                 "B2:=${E1}-A2*${rho1}^${power}; E2:=A2*mat_den^${power}+B2; "
                 "if(mat_den<${rho1},E1,E2)"
    coupled_variables = 'mat_den'
    property_name = E_phys
  []
  [Cost]
    type = DerivativeParsedMaterial
    # ordered multimaterial simp
    expression = "A1:=(${C0}-${C1})/(${rho0}^${power}-${rho1}^${power}); "
                 "B1:=${C0}-A1*${rho0}^${power}; C1:=A1*mat_den^${power}+B1; "
                 "A2:=(${C1}-${C2})/(${rho1}^${power}-${rho2}^${power}); "
                 "B2:=${C1}-A2*${rho1}^${power}; C2:=A2*mat_den^${power}+B2; "
                 "if(mat_den<${rho1},C1,C2)"
    coupled_variables = 'mat_den'
    property_name = Cost
  []
  [poissons_ratio]
    type = GenericConstantMaterial
    prop_names = poissons_ratio
    prop_values = 0.3
  []
  [stress]
    type = ComputeLinearElasticStress
  []
  [dc]
    type = ComplianceSensitivity
    design_density = mat_den
    youngs_modulus = E_phys
  []
  [cc]
    type = CostSensitivity
    design_density = mat_den
    cost = Cost
    outputs = 'exodus'
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[UserObjects]
  [rad_avg]
    type = RadialAverage
    radius = 1.2
    weights = linear
    prop_name = sensitivity
    execute_on = TIMESTEP_END
    force_preaux = true
  []
  [update]
    type = DensityUpdate
    density_sensitivity = Dc
    design_density = mat_den
    volume_fraction = ${vol_frac}
    execute_on = TIMESTEP_BEGIN
  []
  [calc_sense]
    type = SensitivityFilter
    density_sensitivity = Dc
    design_density = mat_den
    filter_UO = rad_avg
    execute_on = TIMESTEP_END
    force_postaux = true
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'
  nl_abs_tol = 1e-8
  dt = 1.0
  num_steps = 70
[]

[Outputs]
  exodus = true
  [out]
    type = CSV
    execute_on = 'TIMESTEP_END'
  []
  print_linear_residuals = false
[]

[Postprocessors]
  [total_vol]
    type = ElementIntegralVariablePostprocessor
    variable = mat_den
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [sensitivity]
    type = ElementIntegralMaterialProperty
    mat_prop = sensitivity
  []
[]

(test/tests/mortar/ad_periodic_segmental_constraint/penalty_periodic_simple3d.i)

[Mesh]
  [left_block]
    type = GeneratedMeshGenerator
    dim = 3
    xmin = -3.0
    xmax = 3.0
    ymin = -3.0
    ymax = 3.0
    zmin = -3.0
    zmax = 3.0
    nx = 3
    ny = 3
    nz = 3
    elem_type = HEX8
  []
  [left_block_sidesets]
    type = RenameBoundaryGenerator
    input = left_block
    old_boundary = '0 1 2 3 4 5'
    new_boundary = '10 11 12 13 14 15'
  []
  [left_block_id]
    type = SubdomainIDGenerator
    input = left_block_sidesets
    subdomain_id = 1
  []
  [left]
    type = LowerDBlockFromSidesetGenerator
    input = left_block_id
    sidesets = '14'
    new_block_id = '10004'
    new_block_name = 'secondary_left'
  []
  [right]
    type = LowerDBlockFromSidesetGenerator
    input = left
    sidesets = '12'
    new_block_id = '10002'
    new_block_name = 'primary_right'
  []
  [bottom]
    type = LowerDBlockFromSidesetGenerator
    input = right
    sidesets = '10'
    new_block_id = '10000'
    new_block_name = 'secondary_bottom'
  []
  [top]
    type = LowerDBlockFromSidesetGenerator
    input = bottom
    sidesets = '15'
    new_block_id = '10005'
    new_block_name = 'primary_top'
  []
  [back]
    type = LowerDBlockFromSidesetGenerator
    input = top
    sidesets = '11'
    new_block_id = '10001'
    new_block_name = 'secondary_back'
  []
  [front]
    type = LowerDBlockFromSidesetGenerator
    input = back
    sidesets = '13'
    new_block_id = '10003'
    new_block_name = 'primary_front'
  []

  [corner_node]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node'
    nodes = '0'
    input = front
  []
[]

[Variables]
  [u]
    order = FIRST
    family = LAGRANGE
  []
  [epsilon]
    order = THIRD
    family = SCALAR
  []
[]

[AuxVariables]
  [sigma]
    order = THIRD
    family = SCALAR
  []
[]

[AuxScalarKernels]
  [sigma]
    type = FunctionScalarAux
    variable = sigma
    function = '1 2 3'
    execute_on = initial #timestep_end
  []
[]

[Kernels]
  [diff1]
    type = ADDiffusion
    variable = u
    block = 1
  []
[]

[Problem]
  kernel_coverage_check = false
  error_on_jacobian_nonzero_reallocation = true
[]

[BCs]
  [fix_right]
    type = DirichletBC
    variable = u
    boundary = pinned_node
    value = 0
  []
[]

[Constraints]
  [mortarlr]
    type = ADPenaltyEqualValueConstraint
    primary_boundary = '12'
    secondary_boundary = '14'
    primary_subdomain = 'primary_right'
    secondary_subdomain = 'secondary_left'
    secondary_variable = u
    correct_edge_dropping = true
    penalty_value = 1.e2
  []
  [periodiclr]
    type = ADPenaltyPeriodicSegmentalConstraint
    primary_boundary = '12'
    secondary_boundary = '14'
    primary_subdomain = 'primary_right'
    secondary_subdomain = 'secondary_left'
    secondary_variable = u
    epsilon = epsilon
    sigma = sigma
    correct_edge_dropping = true
    penalty_value = 1.e2
  []
  [mortarbt]
    type = ADPenaltyEqualValueConstraint
    primary_boundary = '15'
    secondary_boundary = '10'
    primary_subdomain = 'primary_top'
    secondary_subdomain = 'secondary_bottom'
    secondary_variable = u
    correct_edge_dropping = true
    penalty_value = 1.e2
  []
  [periodicbt]
    type = ADPenaltyPeriodicSegmentalConstraint
    primary_boundary = '15'
    secondary_boundary = '10'
    primary_subdomain = 'primary_top'
    secondary_subdomain = 'secondary_bottom'
    secondary_variable = u
    epsilon = epsilon
    sigma = sigma
    correct_edge_dropping = true
    penalty_value = 1.e2
  []
  [mortarbf]
    type = ADPenaltyEqualValueConstraint
    primary_boundary = '13'
    secondary_boundary = '11'
    primary_subdomain = 'primary_front'
    secondary_subdomain = 'secondary_back'
    secondary_variable = u
    correct_edge_dropping = true
    penalty_value = 1.e2
  []
  [periodicbf]
    type = ADPenaltyPeriodicSegmentalConstraint
    primary_boundary = '13'
    secondary_boundary = '11'
    primary_subdomain = 'primary_front'
    secondary_subdomain = 'secondary_back'
    secondary_variable = u
    epsilon = epsilon
    sigma = sigma
    correct_edge_dropping = true
    penalty_value = 1.e2
  []
[]

[Preconditioning]
  [smp]
    full = true
    type = SMP
  []
[]

[Executioner]
  type = Steady
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  solve_type = NEWTON
[]

[Outputs]
#  exodus = true
  csv = true
[]

(modules/combined/test/tests/restart-transient-from-ss-with-stateful/sub_tr.i)

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    nx = 8
    ny = 8
    xmin = -82.627
    xmax = 82.627
    ymin = -82.627
    ymax = 82.627
    dim = 2
  []
  [./extra_nodes_x]
    type = ExtraNodesetGenerator
    input = 'gen'
    new_boundary = 'no_x'
    coord = '0 82.627 0'
  [../]
  [./extra_nodes_y]
    type = ExtraNodesetGenerator
    input = 'extra_nodes_x'
    new_boundary = 'no_y'
    coord = '-82.627 0 0'
  [../]
[]

[Problem]
  type = ReferenceResidualProblem
  reference_vector = 'ref'
  extra_tag_vectors = 'ref'
[]

[AuxVariables]
  [./temp]
  [../]
[]

[Physics/SolidMechanics/QuasiStatic]
  # FINITE strain when strain is large, i.e., visible movement.
  # SMALL strain when things are stressed, but may not move.
  [./fuel]
    add_variables = true
    strain = FINITE
    temperature = temp
    eigenstrain_names = 'thermal_eigenstrain'
    generate_output = 'vonmises_stress stress_xx stress_yy hydrostatic_stress max_principal_stress strain_xy elastic_strain_xx stress_xy'
    extra_vector_tags = 'ref'
    use_finite_deform_jacobian = true
    incremental = true
  [../]
[]

[BCs]
  [./no_x]
    type = DirichletBC
    variable = disp_x
    boundary = 'no_x'
    value = 0.0
    preset = true
  [../]
  [./no_y]
    type = DirichletBC
    preset = true
    variable = disp_y
    boundary = 'no_y'
    value = 0.0
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 3e10   # Pa
    poissons_ratio = 0.33    # unitless
  [../]
  [./thermal_strains]
    type = ComputeThermalExpansionEigenstrain
    temperature = temp
    thermal_expansion_coeff = 2e-6 # 1/K
    stress_free_temperature = 500 # K
    eigenstrain_name = 'thermal_eigenstrain'
  [../]
  [./stress_finite] # goes with FINITE strain formulation
    type = ComputeFiniteStrainElasticStress
  [../]
[]

[Postprocessors]
  [./avg_temp]
    type = ElementAverageValue
    variable = temp
    execute_on = 'initial timestep_end'
  [../]
  [./disp_x_max_element]
    type = ElementExtremeValue
    value_type = max
    variable = disp_x
    execute_on = 'initial timestep_end'
  [../]
  [./disp_y_max_element]
    type = ElementExtremeValue
    value_type = max
    variable = disp_y
    execute_on = 'initial timestep_end'
  [../]
  [./disp_x_max_nodal]
    type = NodalExtremeValue
    value_type = max
    variable = disp_x
    execute_on = 'initial timestep_end'
  [../]
  [./disp_y_max_nodal]
    type = NodalExtremeValue
    value_type = max
    variable = disp_y
    execute_on = 'initial timestep_end'
  [../]
[]

[Executioner]
  type = Transient
  petsc_options_iname = '-pc_type -pc_hypre_type -ksp_gmres_restart'
  petsc_options_value = 'hypre boomeramg 300'
  line_search = 'none'

  l_tol = 1e-02
  nl_rel_tol = 5e-04
  nl_abs_tol = 1e-2

  l_max_its = 50
  nl_max_its = 25

  start_time = 0
  end_time = 40
  dt = 10
[]

[Outputs]
  print_linear_residuals = false
  perf_graph = true
  exodus = true
[]

(modules/solid_mechanics/test/tests/lagrangian/cartesian/total/homogenization/action/2d_pbc_symmetry.i)

# 2D thermomechanical coupling
# strain periodicity in +-x
# symmetry about the -y plane (i.e. bottom)

[GlobalParams]
  displacements = 'disp_x disp_y'
  large_kinematics = true
[]

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 3
    ny = 3
  []
  [pins]
    type = ExtraNodesetGenerator
    input = 'gmg'
    new_boundary = 'pin'
    coord = '0 0 0'
  []
[]

[Variables]
  [T]
    initial_condition = 300
  []
[]

[Kernels]
  [htime]
    type = CoefTimeDerivative
    variable = 'T'
    Coefficient = 1
  []
  [hcond]
    type = MatDiffusion
    variable = 'T'
    diffusivity = 1e-4
  []
  [hsource]
    type = MatBodyForce
    variable = 'T'
    material_property = source
  []
[]

[Physics]
  [SolidMechanics]
    [QuasiStatic]
      [all]
        strain = FINITE
        add_variables = true
        new_system = true
        formulation = TOTAL
        volumetric_locking_correction = false
        temperature = T
        eigenstrain_names = 'thermal_egs'
        constraint_types = 'strain none none none none none none none none'
        targets = '0'
        generate_output = 'strain_xx strain_xy strain_yy'
      []
    []
  []
[]

[BCs]
  [Periodic]
    [x]
      variable = 'disp_x'
      auto_direction = 'x'
    []
    [y]
      variable = 'disp_y'
      auto_direction = 'x'
    []
    [T]
      variable = 'T'
      auto_direction = 'x'
    []
  []
  # remove rigid body modes
  [fix_x]
    type = DirichletBC
    boundary = 'pin'
    variable = 'disp_x'
    value = 0
  []
  # symmetry
  [symmetry]
    type = DirichletBC
    boundary = 'bottom'
    variable = 'disp_y'
    value = 0
  []
[]

[Functions]
  [source]
    type = ParsedFunction
    expression = '3*sin(2*pi*x)-y^2'
  []
[]

[Materials]
  [source]
    type = GenericFunctionMaterial
    prop_names = 'source'
    prop_values = 'source'
  []
  [thermal_egs]
    type = ComputeThermalExpansionEigenstrain
    eigenstrain_name = 'thermal_egs'
    stress_free_temperature = 300
    thermal_expansion_coeff = 5e-3
    temperature = 'T'
  []
  [C]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 1e5
    poissons_ratio = 0.3
  []
  [stress]
    type = ComputeLagrangianLinearElasticStress
    objective_rate = jaumann
  []
[]

[Executioner]
  type = Transient

  solve_type = 'NEWTON'
  line_search = none
  automatic_scaling = true

  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'

  nl_max_its = 10
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-10

  dt = 1
  end_time = 2
[]

[Outputs]
  exodus = true
[]

(modules/solid_mechanics/test/tests/auxkernels/ranktwoscalaraux.i)

[Mesh]
  displacements = 'disp_x disp_y disp_z'
  [generated_mesh]
    type = GeneratedMeshGenerator
    elem_type = HEX8
    dim = 3
    nx = 1
    ny = 1
    nz = 1
    xmin = 0.0
    xmax = 1.0
    ymin = 0.0
    ymax = 1.0
    zmin = 0.0
    zmax = 1.0
  []
  [node]
    type = ExtraNodesetGenerator
    coord = '0.0 0.0 0.0'
    new_boundary = 6
    input = generated_mesh
  []
  [snode]
    type = ExtraNodesetGenerator
    coord = '1.0 0.0 0.0'
    new_boundary = 7
    input = node
  []
[]

[Variables]
  [./disp_x]
    order = FIRST
    family = LAGRANGE
  [../]
 [./disp_y]
    order = FIRST
    family = LAGRANGE
  [../]
  [./disp_z]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [SolidMechanics]
    displacements = 'disp_x disp_y disp_z'
  [../]
[]



[Materials]
  [./fplastic]
    type = FiniteStrainPlasticMaterial
    block = 0
    yield_stress='0. 445. 0.05 610. 0.1 680. 0.38 810. 0.95 920. 2. 950.'
  [../]
  [./elasticity_tensor]
    type = ComputeElasticityTensor
    block = 0
    C_ijkl = '2.827e5 1.21e5 1.21e5 2.827e5 1.21e5 2.827e5 0.808e5 0.808e5 0.808e5'
    fill_method = symmetric9
  [../]
  [./strain]
    type = ComputeFiniteStrain
    block = 0
    displacements = 'disp_x disp_y disp_z'
  [../]
[]

[Functions]
 [./topfunc]
   type = ParsedFunction
   expression = 't'
 [../]
[]

[BCs]
  [./bottom3]
    type = DirichletBC
    variable = disp_z
    boundary = 0
    value = 0.0
  [../]
  [./top]
    type = FunctionDirichletBC
    variable = disp_z
    boundary = 5
    function = topfunc
  [../]
  [./corner1]
    type = DirichletBC
    variable = disp_x
    boundary = 6
    value = 0.0
  [../]
  [./corner2]
    type = DirichletBC
    variable = disp_y
    boundary = 6
    value = 0.0
  [../]
  [./corner3]
    type = DirichletBC
    variable = disp_z
    boundary = 6
    value = 0.0
  [../]
  [./side1]
    type = DirichletBC
    variable = disp_y
    boundary = 7
    value = 0.0
  [../]
  [./side2]
    type = DirichletBC
    variable = disp_z
    boundary = 7
    value = 0.0
  [../]
[]

[AuxVariables]
  [./stress_zz]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./vonmises]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./hydrostatic]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./L2norm]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[AuxKernels]
  [./stress_zz]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_zz
    index_i = 2
    index_j = 2
  [../]
  [./vonmises]
    type = RankTwoScalarAux
    rank_two_tensor = stress
    variable = vonmises
    scalar_type = VonMisesStress
  [../]
  [./hydrostatic]
    type = RankTwoScalarAux
    rank_two_tensor = stress
    variable = hydrostatic
    scalar_type = Hydrostatic
  [../]
  [./L2norm]
    type = RankTwoScalarAux
    rank_two_tensor = stress
    variable = L2norm
    scalar_type = L2norm
  [../]
[]

[Postprocessors]
  [./stress_zz]
    type = ElementAverageValue
    variable = stress_zz
  [../]
  [./vonmises]
    type = ElementAverageValue
    variable = vonmises
  [../]
  [./hydrostatic]
    type = ElementAverageValue
    variable = hydrostatic
  [../]
  [./L2norm]
    type = ElementAverageValue
    variable = L2norm
  [../]
[]

[Executioner]

  type = Transient

  dt=0.1
  dtmin=0.1
  dtmax=1
  end_time=1.0

  #Preconditioned JFNK (default)
  solve_type = 'PJFNK'

  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-10
[]

[Outputs]
  exodus = true
[]

(test/tests/meshgenerators/extra_nodeset_generator/generate_extra_nodeset_multiple_coord.i)

[Mesh]
  [./gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 2
    ny = 2
  []

  [./eng1]
    type = ExtraNodesetGenerator
    input = gen
    new_boundary = 'corner'
    coord = '0.5 1; 1 1; 1 0.5'
  []
  [./eng2]
    type = ExtraNodesetGenerator
    input = eng1
    new_boundary = 'single'
    coord = '0 0'
  []
[]

[Outputs]
  exodus = true
[]

(modules/combined/examples/optimization/multi-load/square_subapp_one.i)

power = 1.0
E0 = 1.0
Emin = 1.0e-6

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  [Bottom]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 100
    ny = 100
    xmin = 0
    xmax = 150
    ymin = 0
    ymax = 150
  []
  [left_load]
    type = ExtraNodesetGenerator
    input = Bottom
    new_boundary = left_load
    coord = '0 150 0'
  []
  [right_load]
    type = ExtraNodesetGenerator
    input = left_load
    new_boundary = right_load
    coord = '150 150 0'
  []
  [left_support]
    type = ExtraNodesetGenerator
    input = right_load
    new_boundary = left_support
    coord = '0 0 0'
  []
  [right_support]
    type = ExtraNodesetGenerator
    input = left_support
    new_boundary = right_support
    coord = '150 0 0'
  []
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
[]

[AuxVariables]
  [Dc]
    family = MONOMIAL
    order = SECOND
    initial_condition = -1.0
  []
  [Cc]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = -1.0
  []
  [mat_den]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = 0.25
  []
  [sensitivity_var]
    family = MONOMIAL
    order = SECOND
    initial_condition = -1.0
  []
[]

[AuxKernels]
  [sensitivity_kernel]
    type = MaterialRealAux
    property = sensitivity
    variable = sensitivity_var
    check_boundary_restricted = false
    execute_on = 'TIMESTEP_END'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = SMALL
    add_variables = true
    incremental = false
  []
[]

[BCs]
  [no_y]
    type = DirichletBC
    variable = disp_y
    boundary = left_support
    value = 0.0
  []
  [no_x]
    type = DirichletBC
    variable = disp_x
    boundary = left_support
    value = 0.0
  []
  [no_y_right]
    type = DirichletBC
    variable = disp_y
    boundary = right_support
    value = 0.0
  []
  [no_x_right]
    type = DirichletBC
    variable = disp_x
    boundary = right_support
    value = 0.0
  []
[]

[NodalKernels]
  [push_left]
    type = NodalGravity
    variable = disp_y
    boundary = left_load
    gravity_value = -1e-3
    mass = 1
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeVariableIsotropicElasticityTensor
    youngs_modulus = E_phys
    poissons_ratio = poissons_ratio
    args = 'mat_den'
  []
  [E_phys]
    type = DerivativeParsedMaterial
    # Emin + (density^penal) * (E0 - Emin)
    expression = '${Emin} + (mat_den ^ ${power}) * (${E0}-${Emin})'
    coupled_variables = 'mat_den'
    property_name = E_phys
  []
  [poissons_ratio]
    type = GenericConstantMaterial
    prop_names = poissons_ratio
    prop_values = 0.3
  []
  [stress]
    type = ComputeLinearElasticStress
  []
  [dc]
    type = ComplianceSensitivity
    design_density = mat_den
    youngs_modulus = E_phys
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[UserObjects]
  # We do averaging in subapps
  [rad_avg]
    type = RadialAverage
    radius = 8
    weights = linear
    prop_name = sensitivity
    force_preaux = true
    execute_on = 'TIMESTEP_END'
  []
  # Provides Dc
  [calc_sense]
    type = SensitivityFilter
    density_sensitivity = Dc
    design_density = mat_den
    filter_UO = rad_avg
    force_postaux = true
    execute_on = 'TIMESTEP_END'
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'
  nl_abs_tol = 1e-10
  dt = 1.0
  num_steps = 10
[]

[Outputs]
  exodus = true
  [out]
    type = CSV
    execute_on = 'TIMESTEP_END'
  []
  print_linear_residuals = false
[]

[Postprocessors]
  [mesh_volume]
    type = VolumePostprocessor
    execute_on = 'initial timestep_end'
  []
  [total_vol]
    type = ElementIntegralVariablePostprocessor
    variable = mat_den
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [vol_frac]
    type = ParsedPostprocessor
    expression = 'total_vol / mesh_volume'
    pp_names = 'total_vol mesh_volume'
  []
  [sensitivity]
    type = ElementIntegralMaterialProperty
    mat_prop = sensitivity
    execute_on = 'TIMESTEP_BEGIN TIMESTEP_END NONLINEAR'
  []
  [objective]
    type = ElementIntegralMaterialProperty
    mat_prop = strain_energy_density
    execute_on = 'INITIAL TIMESTEP_END'
  []
[]

(modules/solid_mechanics/test/tests/finite_strain_elastic_anisotropy/3d_bar_orthotropic_90deg_rotation_ad.i)

[Mesh]
  [generated_mesh]
    type = GeneratedMeshGenerator
    dim = 3
    xmin = 0
    xmax = 2
    ymin = 0
    ymax = 10
    zmin = 0
    zmax = 2
    nx = 1
    ny = 1
    nz = 1
    elem_type = HEX8
  []
  [corner]
    type = ExtraNodesetGenerator
    new_boundary = 101
    coord = '0 0 0'
    input = generated_mesh
  []
  [side]
    type = ExtraNodesetGenerator
    new_boundary = 102
    coord = '2 0 0'
    input = corner
  []
[]

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = FINITE
    add_variables = true
    use_finite_deform_jacobian = true
    volumetric_locking_correction = false
    use_automatic_differentiation = true
    generate_output = 'stress_xx stress_yy stress_zz stress_xy stress_xz'
  []
[]

[Materials]
  [stress]
    type = ADComputeFiniteStrainElasticStress
  []
  [elasticity_tensor]
    type = ADComputeElasticityTensor
    fill_method = orthotropic
    C_ijkl = '2.0e3 2.0e5 2.0e3 0.71428571e3 0.71428571e3 0.71428571e3 0.4 0.2 0.004 0.004 0.2 0.4'
  []
[]

[BCs]
  [fix_z]
    type = ADDirichletBC
    variable = disp_z
    boundary = bottom
    value = 0
  []

  [rot_y]
    type = DisplacementAboutAxis
    boundary = bottom
    function = t
    angle_units = degrees
    axis_origin = '0. 0. 0.'
    axis_direction = '0. 0. 1.'
    component = 1
    variable = disp_y
  []
  #
  [rot_x]
    type = DisplacementAboutAxis
    boundary = bottom
    function = t
    angle_units = degrees
    axis_origin = '0. 0. 0.'
    axis_direction = '0. 0. 1.'
    component = 0
    variable = disp_x
  []

  [rot_y90]
    type = DisplacementAboutAxis
    boundary = bottom
    function = 90
    angle_units = degrees
    axis_origin = '0. 0. 0.'
    axis_direction = '0. 0. 1.'
    component = 1
    variable = disp_y
  []
  #
  [rot_x90]
    type = DisplacementAboutAxis
    boundary = bottom
    function = 90
    angle_units = degrees
    axis_origin = '0. 0. 0.'
    axis_direction = '0. 0. 1.'
    component = 0
    variable = disp_x
  []

  [press]
    boundary = top
    function = '-1.0*(t-90)*10.0'
    use_displaced_mesh = true
    displacements = 'disp_x disp_y disp_z'
    type = Pressure
    variable = disp_x
  []

[]

[Controls]
  [c1]
    type = TimePeriod
    enable_objects = 'BCs::rot_x BCs::rot_y'
    disable_objects = 'BCs::rot_x90 BCs::rot_y90 BCs::press'
    start_time = '0'
    end_time = '90'
  []
  [c190plus]
    type = TimePeriod
    enable_objects = 'BCs::rot_x90 BCs::rot_y90 BCs::press'
    disable_objects = 'BCs::rot_x BCs::rot_y '
    start_time = '90'
    end_time = '390'
  []
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-ksp_gmres_restart'
  petsc_options_value = '101'

  line_search = 'none'

  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-08
  nl_max_its = 50

  l_tol = 1e-4
  l_max_its = 50
  start_time = 0.0

  dt = 5
  dtmin = 5

  num_steps = 78
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Outputs]
  exodus = true
[]

(modules/combined/test/tests/optimization/compliance_sensitivity/2d_mbb.i)

vol_frac = 0.5
E0 = 1
Emin = 1e-8
power = 2
[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  [MeshGenerator]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 150
    ny = 50
    xmin = 0
    xmax = 30
    ymin = 0
    ymax = 10
  []
  [node]
    type = ExtraNodesetGenerator
    input = MeshGenerator
    new_boundary = hold
    nodes = 0
  []
  [push]
    type = ExtraNodesetGenerator
    input = node
    new_boundary = push
    coord = '30 10 0'
  []
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
[]

[AuxVariables]
  [Dc]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = -1.0
  []
  [mat_den]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = ${vol_frac}
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = SMALL
    add_variables = true
    incremental = false
  []
[]

[BCs]
  [no_x]
    type = DirichletBC
    variable = disp_y
    boundary = hold
    value = 0.0
  []
  [no_y]
    type = DirichletBC
    variable = disp_x
    boundary = right
    value = 0.0
  []

[]
[NodalKernels]
  [push]
    type = NodalGravity
    variable = disp_y
    boundary = push
    gravity_value = -1
    mass = 1
  []
[]
[Materials]
  [elasticity_tensor]
    type = ComputeVariableIsotropicElasticityTensor
    youngs_modulus = E_phys
    poissons_ratio = poissons_ratio
    args = 'mat_den'
  []
  [E_phys]
    type = DerivativeParsedMaterial
    # Emin + (density^penal) * (E0 - Emin)
    expression = '${Emin} + (mat_den ^ ${power}) * (${E0}-${Emin})'
    coupled_variables = 'mat_den'
    property_name = E_phys
  []
  [poissons_ratio]
    type = GenericConstantMaterial
    prop_names = poissons_ratio
    prop_values = 0.3
  []
  [stress]
    type = ComputeLinearElasticStress
  []
  [dc]
    type = ComplianceSensitivity
    design_density = mat_den
    youngs_modulus = E_phys
    incremental = false
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]
[UserObjects]
  [rad_avg]
    type = RadialAverage
    radius = 1.2
    weights = linear
    prop_name = sensitivity
    execute_on = TIMESTEP_END
    force_preaux = true
  []
  [update]
    type = DensityUpdate
    density_sensitivity = Dc
    design_density = mat_den
    volume_fraction = ${vol_frac}
    execute_on = TIMESTEP_BEGIN
  []
  [calc_sense]
    type = SensitivityFilter
    density_sensitivity = Dc
    design_density = mat_den
    filter_UO = rad_avg
    execute_on = TIMESTEP_END
    force_postaux = true
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'
  nl_abs_tol = 1e-8
  dt = 1.0
  num_steps = 70
[]

[Outputs]
  [out]
    type = CSV
    execute_on = 'TIMESTEP_END'
  []
  print_linear_residuals = false
[]

[Postprocessors]
  [total_vol]
    type = ElementIntegralVariablePostprocessor
    variable = mat_den
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [sensitivity]
    type = ElementIntegralMaterialProperty
    mat_prop = sensitivity
  []
[]

(modules/combined/examples/optimization/multi-load/single_subapp_one.i)

power = 2
E0 = 1.0
Emin = 1.0e-6

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  # final_generator = 'MoveRight'
  [Bottom]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 80
    ny = 40
    xmin = 0
    xmax = 150
    ymin = 0
    ymax = 75
  []
  [left_load]
    type = ExtraNodesetGenerator
    input = Bottom
    new_boundary = left_load
    coord = '37.5 75 0'
  []
  [right_load]
    type = ExtraNodesetGenerator
    input = left_load
    new_boundary = right_load
    coord = '112.5 75 0'
  []
  [left_support]
    type = ExtraNodesetGenerator
    input = right_load
    new_boundary = left_support
    coord = '0 0 0'
  []
  [right_support]
    type = ExtraNodesetGenerator
    input = left_support
    new_boundary = right_support
    coord = '150 0 0'
  []
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
[]

[AuxVariables]
  [Dc]
    family = MONOMIAL
    order = SECOND
    initial_condition = -1.0
  []
  [Cc]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = -1.0
  []
  [mat_den]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = 0.1
  []
  [sensitivity_var]
    family = MONOMIAL
    order = SECOND
    initial_condition = -1.0
  []
[]

[AuxKernels]
  [sensitivity_kernel]
    type = MaterialRealAux
    property = sensitivity
    variable = sensitivity_var
    check_boundary_restricted = false
    execute_on = 'TIMESTEP_END'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = SMALL
    add_variables = true
    incremental = false
  []
[]

[BCs]
  [no_y]
    type = DirichletBC
    variable = disp_y
    boundary = left_support
    value = 0.0
  []
  [no_x]
    type = DirichletBC
    variable = disp_x
    boundary = left_support
    value = 0.0
  []
  [no_y_right]
    type = DirichletBC
    variable = disp_y
    boundary = right_support
    value = 0.0
  []
[]

[NodalKernels]
  [push_left]
    type = NodalGravity
    variable = disp_y
    boundary = left_load
    gravity_value = -1e-3
    mass = 1
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeVariableIsotropicElasticityTensor
    youngs_modulus = E_phys
    poissons_ratio = poissons_ratio
    args = 'mat_den'
  []
  [E_phys]
    type = DerivativeParsedMaterial
    # Emin + (density^penal) * (E0 - Emin)
    expression = '${Emin} + (mat_den ^ ${power}) * (${E0}-${Emin})'
    coupled_variables = 'mat_den'
    property_name = E_phys
  []
  [poissons_ratio]
    type = GenericConstantMaterial
    prop_names = poissons_ratio
    prop_values = 0.0
  []
  [stress]
    type = ComputeLinearElasticStress
  []
  [dc]
    type = ComplianceSensitivity
    design_density = mat_den
    youngs_modulus = E_phys
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[UserObjects]
  [rad_avg]
    type = RadialAverage
    radius = 3
    weights = linear
    prop_name = sensitivity
    force_preaux = true
    execute_on = 'TIMESTEP_END'
  []
  # No SIMP optimization in subapp
  [calc_sense]
    type = SensitivityFilter
    density_sensitivity = Dc
    design_density = mat_den
    filter_UO = rad_avg
    force_postaux = true
    execute_on = 'TIMESTEP_END'
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'
  nl_abs_tol = 1e-10
  dt = 1.0
  num_steps = 25
[]

[Outputs]
  exodus = true
  [out]
    type = CSV
    execute_on = 'TIMESTEP_END'
  []
  print_linear_residuals = false
[]

[Postprocessors]
  [mesh_volume]
    type = VolumePostprocessor
    execute_on = 'initial timestep_end'
  []
  [total_vol]
    type = ElementIntegralVariablePostprocessor
    variable = mat_den
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [vol_frac]
    type = ParsedPostprocessor
    expression = 'total_vol / mesh_volume'
    pp_names = 'total_vol mesh_volume'
  []
  [sensitivity]
    type = ElementIntegralMaterialProperty
    mat_prop = sensitivity
    execute_on = 'TIMESTEP_BEGIN TIMESTEP_END NONLINEAR'
  []
  [objective]
    type = ElementIntegralMaterialProperty
    mat_prop = strain_energy_density
    execute_on = 'INITIAL TIMESTEP_END'
  []
[]

(modules/navier_stokes/test/tests/finite_element/ins/mms/supg/supg_adv_dominated_mms.i)

mu=1.5e-2
rho=2.5

[GlobalParams]
  gravity = '0 0 0'
  supg = true
  convective_term = true
  integrate_p_by_parts = false
  transient_term = true
  laplace = true
  u = vel_x
  v = vel_y
  pressure = p
  alpha = 1e0
  order = SECOND
  family = LAGRANGE
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 1.0
    ymin = 0
    ymax = 1.0
    elem_type = QUAD9
    nx = 4
    ny = 4
  []
  [./corner_node]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node'
    nodes = '0'
    input = gen
  [../]
[]

[Variables]
  [./vel_x]
  [../]

  [./vel_y]
  [../]

  [./p]
    order = FIRST
  [../]
[]

[Kernels]
  # mass
  [./mass]
    type = INSMass
    variable = p
  [../]

  [./x_time]
    type = INSMomentumTimeDerivative
    variable = vel_x
  [../]
  [./y_time]
    type = INSMomentumTimeDerivative
    variable = vel_y
  [../]

  # x-momentum, space
  [./x_momentum_space]
    type = INSMomentumLaplaceForm
    variable = vel_x
    component = 0
    forcing_func = vel_x_source_func
  [../]

  # y-momentum, space
  [./y_momentum_space]
    type = INSMomentumLaplaceForm
    variable = vel_y
    component = 1
    forcing_func = vel_y_source_func
  [../]

  [./p_source]
    type = BodyForce
    function = p_source_func
    variable = p
  [../]
[]

[BCs]
  [./vel_x]
    type = FunctionDirichletBC
    boundary = 'left right top bottom'
    function = vel_x_func
    variable = vel_x
  [../]
  [./vel_y]
    type = FunctionDirichletBC
    boundary = 'left right top bottom'
    function = vel_y_func
    variable = vel_y
  [../]
  [./p]
    type = FunctionDirichletBC
    boundary = 'left right top bottom'
    function = p_func
    variable = p
  [../]
[]

[Functions]
  [./vel_x_source_func]
    type = ParsedFunction
    expression = '-${mu}*(-0.028*pi^2*x^2*sin(0.2*pi*x*y) - 0.028*pi^2*y^2*sin(0.2*pi*x*y) - 0.1*pi^2*sin(0.5*pi*x) - 0.4*pi^2*sin(pi*y)) + ${rho}*(0.14*pi*x*cos(0.2*pi*x*y) + 0.4*pi*cos(pi*y))*(0.6*sin(0.8*pi*x) + 0.3*sin(0.3*pi*y) + 0.2*sin(0.3*pi*x*y) + 0.3) + ${rho}*(0.14*pi*y*cos(0.2*pi*x*y) + 0.2*pi*cos(0.5*pi*x))*(0.4*sin(0.5*pi*x) + 0.4*sin(pi*y) + 0.7*sin(0.2*pi*x*y) + 0.5) + 0.1*pi*y*cos(0.2*pi*x*y) + 0.25*pi*cos(0.5*pi*x)'
  [../]
  [./vel_y_source_func]
    type = ParsedFunction
    expression = '-${mu}*(-0.018*pi^2*x^2*sin(0.3*pi*x*y) - 0.018*pi^2*y^2*sin(0.3*pi*x*y) - 0.384*pi^2*sin(0.8*pi*x) - 0.027*pi^2*sin(0.3*pi*y)) + ${rho}*(0.06*pi*x*cos(0.3*pi*x*y) + 0.09*pi*cos(0.3*pi*y))*(0.6*sin(0.8*pi*x) + 0.3*sin(0.3*pi*y) + 0.2*sin(0.3*pi*x*y) + 0.3) + ${rho}*(0.06*pi*y*cos(0.3*pi*x*y) + 0.48*pi*cos(0.8*pi*x))*(0.4*sin(0.5*pi*x) + 0.4*sin(pi*y) + 0.7*sin(0.2*pi*x*y) + 0.5) + 0.1*pi*x*cos(0.2*pi*x*y) + 0.3*pi*cos(0.3*pi*y)'
  [../]
  [./p_source_func]
    type = ParsedFunction
    expression = '-0.06*pi*x*cos(0.3*pi*x*y) - 0.14*pi*y*cos(0.2*pi*x*y) - 0.2*pi*cos(0.5*pi*x) - 0.09*pi*cos(0.3*pi*y)'
  [../]
  [./vel_x_func]
    type = ParsedFunction
    expression = '0.4*sin(0.5*pi*x) + 0.4*sin(pi*y) + 0.7*sin(0.2*pi*x*y) + 0.5'
  [../]
  [./vel_y_func]
    type = ParsedFunction
    expression = '0.6*sin(0.8*pi*x) + 0.3*sin(0.3*pi*y) + 0.2*sin(0.3*pi*x*y) + 0.3'
  [../]
  [./p_func]
    type = ParsedFunction
    expression = '0.5*sin(0.5*pi*x) + 1.0*sin(0.3*pi*y) + 0.5*sin(0.2*pi*x*y) + 0.5'
  [../]
  [./vxx_func]
    type = ParsedFunction
    expression = '0.14*pi*y*cos(0.2*pi*x*y) + 0.2*pi*cos(0.5*pi*x)'
  [../]
[]

[Materials]
  [./const]
    type = GenericConstantMaterial
    block = 0
    prop_names = 'rho mu'
    prop_values = '${rho}  ${mu}'
  [../]
[]

[Preconditioning]
  [./SMP]
    type = SMP
    full = true
    solve_type = 'NEWTON'
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 10
  petsc_options = '-snes_converged_reason -ksp_converged_reason'
  petsc_options_iname = '-pc_type -pc_factor_shift_type'
  petsc_options_value = 'lu NONZERO'
  line_search = 'none'
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-14
  nl_max_its = 10
  l_tol = 1e-6
  l_max_its = 10
  [./TimeStepper]
    dt = .05
    type = IterationAdaptiveDT
    cutback_factor = 0.4
    growth_factor = 1.2
    optimal_iterations = 20
  [../]
[]

[Outputs]
  execute_on = 'final'
  [./exodus]
    type = Exodus
  [../]
  [./csv]
    type = CSV
  [../]
[]

[Postprocessors]
  [./L2vel_x]
    type = ElementL2Error
    variable = vel_x
    function = vel_x_func
    outputs = 'console'    execute_on = 'timestep_end'
  [../]
  [./L2vel_y]
    variable = vel_y
    function = vel_y_func
    type = ElementL2Error
    outputs = 'console'    execute_on = 'timestep_end'
  [../]
  [./L2p]
    variable = p
    function = p_func
    type = ElementL2Error
    outputs = 'console'    execute_on = 'timestep_end'
  [../]
  [./L2vxx]
    variable = vxx
    function = vxx_func
    type = ElementL2Error
    outputs = 'console'    execute_on = 'timestep_end'
  [../]
[]

[AuxVariables]
  [./vxx]
    family = MONOMIAL
    order = FIRST
  [../]
[]

[AuxKernels]
  [./vxx]
    type = VariableGradientComponent
    component = x
    variable = vxx
    gradient_variable = vel_x
  [../]
[]

(modules/solid_mechanics/test/tests/cohesive_zone_model/bilinear_mixed.i)

[Mesh]
  [msh]
    type = GeneratedMeshGenerator
    dim = 2
    xmax = 1
    ymax = 2
    nx = 1
    ny = 2
  []
  [block1]
    type = SubdomainBoundingBoxGenerator
    input = 'msh'
    bottom_left = '0 0 0'
    top_right = '1 1 0'
    block_id = 1
    block_name = 'block1'
  []
  [block2]
    type = SubdomainBoundingBoxGenerator
    input = 'block1'
    bottom_left = '0 1 0'
    top_right = '1 2 0'
    block_id = 2
    block_name = 'block2'
  []
  [split]
    type = BreakMeshByBlockGenerator
    input = block2
  []
  [top_node]
    type = ExtraNodesetGenerator
    coord = '0 2 0'
    input = split
    new_boundary = top_node
  []
  [bottom_node]
    type = ExtraNodesetGenerator
    coord = '0 0 0'
    input = top_node
    new_boundary = bottom_node
  []
[]

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Physics]
  [SolidMechanics]
    [QuasiStatic]
      generate_output = 'stress_yy'
      [all]
        strain = FINITE
        add_variables = true
        use_automatic_differentiation = true
        decomposition_method = TaylorExpansion
      []
    []
  []
[]

[BCs]
  [fix_x]
    type = DirichletBC
    preset = true
    value = 0.0
    boundary = bottom_node
    variable = disp_x
  []

  [fix_top]
    type = DirichletBC
    preset = true
    boundary = top
    variable = disp_x
    value = 0
  []

  [top]
    type = FunctionDirichletBC
    boundary = top
    variable = disp_y
    function = 'if(t<=0.3,t,if(t<=0.6,0.3-(t-0.3),0.6-t))'
    preset = true
  []

  [bottom]
    type = DirichletBC
    boundary = bottom
    variable = disp_y
    value = 0
    preset = true
  []
[]

[Physics/SolidMechanics/CohesiveZone]
  [czm_ik]
    boundary = 'interface'
  []
[]

[Materials]
  [stress]
    type = ADComputeFiniteStrainElasticStress
  []
  [elasticity_tensor]
    type = ADComputeElasticityTensor
    fill_method = symmetric9
    C_ijkl = '1.684e5 0.176e5 0.176e5 1.684e5 0.176e5 1.684e5 0.754e5 0.754e5 0.754e5'
  []
  [czm]
    type = BiLinearMixedModeTraction
    boundary = 'interface'
    penalty_stiffness = 1e6
    GI_c = 1e3
    GII_c = 1e2
    normal_strength = 1e4
    shear_strength = 1e3
    displacements = 'disp_x disp_y'
    eta = 2.2
    viscosity = 1e-3
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient

  solve_type = 'NEWTON'
  line_search = none

  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'

  automatic_scaling = true

  l_max_its = 2
  l_tol = 1e-14
  nl_max_its = 30
  nl_rel_tol = 1e-50
  nl_abs_tol = 1e-15
  start_time = 0.0
  dt = 0.1
  end_time = 1.0
  dtmin = 0.1
[]

[Outputs]
  exodus = true
[]

(modules/navier_stokes/test/tests/finite_element/ins/lid_driven/lid_driven_md.i)

[GlobalParams]
  gravity = '0 0 0'

  order = FIRST
  family = LAGRANGE

  u = vel_x
  v = vel_y
  pressure = p
  temperature = T
  porosity = porosity
  eos = eos
[]

[Mesh]
  [./square]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 0.1
    ymin = 0
    ymax = 0.1
    nx = 20
    ny = 20
    elem_type = QUAD4
  []

  [middle_node]
    type = ExtraNodesetGenerator
    input = square
    new_boundary = 'bottom_left_corner'
    coord = '0 0'
  []
[]

[FluidProperties]
  [./eos]
    type = SimpleFluidProperties
    density0 = 100              # kg/m^3
    thermal_expansion = 0       # K^{-1}
    cp =  1272.0
    viscosity = 0.1             # Pa-s, Re=rho*u*L/mu = 100*1*0.1/0.1 = 100
  [../]
[]

[Variables]
  # velocity
  [./vel_x]
    scaling = 1.e-1
    initial_condition = 0.0
  [../]
  [./vel_y]
    scaling = 1.e-1
    initial_condition = 0.0
  [../]
  # Pressure
  [./p]
    scaling = 1
    initial_condition = 1.0e5
  [../]
[]

[AuxVariables]
  [rho]
    # incompressible flow, rho = constant
    initial_condition = 100
  []
  [T]
    # nothing really depends on T, but eos requires temperature
    initial_condition = 800
  []
  [porosity]
    # nothing really depends on porosity, but PINSFEFluidPressureTimeDerivative requires it
    # need make it conditional
    initial_condition = 1
  []
[]

[Materials]
  [flow_mat]
    type = INSFEMaterial
  []
[]

[Kernels]
  # mass eqn
  [mass_time]
    type = PINSFEFluidPressureTimeDerivative
    variable = p
  []
  [mass_space]
    type = INSFEFluidMassKernel
    variable = p
  []

  # x-momentum eqn
  [x_momentum_time]
    type = PINSFEFluidVelocityTimeDerivative
    variable = vel_x
  []
  [x_momentum_space]
    type = INSFEFluidMomentumKernel
    variable = vel_x
    component = 0
  []

  # y-momentum eqn
  [y_momentum_time]
    type = PINSFEFluidVelocityTimeDerivative
    variable = vel_y
  []
  [y_momentum_space]
    type = INSFEFluidMomentumKernel
    variable = vel_y
    component = 1
  []
[]

[BCs]
  [x_zero]
    type = DirichletBC
    variable = vel_x
    boundary = 'bottom left right'
    value = 0
  []
  [x_lid]
    type = DirichletBC
    variable = vel_x
    boundary = 'top'
    value = 1
  []
  [y_zero]
    type = DirichletBC
    variable = vel_y
    boundary = 'bottom top left right'
    value = 0
  []

  [p_anchor]
    type = DirichletBC
    variable = p
    boundary = 'bottom_left_corner'
    value = 1e5
  []
[]

[Preconditioning]
  [SMP_PJFNK]
    type = SMP
    full = true
    solve_type = 'PJFNK'
  []
[]


[Executioner]
  type = Transient

  dt = 0.01
  dtmin = 1.e-4

  petsc_options_iname = '-pc_type -ksp_gmres_restart'
  petsc_options_value = 'lu 100'

  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-8
  nl_max_its = 10

  l_tol = 1e-6
  l_max_its = 100

  start_time = 0.0
  end_time = 2
  num_steps = 5
[]

[Outputs]
  perf_graph = true
  print_linear_residuals = false
  time_step_interval = 1
  execute_on = 'initial timestep_end'
  [./console]
    type = Console
    output_linear = false
  [../]
  [./out]
    type = Exodus
    hide = 'porosity'
  [../]
[]

(modules/solid_mechanics/test/tests/crystal_plasticity/monolithic_material_based/rot-eg1.i)

#
# Rotation Test
#
# This test is designed to compute a uniaxial stress and then follow that
# stress as the mesh is rotated 90 degrees.
#
# The mesh is composed of one block with a single element.  The nodal
# displacements in the x and y directions are prescribed.  Poisson's
# ratio is zero.
#

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 3
    elem_type = HEX8
    displacements = 'ux uy uz'
  []
  [./side1n1]
    input = gen
    type = ExtraNodesetGenerator
    coord = '0.0 0.0 0.0'
    boundary = 6
  [../]
  [./side1n2]
    input = side1n1
    type = ExtraNodesetGenerator
    coord = '1.0 0.0 0.0'
    boundary = 7
  [../]
  [./side2n1]
    input = side1n2
    type = ExtraNodesetGenerator
    coord = '0.0 1.0 0.0'
    boundary = 8
  [../]
  [./side2n2]
    input = side2n1
    type = ExtraNodesetGenerator
    coord = '1.0 1.0 0.0'
    boundary = 9
  [../]
  [./side3n1]
    input = side2n2
    type = ExtraNodesetGenerator
    coord = '0.0 1.0 1.0'
    boundary = 10
  [../]
  [./side3n2]
    input = side3n1
    type = ExtraNodesetGenerator
    coord = '1.0 1.0 1.0'
    boundary = 11
  [../]
  [./side4n1]
    input = side3n2
    type = ExtraNodesetGenerator
    coord = '0.0 0.0 1.0'
    boundary = 12
  [../]
  [./side4n2]
    input = side4n1
    type = ExtraNodesetGenerator
    coord = '1.0 0.0 1.0'
    boundary = 13
  [../]
[]

[Variables]
  [./ux]
    block = 0
  [../]
  [./uy]
    block = 0
  [../]
  [./uz]
    block = 0
  [../]
[]

[Functions]
  [./side2uxfunc]
    type = ParsedFunction
    expression = cos(pi/2*t)-1
  [../]
  [./side2uyfunc]
    type = ParsedFunction
    expression = sin(pi/2*t)
  [../]
  [./side3uxfunc]
    type = ParsedFunction
    expression = cos(pi/2*t)-sin(pi/2*t)-1
  [../]
  [./side3uyfunc]
    type = ParsedFunction
    expression = cos(pi/2*t)+sin(pi/2*t)-1
  [../]
  [./side4uxfunc]
    type = ParsedFunction
    expression = -sin(pi/2*t)
  [../]
  [./side4uyfunc]
    type = ParsedFunction
    expression = cos(pi/2*t)-1
  [../]
[]

[BCs]
  active = 'bcside1 bcside2ux bcside2uy bcside4ux bcside4uy bcside3uy bcside3ux bcx'
  [./bcside1]
    type = DirichletBC
    variable = 'uy uz'
    boundary = '6 7'
    value = 0
  [../]
  [./bcside2ux]
    type = FunctionDirichletBC
    variable = uy
    boundary = '8 9'
    function = side2uxfunc
  [../]
  [./bcside2uy]
    type = FunctionDirichletBC
    variable = uz
    boundary = '8 9'
    function = side2uyfunc
  [../]
  [./bcside3ux]
    type = FunctionDirichletBC
    variable = uy
    boundary = '10 11'
    function = side3uxfunc
  [../]
  [./bcside3uy]
    type = FunctionDirichletBC
    variable = uz
    boundary = '10 11'
    function = side3uyfunc
  [../]
  [./bcside4ux]
    type = FunctionDirichletBC
    variable = uy
    boundary = '12 13'
    function = side4uxfunc
  [../]
  [./bcside4uy]
    type = FunctionDirichletBC
    variable = uz
    boundary = '12 13'
    function = side4uyfunc
  [../]
  [./bot]
    type = DirichletBC
    variable = 'ux uy uz'
    boundary = back
    value = 0
  [../]
  [./topxz]
    type = DirichletBC
    variable = 'ux uz'
    boundary = front
    value = 0
  [../]
  [./topy]
    type = DirichletBC
    variable = uy
    boundary = front
    value = 1
  [../]
  [./bcx]
    type = DirichletBC
    variable = ux
    boundary = '6 7 8 9 10 11 12 13'
    value = 0
  [../]
[]

[Materials]
  [./crysp]
    type = FiniteStrainCrystalPlasticity
    block = 0
    disp_y = uy
    disp_x = ux
    slip_sys_file_name = input_slip_sys.txt
    disp_z = uz
    flowprops = ' 1 12 0.001 0.1'
    C_ijkl = '1.684e5 1.214e5 1.214e5 1.684e5 1.214e5 1.684e5 .754e5 .754e5 .754e5'
    nss = 12
    hprops = '1 541.5 60.8 109.8'
    gprops = '1 12 60.8'
    fill_method = symmetric9
  [../]
[]

[Preconditioning]
  [./smp]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = Transient
  dt = 0.01

  #Preconditioned JFNK (default)
  solve_type = 'PJFNK'



  petsc_options_iname = -pc_hypre_type
  petsc_options_value = boomerang
  dtmax = 0.01
  end_time = 1
  dtmin = 0.01
[]

[Outputs]
  file_base = rot_eg1
  solution_history = true
  [./exodus]
    type = Exodus
    use_displaced = true
  [../]
[]

[SolidMechanics]
  [./tensormech]
    disp_z = uz
    disp_y = uy
    disp_x = ux
  [../]
[]

(modules/combined/test/tests/optimization/compliance_sensitivity/2d_mbb_pde_amr.i)

vol_frac = 0.5
E0 = 1
Emin = 1e-8
power = 3
[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  [MeshGenerator]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 30
    ny = 10
    xmin = 0
    xmax = 30
    ymin = 0
    ymax = 10
  []
  [node]
    type = ExtraNodesetGenerator
    input = MeshGenerator
    new_boundary = hold
    nodes = 0
  []
  [push]
    type = ExtraNodesetGenerator
    input = node
    new_boundary = push
    coord = '30 10 0'
  []

[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [Dc]
    initial_condition = -1.0
  []
[]

[AuxVariables]

  [sensitivity]
    family = MONOMIAL
    order = FIRST
    initial_condition = -1.0
    [AuxKernel]
      type = MaterialRealAux
      variable = sensitivity
      property = sensitivity
      execute_on = LINEAR
    []
  []
  [mat_den]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = ${vol_frac}
  []
  [Dc_elem]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = -1.0
    [AuxKernel]
      type = SelfAux
      variable = Dc_elem
      v = Dc
      execute_on = 'TIMESTEP_END'
    []
  []
  [mat_den_nodal]
    family = L2_LAGRANGE
    order = FIRST
    initial_condition = ${vol_frac}
    [AuxKernel]
      type = SelfAux
      execute_on = TIMESTEP_END
      variable = mat_den_nodal
      v = mat_den
    []
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = SMALL
    add_variables = true
    incremental = false
  []
[]
[Kernels]
  [diffusion]
    type = FunctionDiffusion
    variable = Dc
    function = 0.15 # radius coeff
  []
  [potential]
    type = Reaction
    variable = Dc
  []
  [source]
    type = CoupledForce
    variable = Dc
    v = sensitivity
  []
[]
[BCs]
  [no_x]
    type = DirichletBC
    variable = disp_y
    boundary = hold
    value = 0.0
  []
  [no_y]
    type = DirichletBC
    variable = disp_x
    boundary = right
    value = 0.0
  []
  [boundary_penalty]
    type = ADRobinBC
    variable = Dc
    boundary = 'left top'
    coefficient = 10
  []
  [boundary_penalty_right]
    type = ADRobinBC
    variable = Dc
    boundary = 'right'
    coefficient = 10
  []
[]
[NodalKernels]
  [push]
    type = NodalGravity
    variable = disp_y
    boundary = push
    gravity_value = -1
    mass = 1
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeVariableIsotropicElasticityTensor
    youngs_modulus = E_phys
    poissons_ratio = poissons_ratio
    args = 'mat_den'
  []
  [E_phys]
    type = DerivativeParsedMaterial
    # Emin + (density^penal) * (E0 - Emin)
    expression = '${Emin} + (mat_den ^ ${power}) * (${E0}-${Emin})'
    coupled_variables = 'mat_den'
    property_name = E_phys
  []
  [poissons_ratio]
    type = GenericConstantMaterial
    prop_names = poissons_ratio
    prop_values = 0.3
  []
  [stress]
    type = ComputeLinearElasticStress
  []
  [dc]
    type = ComplianceSensitivity
    design_density = mat_den
    youngs_modulus = E_phys
    incremental = false
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]
[UserObjects]
  [update]
    type = DensityUpdate
    density_sensitivity = Dc_elem
    design_density = mat_den
    volume_fraction = ${vol_frac}
    execute_on = TIMESTEP_BEGIN
    force_postaux = true
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'
  line_search = none
  nl_abs_tol = 1e-4
  l_max_its = 200
  start_time = 0.0
  dt = 1.0
  num_steps = 70
[]

[Outputs]
  [out]
    type = CSV
    execute_on = 'INITIAL TIMESTEP_END'
  []
  print_linear_residuals = false
[]

[Postprocessors]
  [total_vol]
    type = ElementIntegralVariablePostprocessor
    variable = mat_den
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [sensitivity]
    type = ElementIntegralMaterialProperty
    mat_prop = sensitivity
  []
[]

[Controls]
  [first_period]
    type = TimePeriod
    start_time = 0.0
    end_time = 40
    enable_objects = 'BCs::boundary_penalty_right'
    execute_on = 'initial timestep_begin'
  []
[]

[Adaptivity]
  max_h_level = 2
  recompute_markers_during_cycles = true
  interval = 1
  cycles_per_step = 1
  marker = density_marker
  [Indicators]
    [density_jump]
      type = ValueJumpIndicator
      variable = mat_den_nodal
    []
  []
  [Markers]
    [density_marker]
      type = ErrorToleranceMarker
      indicator = density_jump
      coarsen = 0.1
      refine = 0.1
    []
  []
[]

(modules/solid_mechanics/test/tests/lagrangian/cartesian/total/rates/rotation.i)

[Mesh]
  [msh]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 1
    ny = 1
  []
  [bottom_left]
    type = ExtraNodesetGenerator
    input = msh
    new_boundary = 'bottom_left'
    coord = '0 0 0'
  []
  [top_left]
    type = ExtraNodesetGenerator
    input = bottom_left
    new_boundary = 'top_left'
    coord = '0 1 0'
  []
  [top_right]
    type = ExtraNodesetGenerator
    input = top_left
    new_boundary = 'top_right'
    coord = '1 1 0'
  []
  [bottom_right]
    type = ExtraNodesetGenerator
    input = top_right
    new_boundary = 'bottom_right'
    coord = '1 0 0'
  []
[]

[GlobalParams]
  displacements = 'disp_x disp_y'
  large_kinematics = true
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
[]

[Kernels]
  [sdx]
    type = TotalLagrangianStressDivergence
    variable = disp_x
    component = 0
  []
  [sdy]
    type = TotalLagrangianStressDivergence
    variable = disp_y
    component = 1
  []
[]

[AuxVariables]
  [stress_xx]
    order = CONSTANT
    family = MONOMIAL
    [AuxKernel]
      type = RankTwoAux
      rank_two_tensor = cauchy_stress
      index_i = 0
      index_j = 0
      execute_on = TIMESTEP_END
    []
  []
  [stress_yy]
    order = CONSTANT
    family = MONOMIAL
    [AuxKernel]
      type = RankTwoAux
      rank_two_tensor = cauchy_stress
      index_i = 1
      index_j = 1
      execute_on = TIMESTEP_END
    []
  []
[]

[BCs]
  [fix_y]
    type = DirichletBC
    variable = disp_y
    boundary = 'bottom_left'
    value = 0
  []
  [fix_x]
    type = DirichletBC
    variable = disp_x
    boundary = 'bottom_left'
    value = 0
  []
  [top_left_x]
    type = FunctionDirichletBC
    variable = disp_x
    boundary = 'top_left'
    function = 'theta:=if(t<1,0,t-1); -sin(theta)'
  []
  [top_left_y]
    type = FunctionDirichletBC
    variable = disp_y
    boundary = 'top_left'
    function = 'theta:=if(t<1,0,t-1); cos(theta)-1'
  []
  [bottom_right_x]
    type = FunctionDirichletBC
    variable = disp_x
    boundary = 'bottom_right'
    function = 'theta:=if(t<1,0,t-1); if(t<1,t,2*cos(theta)-1)'
  []
  [bottom_right_y]
    type = FunctionDirichletBC
    variable = disp_y
    boundary = 'bottom_right'
    function = 'theta:=if(t<1,0,t-1); if(t<1,0,2*sin(theta))'
  []
  [top_right_x]
    type = FunctionDirichletBC
    variable = disp_x
    boundary = 'top_right'
    function = 'theta:=if(t<1,0,t-1); phi:=theta+atan(0.5); if(t<1,t,sqrt(5)*cos(phi)-1)'
  []
  [top_right_y]
    type = FunctionDirichletBC
    variable = disp_y
    boundary = 'top_right'
    function = 'theta:=if(t<1,0,t-1); phi:=theta+atan(0.5); if(t<1,0,sqrt(5)*sin(phi)-1)'
  []
[]

[Materials]
  [elastic_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 1e5
    poissons_ratio = 0
  []
  [stress]
    type = ComputeLagrangianLinearElasticStress
  []
  [strain]
    type = ComputeLagrangianStrain
  []
[]

[Postprocessors]
  [sxx]
    type = ElementAverageValue
    variable = stress_xx
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [syy]
    type = ElementAverageValue
    variable = stress_yy
    execute_on = 'INITIAL TIMESTEP_END'
  []
[]

[Executioner]
  type = Transient
  dt = 0.01
  end_time = '${fparse pi/2+1}'

  solve_type = NEWTON
  line_search = none

  petsc_options_iname = -pc_type
  petsc_options_value = lu
  automatic_scaling = true

  nl_abs_tol = 1e-10
  nl_rel_tol = 1e-10
[]

[Outputs]
  csv = true
[]

(modules/combined/examples/publications/rapid_dev/fig8.i)

#
# Fig. 8 input for 10.1016/j.commatsci.2017.02.017
# D. Schwen et al./Computational Materials Science 132 (2017) 36-45
# Two growing particles with differnet anisotropic Eigenstrains
#

[Mesh]
  [./gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 80
    ny = 40
    xmin = -20
    xmax = 20
    ymin = 0
    ymax = 20
    elem_type = QUAD4
  [../]
  [./cnode]
    type = ExtraNodesetGenerator
    input = gen
    coord = '0.0 0.0'
    new_boundary = 100
    tolerance = 0.1
  [../]
[]

[GlobalParams]
  # CahnHilliard needs the third derivatives
  derivative_order = 3
  enable_jit = true
  displacements = 'disp_x disp_y'
  int_width = 1
[]

# AuxVars to compute the free energy density for outputting
[AuxVariables]
  [./local_energy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./cross_energy]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[AuxKernels]
  [./local_free_energy]
    type = TotalFreeEnergy
    variable = local_energy
    interfacial_vars = 'c'
    kappa_names = 'kappa_c'
    additional_free_energy = cross_energy
    execute_on = 'INITIAL TIMESTEP_END'
  [../]
  [./cross_terms]
    type = CrossTermGradientFreeEnergy
    variable = cross_energy
    interfacial_vars = 'eta1 eta2 eta3'
    kappa_names = 'kappa11 kappa12 kappa13
                   kappa21 kappa22 kappa23
                   kappa31 kappa32 kappa33'
    execute_on = 'INITIAL TIMESTEP_END'
  [../]
[]

# particle x positions and radius
P1X=8
P2X=-4
PR=2

[Variables]
  # Solute concentration variable
  [./c]
    [./InitialCondition]
      type = SpecifiedSmoothCircleIC
      x_positions = '${P1X} ${P2X}'
      y_positions = '0 0'
      z_positions = '0 0'
      radii = '${PR} ${PR}'
      outvalue = 0.5
      invalue = 0.9
    [../]
  [../]
  [./w]
  [../]

  # Order parameter for the Matrix
  [./eta1]
    [./InitialCondition]
      type = SpecifiedSmoothCircleIC
      x_positions = '${P1X} ${P2X}'
      y_positions = '0 0'
      z_positions = '0 0'
      radii = '${PR} ${PR}'
      outvalue = 1.0
      invalue = 0.0
    [../]
  [../]
  # Order parameters for the 2 different inclusion orientations
  [./eta2]
    [./InitialCondition]
      type = SmoothCircleIC
      x1 = ${P2X}
      y1 = 0
      radius = ${PR}
      invalue = 1.0
      outvalue = 0.0
    [../]
  [../]
  [./eta3]
    [./InitialCondition]
      type = SmoothCircleIC
      x1 = ${P1X}
      y1 = 0
      radius = ${PR}
      invalue = 1.0
      outvalue = 0.0
    [../]
  [../]

  # Lagrange-multiplier
  [./lambda]
    initial_condition = 1.0
  [../]
[]

[Physics/SolidMechanics/QuasiStatic/all]
  add_variables = true
  strain = SMALL
  eigenstrain_names = eigenstrain
[]

[Kernels]
  # Split Cahn-Hilliard kernels
  [./c_res]
    type = SplitCHParsed
    variable = c
    f_name = F
    coupled_variables = 'eta1 eta2 eta3'
    kappa_name = kappa_c
    w = w
  [../]
  [./wres]
    type = SplitCHWRes
    variable = w
    mob_name = M
  [../]
  [./time]
    type = CoupledTimeDerivative
    variable = w
    v = c
  [../]

  # Allen-Cahn and Lagrange-multiplier constraint kernels for order parameter 1
  [./deta1dt]
    type = TimeDerivative
    variable = eta1
  [../]
  [./ACBulk1]
    type = AllenCahn
    variable = eta1
    coupled_variables = 'eta2 eta3 c'
    mob_name = L1
    f_name = F
  [../]
  [./ACInterface1]
    type = ACMultiInterface
    variable = eta1
    etas = 'eta1 eta2 eta3'
    mob_name = L1
    kappa_names = 'kappa11 kappa12 kappa13'
  [../]
  [./lagrange1]
    type = SwitchingFunctionConstraintEta
    variable = eta1
    h_name   = h1
    lambda = lambda
  [../]

  # Allen-Cahn and Lagrange-multiplier constraint kernels for order parameter 2
  [./deta2dt]
    type = TimeDerivative
    variable = eta2
  [../]
  [./ACBulk2]
    type = AllenCahn
    variable = eta2
    coupled_variables = 'eta1 eta3 c'
    mob_name = L2
    f_name = F
  [../]
  [./ACInterface2]
    type = ACMultiInterface
    variable = eta2
    etas = 'eta1 eta2 eta3'
    mob_name = L2
    kappa_names = 'kappa21 kappa22 kappa23'
  [../]
  [./lagrange2]
    type = SwitchingFunctionConstraintEta
    variable = eta2
    h_name   = h2
    lambda = lambda
  [../]

  # Allen-Cahn and Lagrange-multiplier constraint kernels for order parameter 3
  [./deta3dt]
    type = TimeDerivative
    variable = eta3
  [../]
  [./ACBulk3]
    type = AllenCahn
    variable = eta3
    coupled_variables = 'eta1 eta2 c'
    mob_name = L3
    f_name = F
  [../]
  [./ACInterface3]
    type = ACMultiInterface
    variable = eta3
    etas = 'eta1 eta2 eta3'
    mob_name = L3
    kappa_names = 'kappa31 kappa32 kappa33'
  [../]
  [./lagrange3]
    type = SwitchingFunctionConstraintEta
    variable = eta3
    h_name   = h3
    lambda = lambda
  [../]

  # Lagrange-multiplier constraint kernel for lambda
  [./lagrange]
    type = SwitchingFunctionConstraintLagrange
    variable = lambda
    etas    = 'eta1 eta2 eta3'
    h_names = 'h1   h2   h3'
    epsilon = 1e-6
  [../]
[]

[Materials]
  # declare a few constants, such as mobilities (L,M) and interface gradient prefactors (kappa*)
  [./consts]
    type = GenericConstantMaterial
    block = 0
    prop_names  = 'M   kappa_c  L1 L2 L3  kappa11 kappa12 kappa13 kappa21 kappa22 kappa23 kappa31 kappa32 kappa33'
    prop_values = '0.2 0.5      1  1  1   2.00    2.00    2.00    2.00    2.00    2.00    2.00    2.00    2.00   '
  [../]

  # We use this to output the level of constraint enforcement
  # ideally it should be 0 everywhere, if the constraint is fully enforced
  [./etasummat]
    type = ParsedMaterial
    property_name = etasum
    coupled_variables = 'eta1 eta2 eta3'
    material_property_names = 'h1 h2 h3'
    expression = 'h1+h2+h3-1'
    outputs = exodus
  [../]

  # This parsed material creates a single property for visualization purposes.
  # It will be 0 for phase 1, -1 for phase 2, and 1 for phase 3
  [./phasemap]
    type = ParsedMaterial
    property_name = phase
    coupled_variables = 'eta2 eta3'
    expression = 'if(eta3>0.5,1,0)-if(eta2>0.5,1,0)'
    outputs = exodus
  [../]

  # global mechanical properties
  [./elasticity_tensor]
    type = ComputeElasticityTensor
    C_ijkl = '400 400'
    fill_method = symmetric_isotropic
  [../]
  [./stress]
    type = ComputeLinearElasticStress
  [../]

  # eigenstrain
  [./eigenstrain_2]
    type = GenericConstantRankTwoTensor
    tensor_name = s2
    tensor_values = '0 -0.05 0  0 0 0'
  [../]
  [./eigenstrain_3]
    type = GenericConstantRankTwoTensor
    tensor_name = s3
    tensor_values =  '-0.05 0 0  0 0 0'
  [../]
  [./eigenstrain]
    type = CompositeEigenstrain
    weights = 'h2 h3'
    tensors = 's2 s3'
    coupled_variables = 'eta2 eta3'
    eigenstrain_name = eigenstrain
  [../]

  # switching functions
  [./switching1]
    type = SwitchingFunctionMaterial
    function_name = h1
    eta = eta1
    h_order = SIMPLE
  [../]
  [./switching2]
    type = SwitchingFunctionMaterial
    function_name = h2
    eta = eta2
    h_order = SIMPLE
  [../]
  [./switching3]
    type = SwitchingFunctionMaterial
    function_name = h3
    eta = eta3
    h_order = SIMPLE
  [../]

  [./barrier]
    type = MultiBarrierFunctionMaterial
    etas = 'eta1 eta2 eta3'
  [../]

  # chemical free energies
  [./chemical_free_energy_1]
    type = DerivativeParsedMaterial
    property_name = Fc1
    expression = '4*c^2'
    coupled_variables = 'c'
    derivative_order = 2
  [../]
  [./chemical_free_energy_2]
    type = DerivativeParsedMaterial
    property_name = Fc2
    expression = '(c-0.9)^2-0.4'
    coupled_variables = 'c'
    derivative_order = 2
  [../]
  [./chemical_free_energy_3]
    type = DerivativeParsedMaterial
    property_name = Fc3
    expression = '(c-0.9)^2-0.5'
    coupled_variables = 'c'
    derivative_order = 2
  [../]

  # global chemical free energy
  [./chemical_free_energy]
    type = DerivativeMultiPhaseMaterial
    f_name = Fc
    fi_names = 'Fc1  Fc2  Fc3'
    hi_names = 'h1  h2  h3'
    etas     = 'eta1 eta2 eta3'
    coupled_variables = 'c'
    W = 3
  [../]

  # global elastic free energy
  [./elastic_free_energy]
    type = ElasticEnergyMaterial
    f_name = Fe
    coupled_variables = 'eta2 eta3'
    outputs = exodus
    output_properties = Fe
    derivative_order = 2
  [../]

  # Penalize phase 2 and 3 coexistence
  [./multi_phase_penalty]
    type = DerivativeParsedMaterial
    property_name = Fp
    expression = '50*(eta2*eta3)^2'
    coupled_variables = 'eta2 eta3'
    derivative_order = 2
    outputs = exodus
    output_properties = Fp
  [../]

  # free energy
  [./free_energy]
    type = DerivativeSumMaterial
    property_name = F
    sum_materials = 'Fc Fe Fp'
    coupled_variables = 'c eta1 eta2 eta3'
    derivative_order = 2
  [../]
[]

[BCs]
  # fix center point location
  [./centerfix_x]
    type = DirichletBC
    boundary = 100
    variable = disp_x
    value = 0
  [../]

  # fix side point x coordinate to inhibit rotation
  [./angularfix]
    type = DirichletBC
    boundary = bottom
    variable = disp_y
    value = 0
  [../]
[]

[Preconditioning]
  [./SMP]
    type = SMP
    full = true
  [../]
[]

# We monitor the total free energy and the total solute concentration (should be constant)
[Postprocessors]
  [./total_free_energy]
    type = ElementIntegralVariablePostprocessor
    variable = local_energy
    execute_on = 'INITIAL TIMESTEP_END'
  [../]
  [./total_solute]
    type = ElementIntegralVariablePostprocessor
    variable = c
    execute_on = 'INITIAL TIMESTEP_END'
  [../]
[]

[Executioner]
  type = Transient
  scheme = bdf2

  solve_type = 'PJFNK'
  petsc_options_iname = '-pc_type -sub_pc_type'
  petsc_options_value = 'asm      lu'

  l_max_its = 30
  nl_max_its = 10
  l_tol = 1.0e-4
  nl_rel_tol = 1.0e-8
  nl_abs_tol = 1.0e-10
  start_time = 0.0
  end_time = 12.0

  [./TimeStepper]
    type = IterationAdaptiveDT
    optimal_iterations = 8
    iteration_window = 1
    dt = 0.01
  [../]
[]

[Outputs]
  print_linear_residuals = false
  execute_on = 'INITIAL TIMESTEP_END'
  exodus = true
  [./table]
    type = CSV
    delimiter = ' '
  [../]
[]

[Debug]
  # show_var_residual_norms = true
[]

(modules/combined/test/tests/optimization/compliance_sensitivity/three_materials_thermal.i)

vol_frac = 0.4
cost_frac = 0.4

power = 4

# Stiffness (not optimized in this test)
E0 = 1.0e-6
E1 = 0.2
E2 = 0.6
E3 = 1.0

# Densities
rho0 = 1.0e-6
rho1 = 0.4
rho2 = 0.7
rho3 = 1.0

# Costs
C0 = 1.0e-6
C1 = 0.5
C2 = 0.8
C3 = 1.0

# Thermal conductivity
TC0 = 1.0e-6
TC1 = 0.2
TC2 = 0.6
TC3 = 1.0

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  [MeshGenerator]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 40
    ny = 40
    xmin = 0
    xmax = 40
    ymin = 0
    ymax = 40
  []
  [node]
    type = ExtraNodesetGenerator
    input = MeshGenerator
    new_boundary = hold
    nodes = 0
  []
  [push_left]
    type = ExtraNodesetGenerator
    input = node
    new_boundary = push_left
    coord = '20 0 0'
  []
  [push_center]
    type = ExtraNodesetGenerator
    input = push_left
    new_boundary = push_center
    coord = '40 0 0'
  []
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [temp]
    initial_condition = 100.0
  []
[]

[AuxVariables]
  [Dc]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = -1.0
  []
  [Cc]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = -1.0
  []
  [Tc]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = -1.0
  []
  [Cost]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = -1.0
  []
  [mat_den]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = ${vol_frac}
  []
  [thermal_compliance]
    order = CONSTANT
    family = MONOMIAL
  []
[]

# [ICs]
#   [mat_den]
#     type = RandomIC
#     seed = 4
#     variable = mat_den
#     max = '${fparse vol_frac+0.25}'
#     min = '${fparse vol_frac-0.25}'
#   []
# []

[AuxKernels]
  [Cost]
    type = MaterialRealAux
    variable = Cost
    property = Cost_mat
  []
  [thermal_compliance]
    type = MaterialRealAux
    property = thermal_compliance
    variable = thermal_compliance
    execute_on = timestep_end
  []
[]

[Kernels]
  [heat_conduction]
    type = HeatConduction
    variable = temp
    diffusion_coefficient = thermal_cond
  []
  [heat_source]
    type = HeatSource
    value = 1e-2 # W/m^3
    variable = temp
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = SMALL
    add_variables = true
    incremental = false
  []
[]

[BCs]
  [no_y]
    type = DirichletBC
    variable = disp_y
    boundary = hold
    value = 0.0
  []
  [no_x_symm]
    type = DirichletBC
    variable = disp_x
    boundary = right
    value = 0.0
  []
  [top]
    type = DirichletBC
    variable = temp
    boundary = top
    value = 0
  []
  [bottom]
    type = DirichletBC
    variable = temp
    boundary = bottom
    value = 0
  []
  [right]
    type = DirichletBC
    variable = temp
    boundary = right
    value = 0
  []
  [left]
    type = DirichletBC
    variable = temp
    boundary = left
    value = 0
  []
[]

[NodalKernels]
  [push_left]
    type = NodalGravity
    variable = disp_y
    boundary = push_left
    gravity_value = -1e-6 # -3
    mass = 1
  []
  [push_center]
    type = NodalGravity
    variable = disp_y
    boundary = push_center
    gravity_value = -1e-6 # -3
    mass = 1
  []
[]

[Materials]
  [thermal_cond]
    type = DerivativeParsedMaterial
    # ordered multimaterial simp
    expression = "A1:=(${TC0}-${TC1})/(${rho0}^${power}-${rho1}^${power}); "
                 "B1:=${TC0}-A1*${rho0}^${power}; TC1:=A1*mat_den^${power}+B1; "
                 "A2:=(${TC1}-${TC2})/(${rho1}^${power}-${rho2}^${power}); "
                 "B2:=${TC1}-A2*${rho1}^${power}; TC2:=A2*mat_den^${power}+B2; "
                 "A3:=(${TC2}-${TC3})/(${rho2}^${power}-${rho3}^${power}); "
                 "B3:=${TC2}-A3*${rho2}^${power}; TC3:=A3*mat_den^${power}+B3; "
                 "if(mat_den<${rho1},TC1,if(mat_den<${rho2},TC2,TC3))"
    coupled_variables = 'mat_den'
    property_name = thermal_cond
  []
  [thermal_compliance]
    type = ThermalCompliance
    temperature = temp
    thermal_conductivity = thermal_cond
  []
  [elasticity_tensor]
    type = ComputeVariableIsotropicElasticityTensor
    youngs_modulus = E_phys
    poissons_ratio = poissons_ratio
    args = 'mat_den'
  []
  [E_phys]
    type = DerivativeParsedMaterial
    # ordered multimaterial simp
    expression = "A1:=(${E0}-${E1})/(${rho0}^${power}-${rho1}^${power}); "
                 "B1:=${E0}-A1*${rho0}^${power}; E1:=A1*mat_den^${power}+B1; "
                 "A2:=(${E1}-${E2})/(${rho1}^${power}-${rho2}^${power}); "
                 "B2:=${E1}-A2*${rho1}^${power}; E2:=A2*mat_den^${power}+B2; "
                 "A3:=(${E2}-${E3})/(${rho2}^${power}-${rho3}^${power}); "
                 "B3:=${E2}-A3*${rho2}^${power}; E3:=A3*mat_den^${power}+B3; "
                 "if(mat_den<${rho1},E1,if(mat_den<${rho2},E2,E3))"
    coupled_variables = 'mat_den'
    property_name = E_phys
  []
  [Cost_mat]
    type = DerivativeParsedMaterial
    # ordered multimaterial simp
    expression = "A1:=(${C0}-${C1})/(${rho0}^(1/${power})-${rho1}^(1/${power})); "
                 "B1:=${C0}-A1*${rho0}^(1/${power}); C1:=A1*mat_den^(1/${power})+B1; "
                 "A2:=(${C1}-${C2})/(${rho1}^(1/${power})-${rho2}^(1/${power})); "
                 "B2:=${C1}-A2*${rho1}^(1/${power}); C2:=A2*mat_den^(1/${power})+B2; "
                 "A3:=(${C2}-${C3})/(${rho2}^(1/${power})-${rho3}^(1/${power})); "
                 "B3:=${C2}-A3*${rho2}^(1/${power}); C3:=A3*mat_den^(1/${power})+B3; "
                 "if(mat_den<${rho1},C1,if(mat_den<${rho2},C2,C3))"
    coupled_variables = 'mat_den'
    property_name = Cost_mat
  []
  [CostDensity]
    type = ParsedMaterial
    property_name = CostDensity
    coupled_variables = 'mat_den Cost'
    expression = 'mat_den*Cost'
  []
  [poissons_ratio]
    type = GenericConstantMaterial
    prop_names = poissons_ratio
    prop_values = 0.3
  []
  [stress]
    type = ComputeLinearElasticStress
  []
  [dc]
    type = ComplianceSensitivity
    design_density = mat_den
    youngs_modulus = E_phys
  []
  [cc]
    type = CostSensitivity
    design_density = mat_den
    cost = Cost_mat
  []
  [tc]
    type = ThermalSensitivity
    design_density = mat_den
    thermal_conductivity = thermal_cond
    temperature = temp
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[UserObjects]
  [rad_avg]
    type = RadialAverage
    radius = 4
    weights = linear
    prop_name = sensitivity
    execute_on = TIMESTEP_END
    force_preaux = true
  []
  [rad_avg_cost]
    type = RadialAverage
    radius = 4
    weights = linear
    prop_name = cost_sensitivity
    execute_on = TIMESTEP_END
    force_preaux = true
  []
  [rad_avg_thermal]
    type = RadialAverage
    radius = 4
    weights = linear
    prop_name = thermal_sensitivity
    execute_on = TIMESTEP_END
    force_preaux = true
  []
  [update]
    type = DensityUpdateTwoConstraints
    density_sensitivity = Dc
    cost_density_sensitivity = Cc
    cost = Cost
    cost_fraction = ${cost_frac}
    design_density = mat_den
    volume_fraction = ${vol_frac}

    bisection_lower_bound = 0
    bisection_upper_bound = 1.0e12 # 100

    use_thermal_compliance = true
    thermal_sensitivity = Tc
    # Only account for thermal optimizxation
    weight_mechanical_thermal = '0 1'

    relative_tolerance = 1.0e-8
    bisection_move = 0.05
    adaptive_move = false
    execute_on = TIMESTEP_BEGIN
  []
  # Provides Dc
  [calc_sense]
    type = SensitivityFilter
    density_sensitivity = Dc
    design_density = mat_den
    filter_UO = rad_avg
    execute_on = TIMESTEP_END
    force_postaux = true
  []
  # Provides Cc
  [calc_sense_cost]
    type = SensitivityFilter
    density_sensitivity = Cc
    design_density = mat_den
    filter_UO = rad_avg_cost
    execute_on = TIMESTEP_END
    force_postaux = true
  []
  # Provides Tc
  [calc_sense_thermal]
    type = SensitivityFilter
    density_sensitivity = Tc
    design_density = mat_den
    filter_UO = rad_avg_thermal
    execute_on = TIMESTEP_END
    force_postaux = true
  []
[]

[Executioner]
  type = Transient
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'
  nl_abs_tol = 1e-10
  dt = 1.0
  num_steps = 12
[]

[Outputs]
  [out]
    type = CSV
    execute_on = 'TIMESTEP_END'
  []
  print_linear_residuals = false
[]

[Postprocessors]
  [right_flux]
    type = SideDiffusiveFluxAverage
    variable = temp
    boundary = right
    diffusivity = 10
  []
  [mesh_volume]
    type = VolumePostprocessor
    execute_on = 'initial timestep_end'
  []
  [total_vol]
    type = ElementIntegralVariablePostprocessor
    variable = mat_den
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [vol_frac]
    type = ParsedPostprocessor
    expression = 'total_vol / mesh_volume'
    pp_names = 'total_vol mesh_volume'
  []
  [sensitivity]
    type = ElementIntegralMaterialProperty
    mat_prop = sensitivity
  []
  [cost_sensitivity]
    type = ElementIntegralMaterialProperty
    mat_prop = cost_sensitivity
  []
  [cost]
    type = ElementIntegralMaterialProperty
    mat_prop = CostDensity
  []
  [cost_frac]
    type = ParsedPostprocessor
    expression = 'cost / mesh_volume'
    pp_names = 'cost mesh_volume'
  []
  [objective]
    type = ElementIntegralMaterialProperty
    mat_prop = strain_energy_density
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [objective_thermal]
    type = ElementIntegralMaterialProperty
    mat_prop = thermal_compliance
    execute_on = 'INITIAL TIMESTEP_END'
  []
[]

(modules/navier_stokes/test/tests/finite_element/ins/coupled-force/gravity-object.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 1.0
    ymin = 0
    ymax = 1.0
    nx = 16
    ny = 16
  []
  [./corner_node]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node'
    nodes = '0'
    input = gen
  [../]
[]

[Variables]
  [./velocity]
    family = LAGRANGE_VEC
  [../]
  [./p]
  [../]
  [u]
    family = LAGRANGE_VEC
  []
[]

[ICs]
  [velocity]
    type = VectorConstantIC
    x_value = 1e-15
    y_value = 1e-15
    variable = velocity
  []
[]

[Kernels]
  [./mass]
    type = INSADMass
    variable = p
  [../]
  [./mass_pspg]
    type = INSADMassPSPG
    variable = p
  [../]

  [./momentum_convection]
    type = INSADMomentumAdvection
    variable = velocity
  [../]

  [./momentum_viscous]
    type = INSADMomentumViscous
    variable = velocity
  [../]

  [./momentum_pressure]
    type = INSADMomentumPressure
    variable = velocity
    pressure = p
    integrate_p_by_parts = true
  [../]

  [momentum_coupled_force]
    type = INSADMomentumCoupledForce
    variable = velocity
    coupled_vector_var = u
  []

  [gravity]
    type = INSADGravityForce
    variable = velocity
    gravity = '0 -9.81 0'
  []

  [./momentum_supg]
    type = INSADMomentumSUPG
    variable = velocity
    velocity = velocity
  [../]

  [u_diff]
    type = VectorDiffusion
    variable = u
  []
[]

[BCs]
  [./no_slip]
    type = VectorFunctionDirichletBC
    variable = velocity
    boundary = 'bottom right left top'
  [../]

  [./pressure_pin]
    type = DirichletBC
    variable = p
    boundary = 'pinned_node'
    value = 0
  [../]

  [u_left]
    type = VectorFunctionDirichletBC
    variable = u
    boundary = 'left'
    function_x = 1
    function_y = 1
  []

  [u_right]
    type = VectorFunctionDirichletBC
    variable = u
    boundary = 'right'
    function_x = -1
    function_y = -1
  []
[]

[Materials]
  [./const]
    type = ADGenericConstantMaterial
    prop_names = 'rho mu'
    prop_values = '1  1'
  [../]
  [ins_mat]
    type = INSADTauMaterial
    velocity = velocity
    pressure = p
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -sub_pc_factor_levels -ksp_gmres_restart'
  petsc_options_value = 'asm      6                     200'
  line_search = 'none'
  nl_rel_tol = 1e-12
  nl_max_its = 6
[]

[Outputs]
  exodus = true
[]

(test/tests/bcs/ad_nodal_bc_nonlocal_dependence/test.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 1
    nx = 20
  []
  [pin]
    type = ExtraNodesetGenerator
    input = gen
    new_boundary = 'pin'
    nodes = '0'
  []
[]

[Variables]
  [u][]
[]

[Kernels]
  [diff]
    type = Diffusion
    variable = u
  []
[]

[BCs]
  [left_neumann]
    type = NeumannBC
    boundary = 'left'
    value = -1
    variable = u
  []
  [right_neumann]
    type = NeumannBC
    boundary = 'right'
    value = 1
    variable = u
  []
  [pin]
    type = ADAverageValuePin
    variable = u
    # This BC constrains a single degree of freedom on the node specified by the boundary name 'pin' but
    # since only gradients of 'u' appear in the weak form and we have no other Dirichlet boundary conditions,
    # constraining the single degree of freedom will make it appear as if we have constrained all the degrees of
    # freedom in the system such that we have an average value of 0.
    boundary = 'pin'
  []
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
[]

[Problem]
  # We have to close the matrix before enforcing boundary conditions, which destroys our sparsity pattern
  use_hash_table_matrix_assembly = true
[]

[Outputs]
  exodus = true
[]

(modules/solid_mechanics/test/tests/ad_anisotropic_creep/aniso_creep_integration_error.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 10
    ny = 2
    nz = 2
    xmin = 0.0
    ymin = 0.0
    zmin = 0.0

    xmax = 10.0
    ymax = 1.0
    zmax = 1.0
  []
  [corner_node]
    type = ExtraNodesetGenerator
    new_boundary = '100'
    nodes = '3 69'
    input = gen
  []
  [corner_node_2]
    type = ExtraNodesetGenerator
    new_boundary = '101'
    nodes = '4 47'
    input = corner_node
  []
[]

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  volumetric_locking_correction = true
[]

[AuxVariables]
  [hydrostatic_stress]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_xx]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_xy]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [hydrostatic_stress]
    type = RankTwoScalarAux
    variable = hydrostatic_stress
    rank_two_tensor = stress
    scalar_type = Hydrostatic
  []
  [creep_strain_xx]
    type = RankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_xx
    index_i = 0
    index_j = 0
  []
  [creep_strain_xy]
    type = RankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_xy
    index_i = 0
    index_j = 1
  []
  [creep_strain_yy]
    type = RankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_yy
    index_i = 1
    index_j = 1
  []
  [sigma_xx]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_xx
    index_i = 1
    index_j = 1
  []
[]

[Functions]
  [pull]
    type = PiecewiseLinear
    x = '0 1.0'
    y = '0 -4e1'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = FINITE
    generate_output = 'elastic_strain_xx stress_xx'
    use_automatic_differentiation = false
    add_variables = true
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 7000
    poissons_ratio = 0.0
  []

  [elastic_strain]
    type = ComputeMultipleInelasticStress
    inelastic_models = "trial_creep_two"
    max_iterations = 50
    absolute_tolerance = 1e-16
  []

  [hill_tensor]
    type = HillConstants
    # F G H L M N
    hill_constants = "0.5 0.25 0.3866 1.6413 1.6413 1.2731"
  []

  [trial_creep_two]
    type = HillCreepStressUpdate
    coefficient = 1e-16
    n_exponent = 9
    m_exponent = 0
    activation_energy = 0
    max_inelastic_increment = 1.0e-4
    absolute_tolerance = 1e-20
    relative_tolerance = 1e-20
    max_integration_error = 1.0e-5
  []
[]

[BCs]
  [no_disp_x]
    type = DirichletBC
    variable = disp_x
    boundary = left
    value = 0.0
  []

  [no_disp_y]
    type = DirichletBC
    variable = disp_y
    boundary = 100
    value = 0.0
  []

  [no_disp_z]
    type = DirichletBC
    variable = disp_z
    boundary = 101
    value = 0.0
  []

  [Pressure]
    [Side1]
      boundary = right
      function = pull
    []
  []

[]

[Executioner]
  type = Transient

  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu     superlu_dist'

  nl_rel_tol = 1.0e-13
  nl_abs_tol = 1.0e-13
  l_max_its = 10
  end_time = 1.65e-1
  dt = 2.5e-2
  start_time = 0
  automatic_scaling = true

  [./TimeStepper]
  type = IterationAdaptiveDT
  dt = 2.5e-2
  time_t = '0.0  10.0'
  time_dt = '2.5e-2 2.5e-2 '
  optimal_iterations = 30
  iteration_window = 9
  growth_factor = 1.5
  cutback_factor = 0.5
  timestep_limiting_postprocessor = matl_ts_min
  reject_large_step = true
  reject_large_step_threshold = 0.999
[../]
[]

[Postprocessors]
  [time_step_size]
    type = TimestepSize
  []
  [matl_ts_min]
    type = MaterialTimeStepPostprocessor
  []
  [max_disp_x]
    type = ElementExtremeValue
    variable = disp_x
  []
  [max_disp_y]
    type = ElementExtremeValue
    variable = disp_y
  []
  [max_hydro]
    type = ElementAverageValue
    variable = hydrostatic_stress
  []
  [dt]
    type = TimestepSize
  []
  [num_lin]
    type = NumLinearIterations
    outputs = console
  []
  [num_nonlin]
    type = NumNonlinearIterations
    outputs = console
  []
  [creep_strain_xx]
    type = ElementalVariableValue
    variable = creep_strain_xx
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [elastic_strain_xx]
    type = ElementalVariableValue
    variable = elastic_strain_xx
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [sigma_xx]
    type = ElementalVariableValue
    variable = stress_xx
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
[]

[Outputs]
  csv = true
  exodus = true
  perf_graph = true
[]

(modules/navier_stokes/test/tests/finite_volume/ins/lid-driven/transient-lid-driven-with-energy.i)

mu = 1
rho = 1
k = .01
cp = 1
velocity_interp_method = 'rc'
advected_interp_method = 'average'

[GlobalParams]
  rhie_chow_user_object = 'rc'
[]

[UserObjects]
  [rc]
    type = INSFVRhieChowInterpolator
    u = u
    v = v
    pressure = pressure
  []
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 1
    ymin = 0
    ymax = 1
    nx = 32
    ny = 32
  []
  [pin]
    type = ExtraNodesetGenerator
    input = gen
    new_boundary = 'pin'
    nodes = '0'
  []
[]

[Variables]
  [u]
    type = INSFVVelocityVariable
  []
  [v]
    type = INSFVVelocityVariable
  []
  [pressure]
    type = INSFVPressureVariable
  []
  [T]
    type = INSFVEnergyVariable
  []
  [lambda]
    family = SCALAR
    order = FIRST
  []
[]

[ICs]
  [T]
    type = ConstantIC
    variable = T
    value = 1
  []
[]

[AuxVariables]
  [U]
    order = CONSTANT
    family = MONOMIAL
    fv = true
  []
[]

[AuxKernels]
  [mag]
    type = VectorMagnitudeAux
    variable = U
    x = u
    y = v
  []
[]

[FVKernels]
  [mass]
    type = INSFVMassAdvection
    variable = pressure
    advected_interp_method = ${advected_interp_method}
    velocity_interp_method = ${velocity_interp_method}
    rho = ${rho}
  []
  [mean_zero_pressure]
    type = FVIntegralValueConstraint
    variable = pressure
    lambda = lambda
  []

  [u_time]
    type = INSFVMomentumTimeDerivative
    variable = 'u'
    rho = ${rho}
    momentum_component = 'x'
  []
  [u_advection]
    type = INSFVMomentumAdvection
    variable = u
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
    rho = ${rho}
    momentum_component = 'x'
  []
  [u_viscosity]
    type = INSFVMomentumDiffusion
    variable = u
    mu = ${mu}
    momentum_component = 'x'
  []
  [u_pressure]
    type = INSFVMomentumPressure
    variable = u
    momentum_component = 'x'
    pressure = pressure
  []

  [v_time]
    type = INSFVMomentumTimeDerivative
    variable = v
    rho = ${rho}
    momentum_component = 'y'
  []
  [v_advection]
    type = INSFVMomentumAdvection
    variable = v
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
    rho = ${rho}
    momentum_component = 'y'
  []
  [v_viscosity]
    type = INSFVMomentumDiffusion
    variable = v
    mu = ${mu}
    momentum_component = 'y'
  []
  [v_pressure]
    type = INSFVMomentumPressure
    variable = v
    momentum_component = 'y'
    pressure = pressure
  []

  [temp_time]
    type = INSFVEnergyTimeDerivative
    variable = T
    rho = ${rho}
    dh_dt = dh_dt
  []
  [temp_conduction]
    type = FVDiffusion
    coeff = 'k'
    variable = T
  []
  [temp_advection]
    type = INSFVEnergyAdvection
    variable = T
    velocity_interp_method = ${velocity_interp_method}
    advected_interp_method = ${advected_interp_method}
  []
[]

[FVBCs]
  [top_x]
    type = INSFVNoSlipWallBC
    variable = u
    boundary = 'top'
    function = 'lid_function'
  []

  [no_slip_x]
    type = INSFVNoSlipWallBC
    variable = u
    boundary = 'left right bottom'
    function = 0
  []

  [no_slip_y]
    type = INSFVNoSlipWallBC
    variable = v
    boundary = 'left right top bottom'
    function = 0
  []

  [T_hot]
    type = FVDirichletBC
    variable = T
    boundary = 'bottom'
    value = 1
  []

  [T_cold]
    type = FVDirichletBC
    variable = T
    boundary = 'top'
    value = 0
  []
[]

[FunctorMaterials]
  [functor_constants]
    type = ADGenericFunctorMaterial
    prop_names = 'cp k'
    prop_values = '${cp} ${k}'
  []
  [ins_fv]
    type = INSFVEnthalpyFunctorMaterial
    temperature = 'T'
    rho = ${rho}
  []
[]

[Functions]
  [lid_function]
    type = ParsedFunction
    expression = '4*x*(1-x)'
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  # Run for 100+ timesteps to reach steady state.
  num_steps = 5
  dt = .5
  dtmin = .5
  petsc_options_iname = '-pc_type -pc_factor_shift_type'
  petsc_options_value = 'lu NONZERO'
  line_search = 'none'
  nl_rel_tol = 1e-12
  nl_max_its = 6
[]

[Outputs]
  exodus = true
[]

(modules/navier_stokes/test/tests/finite_element/ins/lid_driven/ad_lid_driven.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 1.0
    ymin = 0
    ymax = 1.0
    nx = 16
    ny = 16
    elem_type = QUAD9
  []
  [./corner_node]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node'
    nodes = '0'
    input = gen
  [../]
[]

[AuxVariables]
  [vel_x]
    order = SECOND
  []
  [vel_y]
    order = SECOND
  []
[]

[AuxKernels]
  [vel_x]
    type = VectorVariableComponentAux
    variable = vel_x
    vector_variable = velocity
    component = 'x'
  []
  [vel_y]
    type = VectorVariableComponentAux
    variable = vel_y
    vector_variable = velocity
    component = 'y'
  []
[]

[Variables]
  [./velocity]
    order = SECOND
    family = LAGRANGE_VEC
  [../]

  [./T]
    order = SECOND
    [./InitialCondition]
      type = ConstantIC
      value = 1.0
    [../]
  [../]

  [./p]
  [../]
[]

[Kernels]
  [./mass]
    type = INSADMass
    variable = p
  [../]

  [./momentum_time]
    type = INSADMomentumTimeDerivative
    variable = velocity
  [../]

  [./momentum_convection]
    type = INSADMomentumAdvection
    variable = velocity
  [../]

  [./momentum_viscous]
    type = INSADMomentumViscous
    variable = velocity
  [../]

  [./momentum_pressure]
    type = INSADMomentumPressure
    variable = velocity
    pressure = p
    integrate_p_by_parts = true
  [../]

 [./temperature_time]
   type = INSADHeatConductionTimeDerivative
   variable = T
 [../]

 [./temperature_advection]
   type = INSADEnergyAdvection
   variable = T
 [../]

 [./temperature_conduction]
   type = ADHeatConduction
   variable = T
   thermal_conductivity = 'k'
 [../]
[]

[BCs]
  [./no_slip]
    type = VectorFunctionDirichletBC
    variable = velocity
    boundary = 'bottom right left'
  [../]

  [./lid]
    type = VectorFunctionDirichletBC
    variable = velocity
    boundary = 'top'
    function_x = 'lid_function'
  [../]

  [./T_hot]
    type = DirichletBC
    variable = T
    boundary = 'bottom'
    value = 1
  [../]

  [./T_cold]
    type = DirichletBC
    variable = T
    boundary = 'top'
    value = 0
  [../]

  [./pressure_pin]
    type = DirichletBC
    variable = p
    boundary = 'pinned_node'
    value = 0
  [../]
[]

[Materials]
  [./const]
    type = ADGenericConstantMaterial
    prop_names = 'rho mu cp k'
    prop_values = '1  1  1  .01'
  [../]
  [ins_mat]
    type = INSAD3Eqn
    velocity = velocity
    pressure = p
    temperature = T
  []
[]

[Functions]
  [./lid_function]
    # We pick a function that is exactly represented in the velocity
    # space so that the Dirichlet conditions are the same regardless
    # of the mesh spacing.
    type = ParsedFunction
    expression = '4*x*(1-x)'
  [../]
[]

[Preconditioning]
  [./SMP]
    type = SMP
    full = true
    solve_type = 'NEWTON'
  [../]
[]

[Executioner]
  type = Transient
  # Run for 100+ timesteps to reach steady state.
  num_steps = 5
  dt = .5
  dtmin = .5
  petsc_options_iname = '-pc_type -pc_asm_overlap -sub_pc_type -sub_pc_factor_levels'
  petsc_options_value = 'asm      2               ilu          4'
  line_search = 'none'
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-13
  nl_max_its = 6
  l_tol = 1e-6
  l_max_its = 500
[]

[Outputs]
  file_base = lid_driven_out
  exodus = true
  perf_graph = true
[]

(modules/solid_mechanics/test/tests/ad_anisotropic_creep/3d_bar_orthotropic_90deg_rotation_ad_creep_x_no_rotation.i)

[Mesh]
  [generated_mesh]
    type = GeneratedMeshGenerator
    dim = 3
    xmin = 0
    xmax = 2
    ymin = 0
    ymax = 10
    zmin = 0
    zmax = 2
    nx = 1
    ny = 1
    nz = 1
    elem_type = HEX8
  []
  [corner]
    type = ExtraNodesetGenerator
    new_boundary = 101
    coord = '0 0 0'
    input = generated_mesh
  []
  [side]
    type = ExtraNodesetGenerator
    new_boundary = 102
    coord = '2 0 0'
    input = corner
  []
[]

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = FINITE
    add_variables = true
    volumetric_locking_correction = true
    use_automatic_differentiation = true
    generate_output = 'elastic_strain_xx stress_xx creep_strain_xx creep_strain_yy creep_strain_zz'
  []
[]

[Materials]
  [elastic_strain]
    type = ADComputeMultipleInelasticStress
    inelastic_models = "trial_creep"
    max_iterations = 50
    absolute_tolerance = 1e-18
  []
  [hill_tensor]
    type = ADHillConstants
    # F G H L M N
    hill_constants = "0.25 0.4 0.65 1.5 1.5 1.5"
  []
  [trial_creep]
    type = ADHillCreepStressUpdate
    coefficient = 5e-14
    n_exponent = 10
    m_exponent = 0
    activation_energy = 0
    max_inelastic_increment = 0.00003
    absolute_tolerance = 1e-18
    relative_tolerance = 1e-18
    # Force it to not use integration error
    max_integration_error = 100.0
  []
  [elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    youngs_modulus = 500
    poissons_ratio = 0.0
  []
[]

[BCs]
  [fix_x]
    type = ADDirichletBC
    variable = disp_x
    boundary = bottom
    value = 0
  []

  [rot_z]
    type = DisplacementAboutAxis
    boundary = bottom
    function = 0
    angle_units = degrees
    axis_origin = '0. 0. 0.'
    axis_direction = '1. 0. 1.0e-13'
    component = 2
    variable = disp_z
  []
  #
  [rot_y]
    type = DisplacementAboutAxis
    boundary = bottom
    function = 0
    angle_units = degrees
    axis_origin = '0. 0. 0.'
    axis_direction = '1. 0. 1.0e-13'
    component = 1
    variable = disp_y
  []

  [rot_z90]
    type = DisplacementAboutAxis
    boundary = bottom
    function = 0
    angle_units = degrees
    axis_origin = '0. 0. 0.'
    axis_direction = '1. 0. 1.0e-13'
    component = 2
    variable = disp_z
  []
  #
  [rot_y90]
    type = DisplacementAboutAxis
    boundary = bottom
    function = 0
    angle_units = degrees
    axis_origin = '0. 0. 0.'
    axis_direction = '1. 0. 1.0e-13'
    component = 1
    variable = disp_y
  []

  [press]
    type = Pressure
    boundary = top
    function = '-1.0*(t-90)*0.1'
    use_displaced_mesh = true
    displacements = 'disp_x disp_y disp_z'
    variable = disp_y
  []
[]

[Postprocessors]
  [creep_strain_yy]
    type = ADElementAverageMaterialProperty
    mat_prop = creep_strain_yy
  []
[]

[Controls]
  [c1]
    type = TimePeriod
    enable_objects = 'BCs::rot_z BCs::rot_y'
    disable_objects = 'BCs::rot_z90 BCs::rot_y90 BCs::press'
    start_time = '0'
    end_time = '90'
  []
  [c190plus]
    type = TimePeriod
    enable_objects = 'BCs::rot_z90 BCs::rot_y90 BCs::press'
    disable_objects = 'BCs::rot_z BCs::rot_y '
    start_time = '90'
    end_time = '390'
  []
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-ksp_gmres_restart'
  petsc_options_value = '101'

  line_search = 'none'

  nl_rel_tol = 1e-11
  nl_abs_tol = 1e-11
  nl_max_its = 50

  l_tol = 1e-4
  l_max_its = 50
  start_time = 0.0

  dt = 0.1
  dtmin = 0.1

  num_steps = 1200
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Outputs]
  exodus = false
  csv = true
[]

(modules/navier_stokes/test/tests/auxkernels/reynolds-number-functor-aux/fe.i)

rho=1
mu=1

[GlobalParams]
  gravity = '0 0 0'
  pspg = true
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 10
  []
  [corner_node]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node'
    nodes = '0'
    input = gen
  []
[]

[AuxVariables]
  [Reynolds]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[AuxKernels]
  [Reynolds]
    type = ReynoldsNumberFunctorAux
    variable = Reynolds
    speed = speed
    rho = ${rho}
    mu = ${mu}
  []
[]

[Variables]
  [vel_x]
  []
  [vel_y]
  []
  [p]
  []
[]

[Kernels]
  # mass
  [mass]
    type = INSMass
    variable = p
    u = vel_x
    v = vel_y
    pressure = p
  []
  # x-momentum, space
  [x_momentum_space]
    type = INSMomentumLaplaceForm
    variable = vel_x
    u = vel_x
    v = vel_y
    pressure = p
    component = 0
  []
  # y-momentum, space
  [y_momentum_space]
    type = INSMomentumLaplaceForm
    variable = vel_y
    u = vel_x
    v = vel_y
    pressure = p
    component = 1
  []
[]

[BCs]
  [x_no_slip]
    type = DirichletBC
    variable = vel_x
    boundary = 'bottom right left'
    value = 0.0
  []
  [lid]
    type = FunctionDirichletBC
    variable = vel_x
    boundary = 'top'
    function = 'lid_function'
  []
  [y_no_slip]
    type = DirichletBC
    variable = vel_y
    boundary = 'bottom right top left'
    value = 0.0
  []
  [pressure_pin]
    type = DirichletBC
    variable = p
    boundary = 'pinned_node'
    value = 0
  []
[]

[Materials]
  [const]
    type = GenericConstantMaterial
    block = 0
    prop_names = 'rho mu'
    prop_values = '${rho}  ${mu}'
  []
  [speed]
    type = ADVectorMagnitudeFunctorMaterial
    x_functor = vel_x
    y_functor = vel_y
    vector_magnitude_name = speed
  []
[]

[Functions]
  [lid_function]
    # We pick a function that is exactly represented in the velocity
    # space so that the Dirichlet conditions are the same regardless
    # of the mesh spacing.
    type = ParsedFunction
    expression = '4*x*(1-x)'
  []
[]

[Preconditioning]
  [SMP]
    type = SMP
    full = true
    solve_type = 'NEWTON'
  []
[]

[Executioner]
  type = Steady
  petsc_options_iname = '-pc_type -pc_asm_overlap -sub_pc_type'
  petsc_options_value = 'asm      2               lu'
  line_search = 'none'
  nl_rel_tol = 1e-12
[]

[Outputs]
  exodus = true
[]

(modules/solid_mechanics/test/tests/ad_anisotropic_creep/3d_bar_orthotropic_90deg_rotation_ad_creep_z.i)

[Mesh]
  [generated_mesh]
    type = GeneratedMeshGenerator
    dim = 3
    xmin = 0
    xmax = 2
    ymin = 0
    ymax = 10
    zmin = 0
    zmax = 2
    nx = 1
    ny = 1
    nz = 1
    elem_type = HEX8
  []
  [corner]
    type = ExtraNodesetGenerator
    new_boundary = 101
    coord = '0 0 0'
    input = generated_mesh
  []
  [side]
    type = ExtraNodesetGenerator
    new_boundary = 102
    coord = '2 0 0'
    input = corner
  []
[]

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = FINITE
    add_variables = true
    volumetric_locking_correction = true
    use_automatic_differentiation = true
    generate_output = 'elastic_strain_xx stress_xx creep_strain_xx'
  []
[]

[Materials]
  [elastic_strain]
    type = ADComputeMultipleInelasticStress
    inelastic_models = "trial_creep"
    max_iterations = 50
    absolute_tolerance = 1e-18
  []
  [hill_tensor]
    type = ADHillConstants
    # F G H L M N
    hill_constants = "0.5 1.0 0.5 1.5 1.5 1.5"
    use_large_rotation = true
  []
  [trial_creep]
    type = ADHillCreepStressUpdate
    coefficient = 5e-14
    n_exponent = 10
    m_exponent = 0
    activation_energy = 0
    max_inelastic_increment = 0.00003
    absolute_tolerance = 1e-18
    relative_tolerance = 1e-18
    # Force it to not use integration error
    max_integration_error = 100.0
    use_transformation = true
  []
  [elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    youngs_modulus = 500
    poissons_ratio = 0.0
  []
[]

[BCs]
  [fix_z]
    type = ADDirichletBC
    variable = disp_z
    boundary = bottom
    value = 0
  []

  [rot_y]
    type = DisplacementAboutAxis
    boundary = bottom
    function = t
    angle_units = degrees
    axis_origin = '0. 0. 0.'
    axis_direction = '0. 0. 1.'
    component = 1
    variable = disp_y
  []
  #
  [rot_x]
    type = DisplacementAboutAxis
    boundary = bottom
    function = t
    angle_units = degrees
    axis_origin = '0. 0. 0.'
    axis_direction = '0. 0. 1.'
    component = 0
    variable = disp_x
  []

  [rot_y90]
    type = DisplacementAboutAxis
    boundary = bottom
    function = 90
    angle_units = degrees
    axis_origin = '0. 0. 0.'
    axis_direction = '0. 0. 1.'
    component = 1
    variable = disp_y
  []
  #
  [rot_x90]
    type = DisplacementAboutAxis
    boundary = bottom
    function = 90
    angle_units = degrees
    axis_origin = '0. 0. 0.'
    axis_direction = '0. 0. 1.'
    component = 0
    variable = disp_x
  []

  [press]
    boundary = top
    function = '-1.0*(t-90)*0.1'
    use_displaced_mesh = true
    displacements = 'disp_x disp_y disp_z'
    type = Pressure
    variable = disp_x
  []
[]

[Postprocessors]
  [creep_strain_xx]
    type = ADElementAverageMaterialProperty
    mat_prop = creep_strain_xx
  []
[]

[Controls]
  [c1]
    type = TimePeriod
    enable_objects = 'BCs::rot_x BCs::rot_y'
    disable_objects = 'BCs::rot_x90 BCs::rot_y90 BCs::press'
    start_time = '0'
    end_time = '90'
  []
  [c190plus]
    type = TimePeriod
    enable_objects = 'BCs::rot_x90 BCs::rot_y90 BCs::press'
    disable_objects = 'BCs::rot_x BCs::rot_y '
    start_time = '90'
    end_time = '390'
  []
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-ksp_gmres_restart'
  petsc_options_value = '101'

  line_search = 'none'

  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-12
  nl_max_its = 50

  automatic_scaling = true
  l_tol = 1e-4
  l_max_its = 50
  start_time = 0.0

  dt = 0.1
  dtmin = 0.1

  num_steps = 1200
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Outputs]
  exodus = false
  csv = true
[]

(modules/navier_stokes/test/tests/finite_element/ins/wall_convection/steady.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 1.0
    ymin = 0
    ymax = 1.0
    nx = 16
    ny = 16
  []
  [./corner_node]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node'
    nodes = '0'
    input = gen
  [../]
[]

[Variables]
  [./velocity]
    family = LAGRANGE_VEC
  [../]
  [./p]
  [../]
  [temperature][]
[]

[ICs]
  [velocity]
    type = VectorConstantIC
    x_value = 1e-15
    y_value = 1e-15
    variable = velocity
  []
[]

[Kernels]
  [./mass]
    type = INSADMass
    variable = p
  [../]
  [./mass_pspg]
    type = INSADMassPSPG
    variable = p
  [../]

  [./momentum_convection]
    type = INSADMomentumAdvection
    variable = velocity
  [../]

  [./momentum_viscous]
    type = INSADMomentumViscous
    variable = velocity
  [../]

  [./momentum_pressure]
    type = INSADMomentumPressure
    variable = velocity
    pressure = p
    integrate_p_by_parts = true
  [../]

  [./momentum_supg]
    type = INSADMomentumSUPG
    variable = velocity
    velocity = velocity
  [../]

 [./temperature_advection]
   type = INSADEnergyAdvection
   variable = temperature
 [../]

  [./temperature_conduction]
    type = ADHeatConduction
    variable = temperature
    thermal_conductivity = 'k'
  [../]

  [temperature_ambient_convection]
    type = INSADEnergyAmbientConvection
    variable = temperature
    alpha = 1
    T_ambient = 0.5
  []

  [temperature_supg]
    type = INSADEnergySUPG
    variable = temperature
    velocity = velocity
  []
[]

[BCs]
  [./no_slip]
    type = VectorFunctionDirichletBC
    variable = velocity
    boundary = 'bottom right left'
  [../]

  [./lid]
    type = VectorFunctionDirichletBC
    variable = velocity
    boundary = 'top'
    function_x = 'lid_function'
  [../]

  [./pressure_pin]
    type = DirichletBC
    variable = p
    boundary = 'pinned_node'
    value = 0
  [../]

  [./temperature_hot]
    type = DirichletBC
    variable = temperature
    boundary = 'bottom'
    value = 1
  [../]

  [./temperature_cold]
    type = DirichletBC
    variable = temperature
    boundary = 'top'
    value = 0
  [../]
[]

[Materials]
  [./const]
    type = ADGenericConstantMaterial
    prop_names = 'rho mu cp k'
    prop_values = '1  1  1  .01'
  [../]
  [ins_mat]
    type = INSADStabilized3Eqn
    velocity = velocity
    pressure = p
    temperature = temperature
  []
[]

[Functions]
  [./lid_function]
    # We pick a function that is exactly represented in the velocity
    # space so that the Dirichlet conditions are the same regardless
    # of the mesh spacing.
    type = ParsedFunction
    expression = '4*x*(1-x)'
  [../]
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -sub_pc_factor_levels -ksp_gmres_restart'
  petsc_options_value = 'asm      6                     200'
  line_search = 'none'
  nl_rel_tol = 1e-12
  nl_max_its = 6
[]

[Outputs]
  exodus = true
[]

(test/tests/mortar/periodic_segmental_constraint/penalty_periodic_split.i)

[Mesh]
  [left_block]
    type = GeneratedMeshGenerator
    dim = 3
    xmin = -3.0
    xmax = 3.0
    ymin = -3.0
    ymax = 3.0
    zmin = -3.0
    zmax = 3.0
    nx = 3
    ny = 3
    nz = 3
    elem_type = HEX8
  []
  [left_block_sidesets]
    type = RenameBoundaryGenerator
    input = left_block
    old_boundary = '0 1 2 3 4 5'
    new_boundary = '10 11 12 13 14 15'
  []
  [left_block_id]
    type = SubdomainIDGenerator
    input = left_block_sidesets
    subdomain_id = 1
  []
  [left]
    type = LowerDBlockFromSidesetGenerator
    input = left_block_id
    sidesets = '14'
    new_block_id = '10004'
    new_block_name = 'secondary_left'
  []
  [right]
    type = LowerDBlockFromSidesetGenerator
    input = left
    sidesets = '12'
    new_block_id = '10002'
    new_block_name = 'primary_right'
  []
  [bottom]
    type = LowerDBlockFromSidesetGenerator
    input = right
    sidesets = '10'
    new_block_id = '10000'
    new_block_name = 'secondary_bottom'
  []
  [top]
    type = LowerDBlockFromSidesetGenerator
    input = bottom
    sidesets = '15'
    new_block_id = '10005'
    new_block_name = 'primary_top'
  []
  [back]
    type = LowerDBlockFromSidesetGenerator
    input = top
    sidesets = '11'
    new_block_id = '10001'
    new_block_name = 'secondary_back'
  []
  [front]
    type = LowerDBlockFromSidesetGenerator
    input = back
    sidesets = '13'
    new_block_id = '10003'
    new_block_name = 'primary_front'
  []

  [corner_node]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node'
    nodes = '0'
    input = front
  []
[]

[Variables]
  [u]
    order = FIRST
    family = LAGRANGE
  []
  [epsilon]
    order = THIRD
    family = SCALAR
  []
[]

[AuxVariables]
  [sigma]
    order = THIRD
    family = SCALAR
  []
[]

[AuxScalarKernels]
  [sigma]
    type = FunctionScalarAux
    variable = sigma
    function = '1 2 3'
    execute_on = initial #timestep_end
  []
[]

[Kernels]
  [diff1]
    type = Diffusion
    variable = u
    block = 1
  []
[]

[Problem]
  kernel_coverage_check = false
  error_on_jacobian_nonzero_reallocation = true
[]

[BCs]
  [fix_right]
    type = DirichletBC
    variable = u
    boundary = pinned_node
    value = 0
  []
[]

[Constraints]
  [mortarlr]
    type = PenaltyEqualValueConstraint
    primary_boundary = '12'
    secondary_boundary = '14'
    primary_subdomain = 'primary_right'
    secondary_subdomain = 'secondary_left'
    secondary_variable = u
    correct_edge_dropping = true
    penalty_value = 1.e2
  []
  [periodiclr]
    type = PenaltyPeriodicSegmentalConstraint
    primary_boundary = '12'
    secondary_boundary = '14'
    primary_subdomain = 'primary_right'
    secondary_subdomain = 'secondary_left'
    secondary_variable = u
    epsilon = epsilon
    sigma = sigma
    correct_edge_dropping = true
    penalty_value = 1.e2
  []
  [mortarbt]
    type = PenaltyEqualValueConstraint
    primary_boundary = '15'
    secondary_boundary = '10'
    primary_subdomain = 'primary_top'
    secondary_subdomain = 'secondary_bottom'
    secondary_variable = u
    correct_edge_dropping = true
    penalty_value = 1.e2
  []
  [periodicbt]
    type = PenaltyPeriodicSegmentalConstraint
    primary_boundary = '15'
    secondary_boundary = '10'
    primary_subdomain = 'primary_top'
    secondary_subdomain = 'secondary_bottom'
    secondary_variable = u
    epsilon = epsilon
    sigma = sigma
    correct_edge_dropping = true
    penalty_value = 1.e2
  []
  [mortarbf]
    type = PenaltyEqualValueConstraint
    primary_boundary = '13'
    secondary_boundary = '11'
    primary_subdomain = 'primary_front'
    secondary_subdomain = 'secondary_back'
    secondary_variable = u
    correct_edge_dropping = true
    penalty_value = 1.e2
  []
  [periodicbf]
    type = PenaltyPeriodicSegmentalConstraint
    primary_boundary = '13'
    secondary_boundary = '11'
    primary_subdomain = 'primary_front'
    secondary_subdomain = 'secondary_back'
    secondary_variable = u
    epsilon = epsilon
    sigma = sigma
    correct_edge_dropping = true
    penalty_value = 1.e2
  []
[]

[Preconditioning]
  [FSP]
    type = FSP
    topsplit = 'uv' # 'uv' should match the following block name
    [uv]
      splitting = 'u v' # 'u' and 'v' are the names of subsolvers
      splitting_type = additive
    []
    [u]
      vars = 'u'
      petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
      petsc_options_value = '  201               hypre    boomeramg      10'
    []
    [v]
      vars = 'epsilon'
      petsc_options_iname = '-ksp_type -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
      petsc_options_value = ' preonly   hypre    boomeramg      10'
    []
  []
[]

[Executioner]
  type = Steady
  solve_type = NEWTON
[]

[Outputs]
  csv = true
[]

(modules/contact/test/tests/cohesive_zone_model/mortar_czm.i)

[Mesh]
  [msh]
    type = GeneratedMeshGenerator
    dim = 2
    xmax = 1
    ymax = 1
    nx = 5
    ny = 5
    boundary_name_prefix = bottom
  []
  [msh_id]
    type = SubdomainIDGenerator
    input = msh
    subdomain_id = 1
  []

  [msh_two]
    type = GeneratedMeshGenerator
    dim = 2
    xmax = 1
    ymin = 1
    ymax = 2
    nx = 5
    ny = 5
    boundary_name_prefix = top
    boundary_id_offset = 10
  []
  [msh_two_id]
    type = SubdomainIDGenerator
    input = msh_two
    subdomain_id = 2
  []
  [combined]
    type = MeshCollectionGenerator
    inputs = 'msh_id msh_two_id'
  []
  [top_node]
    type = ExtraNodesetGenerator
    coord = '0 2 0'
    input = combined
    new_boundary = top_node
  []
  [bottom_node]
    type = ExtraNodesetGenerator
    coord = '0 0 0'
    input = top_node
    new_boundary = bottom_node
  []
  # Build subdomains
  [secondary]
    type = LowerDBlockFromSidesetGenerator
    new_block_id = 10001
    new_block_name = 'secondary_lower'
    sidesets = 'bottom_top'
    input = bottom_node
  []
  [primary]
    type = LowerDBlockFromSidesetGenerator
    new_block_id = 10000
    sidesets = 'top_bottom'
    new_block_name = 'primary_lower'
    input = secondary
  []
  allow_renumbering = false
[]

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Physics]
  [SolidMechanics]
    [QuasiStatic]
      generate_output = 'stress_yy'
      [all]
        strain = FINITE
        add_variables = true
        use_automatic_differentiation = true
        decomposition_method = TaylorExpansion
        block = '1 2'
      []
    []
  []
[]

[BCs]
  [fix_x]
    type = DirichletBC
    preset = true
    value = 0.0
    boundary = bottom_node
    variable = disp_x
  []

  [fix_top]
    type = DirichletBC
    preset = true
    boundary = top_top
    variable = disp_x
    value = 0
  []

  [top]
    type = FunctionDirichletBC
    boundary = top_top
    variable = disp_y
    function = 'if(t<=0.3,t,if(t<=0.6,0.3-(t-0.3),0.6-t))'
    preset = true
  []

  [bottom]
    type = DirichletBC
    boundary = bottom_bottom
    variable = disp_y
    value = 0
    preset = true
  []
[]

[AuxVariables]
[]

[AuxKernels]
[]

[Materials]
  [stress]
    type = ADComputeFiniteStrainElasticStress
    block = '1 2'
  []
  [elasticity_tensor]
    type = ADComputeElasticityTensor
    fill_method = symmetric9
    C_ijkl = '1.684e5 0.176e5 0.176e5 1.684e5 0.176e5 1.684e5 0.754e5 0.754e5 0.754e5'
    block = '1 2'
  []
  [normal_strength]
    type = GenericFunctionMaterial
    prop_names = 'N'
    prop_values = 'if(x<0.5,1,100)*1e4'
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient

  solve_type = 'NEWTON'
  line_search = none

  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'

  automatic_scaling = true

  l_max_its = 2
  l_tol = 1e-14
  nl_max_its = 30
  nl_rel_tol = 1e-11
  nl_abs_tol = 1e-11
  start_time = 0.0
  dt = 0.01
  end_time = 0.05
  dtmin = 0.01
[]

[Outputs]
  exodus = true
[]

[UserObjects]
  [czm_uo]
    type = BilinearMixedModeCohesiveZoneModel
    primary_boundary = 'top_bottom'
    secondary_boundary = 'bottom_top'
    primary_subdomain = 10000
    secondary_subdomain = 10001

    disp_x = disp_x
    disp_y = disp_y
    friction_coefficient = 0.1 # with 2.0 works
    secondary_variable = disp_x

    penalty = 0e6
    penalty_friction = 1e4
    use_physical_gap = true

    correct_edge_dropping = true
    normal_strength = N
    shear_strength = 1e3
    viscosity = 1e-3
    penalty_stiffness = 1e6

    power_law_parameter = 2.2
    GI_c = 1e3
    GII_c = 1e2
    displacements = 'disp_x disp_y'
  []
[]

[Constraints]
  [x]
    type = NormalMortarMechanicalContact
    primary_boundary = 'top_bottom'
    secondary_boundary = 'bottom_top'
    primary_subdomain = 10000
    secondary_subdomain = 10001
    secondary_variable = disp_x
    component = x
    use_displaced_mesh = true
    compute_lm_residuals = false
    weighted_gap_uo = czm_uo
    correct_edge_dropping = true
  []
  [y]
    type = NormalMortarMechanicalContact
    primary_boundary = 'top_bottom'
    secondary_boundary = 'bottom_top'
    primary_subdomain = 10000
    secondary_subdomain = 10001
    secondary_variable = disp_y
    component = y
    use_displaced_mesh = true
    compute_lm_residuals = false
    weighted_gap_uo = czm_uo
    correct_edge_dropping = true
  []
  [c_x]
    type = MortarGenericTraction
    primary_boundary = 'top_bottom'
    secondary_boundary = 'bottom_top'
    primary_subdomain = 10000
    secondary_subdomain = 10001
    secondary_variable = disp_x
    component = x
    use_displaced_mesh = true
    compute_lm_residuals = false
    cohesive_zone_uo = czm_uo
    correct_edge_dropping = true
  []
  [c_y]
    type = MortarGenericTraction
    primary_boundary = 'top_bottom'
    secondary_boundary = 'bottom_top'
    primary_subdomain = 10000
    secondary_subdomain = 10001
    secondary_variable = disp_y
    component = y
    use_displaced_mesh = true
    compute_lm_residuals = false
    cohesive_zone_uo = czm_uo
    correct_edge_dropping = true
  []
[]

(modules/combined/test/tests/optimization/compliance_sensitivity/3d_mbb.i)

vol_frac = 0.5
E0 = 1
Emin = 1e-8
power = 3
[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
[]

[Mesh]
  [MeshGenerator]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 30
    ny = 10
    nz = 10
    xmin = 0
    xmax = 30
    ymin = 0
    ymax = 10
    zmin = 0
    zmax = 10
  []
  [node]
    type = ExtraNodesetGenerator
    input = MeshGenerator
    new_boundary = hold_y
    coord = '0 0 0; 0 0 10'
  []
  [push]
    type = ExtraNodesetGenerator
    input = node
    new_boundary = push
    coord = '30 10 5'
  []
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [disp_z]
  []
  [Dc]
    initial_condition = -1.0
  []
[]

[AuxVariables]
  [sensitivity]
    family = MONOMIAL
    order = FIRST
    initial_condition = -1.0
    [AuxKernel]
      type = MaterialRealAux
      variable = sensitivity
      property = sensitivity
      execute_on = LINEAR
    []
  []
  [mat_den]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = ${vol_frac}
  []
  [Dc_elem]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = -1.0
    [AuxKernel]
      type = SelfAux
      variable = Dc_elem
      v = Dc
      execute_on = 'TIMESTEP_END'
    []
  []
  [mat_den_nodal]
    family = L2_LAGRANGE
    order = FIRST
    initial_condition = ${vol_frac}
    [AuxKernel]
      type = SelfAux
      execute_on = TIMESTEP_END
      variable = mat_den_nodal
      v = mat_den
    []
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = SMALL
    add_variables = true
    incremental = false
  []
[]
[Kernels]
  [diffusion]
    type = FunctionDiffusion
    variable = Dc
    function = 0.15 # radius coeff
  []
  [potential]
    type = Reaction
    variable = Dc
  []
  [source]
    type = CoupledForce
    variable = Dc
    v = sensitivity
  []
[]
[BCs]
  [no_x]
    type = DirichletBC
    variable = disp_y
    boundary = hold_y
    value = 0.0
  []
  [no_y]
    type = DirichletBC
    variable = disp_x
    boundary = right
    value = 0.0
  []
  [boundary_penalty]
    type = ADRobinBC
    variable = Dc
    boundary = 'left top front back'
    coefficient = 10
  []
  [boundary_penalty_right]
    type = ADRobinBC
    variable = Dc
    boundary = 'right'
    coefficient = 10
  []
[]
[NodalKernels]
  [push]
    type = NodalGravity
    variable = disp_y
    boundary = push
    gravity_value = -1
    mass = 1
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeVariableIsotropicElasticityTensor
    youngs_modulus = E_phys
    poissons_ratio = poissons_ratio
    args = 'mat_den'
  []
  [E_phys]
    type = DerivativeParsedMaterial
    # Emin + (density^penal) * (E0 - Emin)
    expression = '${Emin} + (mat_den ^ ${power}) * (${E0}-${Emin})'
    coupled_variables = 'mat_den'
    property_name = E_phys
  []
  [poissons_ratio]
    type = GenericConstantMaterial
    prop_names = poissons_ratio
    prop_values = 0.3
  []
  [stress]
    type = ComputeLinearElasticStress
  []
  [dc]
    type = ComplianceSensitivity
    design_density = mat_den
    youngs_modulus = E_phys
    incremental = false
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]
[UserObjects]
  [update]
    type = DensityUpdate
    density_sensitivity = Dc_elem
    design_density = mat_den
    volume_fraction = ${vol_frac}
    execute_on = TIMESTEP_BEGIN
    force_postaux = true
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'
  line_search = none
  nl_abs_tol = 1e-4
  l_max_its = 200
  start_time = 0.0
  dt = 1.0
  num_steps = 2
[]

[Outputs]
  [out]
    type = CSV
    execute_on = 'INITIAL TIMESTEP_END'
  []
  print_linear_residuals = false
[]

[Postprocessors]
  [total_vol]
    type = ElementIntegralVariablePostprocessor
    variable = mat_den
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [sensitivity]
    type = ElementIntegralMaterialProperty
    mat_prop = sensitivity
  []
[]

[Controls]
  [first_period]
    type = TimePeriod
    start_time = 0.0
    end_time = 10
    enable_objects = 'BCs::boundary_penalty_right'
    execute_on = 'initial timestep_begin'
  []
[]

(modules/combined/tutorials/introduction/thermal_mechanical/thermomech_step01.i)

#
# Single block coupled thermal/mechanical
# https://mooseframework.inl.gov/modules/combined/tutorials/introduction/thermoech_step01.html
#

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  [generated]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 10
    xmax = 2
    ymax = 1
  []
  [pin]
    type = ExtraNodesetGenerator
    input = generated
    new_boundary = pin
    coord = '0 0 0'
  []
[]

[Variables]
  [T]
    initial_condition = 300.0
  []
[]

[Kernels]
  [heat_conduction]
    type = HeatConduction
    variable = T
  []
  [time_derivative]
    type = HeatConductionTimeDerivative
    variable = T
  []
  [heat_source]
    type = HeatSource
    variable = T
    value = 5e4
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    add_variables = true
    strain = FINITE
    automatic_eigenstrain_names = true
    generate_output = 'vonmises_stress'
  []
[]

[Materials]
  [thermal]
    type = HeatConductionMaterial
    thermal_conductivity = 45.0
    specific_heat = 0.5
  []
  [density]
    type = GenericConstantMaterial
    prop_names = 'density'
    prop_values = 8000.0
  []
  [elasticity]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 1e9
    poissons_ratio = 0.3
  []
  [expansion1]
    type = ComputeThermalExpansionEigenstrain
    temperature = T
    thermal_expansion_coeff = 0.001
    stress_free_temperature = 300
    eigenstrain_name = thermal_expansion
  []
  [stress]
    type = ComputeFiniteStrainElasticStress
  []
[]

[BCs]
  [t_left]
    type = DirichletBC
    variable = T
    value = 300
    boundary = 'left'
  []
  [t_right]
    type = FunctionDirichletBC
    variable = T
    function = '300+5*t'
    boundary = 'right'
  []
  [pin_x]
    type = DirichletBC
    variable = disp_x
    boundary = pin
    value = 0
  []
  [bottom_y]
    type = DirichletBC
    variable = disp_y
    boundary = bottom
    value = 0
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  end_time = 5
  dt = 1
[]

[Outputs]
  exodus = true
[]

(modules/combined/examples/optimization/2d_mbb.i)

vol_frac = 0.5
E0 = 1
Emin = 1e-8
power = 2
[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  [MeshGenerator]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 150
    ny = 50
    xmin = 0
    xmax = 30
    ymin = 0
    ymax = 10
  []
  [node]
    type = ExtraNodesetGenerator
    input = MeshGenerator
    new_boundary = pull
    nodes = 0
  []
  [push]
    type = ExtraNodesetGenerator
    input = node
    new_boundary = push
    coord = '30 10 0'
  []

[]

[AuxVariables]

  [Emin]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = ${Emin}
  []
  [power]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = ${power}
  []
  [E0]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = ${E0}
  []
  [Dc]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = -1.0
  []
  [mat_den]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = ${vol_frac}
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = SMALL
    add_variables = true
    incremental = false
  []
[]

[BCs]
  [no_x]
    type = DirichletBC
    variable = disp_y
    boundary = pull
    value = 0.0
  []
  [no_y]
    type = DirichletBC
    variable = disp_x
    boundary = right
    value = 0.0
  []

[]
[NodalKernels]
  [pull]
    type = NodalGravity
    variable = disp_y
    boundary = push
    gravity_value = -1
    mass = 1
  []
[]
[Materials]
  [elasticity_tensor]
    type = ComputeVariableIsotropicElasticityTensor
    youngs_modulus = E_phys
    poissons_ratio = poissons_ratio
    args = 'Emin mat_den power E0'
  []
  [E_phys]
    type = DerivativeParsedMaterial
    # Emin + (density^penal) * (E0 - Emin)
    expression = '${Emin} + (mat_den ^ ${power}) * (${E0}-${Emin})'
    coupled_variables = 'mat_den'
    property_name = E_phys
  []
  [poissons_ratio]
    type = GenericConstantMaterial
    prop_names = poissons_ratio
    prop_values = 0.3
  []
  [stress]
    type = ComputeLinearElasticStress
  []
  [dc]
    type = ComplianceSensitivity
    design_density = mat_den
    youngs_modulus = E_phys
    incremental = false
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]
[UserObjects]
  [rad_avg]
    type = RadialAverage
    radius = 1.2
    weights = linear
    prop_name = sensitivity
    execute_on = TIMESTEP_END
    force_preaux = true
  []
  [update]
    type = DensityUpdate
    density_sensitivity = Dc
    design_density = mat_den
    volume_fraction = ${vol_frac}
    execute_on = TIMESTEP_BEGIN
  []
  [calc_sense]
    type = SensitivityFilter
    density_sensitivity = Dc
    design_density = mat_den
    filter_UO = rad_avg
    execute_on = TIMESTEP_END
    force_postaux = true
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'
  nl_abs_tol = 1e-8
  dt = 1.0
  num_steps = 70
[]

[Outputs]
  [out]
    type = Exodus
    execute_on = 'TIMESTEP_END'
  []
  print_linear_residuals = false
[]

[Postprocessors]
  [total_vol]
    type = ElementIntegralVariablePostprocessor
    variable = mat_den
    execute_on = 'INITIAL TIMESTEP_END'
  []
[]

(modules/navier_stokes/test/tests/finite_element/ins/energy_source/steady.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 1.0
    ymin = 0
    ymax = 1.0
    nx = 16
    ny = 16
  []
  [./corner_node]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node'
    nodes = '0'
    input = gen
  [../]
[]

[Variables]
  [./velocity]
    family = LAGRANGE_VEC
  [../]
  [./p]
  [../]
  [temperature][]
[]

[ICs]
  [velocity]
    type = VectorConstantIC
    x_value = 1e-15
    y_value = 1e-15
    variable = velocity
  []
[]

[Kernels]
  [./mass]
    type = INSADMass
    variable = p
  [../]
  [./mass_pspg]
    type = INSADMassPSPG
    variable = p
  [../]

  [./momentum_convection]
    type = INSADMomentumAdvection
    variable = velocity
  [../]

  [./momentum_viscous]
    type = INSADMomentumViscous
    variable = velocity
  [../]

  [./momentum_pressure]
    type = INSADMomentumPressure
    variable = velocity
    pressure = p
    integrate_p_by_parts = true
  [../]

  [./momentum_supg]
    type = INSADMomentumSUPG
    variable = velocity
    velocity = velocity
  [../]

 [./temperature_advection]
   type = INSADEnergyAdvection
   variable = temperature
 [../]

  [./temperature_conduction]
    type = ADHeatConduction
    variable = temperature
    thermal_conductivity = 'k'
  [../]

  [temperature_source]
    type = INSADEnergySource
    variable = temperature
    source_function = 1
  []

  [temperature_supg]
    type = INSADEnergySUPG
    variable = temperature
    velocity = velocity
  []
[]

[BCs]
  [./no_slip]
    type = VectorFunctionDirichletBC
    variable = velocity
    boundary = 'bottom right left'
  [../]

  [./lid]
    type = VectorFunctionDirichletBC
    variable = velocity
    boundary = 'top'
    function_x = 'lid_function'
  [../]

  [./pressure_pin]
    type = DirichletBC
    variable = p
    boundary = 'pinned_node'
    value = 0
  [../]

  [./temperature_hot]
    type = DirichletBC
    variable = temperature
    boundary = 'bottom'
    value = 1
  [../]

  [./temperature_cold]
    type = DirichletBC
    variable = temperature
    boundary = 'top'
    value = 0
  [../]
[]

[Materials]
  [./const]
    type = ADGenericConstantMaterial
    prop_names = 'rho mu cp k'
    prop_values = '1  1  1  .01'
  [../]
  [ins_mat]
    type = INSADStabilized3Eqn
    velocity = velocity
    pressure = p
    temperature = temperature
  []
[]

[Functions]
  [./lid_function]
    # We pick a function that is exactly represented in the velocity
    # space so that the Dirichlet conditions are the same regardless
    # of the mesh spacing.
    type = ParsedFunction
    expression = '4*x*(1-x)'
  [../]
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -sub_pc_factor_levels -ksp_gmres_restart'
  petsc_options_value = 'asm      6                     200'
  line_search = 'none'
  nl_rel_tol = 1e-12
  nl_max_its = 6
[]

[Outputs]
  exodus = true
[]

(test/tests/meshgenerators/extra_nodeset_generator/closest_point_nodeset.i)

[Mesh]
  parallel_type = distributed
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 10
  []

  [eng1]
    type = ExtraNodesetGenerator
    input = gen
    new_boundary = 'corner'
    coord = '0.99 0.99; -0.1 -0.1; 1.1 0'
    use_closest_node = true
  []
[]

[Outputs]
  exodus = true
[]

(test/tests/mortar/periodic_segmental_constraint/penalty_periodic_checker2d.i)

[Mesh]
  [left_block]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = -1.0
    xmax = 1.0
    ymin = -1.0
    ymax = 1.0
    nx = 16
    ny = 16
    elem_type = QUAD4
  []
  [left_block_sidesets]
    type = RenameBoundaryGenerator
    input = left_block
    old_boundary = '0 1 2 3'
    new_boundary = '10 11 12 13'
  []
  [left_block_id]
    type = SubdomainIDGenerator
    input = left_block_sidesets
    subdomain_id = 1
  []
  [./lowrig]
    type = SubdomainBoundingBoxGenerator
    input = 'left_block_id'
    block_id = 2
    bottom_left = '0 -1 0'
    top_right = '1 0 0'
  [../]
  [./upplef]
    type = SubdomainBoundingBoxGenerator
    input = 'lowrig'
    block_id = 3
    bottom_left = '-1 0 0'
    top_right = '0 1 0'
  [../]
  [./upprig]
    type = SubdomainBoundingBoxGenerator
    input = 'upplef'
    block_id = 4
    bottom_left = '0 0 0'
    top_right = '1 1 0'
  [../]
  [left]
    type = LowerDBlockFromSidesetGenerator
    input = upprig
    sidesets = '13'
    new_block_id = '10003'
    new_block_name = 'secondary_left'
  []
  [right]
    type = LowerDBlockFromSidesetGenerator
    input = left
    sidesets = '11'
    new_block_id = '10001'
    new_block_name = 'primary_right'
  []
  [bottom]
    type = LowerDBlockFromSidesetGenerator
    input = right
    sidesets = '10'
    new_block_id = '10000'
    new_block_name = 'secondary_bottom'
  []
  [top]
    type = LowerDBlockFromSidesetGenerator
    input = bottom
    sidesets = '12'
    new_block_id = '10002'
    new_block_name = 'primary_top'
  []

  [corner_node]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node'
    nodes = '0'
    input = top
  []
[]

[Variables]
  [u]
    order = FIRST
    family = LAGRANGE
  []
  [epsilon]
    order = SECOND
    family = SCALAR
  []
[]

[AuxVariables]
  [sigma]
    order = SECOND
    family = SCALAR
  []
  [./flux_x]
      order = FIRST
      family = MONOMIAL
  [../]
  [./flux_y]
      order = FIRST
      family = MONOMIAL
  [../]
[]

[AuxScalarKernels]
  [sigma]
    type = FunctionScalarAux
    variable = sigma
    function = '1 3'
    execute_on = initial #timestep_end
  []
[]

[AuxKernels]
  [./flux_x]
    type = DiffusionFluxAux
    diffusivity = 'conductivity'
    variable = flux_x
    diffusion_variable = u
    component = x
    block = '1 2 3 4'
  [../]
  [./flux_y]
    type = DiffusionFluxAux
    diffusivity = 'conductivity'
    variable = flux_y
    diffusion_variable = u
    component = y
    block = '1 2 3 4'
  [../]
[]

[Kernels]
  [diff1]
    type = Diffusion
    variable = u
    block = '1 4'
  []
  [diff2]
    type = MatDiffusion
    variable = u
    block = '2 3'
    diffusivity = conductivity
  []
[]

[Materials]
  [k1]
    type = GenericConstantMaterial
    prop_names = 'conductivity'
    prop_values = 1.0
    block = '1 4'
  []
  [k2]
    type = GenericConstantMaterial
    prop_names = 'conductivity'
    prop_values = 10.0
    block = '2 3'
  []
[]

[Problem]
  kernel_coverage_check = false
  error_on_jacobian_nonzero_reallocation = true
[]

[BCs]
  [fix_right]
    type = DirichletBC
    variable = u
    boundary = pinned_node
    value = 0
  []
[]

[Constraints]
  [mortarlr]
    type = PenaltyEqualValueConstraint
    primary_boundary = '11'
    secondary_boundary = '13'
    primary_subdomain = 'primary_right'
    secondary_subdomain = 'secondary_left'
    secondary_variable = u
    correct_edge_dropping = true
    penalty_value = 1.e2
  []
  [periodiclr]
    type = PenaltyPeriodicSegmentalConstraint
    primary_boundary = '11'
    secondary_boundary = '13'
    primary_subdomain = 'primary_right'
    secondary_subdomain = 'secondary_left'
    secondary_variable = u
    epsilon = epsilon
    sigma = sigma
    correct_edge_dropping = true
    penalty_value = 1.e2
  []
  [mortarbt]
    type = PenaltyEqualValueConstraint
    primary_boundary = '12'
    secondary_boundary = '10'
    primary_subdomain = 'primary_top'
    secondary_subdomain = 'secondary_bottom'
    secondary_variable = u
    correct_edge_dropping = true
    penalty_value = 1.e2
  []
  [periodicbt]
    type = PenaltyPeriodicSegmentalConstraint
    primary_boundary = '12'
    secondary_boundary = '10'
    primary_subdomain = 'primary_top'
    secondary_subdomain = 'secondary_bottom'
    secondary_variable = u
    epsilon = epsilon
    sigma = sigma
    correct_edge_dropping = true
    penalty_value = 1.e2
  []
[]

[Preconditioning]
  [smp]
    full = true
    type = SMP
  []
[]

[Executioner]
  type = Steady
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  solve_type = NEWTON
[]

[Postprocessors]
  [max]
    type = ElementExtremeValue
    variable = 'flux_x'
  []
[]

[Outputs]
  csv = true
[]

(modules/combined/examples/optimization/3d_mbb.i)

vol_frac = 0.5
E0 = 1
Emin = 1e-8
power = 2
[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
[]

[Mesh]
  [MeshGenerator]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 60
    ny = 20
    nz = 20
    xmin = 0
    xmax = 30
    ymin = 0
    ymax = 10
    zmin = 0
    zmax = 10
  []
  [node]
    type = ExtraNodesetGenerator
    input = MeshGenerator
    new_boundary = hold_y
    coord = '0 0 0; 0 0 10'
  []
  [push]
    type = ExtraNodesetGenerator
    input = node
    new_boundary = push
    coord = '30 10 5'
  []
[]

[Variables]
  [disp_z]
  []
  [Dc]
    initial_condition = -1.0
  []
[]

[AuxVariables]
  [Emin]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = ${Emin}
  []
  [power]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = ${power}
  []
  [E0]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = ${E0}
  []
  [sensitivity]
    family = MONOMIAL
    order = FIRST
    initial_condition = -1.0
    [AuxKernel]
      type = MaterialRealAux
      variable = sensitivity
      property = sensitivity
      execute_on = LINEAR
    []
  []
  [mat_den]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = ${vol_frac}
  []
  [Dc_elem]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = -1.0
    [AuxKernel]
      type = SelfAux
      variable = Dc_elem
      v = Dc
      execute_on = 'TIMESTEP_END'
    []
  []
  [mat_den_nodal]
    family = L2_LAGRANGE
    order = FIRST
    initial_condition = ${vol_frac}
    [AuxKernel]
      type = SelfAux
      execute_on = TIMESTEP_END
      variable = mat_den_nodal
      v = mat_den
    []
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = SMALL
    add_variables = true
    incremental = false
  []
[]
[Kernels]
  [diffusion]
    type = FunctionDiffusion
    variable = Dc
    function = 0.15 # radius coeff
  []
  [potential]
    type = Reaction
    variable = Dc
  []
  [source]
    type = CoupledForce
    variable = Dc
    v = sensitivity
  []
[]
[BCs]
  [no_x]
    type = DirichletBC
    variable = disp_y
    boundary = hold_y
    value = 0.0
  []
  [no_y]
    type = DirichletBC
    variable = disp_x
    boundary = right
    value = 0.0
  []
  [boundary_penalty]
    type = ADRobinBC
    variable = Dc
    boundary = 'left top front back'
    coefficient = 10
  []
  [boundary_penalty_right]
    type = ADRobinBC
    variable = Dc
    boundary = 'right'
    coefficient = 10
  []
[]
[NodalKernels]
  [push]
    type = NodalGravity
    variable = disp_y
    boundary = push
    gravity_value = -1
    mass = 1
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeVariableIsotropicElasticityTensor
    youngs_modulus = E_phys
    poissons_ratio = poissons_ratio
    args = 'Emin mat_den power E0'
  []
  [E_phys]
    type = DerivativeParsedMaterial
    # Emin + (density^penal) * (E0 - Emin)
    expression = '${Emin} + (mat_den ^ ${power}) * (${E0}-${Emin})'
    coupled_variables = 'mat_den'
    property_name = E_phys
  []
  [poissons_ratio]
    type = GenericConstantMaterial
    prop_names = poissons_ratio
    prop_values = 0.3
  []
  [stress]
    type = ComputeLinearElasticStress
  []
  [dc]
    type = ComplianceSensitivity
    design_density = mat_den
    youngs_modulus = E_phys
    incremental = false
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]
[UserObjects]
  [update]
    type = DensityUpdate
    density_sensitivity = Dc_elem
    design_density = mat_den
    volume_fraction = ${vol_frac}
    execute_on = TIMESTEP_BEGIN
    force_postaux = true
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'
  line_search = none
  nl_abs_tol = 1e-4
  l_max_its = 200
  start_time = 0.0
  dt = 1.0
  num_steps = 70
[]

[Outputs]
  [out]
    type = Exodus
    execute_on = 'INITIAL TIMESTEP_END'
  []
  print_linear_residuals = false
[]

[Postprocessors]
  [total_vol]
    type = ElementIntegralVariablePostprocessor
    variable = mat_den
    execute_on = 'INITIAL TIMESTEP_END'
  []
[]

[Controls]
  [first_period]
    type = TimePeriod
    start_time = 0.0
    end_time = 10
    enable_objects = 'BCs::boundary_penalty_right'
    execute_on = 'initial timestep_begin'
  []
[]

(test/tests/meshgenerators/extra_nodeset_generator/generate_extra_nodeset_coord.i)

[Mesh]
  [./square]
    type = GeneratedMeshGenerator
    nx = 2
    ny = 2
    dim = 2
  [../]

  [./extra_nodeset]
    type = ExtraNodesetGenerator
    input = square
    new_boundary = 'middle_node'
    coord = '0.5 0.5'
  []
[]

[Outputs]
  exodus = true
[]

(modules/combined/examples/periodic_strain/global_strain_pfm_3D.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 20
    ny = 20
    nz = 20
    xmin = -0.5
    xmax = 0.5
    ymin = -0.5
    ymax = 0.5
    zmin = -0.5
    zmax = 0.5
  []
  [./cnode]
    input = gen
    type = ExtraNodesetGenerator
    coord = '0.0 0.0 0.0'
    new_boundary = 100
  [../]
[]

[Variables]
  [./u_x]
  [../]
  [./u_y]
  [../]
  [./u_z]
  [../]
  [./global_strain]
    order = SIXTH
    family = SCALAR
  [../]
  [./c]
    [./InitialCondition]
      type = FunctionIC
      function = 'sin(2*x*pi)*sin(2*y*pi)*sin(2*z*pi)*0.05+0.6'
    [../]
  [../]
  [./w]
  [../]
[]

[AuxVariables]
  [./local_energy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./disp_x]
  [../]
  [./disp_y]
  [../]
  [./disp_z]
  [../]
  [./s00]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./s01]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./s10]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./s11]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./e00]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./e01]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./e10]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./e11]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[AuxKernels]
  [./disp_x]
    type = GlobalDisplacementAux
    variable = disp_x
    scalar_global_strain = global_strain
    global_strain_uo = global_strain_uo
    component = 0
  [../]
  [./disp_y]
    type = GlobalDisplacementAux
    variable = disp_y
    scalar_global_strain = global_strain
    global_strain_uo = global_strain_uo
    component = 1
  [../]
  [./disp_z]
    type = GlobalDisplacementAux
    variable = disp_z
    scalar_global_strain = global_strain
    global_strain_uo = global_strain_uo
    component = 2
  [../]
  [./local_free_energy]
    type = TotalFreeEnergy
    execute_on = 'initial LINEAR'
    variable = local_energy
    interfacial_vars = 'c'
    kappa_names = 'kappa_c'
  [../]
  [./s00]
    type = RankTwoAux
    variable = s00
    rank_two_tensor = stress
    index_i = 0
    index_j = 0
  [../]
  [./s01]
    type = RankTwoAux
    variable = s01
    rank_two_tensor = stress
    index_i = 0
    index_j = 1
  [../]
  [./s10]
    type = RankTwoAux
    variable = s10
    rank_two_tensor = stress
    index_i = 1
    index_j = 0
  [../]
  [./s11]
    type = RankTwoAux
    variable = s11
    rank_two_tensor = stress
    index_i = 1
    index_j = 1
  [../]
  [./e00]
    type = RankTwoAux
    variable = e00
    rank_two_tensor = total_strain
    index_i = 0
    index_j = 0
  [../]
  [./e01]
    type = RankTwoAux
    variable = e01
    rank_two_tensor = total_strain
    index_i = 0
    index_j = 1
  [../]
  [./e10]
    type = RankTwoAux
    variable = e10
    rank_two_tensor = total_strain
    index_i = 1
    index_j = 0
  [../]
  [./e11]
    type = RankTwoAux
    variable = e11
    rank_two_tensor = total_strain
    index_i = 1
    index_j = 1
  [../]
[]

[GlobalParams]
  derivative_order = 2
  enable_jit = true
  displacements = 'u_x u_y u_z'
  block = 0
[]

[Kernels]
  [./TensorMechanics]
  [../]

  # Cahn-Hilliard kernels
  [./c_dot]
    type = CoupledTimeDerivative
    variable = w
    v = c
    block = 0
  [../]
  [./c_res]
    type = SplitCHParsed
    variable = c
    f_name = F
    kappa_name = kappa_c
    w = w
    block = 0
  [../]
  [./w_res]
    type = SplitCHWRes
    variable = w
    mob_name = M
    block = 0
  [../]
[]

[ScalarKernels]
  [./global_strain]
    type = GlobalStrain
    variable = global_strain
    global_strain_uo = global_strain_uo
  [../]
[]

[BCs]
  [./Periodic]
    [./all]
      auto_direction = 'x y z'
      variable = 'c w u_x u_y u_z'
    [../]
  [../]

  # fix center point location
  [./centerfix_x]
    type = DirichletBC
    boundary = 100
    variable = u_x
    value = 0
  [../]
  [./centerfix_y]
    type = DirichletBC
    boundary = 100
    variable = u_y
    value = 0
  [../]
  [./centerfix_z]
    type = DirichletBC
    boundary = 100
    variable = u_z
    value = 0
  [../]
[]

[Materials]
  [./consts]
    type = GenericConstantMaterial
    prop_names  = 'M   kappa_c'
    prop_values = '0.2 0.01   '
  [../]

  [./shear1]
    type = GenericConstantRankTwoTensor
    tensor_values = '0 0 0 0.5 0.5 0.5'
    tensor_name = shear1
  [../]
  [./shear2]
    type = GenericConstantRankTwoTensor
    tensor_values = '0 0 0 -0.5 -0.5 -0.5'
    tensor_name = shear2
  [../]
  [./expand3]
    type = GenericConstantRankTwoTensor
    tensor_values = '1 1 1 0 0 0'
    tensor_name = expand3
  [../]

  [./weight1]
    type = DerivativeParsedMaterial
    expression = '0.3*c^2'
    property_name = weight1
    coupled_variables = c
  [../]
  [./weight2]
    type = DerivativeParsedMaterial
    expression = '0.3*(1-c)^2'
    property_name = weight2
    coupled_variables = c
  [../]
  [./weight3]
    type = DerivativeParsedMaterial
    expression = '4*(0.5-c)^2'
    property_name = weight3
    coupled_variables = c
  [../]

  [./elasticity_tensor]
    type = ComputeElasticityTensor
    C_ijkl = '1 1'
    fill_method = symmetric_isotropic
  [../]
  [./strain]
    type = ComputeSmallStrain
    global_strain = global_strain
    eigenstrain_names = eigenstrain
  [../]

  [./eigenstrain]
    type = CompositeEigenstrain
    tensors = 'shear1  shear2  expand3'
    weights = 'weight1 weight2 weight3'
    coupled_variables = c
    eigenstrain_name = eigenstrain
  [../]

  [./global_strain]
    type = ComputeGlobalStrain
    scalar_global_strain = global_strain
    global_strain_uo = global_strain_uo
  [../]

  [./stress]
    type = ComputeLinearElasticStress
  [../]

  # chemical free energies
  [./chemical_free_energy]
    type = DerivativeParsedMaterial
    property_name = Fc
    expression = '4*c^2*(1-c)^2'
    coupled_variables = 'c'
    outputs = exodus
    output_properties = Fc
  [../]

  # elastic free energies
  [./elastic_free_energy]
    type = ElasticEnergyMaterial
    f_name = Fe
    coupled_variables = 'c'
    outputs = exodus
    output_properties = Fe
  [../]

  # free energy (chemical + elastic)
  [./free_energy]
    type = DerivativeSumMaterial
    block = 0
    property_name = F
    sum_materials = 'Fc Fe'
    coupled_variables = 'c'
  [../]
[]

[UserObjects]
  [./global_strain_uo]
    type = GlobalStrainUserObject
    execute_on = 'Initial Linear Nonlinear'
  [../]
[]

[Postprocessors]
  [./total_free_energy]
    type = ElementIntegralVariablePostprocessor
    execute_on = 'initial TIMESTEP_END'
    variable = local_energy
  [../]
  [./total_solute]
    type = ElementIntegralVariablePostprocessor
    execute_on = 'initial TIMESTEP_END'
    variable = c
  [../]
  [./min]
    type = ElementExtremeValue
    execute_on = 'initial TIMESTEP_END'
    value_type = min
    variable = c
  [../]
  [./max]
    type = ElementExtremeValue
    execute_on = 'initial TIMESTEP_END'
    value_type = max
    variable = c
  [../]
[]

[Preconditioning]
  [./SMP]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = Transient
  scheme = bdf2
  solve_type = 'PJFNK'

  line_search = basic

  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_ksp_type -sub_pc_type -pc_asm_overlap'
  petsc_options_value = 'asm         31   preonly   lu      1'

  l_max_its = 30
  nl_max_its = 12

  l_tol = 1.0e-4

  nl_rel_tol = 1.0e-8
  nl_abs_tol = 1.0e-10

  start_time = 0.0
  end_time = 2.0

  [./TimeStepper]
    type = IterationAdaptiveDT
    dt = 0.01
    growth_factor = 1.5
    cutback_factor = 0.8
    optimal_iterations = 9
    iteration_window = 2
  [../]
[]

[Outputs]
  execute_on = 'timestep_end'
  print_linear_residuals = false
  exodus = true
  [./table]
    type = CSV
    delimiter = ' '
  [../]
[]

(modules/navier_stokes/test/tests/finite_element/pins/expansion-channel/expansion-channel-slip-wall.i)

# This is an example showing the conservative form with combined velocity inlet condition,
# pressure outlet condition and slip wall boundary condition.

[GlobalParams]
  gravity = '0 -9.8 0'

  order = FIRST
  family = LAGRANGE

  u = vel_x
  v = vel_y
  pressure = p
  temperature = T
  porosity = porosity
  eos = eos

  conservative_form = true
  p_int_by_parts = true
[]

[Mesh]
  [file]
    type = FileMeshGenerator
    file = expansion-channel.e
  []
  [add_corners]
    type = ExtraNodesetGenerator
    input = file
    new_boundary = 'corners'
    coord = '-0.05 -0.5 0; 0.05 -0.5 0; -0.1 0.5 0; 0.1 0.5 0'
  []
[]

[NodalNormals]
  # boundaries 3 (left) and 4 (right) are walls
  boundary = '3 4'
  corner_boundary = 'corners'
[]

[FluidProperties]
  [eos]
    type = SimpleFluidProperties
    density0 = 100              # kg/m^3
    thermal_expansion = 0.001   # K^{-1}
    cp =  100
    viscosity = 0.1             # Pa-s, Re=rho*u*L/mu = 100*1*0.1/0.1 = 100
    thermal_conductivity = 72
  []
[]


[Variables]
  # velocities
  [vel_x]
    scaling = 1e-1
    initial_condition = 0
  []
  [vel_y]
    scaling = 1e-2
    initial_condition = 1
  []

  # Pressure
  [p]
    initial_condition = 1.01e5
  []
  # Temperature
  [T]
    scaling = 1e-4
    initial_condition = 630
  []
[]

[AuxVariables]
  [rho]
    initial_condition = 77.0
  []
  [porosity]
    initial_condition = 0.6
  []
  [vol_heat]
    initial_condition = 1e3
  []
[]

[Materials]
  [mat]
    type = PINSFEMaterial
    alpha = 1e3
    beta = 100
  []
[]


[Kernels]
  # mass balance (continuity) equation
  [mass_time]
    type = PINSFEFluidPressureTimeDerivative
    variable = p
  []
  [mass_space]
    type = INSFEFluidMassKernel
    variable = p
  []

  # momentum equations for x- and y- velocities
  [x_momentum_time]
    type = PINSFEFluidVelocityTimeDerivative
    variable = vel_x
  []
  [x_momentum_space]
    type = INSFEFluidMomentumKernel
    variable = vel_x
    component = 0
  []

  [y_momentum_time]
    type = PINSFEFluidVelocityTimeDerivative
    variable = vel_y
  []
  [y_momentum_space]
    type = INSFEFluidMomentumKernel
    variable = vel_y
    component = 1
  []

  # fluid energy equation
  [temperature_time]
    type = PINSFEFluidTemperatureTimeDerivative
    variable = T
  []
  [temperature_space]
    type = INSFEFluidEnergyKernel
    variable = T
    power_density = vol_heat
  []
[]

[AuxKernels]
  [rho_aux]
    type = FluidDensityAux
    variable = rho
    p = p
    T = T
    fp = eos
  []
[]

[BCs]
  # BCs for mass equation
  # Inlet
  [mass_inlet]
    type = INSFEFluidMassBC
    variable = p
    boundary = '1'
  []
  # Outlet
  [mass_out]
    type = INSFEFluidMassBC
    variable = p
    boundary = '2'
  []

  # BCs for x-momentum equation
  # Inlet
  [vx_in]
    type = INSFEFluidMomentumBC
    variable = vel_x
    boundary = '1'
    component   = 0
    #p_fn = 1.05e5
    v_fn = 1
  []
  # Outlet
  [vx_out]
    type = INSFEFluidMomentumBC
    variable = vel_x
    boundary = '2'
    component   = 0
    p_fn = 1e5
  []
  # Walls (left and right walls)
  [vx_wall]
    type = INSFEFluidWallMomentumBC
    variable = vel_x
    boundary = '3 4'
    component = 0
  []

  # BCs for y-momentum equation
  # Inlet
  [vy_in]
    type = INSFEFluidMomentumBC
    variable = vel_y
    boundary = '1'
    component   = 1
    v_fn = 1
  []
  # Outlet
  [vy_out]
    type = INSFEFluidMomentumBC
    variable = vel_y
    boundary = '2'
    component   = 1
    p_fn = 1e5
  []
  # Walls (left and right walls)
  [vy_wall]
    type = INSFEFluidWallMomentumBC
    variable = vel_y
    boundary = '3 4'
    component = 1
  []

  # Special slip-wall BCs for both x- and y- velocities
  [slipwall]
    type = INSFEMomentumFreeSlipBC
    boundary = '3 4'
    variable = vel_x
    u = vel_x
    v = vel_y
  []

  # BCs for fluid energy equation
  # Inlet
  [T_in]
    type = INSFEFluidEnergyBC
    variable = T
    boundary = '1'
    T_fn = 630
  []
  # Outlet
  [T_out]
    type = INSFEFluidEnergyBC
    variable = T
    boundary = '2'
    T_fn = 630
  []
[]

[Preconditioning]
  [SMP_PJFNK]
    type = FDP
    full = true
    solve_type = 'PJFNK'
  []
[]

[Executioner]
  type = Transient

  dt = 0.2
  dtmin = 1.e-6
  [TimeStepper]
    type = IterationAdaptiveDT
    growth_factor = 1.25
    optimal_iterations = 15
    linear_iteration_ratio = 100
    dt = 0.1

    cutback_factor = 0.5
    cutback_factor_at_failure = 0.5
  []
  dtmax = 25

  petsc_options_iname = '-pc_type -ksp_gmres_restart'
  petsc_options_value = 'lu 100'

  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-8
  nl_max_its = 12

  l_tol = 1e-5
  l_max_its = 100

  start_time = 0.0
  end_time = 500
  num_steps = 2
[]

[Outputs]
  perf_graph = true
  print_linear_residuals = false
  time_step_interval = 1
  execute_on = 'initial timestep_end'
  [console]
    type = Console
    output_linear = false
  []
  [out]
    type = Exodus
    use_displaced = false
  []
[]

(modules/combined/examples/optimization/multi-load/single_main.i)

vol_frac = 0.3

power = 1.1
E0 = 1.0
Emin = 1.0e-6

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  # final_generator = 'MoveRight'
  [Bottom]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 80
    ny = 40
    xmin = 0
    xmax = 150
    ymin = 0
    ymax = 75
  []
  [left_load]
    type = ExtraNodesetGenerator
    input = Bottom
    new_boundary = left_load
    coord = '37.5 75 0'
  []
  [right_load]
    type = ExtraNodesetGenerator
    input = left_load
    new_boundary = right_load
    coord = '112.5 75 0'
  []
  [left_support]
    type = ExtraNodesetGenerator
    input = right_load
    new_boundary = left_support
    coord = '0 0 0'
  []
  [right_support]
    type = ExtraNodesetGenerator
    input = left_support
    new_boundary = right_support
    coord = '150 0 0'
  []
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
[]

[AuxVariables]
  [mat_den]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = 0.02
  []
  [sensitivity_one]
    family = MONOMIAL
    order = SECOND
    initial_condition = -1.0
  []
  [sensitivity_two]
    family = MONOMIAL
    order = SECOND
    initial_condition = -1.0
  []
  [total_sensitivity]
    family = MONOMIAL
    order = SECOND
    initial_condition = -1.0
  []
[]

[AuxKernels]
  [total_sensitivity]
    type = ParsedAux
    variable = total_sensitivity
    expression = '0.5*sensitivity_one + 0.5*sensitivity_two'
    coupled_variables = 'sensitivity_one sensitivity_two'
    execute_on = 'LINEAR TIMESTEP_END'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = SMALL
    add_variables = true
    incremental = false
  []
[]

[BCs]
  [no_y]
    type = DirichletBC
    variable = disp_y
    boundary = left_support
    value = 0.0
  []
  [no_x]
    type = DirichletBC
    variable = disp_x
    boundary = left_support
    value = 0.0
  []
  [no_y_right]
    type = DirichletBC
    variable = disp_y
    boundary = right_support
    value = 0.0
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeVariableIsotropicElasticityTensor
    youngs_modulus = E_phys
    poissons_ratio = poissons_ratio
    args = 'mat_den'
  []
  [E_phys]
    type = DerivativeParsedMaterial
    # Emin + (density^penal) * (E0 - Emin)
    expression = '${Emin} + (mat_den ^ ${power}) * (${E0}-${Emin})'
    coupled_variables = 'mat_den'
    property_name = E_phys
  []
  [poissons_ratio]
    type = GenericConstantMaterial
    prop_names = poissons_ratio
    prop_values = 0.0
  []
  [stress]
    type = ComputeLinearElasticStress
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[UserObjects]
  # We do filtering in the subapps
  [update]
    type = DensityUpdate
    density_sensitivity = total_sensitivity
    design_density = mat_den
    volume_fraction = ${vol_frac}
    execute_on = MULTIAPP_FIXED_POINT_BEGIN
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'
  nl_abs_tol = 1e-10
  dt = 1.0
  num_steps = 25
[]

[Outputs]
  exodus = true
  [out]
    type = CSV
    execute_on = 'TIMESTEP_END'
  []
  print_linear_residuals = false
[]

[Postprocessors]
  [mesh_volume]
    type = VolumePostprocessor
    execute_on = 'initial timestep_end'
  []
  [total_vol]
    type = ElementIntegralVariablePostprocessor
    variable = mat_den
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [vol_frac]
    type = ParsedPostprocessor
    expression = 'total_vol / mesh_volume'
    pp_names = 'total_vol mesh_volume'
  []
  [sensitivity]
    type = ElementIntegralVariablePostprocessor
    variable = total_sensitivity
  []
[]

[MultiApps]
  [sub_app_one]
    type = TransientMultiApp
    input_files = single_subapp_one.i
  []
  [sub_app_two]
    type = TransientMultiApp
    input_files = single_subapp_two.i
  []
[]

[Transfers]
  # First SUB-APP
  # To subapp densities
  [subapp_one_density]
    type = MultiAppCopyTransfer
    to_multi_app = sub_app_one
    source_variable = mat_den # Here
    variable = mat_den
  []
  # From subapp sensitivity
  [subapp_one_sensitivity]
    type = MultiAppCopyTransfer
    from_multi_app = sub_app_one
    source_variable = Dc # sensitivity_var
    variable = sensitivity_one # Here
  []
  # Second SUB-APP
  # To subapp densities
  [subapp_two_density]
    type = MultiAppCopyTransfer
    to_multi_app = sub_app_two
    source_variable = mat_den # Here
    variable = mat_den
  []
  # From subapp sensitivity
  [subapp_two_sensitivity]
    type = MultiAppCopyTransfer
    from_multi_app = sub_app_two
    source_variable = Dc # sensitivity_var
    variable = sensitivity_two # Here
  []
[]

(test/tests/transfers/multiapp_variable_value_sample_transfer/full_domain_primary.i)

[Mesh]
  type = MeshGeneratorMesh

  [cartesian_basic_mesh]
    type = CartesianMeshGenerator
    dim = 2

    dx = '0.25 0.25 0.25 0.25'
    ix = '1 1 1 1 '

    dy = '0.25 0.25 0.25 0.25'
    iy = '1 1 1 1'

    subdomain_id = '1 2 2 2
                    1 1 2 2
                    1 1 2 2
                    1 1 1 2'
  []
  [central_node]
    type = ExtraNodesetGenerator
    coord = '0.5 0.5'
    input = cartesian_basic_mesh
    new_boundary = 'central_node'
  []
[]

[Variables]
  [to_subapp]
    initial_condition = -1.0
  []
[]

[AuxKernels]
  [discretize_to_subapp]
    type = ParsedAux
    variable = from_subapp_check
    expression = 'to_subapp'
    coupled_variables = 'to_subapp'
  []
  [subapp_primary_diff]
    type = ParsedAux
    variable = subapp_primary_diff
    expression = 'from_subapp_check - from_subapp'
    coupled_variables = 'from_subapp_check from_subapp'
  []
[]

[AuxVariables]
  [from_subapp]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = -2.0
  []
  [from_subapp_check]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = -2.0
  []
  [subapp_primary_diff]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = -2.0
  []
  [array_var]
    family = MONOMIAL
    order = CONSTANT
    components = 3
    initial_condition = '-2 -1 0'
  []
[]

[Kernels]
  [diff]
    type = Diffusion
    variable = to_subapp
  []
[]

[BCs]
  [edge]
    type = DirichletBC
    variable = to_subapp
    boundary = 'top right left bottom'
    value = 1
  []
  [center]
    type = DirichletBC
    variable = to_subapp
    boundary = 'central_node'
    value = 0
  []
[]

[Executioner]
  type = Transient
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'

  num_steps = 3
  dt = 1.0

  nl_abs_tol = 1e-13
  nl_rel_tol = 1e-12
[]

[Outputs]
  exodus = true
[]

[MultiApps]
  [sub]
    type = CentroidMultiApp
    input_files = subapp.i
  []
[]

[Transfers]
  [from_primary_to_sub_pp]
    type = MultiAppVariableValueSamplePostprocessorTransfer
    to_multi_app = sub
    source_variable = to_subapp
    postprocessor = from_primary_pp
  []
  [primary_average]
    type = MultiAppVariableValueSamplePostprocessorTransfer
    from_multi_app = sub
    source_variable = from_subapp
    postprocessor = to_primary_pp
  []
  [array_var]
    type = MultiAppVariableValueSamplePostprocessorTransfer
    from_multi_app = sub
    source_variable = array_var
    source_variable_component = 2
    postprocessor = to_primary_pp
  []
[]

(modules/navier_stokes/test/tests/finite_element/ins/boussinesq/boussinesq_square_constant_names.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmax = .05
    ymax = .05
    nx = 20
    ny = 20
    elem_type = QUAD9
  []
  [bottom_left]
    type = ExtraNodesetGenerator
    new_boundary = corner
    coord = '0 0'
    input = gen
  []
[]


[Executioner]
  type = Steady
  solve_type = NEWTON
  nl_rel_tol = 1e-12
  petsc_options_iname = '-pc_type -pc_factor_shift_type'
  petsc_options_value = 'lu       NONZERO'
[]

[Debug]
  show_var_residual_norms = true
[]

[Outputs]
  [out]
    type = Exodus
    execute_on = 'final'
  []
[]

[Variables]
  [velocity]
    family = LAGRANGE_VEC
    order = SECOND
  []
  [p][]
  [temp]
    order = SECOND
    initial_condition = 340
    scaling = 1e-4
  []
[]


[BCs]
  [velocity_dirichlet]
    type = VectorDirichletBC
    boundary = 'left right bottom top'
    variable = velocity
    # The third entry is to satisfy RealVectorValue
    values = '0 0 0'
  []
  # Even though we are integrating by parts, because there are no integrated
  # boundary conditions on the velocity p doesn't appear in the system of
  # equations. Thus we must pin the pressure somewhere in order to ensure a
  # unique solution
  [p_zero]
    type = DirichletBC
    boundary = corner
    variable = p
    value = 0
  []
  [cold]
    type = DirichletBC
    variable = temp
    boundary = left
    value = 300
  []
  [hot]
    type = DirichletBC
    variable = temp
    boundary = right
    value = 400
  []
[]


[Kernels]
  [mass]
    type = INSADMass
    variable = p
  []
  [momentum_viscous]
    type = INSADMomentumViscous
    variable = velocity
  []
  [momentum_advection]
    type = INSADMomentumAdvection
    variable = velocity
  []
  [momentum_pressure]
    type = INSADMomentumPressure
    variable = velocity
    pressure = p
    integrate_p_by_parts = true
  []
  [temp_advection]
    type = INSADEnergyAdvection
    variable = temp
  []
  [temp_conduction]
    type = ADHeatConduction
    variable = temp
    thermal_conductivity = 'k'
  []
  [buoyancy]
    type = INSADBoussinesqBodyForce
    variable = velocity
    temperature = temp
    gravity = '0 -9.81 0'
    ref_temp = 900
    alpha_name = 2.9e-3
  []
  [gravity]
    type = INSADGravityForce
    variable = velocity
    gravity = '0 -9.81 0'
  []
[]

[Materials]
  [ad_const]
    type = ADGenericConstantMaterial
    prop_names =  'mu        rho    k        cp'
    prop_values = '30.74e-6  .5757  46.38e-3 1054'
  []
  [ins_mat]
    type = INSAD3Eqn
    velocity = velocity
    pressure = p
    temperature = temp
  []
[]

(test/tests/mortar/periodic_segmental_constraint/penalty_periodic_aux.i)

[Mesh]
  [left_block]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = -1.0
    xmax = 1.0
    ymin = -1.0
    ymax = 1.0
    nx = 2
    ny = 2
    elem_type = QUAD4
  []
  [left_block_sidesets]
    type = RenameBoundaryGenerator
    input = left_block
    old_boundary = '0 1 2 3'
    new_boundary = '10 11 12 13'
  []
  [left_block_id]
    type = SubdomainIDGenerator
    input = left_block_sidesets
    subdomain_id = 1
  []
  [left]
    type = LowerDBlockFromSidesetGenerator
    input = left_block_id
    sidesets = '13'
    new_block_id = '10003'
    new_block_name = 'secondary_left'
  []
  [right]
    type = LowerDBlockFromSidesetGenerator
    input = left
    sidesets = '11'
    new_block_id = '10001'
    new_block_name = 'primary_right'
  []
  [bottom]
    type = LowerDBlockFromSidesetGenerator
    input = right
    sidesets = '10'
    new_block_id = '10000'
    new_block_name = 'secondary_bottom'
  []
  [top]
    type = LowerDBlockFromSidesetGenerator
    input = bottom
    sidesets = '12'
    new_block_id = '10002'
    new_block_name = 'primary_top'
  []

  [corner_node]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node'
    nodes = '0'
    input = top
  []
[]

[Variables]
  [u]
    order = FIRST
    family = LAGRANGE
  []
  [epsilon]
    order = SECOND
    family = SCALAR
  []
  [sigma]
    order = SECOND
    family = SCALAR
  []
[]

[Kernels]
  [diff1]
    type = Diffusion
    variable = u
    block = 1
  []
[]

[Problem]
  kernel_coverage_check = false
  error_on_jacobian_nonzero_reallocation = true
[]

[BCs]
  [fix_right]
    type = DirichletBC
    variable = u
    boundary = pinned_node
    value = 0
  []
[]

[Constraints]
  [mortarlr]
    type = PenaltyEqualValueConstraint
    primary_boundary = '11'
    secondary_boundary = '13'
    primary_subdomain = 'primary_right'
    secondary_subdomain = 'secondary_left'
    secondary_variable = u
    correct_edge_dropping = true
    penalty_value = 1.e2
  []
  [periodiclr]
    type = PenaltyPeriodicSegmentalConstraint
    primary_boundary = '11'
    secondary_boundary = '13'
    primary_subdomain = 'primary_right'
    secondary_subdomain = 'secondary_left'
    secondary_variable = u
    epsilon = epsilon
    sigma = sigma
    correct_edge_dropping = true
    penalty_value = 1.e2
  []
  [mortarbt]
    type = PenaltyEqualValueConstraint
    primary_boundary = '12'
    secondary_boundary = '10'
    primary_subdomain = 'primary_top'
    secondary_subdomain = 'secondary_bottom'
    secondary_variable = u
    correct_edge_dropping = true
    penalty_value = 1.e2
  []
  [periodicbt]
    type = PenaltyPeriodicSegmentalConstraint
    primary_boundary = '12'
    secondary_boundary = '10'
    primary_subdomain = 'primary_top'
    secondary_subdomain = 'secondary_bottom'
    secondary_variable = u
    epsilon = epsilon
    sigma = sigma
    correct_edge_dropping = true
    penalty_value = 1.e2
  []
[]

[Executioner]
  type = Steady
  solve_type = 'PJFNK'
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  csv = true
[]

(modules/xfem/test/tests/checkpoint/checkpoint.i)

# This test is for two layer materials with different youngs modulus
# The global stress is determined by switching the stress based on level set values
# The material interface is marked by a level set function
# The two layer materials are glued together

[GlobalParams]
  order = FIRST
  family = LAGRANGE
  displacements = 'disp_x disp_y'
[]

[XFEM]
  qrule = volfrac
  output_cut_plane = true
[]

[UserObjects]
  [./level_set_cut_uo]
    type = LevelSetCutUserObject
    level_set_var = ls
  [../]
[]

[Mesh]
  displacements = 'disp_x disp_y'
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 5
    ny = 5
    xmin = 0.0
    xmax = 5.
    ymin = 0.0
    ymax = 5.
    elem_type = QUAD4
  []
  [./left_bottom]
    type = ExtraNodesetGenerator
    new_boundary = 'left_bottom'
    coord = '0.0 0.0'
    input = gen
  [../]
  [./left_top]
    type = ExtraNodesetGenerator
    new_boundary = 'left_top'
    coord = '0.0 5.'
    input = left_bottom
  [../]
[]

[AuxVariables]
  [./ls]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxKernels]
  [./ls_function]
    type = FunctionAux
    variable = ls
    function = ls_func
  [../]
[]

[Variables]
  [./disp_x]
  [../]
  [./disp_y]
  [../]
[]

[Functions]
  [./ls_func]
    type = ParsedFunction
    expression = 'y-2.5'
  [../]
[]

[AuxVariables]
  [./stress_xx]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./stress_yy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./stress_xy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./a_strain_xx]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./a_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./a_strain_xy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./b_strain_xx]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./b_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./b_strain_xy]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[Kernels]
  [./TensorMechanics]
  [../]
[]

[AuxKernels]
  [./stress_xx]
    type = RankTwoAux
    rank_two_tensor = stress
    index_i = 0
    index_j = 0
    variable = stress_xx
  [../]
  [./stress_yy]
    type = RankTwoAux
    rank_two_tensor = stress
    index_i = 1
    index_j = 1
    variable = stress_yy
  [../]
  [./stress_xy]
    type = RankTwoAux
    rank_two_tensor = stress
    index_i = 0
    index_j = 1
    variable = stress_xy
  [../]
  [./a_strain_xx]
    type = RankTwoAux
    rank_two_tensor = A_total_strain
    index_i = 0
    index_j = 0
    variable = a_strain_xx
  [../]
  [./a_strain_yy]
    type = RankTwoAux
    rank_two_tensor = A_total_strain
    index_i = 1
    index_j = 1
    variable = a_strain_yy
  [../]
  [./a_strain_xy]
    type = RankTwoAux
    rank_two_tensor = A_total_strain
    index_i = 0
    index_j = 1
    variable = a_strain_xy
  [../]
  [./b_strain_xx]
    type = RankTwoAux
    rank_two_tensor = B_total_strain
    index_i = 0
    index_j = 0
    variable = b_strain_xx
  [../]
  [./b_strain_yy]
    type = RankTwoAux
    rank_two_tensor = B_total_strain
    index_i = 1
    index_j = 1
    variable = b_strain_yy
  [../]
  [./b_strain_xy]
    type = RankTwoAux
    rank_two_tensor = B_total_strain
    index_i = 0
    index_j = 1
    variable = b_strain_xy
  [../]
[]

[Constraints]
  [./dispx_constraint]
    type = XFEMSingleVariableConstraint
    use_displaced_mesh = false
    variable = disp_x
    alpha = 1e8
    geometric_cut_userobject = 'level_set_cut_uo'
  [../]
  [./dispy_constraint]
    type = XFEMSingleVariableConstraint
    use_displaced_mesh = false
    variable = disp_y
    alpha = 1e8
    geometric_cut_userobject = 'level_set_cut_uo'
  [../]
[]

[BCs]
  [./bottomx]
    type = DirichletBC
    boundary = bottom
    variable = disp_x
    value = 0.0
  [../]
  [./bottomy]
    type = DirichletBC
    boundary = bottom
    variable = disp_y
    value = 0.0
  [../]
  [./topx]
    type = FunctionDirichletBC
    boundary = top
    variable = disp_x
    function = 0.03*t
  [../]
  [./topy]
    type = FunctionDirichletBC
    boundary = top
    variable = disp_y
    function = '0.03*t'
  [../]
[]

[Materials]
  [./elasticity_tensor_A]
    type = ComputeIsotropicElasticityTensor
    base_name = A
    youngs_modulus = 1e9
    poissons_ratio = 0.3
  [../]
  [./strain_A]
    type = ComputeSmallStrain
    base_name = A
  [../]
  [./stress_A]
    type = ComputeLinearElasticStress
    base_name = A
  [../]
  [./elasticity_tensor_B]
    type = ComputeIsotropicElasticityTensor
    base_name = B
    youngs_modulus = 1e5
    poissons_ratio = 0.3
  [../]
  [./strain_B]
    type = ComputeSmallStrain
    base_name = B
  [../]
  [./stress_B]
    type = ComputeLinearElasticStress
    base_name = B
  [../]
  [./combined_stress]
    type = LevelSetBiMaterialRankTwo
    levelset_positive_base = 'A'
    levelset_negative_base = 'B'
    level_set_var = ls
    prop_name = stress
  [../]
  [./combined_dstressdstrain]
    type = LevelSetBiMaterialRankFour
    levelset_positive_base = 'A'
    levelset_negative_base = 'B'
    level_set_var = ls
    prop_name = Jacobian_mult
  [../]
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'
  petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
  petsc_options_value = '201                hypre    boomeramg      8'

  line_search = 'bt'

# controls for linear iterations
  l_max_its = 20
  l_tol = 1e-3

# controls for nonlinear iterations
  nl_max_its = 15
  nl_rel_tol = 1e-14
  nl_abs_tol = 1e-7

# time control
  start_time = 0.0
  dt = 0.1
  num_steps = 2

  max_xfem_update = 1
[]

[Outputs]
  checkpoint = true
  exodus = true
  execute_on = timestep_end
  csv = true
  [./console]
    type = Console
    output_linear = true
  [../]
[]

(modules/solid_mechanics/test/tests/global_strain/global_strain_uniaxial.i)

[Mesh]
  [generated_mesh]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 2
    ny = 2
    nz = 2
  []
  [cnode]
    type = ExtraNodesetGenerator
    coord = '0.0 0.0 0.0'
    new_boundary = 100
    input = generated_mesh
  []
[]

[Variables]
  [./u_x]
  [../]
  [./u_y]
  [../]
  [./u_z]
  [../]
  [./global_strain]
    order = SIXTH
    family = SCALAR
  [../]
[]

[AuxVariables]
  [./disp_x]
  [../]
  [./disp_y]
  [../]
  [./disp_z]
  [../]
  [./s00]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./s11]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./e00]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./e11]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[AuxKernels]
  [./disp_x]
    type = GlobalDisplacementAux
    variable = disp_x
    scalar_global_strain = global_strain
    global_strain_uo = global_strain_uo
    component = 0
  [../]
  [./disp_y]
    type = GlobalDisplacementAux
    variable = disp_y
    scalar_global_strain = global_strain
    global_strain_uo = global_strain_uo
    component = 1
  [../]
  [./disp_z]
    type = GlobalDisplacementAux
    variable = disp_z
    scalar_global_strain = global_strain
    global_strain_uo = global_strain_uo
    component = 2
  [../]
  [./s00]
    type = RankTwoAux
    variable = s00
    rank_two_tensor = stress
    index_i = 0
    index_j = 0
  [../]
  [./s11]
    type = RankTwoAux
    variable = s11
    rank_two_tensor = stress
    index_i = 1
    index_j = 1
  [../]
  [./e00]
    type = RankTwoAux
    variable = e00
    rank_two_tensor = total_strain
    index_i = 0
    index_j = 0
  [../]
  [./e11]
    type = RankTwoAux
    variable = e11
    rank_two_tensor = total_strain
    index_i = 1
    index_j = 1
  [../]
[]

[GlobalParams]
  displacements = 'u_x u_y u_z'
  block = 0
[]

[Kernels]
  [SolidMechanics]
  [../]
[]

[ScalarKernels]
  [./global_strain]
    type = GlobalStrain
    variable = global_strain
    global_strain_uo = global_strain_uo
  [../]
[]

[BCs]
  [./Periodic]
    [./all]
      auto_direction = 'x y z'
      variable = ' u_x u_y u_z'
    [../]
  [../]

  # fix center point location
  [./centerfix_x]
    type = DirichletBC
    boundary = 100
    variable = u_x
    value = 0
  [../]
  [./centerfix_y]
    type = DirichletBC
    boundary = 100
    variable = u_y
    value = 0
  [../]
  [./centerfix_z]
    type = DirichletBC
    boundary = 100
    variable = u_z
    value = 0
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeElasticityTensor
    block = 0
    C_ijkl = '70e9 0.33'
    fill_method = symmetric_isotropic_E_nu
  [../]
  [./strain]
    type = ComputeSmallStrain
    global_strain = global_strain
  [../]
  [./global_strain]
    type = ComputeGlobalStrain
    scalar_global_strain = global_strain
    global_strain_uo = global_strain_uo
  [../]
  [./stress]
    type = ComputeLinearElasticStress
  [../]
[]

[UserObjects]
  [./global_strain_uo]
    type = GlobalStrainUserObject
    applied_stress_tensor = '5e9 0 0 0 0 0'
    execute_on = 'Initial Linear Nonlinear'
  [../]
[]

[Postprocessors]
  [./l2err_e00]
    type = ElementL2Error
    variable = e00
    function = 0.07142857 #strain_xx = C1111/sigma_xx
  [../]
  [./l2err_e11]
    type = ElementL2Error
    variable = e11
    function = -0.07142857*0.33 #strain_yy = -nu*strain_xx
  [../]
[]

[Preconditioning]
  [./SMP]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = Transient
  scheme = bdf2
  solve_type = 'PJFNK'

  line_search = basic

  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_ksp_type -sub_pc_type -pc_asm_overlap'
  petsc_options_value = 'asm         31   preonly   lu      1'

  l_max_its = 30
  nl_max_its = 12

  nl_rel_tol = 1.0e-10

  start_time = 0.0
  num_steps = 1
[]

[Outputs]
  exodus = true
[]

(modules/solid_mechanics/test/tests/ad_viscoplasticity_stress_update/exact.i)

# This test provides comparison to calculated values from Leblond:1994kl

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  pore_shape_model = spherical
[]

[Mesh]
  [./msh]
    type = CartesianMeshGenerator
    dim = 3
    dx = 0.01
    dy = 0.01
    dz = 0.01
    iz = 1
    ix = 1
    iy = 1
  [../]
  [./extra_nodeset]
    type = ExtraNodesetGenerator
    input = msh
    new_boundary = 'origin'
    coord = '0 0 0'
  []
[]

[Physics/SolidMechanics/QuasiStatic/All]
  strain = FINITE
  add_variables = true
  generate_output = 'strain_xx strain_yy strain_xy hydrostatic_stress vonmises_stress'
  use_automatic_differentiation = true
[]

[Functions]
  [./Q_gtn]
    type = ParsedFunction
    symbol_names = 'avg_vonmises gtn_gauge_stress'
    symbol_values = 'avg_vonmises gtn_gauge_stress'
    expression = 'avg_vonmises/gtn_gauge_stress'
  [../]
  [./M_gtn]
    type = ParsedFunction
    symbol_names = 'avg_hydro gtn_gauge_stress'
    symbol_values = 'avg_hydro gtn_gauge_stress'
    expression = 'abs(avg_hydro) / gtn_gauge_stress'
  [../]
  [./Q_ten]
    type = ParsedFunction
    symbol_names = 'avg_vonmises ten_gauge_stress'
    symbol_values = 'avg_vonmises ten_gauge_stress'
    expression = 'avg_vonmises/ten_gauge_stress'
  [../]
  [./M_ten]
    type = ParsedFunction
    symbol_names = 'avg_hydro ten_gauge_stress'
    symbol_values = 'avg_hydro ten_gauge_stress'
    expression = 'abs(avg_hydro) / ten_gauge_stress'
  [../]
  [./Q_five]
    type = ParsedFunction
    symbol_names = 'avg_vonmises five_gauge_stress'
    symbol_values = 'avg_vonmises five_gauge_stress'
    expression = 'avg_vonmises/five_gauge_stress'
  [../]
  [./M_five]
    type = ParsedFunction
    symbol_names = 'avg_hydro five_gauge_stress'
    symbol_values = 'avg_hydro five_gauge_stress'
    expression = 'abs(avg_hydro) / five_gauge_stress'
  [../]
  [./Q_three]
    type = ParsedFunction
    symbol_names = 'avg_vonmises three_gauge_stress'
    symbol_values = 'avg_vonmises three_gauge_stress'
    expression = 'avg_vonmises / three_gauge_stress'
  [../]
  [./M_three]
    type = ParsedFunction
    symbol_names = 'avg_hydro three_gauge_stress'
    symbol_values = 'avg_hydro three_gauge_stress'
    expression = 'abs(avg_hydro) / three_gauge_stress'
  [../]
  [./Q_two]
    type = ParsedFunction
    symbol_names = 'avg_vonmises two_gauge_stress'
    symbol_values = 'avg_vonmises two_gauge_stress'
    expression = 'avg_vonmises/two_gauge_stress'
  [../]
  [./M_two]
    type = ParsedFunction
    symbol_names = 'avg_hydro two_gauge_stress'
    symbol_values = 'avg_hydro two_gauge_stress'
    expression = 'abs(avg_hydro) / two_gauge_stress'
  [../]
  [./Q_onepointfive]
    type = ParsedFunction
    symbol_names = 'avg_vonmises onepointfive_gauge_stress'
    symbol_values = 'avg_vonmises onepointfive_gauge_stress'
    expression = 'avg_vonmises / onepointfive_gauge_stress'
  [../]
  [./M_onepointfive]
    type = ParsedFunction
    symbol_names = 'avg_hydro onepointfive_gauge_stress'
    symbol_values = 'avg_hydro onepointfive_gauge_stress'
    expression = 'abs(avg_hydro) / onepointfive_gauge_stress'
  [../]
  [./Q_one]
    type = ParsedFunction
    symbol_names = 'avg_vonmises one_gauge_stress'
    symbol_values = 'avg_vonmises one_gauge_stress'
    expression = 'avg_vonmises / one_gauge_stress'
  [../]
  [./M_one]
    type = ParsedFunction
    symbol_names = 'avg_hydro one_gauge_stress'
    symbol_values = 'avg_hydro one_gauge_stress'
    expression = 'abs(avg_hydro) / one_gauge_stress'
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    youngs_modulus = 1e10
    poissons_ratio = 0.3
  [../]
  [./stress]
    type = ADComputeMultipleInelasticStress
    inelastic_models = 'gtn lps_ten lps_five lps_three lps_two lps_onepointfive lps_one'
    outputs = all
    extra_stress_names = extra_stress
  [../]
  [./porosity]
    type = ADPorosityFromStrain
    initial_porosity = 1e-3
    inelastic_strain = 'combined_inelastic_strain'
    outputs = 'all'
  [../]
  [./gtn]
    type = ADViscoplasticityStressUpdate
    coefficient = 0
    power = 1 # arbitrary
    viscoplasticity_model = GTN
    base_name = gtn
    outputs = all
    relative_tolerance = 1e-30
  [../]
  [./lps_ten]
    type = ADViscoplasticityStressUpdate
    coefficient = 0
    power = 10
    base_name = ten
    outputs = all
    relative_tolerance = 1e-30
  [../]
  [./lps_five]
    type = ADViscoplasticityStressUpdate
    coefficient = 0
    power = 5
    base_name = five
    outputs = all
    relative_tolerance = 1e-30
  [../]
  [./lps_three]
    type = ADViscoplasticityStressUpdate
    coefficient = 0
    power = 3
    base_name = three
    outputs = all
    relative_tolerance = 1e-30
  [../]
  [./lps_two]
    type = ADViscoplasticityStressUpdate
    coefficient = 0
    power = 2
    base_name = two
    outputs = all
    relative_tolerance = 1e-30
  [../]
  [./lps_onepointfive]
    type = ADViscoplasticityStressUpdate
    coefficient = 0
    power = 1.5
    base_name = onepointfive
    outputs = all
    relative_tolerance = 1e-30
  [../]
  [./lps_one]
    type = ADViscoplasticityStressUpdate
    coefficient = 0
    power = 1
    base_name = one
    outputs = all
    relative_tolerance = 1e-30
  [../]

  [./const_stress]
    type = ComputeExtraStressConstant
    extra_stress_tensor = '1 1 1 1 1 1 1 1 1'
    outputs = all
  [../]
[]

[BCs]
  [./no_disp_x]
    type = ADDirichletBC
    variable = disp_x
    boundary = left
    value = 0.0
  [../]
  [./no_disp_y]
    type = ADDirichletBC
    variable = disp_y
    boundary = bottom
    value = 0.0
  [../]
  [./no_disp_z]
    type = ADDirichletBC
    variable = disp_z
    boundary = back
    value = 0.0
  [../]
  [./Pressure]
    [./bcs]
      boundary = 'top right front'
      function = '10^(t/4.5)'
      use_automatic_differentiation = true
    [../]
  [../]
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  num_steps = 10
  nl_abs_tol = 1e-8
[]

[Postprocessors]
  [./avg_hydro]
    type = ElementAverageValue
    variable = hydrostatic_stress
  [../]
  [./avg_vonmises]
    type = ElementAverageValue
    variable = vonmises_stress
  [../]
  [./gtn_gauge_stress]
    type = ElementAverageValue
    variable = gtn_gauge_stress
    outputs = none
  [../]
  [./0Q_gtn]
    type = FunctionValuePostprocessor
    function = Q_gtn
  [../]
  [./0M_gtn]
    type = FunctionValuePostprocessor
    function = M_gtn
  [../]
  [./ten_gauge_stress]
    type = ElementAverageValue
    variable = ten_gauge_stress
    outputs = none
  [../]
  [./1Q_ten]
    type = FunctionValuePostprocessor
    function = Q_ten
  [../]
  [./1M_ten]
    type = FunctionValuePostprocessor
    function = M_ten
  [../]
  [./five_gauge_stress]
    type = ElementAverageValue
    variable = five_gauge_stress
    outputs = none
  [../]
  [./2Q_five]
    type = FunctionValuePostprocessor
    function = Q_five
  [../]
  [./2M_five]
    type = FunctionValuePostprocessor
    function = M_five
  [../]
  [./three_gauge_stress]
    type = ElementAverageValue
    variable = three_gauge_stress
    outputs = none
  [../]
  [./3Q_three]
    type = FunctionValuePostprocessor
    function = Q_three
  [../]
  [./3M_three]
    type = FunctionValuePostprocessor
    function = M_three
  [../]
  [./two_gauge_stress]
    type = ElementAverageValue
    variable = two_gauge_stress
    outputs = none
  [../]
  [./4Q_two]
    type = FunctionValuePostprocessor
    function = Q_two
  [../]
  [./4M_two]
    type = FunctionValuePostprocessor
    function = M_two
  [../]
  [./onepointfive_gauge_stress]
    type = ElementAverageValue
    variable = onepointfive_gauge_stress
    outputs = none
  [../]
  [./5Q_onepointfive]
    type = FunctionValuePostprocessor
    function = Q_onepointfive
  [../]
  [./5M_onepointfive]
    type = FunctionValuePostprocessor
    function = M_onepointfive
  [../]
  [./one_gauge_stress]
    type = ElementAverageValue
    variable = one_gauge_stress
    outputs = none
  [../]
  [./6Q_one]
    type = FunctionValuePostprocessor
    function = Q_one
  [../]
  [./6M_one]
    type = FunctionValuePostprocessor
    function = M_one
  [../]
[]

[Outputs]
  csv = true
  file_base = exact_spherical_out
[]

(test/tests/mortar/ad_periodic_segmental_constraint/testperiodicsole.i)

[Mesh]
  [left_block]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = -1.0
    xmax = 1.0
    ymin = -1.0
    ymax = 1.0
    nx = 2
    ny = 2
    elem_type = QUAD4
  []
  [left_block_sidesets]
    type = RenameBoundaryGenerator
    input = left_block
    old_boundary = '0 1 2 3'
    new_boundary = '10 11 12 13'
  []
  [left_block_id]
    type = SubdomainIDGenerator
    input = left_block_sidesets
    subdomain_id = 1
  []
  [left]
    type = LowerDBlockFromSidesetGenerator
    input = left_block_id
    sidesets = '13'
    new_block_id = '10003'
    new_block_name = 'secondary_left'
  []
  [right]
    type = LowerDBlockFromSidesetGenerator
    input = left
    sidesets = '11'
    new_block_id = '10001'
    new_block_name = 'primary_right'
  []
  [bottom]
    type = LowerDBlockFromSidesetGenerator
    input = right
    sidesets = '10'
    new_block_id = '10000'
    new_block_name = 'secondary_bottom'
  []
  [top]
    type = LowerDBlockFromSidesetGenerator
    input = bottom
    sidesets = '12'
    new_block_id = '10002'
    new_block_name = 'primary_top'
  []

  [corner_node]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node'
    nodes = '0'
    input = top
  []
[]

[Variables]
  [u]
    order = FIRST
    family = LAGRANGE
  []
  [kappa_x]
    order = FIRST
    family = SCALAR
  []
  [kappa_y]
    order = FIRST
    family = SCALAR
  []
[]

[AuxVariables]
  [kappa_aux]
    order = SECOND
    family = SCALAR
  []
  [./flux_x]
      order = FIRST
      family = MONOMIAL
  [../]
  [./flux_y]
      order = FIRST
      family = MONOMIAL
  [../]
[]

[AuxScalarKernels]
  [kappa]
    type = FunctionScalarAux
    variable = kappa_aux
    function = '1 3'
    execute_on = initial #timestep_end
  []
[]

[AuxKernels]
  [./flux_x]
    type = DiffusionFluxAux
    diffusivity = 'conductivity'
    variable = flux_x
    diffusion_variable = u
    component = x
    block = 1
  [../]
  [./flux_y]
    type = DiffusionFluxAux
    diffusivity = 'conductivity'
    variable = flux_y
    diffusion_variable = u
    component = y
    block = 1
  [../]
[]

[Kernels]
  [diff1]
    type = ADDiffusion
    variable = u
    block = 1
  []
[]

[Materials]
  [k1]
    type = GenericConstantMaterial
    prop_names = 'conductivity'
    prop_values = 1.0
    block = 1
  []
[]

[Problem]
  kernel_coverage_check = false
  error_on_jacobian_nonzero_reallocation = true
[]

[BCs]
  [fix_right]
    type = DirichletBC
    variable = u
    boundary = pinned_node
    value = 0
  []
[]

[Constraints]
  [mortarlr]
    type = ADPenaltyEqualValueConstraint
    primary_boundary = '11'
    secondary_boundary = '13'
    primary_subdomain = 'primary_right'
    secondary_subdomain = 'secondary_left'
    secondary_variable = u
    correct_edge_dropping = true
    penalty_value = 1.e3
  []
  [periodiclrx]
    type = ADTestPeriodicSole
    primary_boundary = '11'
    secondary_boundary = '13'
    primary_subdomain = 'primary_right'
    secondary_subdomain = 'secondary_left'
    secondary_variable = u
    kappa = kappa_x
    kappa_aux = kappa_aux
    component = 0
    kappa_other = kappa_y
    correct_edge_dropping = true
    pen_scale = 1.e3
  []
  [periodiclry]
    type = ADTestPeriodicSole
    primary_boundary = '11'
    secondary_boundary = '13'
    primary_subdomain = 'primary_right'
    secondary_subdomain = 'secondary_left'
    secondary_variable = u
    kappa = kappa_y
    kappa_aux = kappa_aux
    component = 1
    kappa_other = kappa_x
    correct_edge_dropping = true
    pen_scale = 1.e3
  []
  [mortarbt]
    type = ADPenaltyEqualValueConstraint
    primary_boundary = '12'
    secondary_boundary = '10'
    primary_subdomain = 'primary_top'
    secondary_subdomain = 'secondary_bottom'
    secondary_variable = u
    correct_edge_dropping = true
    penalty_value = 1.e3
  []
  [periodicbtx]
    type = ADTestPeriodicSole
    primary_boundary = '12'
    secondary_boundary = '10'
    primary_subdomain = 'primary_top'
    secondary_subdomain = 'secondary_bottom'
    secondary_variable = u
    kappa = kappa_x
    kappa_aux = kappa_aux
    component = 0
    kappa_other = kappa_y
    correct_edge_dropping = true
    pen_scale = 1.e3
  []
  [periodicbty]
    type = ADTestPeriodicSole
    primary_boundary = '12'
    secondary_boundary = '10'
    primary_subdomain = 'primary_top'
    secondary_subdomain = 'secondary_bottom'
    secondary_variable = u
    kappa = kappa_y
    kappa_aux = kappa_aux
    component = 1
    kappa_other = kappa_x
    correct_edge_dropping = true
    compute_scalar_residuals = true
    pen_scale = 1.e3
  []
[]

[Preconditioning]
  [smp]
    full = true
    type = SMP
  []
[]

[Executioner]
  type = Steady
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  solve_type = NEWTON
[]

[Postprocessors]
  [max]
    type = ElementExtremeValue
    variable = 'flux_x'
  []
[]

[Outputs]
  csv = true
[]

(modules/solid_mechanics/test/tests/uel/uel_test_print.i)

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
[]

[Mesh]
  [mesh]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 3
    ny = 3
    nz = 3
    elem_type = HEX8
  []
  [extra_nodeset]
    type = ExtraNodesetGenerator
    input = mesh
    new_boundary = 'master'
    coord = '1.0 1.0 1.0'
  []
[]

[AuxVariables]
  [temperature]
    initial_condition = 1500
  []
  [voltage]
    initial_condition = 210
  []
[]

[AuxKernels]
  [temperature]
    type = FunctionAux
    function = temperature_function
    variable = temperature
  []
  [voltage]
    type = FunctionAux
    function = voltage_function
    variable = voltage
  []
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [disp_z]
  []
[]

[Functions]
  [function_pull]
    type = PiecewiseLinear
    x = '0 100'
    y = '0 0.1'
  []
  [pressure_function]
    type = PiecewiseLinear
    x = '0 100'
    y = '0 2.0e4'
  []
  [voltage_function]
    type = PiecewiseLinear
    x = '0 100'
    y = '210 450'
  []
  [temperature_function]
    type = PiecewiseLinear
    x = '0 100'
    y = '1500 800'
  []
[]

[Constraints]
  [one]
    type = LinearNodalConstraint
    variable = disp_x
    primary = '6'
    secondary_node_ids = '1 2 5'
    penalty = 1.0e8
    formulation = kinematic
    weights = '1'
  []
  [two]
    type = LinearNodalConstraint
    variable = disp_z
    primary = '6'
    secondary_node_ids = '4 5 7'
    penalty = 1.0e8
    formulation = kinematic
    weights = '1'
  []
[]

[BCs]
  [symmy]
    type = DirichletBC
    variable = disp_y
    boundary = bottom
    value = 0
  []
  [symmx]
    type = DirichletBC
    variable = disp_x
    boundary = left
    value = 0
  []
  [symmz]
    type = DirichletBC
    variable = disp_z
    boundary = back
    value = 0
  []

  [Pressure]
    [press]
      boundary = 'top'
      displacements = 'disp_x disp_y disp_z'
      function = pressure_function
    []
  []
[]

[UserObjects]
  [uel]
    type = AbaqusUserElement
    variables = 'disp_x disp_y disp_z'
    plugin = '../../../../solid_mechanics/examples/uel_build_tests/uel'
    use_displaced_mesh = false

    external_fields = 'temperature voltage'
    jtype = 10

    num_state_vars = 96 #
    constant_properties = '2 1 2 210000 0.3'
    extra_vector_tags = 'kernel_residual'
  []
[]

[Problem]
  kernel_coverage_check = false
  extra_tag_vectors = 'kernel_residual'
[]

[AuxVariables]
  [res_x]
  []
  [res_y]
  []
[]

[AuxKernels]
  [res_x]
    type = TagVectorAux
    variable = res_x
    v = disp_x
    vector_tag = kernel_residual
  []
  [res_y]
    type = TagVectorAux
    variable = res_y
    v = disp_y
    vector_tag = kernel_residual
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient

  petsc_options = '-snes_converged_reason'
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_type'
  petsc_options_value = ' lu       superlu_dist'
  line_search = none

  l_max_its = 100
  l_tol = 1e-8
  nl_max_its = 1
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-8

  error_on_dtmin = false
  dtmin = 10
  dt = 10
  end_time = 10
[]

[Outputs]
  exodus = true
[]

(modules/combined/examples/geochem-porous_flow/geotes_2D/porous_flow.i)

# PorousFlow simulation of injection and production in a 2D aquifer
# Much of this file is standard porous-flow stuff.  The unusual aspects are:
# - transfer of the rates of changes of each species (kg/s) to the aquifer_geochemistry.i simulation.  This is achieved by saving these changes from the PorousFlowMassTimeDerivative residuals
# - transfer of the temperature field to the aquifer_geochemistry.i simulation
# Interesting behaviour can be simulated by this file without its "parent" simulation, exchanger.i.  exchanger.i provides mass-fractions injected via the injection_rate_massfrac_* variables, but since these are more-or-less constant throughout the duration of the exchanger.i simulation, the initial_conditions specified below may be used.  Similar, exchanger.i provides injection_temperature, but that is also constant.

injection_rate = -1.0 # kg/s/m, negative because injection as a source
production_rate = 1.0 # kg/s/m
[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 14 # for better resolution, use 56 or 112
    ny = 8  # for better resolution, use 32 or 64
    xmin = -70
    xmax = 70
    ymin = -40
    ymax = 40
  []
  [injection_node]
    input = gen
    type = ExtraNodesetGenerator
    new_boundary = injection_node
    coord = '-30 0 0'
  []
[]

[GlobalParams]
  PorousFlowDictator = dictator
  gravity = '0 0 0'
[]

[Variables]
  [f0]
    initial_condition = 0.002285946
  []
  [f1]
    initial_condition = 0.0035252
  []
  [f2]
    initial_condition = 1.3741E-05
  []
  [porepressure]
    initial_condition = 2E6
  []
  [temperature]
    initial_condition = 50
    scaling = 1E-6 # fluid enthalpy is roughly 1E6
  []
[]

[BCs]
  [injection_temperature]
    type = MatchedValueBC
    variable = temperature
    v = injection_temperature
    boundary = injection_node
  []
[]

[DiracKernels]
  [inject_Na]
    type = PorousFlowPolyLineSink
    SumQuantityUO = injected_mass
    fluxes = ${injection_rate}
    p_or_t_vals = 0.0
    line_length = 1.0
    multiplying_var = injection_rate_massfrac_Na
    point_file = injection.bh
    variable = f0
  []
  [inject_Cl]
    type = PorousFlowPolyLineSink
    SumQuantityUO = injected_mass
    fluxes = ${injection_rate}
    p_or_t_vals = 0.0
    line_length = 1.0
    multiplying_var = injection_rate_massfrac_Cl
    point_file = injection.bh
    variable = f1
  []
  [inject_SiO2]
    type = PorousFlowPolyLineSink
    SumQuantityUO = injected_mass
    fluxes = ${injection_rate}
    p_or_t_vals = 0.0
    line_length = 1.0
    multiplying_var = injection_rate_massfrac_SiO2
    point_file = injection.bh
    variable = f2
  []
  [inject_H2O]
    type = PorousFlowPolyLineSink
    SumQuantityUO = injected_mass
    fluxes = ${injection_rate}
    p_or_t_vals = 0.0
    line_length = 1.0
    multiplying_var = injection_rate_massfrac_H2O
    point_file = injection.bh
    variable = porepressure
  []

  [produce_Na]
    type = PorousFlowPolyLineSink
    SumQuantityUO = produced_mass_Na
    fluxes = ${production_rate}
    p_or_t_vals = 0.0
    line_length = 1.0
    mass_fraction_component = 0
    point_file = production.bh
    variable = f0
  []
  [produce_Cl]
    type = PorousFlowPolyLineSink
    SumQuantityUO = produced_mass_Cl
    fluxes = ${production_rate}
    p_or_t_vals = 0.0
    line_length = 1.0
    mass_fraction_component = 1
    point_file = production.bh
    variable = f1
  []
  [produce_SiO2]
    type = PorousFlowPolyLineSink
    SumQuantityUO = produced_mass_SiO2
    fluxes = ${production_rate}
    p_or_t_vals = 0.0
    line_length = 1.0
    mass_fraction_component = 2
    point_file = production.bh
    variable = f2
  []
  [produce_H2O]
    type = PorousFlowPolyLineSink
    SumQuantityUO = produced_mass_H2O
    fluxes = ${production_rate}
    p_or_t_vals = 0.0
    line_length = 1.0
    mass_fraction_component = 3
    point_file = production.bh
    variable = porepressure
  []
  [produce_heat]
    type = PorousFlowPolyLineSink
    SumQuantityUO = produced_heat
    fluxes = ${production_rate}
    p_or_t_vals = 0.0
    line_length = 1.0
    use_enthalpy = true
    point_file = production.bh
    variable = temperature
  []
[]

[UserObjects]
  [injected_mass]
    type = PorousFlowSumQuantity
  []
  [produced_mass_Na]
    type = PorousFlowSumQuantity
  []
  [produced_mass_Cl]
    type = PorousFlowSumQuantity
  []
  [produced_mass_SiO2]
    type = PorousFlowSumQuantity
  []
  [produced_mass_H2O]
    type = PorousFlowSumQuantity
  []
  [produced_heat]
    type = PorousFlowSumQuantity
  []
[]

[Postprocessors]
  [dt]
    type = TimestepSize
    execute_on = TIMESTEP_BEGIN
  []
  [tot_kg_injected_this_timestep]
    type = PorousFlowPlotQuantity
    uo = injected_mass
  []
  [kg_Na_produced_this_timestep]
    type = PorousFlowPlotQuantity
    uo = produced_mass_Na
  []
  [kg_Cl_produced_this_timestep]
    type = PorousFlowPlotQuantity
    uo = produced_mass_Cl
  []
  [kg_SiO2_produced_this_timestep]
    type = PorousFlowPlotQuantity
    uo = produced_mass_SiO2
  []
  [kg_H2O_produced_this_timestep]
    type = PorousFlowPlotQuantity
    uo = produced_mass_H2O
  []
  [mole_rate_Na_produced]
    type = FunctionValuePostprocessor
    function = moles_Na
    indirect_dependencies = 'kg_Na_produced_this_timestep dt'
  []
  [mole_rate_Cl_produced]
    type = FunctionValuePostprocessor
    function = moles_Cl
    indirect_dependencies = 'kg_Cl_produced_this_timestep dt'
  []
  [mole_rate_SiO2_produced]
    type = FunctionValuePostprocessor
    function = moles_SiO2
    indirect_dependencies = 'kg_SiO2_produced_this_timestep dt'
  []
  [mole_rate_H2O_produced]
    type = FunctionValuePostprocessor
    function = moles_H2O
    indirect_dependencies = 'kg_H2O_produced_this_timestep dt'
  []
  [heat_joules_extracted_this_timestep]
    type = PorousFlowPlotQuantity
    uo = produced_heat
  []
  [production_temperature]
    type = PointValue
    point = '30 0 0'
    variable = temperature
  []
[]

[Functions]
  [moles_Na]
    type = ParsedFunction
    symbol_names = 'kg_Na dt'
    symbol_values = 'kg_Na_produced_this_timestep dt'
    expression = 'kg_Na * 1000 / 22.9898 / dt'
  []
  [moles_Cl]
    type = ParsedFunction
    symbol_names = 'kg_Cl dt'
    symbol_values = 'kg_Cl_produced_this_timestep dt'
    expression = 'kg_Cl * 1000 / 35.453 / dt'
  []
  [moles_SiO2]
    type = ParsedFunction
    symbol_names = 'kg_SiO2 dt'
    symbol_values = 'kg_SiO2_produced_this_timestep dt'
    expression = 'kg_SiO2 * 1000 / 60.0843 / dt'
  []
  [moles_H2O]
    type = ParsedFunction
    symbol_names = 'kg_H2O dt'
    symbol_values = 'kg_H2O_produced_this_timestep dt'
    expression = 'kg_H2O * 1000 / 18.0152 / dt'
  []
[]

[FluidProperties]
  [the_simple_fluid]
    type = SimpleFluidProperties
    thermal_expansion = 0
    bulk_modulus = 2E9
    viscosity = 1E-3
    density0 = 1000
    cv = 4000.0
    cp = 4000.0
  []
[]

[PorousFlowFullySaturated]
  coupling_type = ThermoHydro
  porepressure = porepressure
  temperature = temperature
  mass_fraction_vars = 'f0 f1 f2'
  save_component_rate_in = 'rate_Na rate_Cl rate_SiO2 rate_H2O' # change in kg at every node / dt
  fp = the_simple_fluid
  temperature_unit = Celsius
[]

[AuxVariables]
  [injection_temperature]
    initial_condition = 200
  []
  [injection_rate_massfrac_Na]
    initial_condition = 0.002285946
  []
  [injection_rate_massfrac_Cl]
    initial_condition = 0.0035252
  []
  [injection_rate_massfrac_SiO2]
    initial_condition = 1.3741E-05
  []
  [injection_rate_massfrac_H2O]
    initial_condition = 0.994175112
  []
  [rate_H2O]
  []
  [rate_Na]
  []
  [rate_Cl]
  []
  [rate_SiO2]
  []
[]

[Materials]
  [porosity]
    type = PorousFlowPorosityConst # this simulation has no porosity changes from dissolution
    porosity = 0.1
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1E-12 0 0   0 1E-12 0   0 0 1E-12'
  []
  [thermal_conductivity]
    type = PorousFlowThermalConductivityIdeal
    dry_thermal_conductivity = '0 0 0  0 0 0  0 0 0'
  []
  [rock_heat]
    type = PorousFlowMatrixInternalEnergy
    density = 2500.0
    specific_heat_capacity = 1200.0
  []
[]

[Preconditioning]
  active = typically_efficient
  [typically_efficient]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -pc_hypre_type'
    petsc_options_value = ' hypre    boomeramg'
  []
  [strong]
    type = SMP
    full = true
    petsc_options = '-ksp_diagonal_scale -ksp_diagonal_scale_fix'
    petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type -pc_asm_overlap'
    petsc_options_value = ' asm      ilu           NONZERO                   2'
  []
  [probably_too_strong]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
    petsc_options_value = ' lu       mumps'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  end_time = 7.76E6 # 90 days
  dt = 1E5
[]

[Outputs]
  exodus = true
[]

[MultiApps]
  [react]
    type = TransientMultiApp
    input_files = aquifer_geochemistry.i
    clone_master_mesh = true
    execute_on = 'timestep_end'
  []
[]

[Transfers]
  [changes_due_to_flow]
    type = MultiAppCopyTransfer
    source_variable = 'rate_H2O rate_Na rate_Cl rate_SiO2 temperature'
    variable = 'pf_rate_H2O pf_rate_Na pf_rate_Cl pf_rate_SiO2 temperature'
    to_multi_app = react
  []
  [massfrac_from_geochem]
    type = MultiAppCopyTransfer
    source_variable = 'massfrac_Na massfrac_Cl massfrac_SiO2'
    variable = 'f0 f1 f2'
    from_multi_app = react
  []
[]

(modules/navier_stokes/test/tests/finite_element/ins/block-restriction/two-mats-one-eqn-set.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 2
    ymin = 0
    ymax = 1
    nx = 16
    ny = 8
    elem_type = QUAD9
  []
  [./corner_node_0]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node_0'
    coord = '0 0 0'
    input = gen
  [../]
  [./corner_node_1]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node_1'
    coord = '1 0 0'
    input = corner_node_0
  [../]
  [./subdomain1]
    input = corner_node_1
    type = SubdomainBoundingBoxGenerator
    bottom_left = '1 0 0'
    top_right = '2 1 0'
    block_id = 1
  [../]
  [./break_boundary]
    input = subdomain1
    type = BreakBoundaryOnSubdomainGenerator
  [../]
  [./interface0]
    type = SideSetsBetweenSubdomainsGenerator
    input = break_boundary
    primary_block = '0'
    paired_block = '1'
    new_boundary = 'interface0'
  [../]
  [./interface1]
    type = SideSetsBetweenSubdomainsGenerator
    input = interface0
    primary_block = '1'
    paired_block = '0'
    new_boundary = 'interface1'
  [../]
[]

[Variables]
  [velocity0]
    order = SECOND
    family = LAGRANGE_VEC
  []
  [T0]
    order = SECOND
    [InitialCondition]
      type = ConstantIC
      value = 1.0
    []
  []
  [p0]
  []
[]

[Kernels]
  [./mass0]
    type = INSADMass
    variable = p0
  [../]
  [./momentum_time0]
    type = INSADMomentumTimeDerivative
    variable = velocity0
  [../]
  [./momentum_convection0]
    type = INSADMomentumAdvection
    variable = velocity0
  [../]
  [./momentum_viscous0]
    type = INSADMomentumViscous
    variable = velocity0
  [../]
  [./momentum_pressure0]
    type = INSADMomentumPressure
    variable = velocity0
    pressure = p0
    integrate_p_by_parts = true
  [../]
  [./temperature_time0]
    type = INSADHeatConductionTimeDerivative
    variable = T0
  [../]
  [./temperature_advection0]
    type = INSADEnergyAdvection
    variable = T0
  [../]
  [./temperature_conduction0]
    type = ADHeatConduction
    variable = T0
    thermal_conductivity = 'k'
  [../]
[]

[BCs]
  [./no_slip0]
    type = VectorFunctionDirichletBC
    variable = velocity0
    boundary = 'bottom_to_0 interface0 left'
  [../]
  [./lid0]
    type = VectorFunctionDirichletBC
    variable = velocity0
    boundary = 'top_to_0'
    function_x = 'lid_function0'
  [../]
  [./T_hot0]
    type = DirichletBC
    variable = T0
    boundary = 'bottom_to_0'
    value = 1
  [../]
  [./T_cold0]
    type = DirichletBC
    variable = T0
    boundary = 'top_to_0'
    value = 0
  [../]
  [./pressure_pin0]
    type = DirichletBC
    variable = p0
    boundary = 'pinned_node_0'
    value = 0
  [../]

  [./no_slip1]
    type = VectorFunctionDirichletBC
    variable = velocity0
    boundary = 'bottom_to_1 interface1 right'
  [../]
  [./lid1]
    type = VectorFunctionDirichletBC
    variable = velocity0
    boundary = 'top_to_1'
    function_x = 'lid_function1'
  [../]
  [./T_hot1]
    type = DirichletBC
    variable = T0
    boundary = 'bottom_to_1'
    value = 1
  [../]
  [./T_cold1]
    type = DirichletBC
    variable = T0
    boundary = 'top_to_1'
    value = 0
  [../]
[]

[Materials]
  [./const]
    type = ADGenericConstantMaterial
    prop_names = 'rho mu cp k'
    prop_values = '1  1  1  .01'
  [../]
  [ins_mat0]
    type = INSAD3Eqn
    velocity = velocity0
    pressure = p0
    temperature = T0
    block = '0'
  []
  [ins_mat1]
    type = INSAD3Eqn
    velocity = velocity0
    pressure = p0
    temperature = T0
    block = '1'
  []
[]

[Functions]
    # We pick a function that is exactly represented in the velocity
    # space so that the Dirichlet conditions are the same regardless
    # of the mesh spacing.
  [./lid_function0]
    type = ParsedFunction
    expression = '4*x*(1-x)'
  [../]
  [./lid_function1]
    type = ParsedFunction
    expression = '4*(x-1)*(2-x)'
  [../]
[]

[Preconditioning]
  [./SMP]
    type = SMP
    full = true
    solve_type = 'NEWTON'
  [../]
[]

[Executioner]
  type = Transient
  # Run for 100+ timesteps to reach steady state.
  num_steps = 5
  dt = .5
  dtmin = .5
  petsc_options_iname = '-pc_type -pc_asm_overlap -sub_pc_type -sub_pc_factor_levels -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      2               ilu          4                     NONZERO'
  line_search = 'none'
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-13
  nl_max_its = 6
  l_tol = 1e-6
  l_max_its = 500
[]

[Outputs]
  exodus = true
[]

(modules/combined/test/tests/restart-transient-from-ss-with-stateful/sub_ss.i)

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    nx = 8
    ny = 8
    xmin = -82.627
    xmax = 82.627
    ymin = -82.627
    ymax = 82.627
    dim = 2
  []
  [./extra_nodes_x]
    type = ExtraNodesetGenerator
    input = 'gen'
    new_boundary = 'no_x'
    coord = '0 82.627 0'
  [../]
  [./extra_nodes_y]
    type = ExtraNodesetGenerator
    input = 'extra_nodes_x'
    new_boundary = 'no_y'
    coord = '-82.627 0 0'
  [../]
[]

[Problem]
  type = ReferenceResidualProblem
  reference_vector = 'ref'
  extra_tag_vectors = 'ref'
[]

[AuxVariables]
  [./temp]
  [../]
[]

[Physics/SolidMechanics/QuasiStatic]
  # FINITE strain when strain is large, i.e., visible movement.
  # SMALL strain when things are stressed, but may not move.
  [./fuel]
    add_variables = true
    strain = FINITE
    temperature = temp
    eigenstrain_names = 'thermal_eigenstrain'
    generate_output = 'vonmises_stress stress_xx stress_yy hydrostatic_stress max_principal_stress strain_xy elastic_strain_xx stress_xy'
    extra_vector_tags = 'ref'
    use_finite_deform_jacobian = true
    incremental = true
  [../]
[]

[BCs]
  [./no_x]
    type = DirichletBC
    variable = disp_x
    boundary = 'no_x'
    value = 0.0
    preset = true
  [../]
  [./no_y]
    type = DirichletBC
    preset = true
    variable = disp_y
    boundary = 'no_y'
    value = 0.0
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 3e10   # Pa
    poissons_ratio = 0.33    # unitless
  [../]
  [./thermal_strains]
    type = ComputeThermalExpansionEigenstrain
    temperature = temp
    thermal_expansion_coeff = 2e-6 # 1/K
    stress_free_temperature = 500 # K
    eigenstrain_name = 'thermal_eigenstrain'
  [../]
  [./stress_finite] # goes with FINITE strain formulation
    type = ComputeFiniteStrainElasticStress
  [../]
[]

[Postprocessors]
  [./avg_temp]
    type = ElementAverageValue
    variable = temp
  [../]
  [./disp_x_max_element]
    type = ElementExtremeValue
    value_type = max
    variable = disp_x
    execute_on = 'initial timestep_end'
  [../]
  [./disp_y_max_element]
    type = ElementExtremeValue
    value_type = max
    variable = disp_y
    execute_on = 'initial timestep_end'
  [../]
  [./disp_x_max_nodal]
    type = NodalExtremeValue
    value_type = max
    variable = disp_x
    execute_on = 'initial timestep_end'
  [../]
  [./disp_y_max_nodal]
    type = NodalExtremeValue
    value_type = max
    variable = disp_y
    execute_on = 'initial timestep_end'
  [../]
[]

[Executioner]
  type = Steady
  petsc_options_iname = '-pc_type -pc_hypre_type -ksp_gmres_restart'
  petsc_options_value = 'hypre boomeramg 300'
  line_search = 'none'

  l_tol = 1e-02
  nl_rel_tol = 5e-04
  nl_abs_tol = 1e-2

  l_max_its = 50
  nl_max_its = 25
[]

[Outputs]
  exodus = true
  print_linear_residuals = false
  perf_graph = true
[]

(modules/combined/test/tests/optimization/compliance_sensitivity/2d_mmb_2material_cost_initial.i)

vol_frac = 0.4
cost_frac = 0.22 # Change back to 0.4

power = 2.0

E0 = 1.0e-6
E1 = 0.3
E2 = 1.0

rho0 = 1.0e-6
rho1 = 0.3
rho2 = 1.0

C0 = 1.0e-6
C1 = 0.5
C2 = 1.0

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  [MeshGenerator]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 150
    ny = 50
    xmin = 0
    xmax = 30
    ymin = 0
    ymax = 10
  []
  [node]
    type = ExtraNodesetGenerator
    input = MeshGenerator
    new_boundary = hold
    nodes = 0
  []
  [push]
    type = ExtraNodesetGenerator
    input = node
    new_boundary = push
    coord = '30 10 0'
  []
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
[]

[AuxVariables]
  [Dc]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = -1.0
  []
  [Cc]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = -1.0
  []
  [Cost]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = -1.0
  []
  [mat_den]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = ${vol_frac}
  []
[]

[AuxKernels]
  [Cost]
    type = MaterialRealAux
    variable = Cost
    property = Cost_mat
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = SMALL
    add_variables = true
    incremental = false
  []
[]

[BCs]
  [no_x]
    type = DirichletBC
    variable = disp_y
    boundary = hold
    value = 0.0
  []
  [no_y]
    type = DirichletBC
    variable = disp_x
    boundary = right
    value = 0.0
  []

[]
[NodalKernels]
  [push]
    type = NodalGravity
    variable = disp_y
    boundary = push
    gravity_value = -1
    mass = 1
  []
[]
[Materials]
  [elasticity_tensor]
    type = ComputeVariableIsotropicElasticityTensor
    youngs_modulus = E_phys
    poissons_ratio = poissons_ratio
    args = 'mat_den'
  []
  [E_phys]
    type = DerivativeParsedMaterial
    # ordered multimaterial simp
    expression = "A1:=(${E0}-${E1})/(${rho0}^${power}-${rho1}^${power}); "
                 "B1:=${E0}-A1*${rho0}^${power}; E1:=A1*mat_den^${power}+B1; "
                 "A2:=(${E1}-${E2})/(${rho1}^${power}-${rho2}^${power}); "
                 "B2:=${E1}-A2*${rho1}^${power}; E2:=A2*mat_den^${power}+B2; "
                 "if(mat_den<${rho1},E1,E2)"
    coupled_variables = 'mat_den'
    property_name = E_phys
    epsilon = 1e-12
  []

  [Cost_mat]
    type = DerivativeParsedMaterial
    # ordered multimaterial simp
    expression = "A1:=(${C0}-${C1})/(${rho0}^(1/${power})-${rho1}^(1/${power})); "
                 "B1:=${C0}-A1*${rho0}^(1/${power}); C1:=A1*mat_den^(1/${power})+B1; "
                 "A2:=(${C1}-${C2})/(${rho1}^(1/${power})-${rho2}^(1/${power})); "
                 "B2:=${C1}-A2*${rho1}^(1/${power}); C2:=A2*mat_den^(1/${power})+B2; "
                 "if(mat_den<${rho1},C1,C2)"
    coupled_variables = 'mat_den'
    property_name = Cost_mat
    epsilon = 1e-12
  []

  [poissons_ratio]
    type = GenericConstantMaterial
    prop_names = poissons_ratio
    prop_values = 0.3
  []
  [stress]
    type = ComputeLinearElasticStress
  []
  [dc]
    type = ComplianceSensitivity
    design_density = mat_den
    youngs_modulus = E_phys
  []
  [cc]
    type = CostSensitivity
    design_density = mat_den
    cost = Cost_mat
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[UserObjects]
  [rad_avg]
    type = RadialAverage
    radius = 1.2
    weights = linear
    prop_name = sensitivity
    execute_on = TIMESTEP_END
    force_preaux = true
  []
  [rad_avg_cost]
    type = RadialAverage
    radius = 1.2
    weights = linear
    prop_name = cost_sensitivity
    execute_on = TIMESTEP_END
    force_preaux = true
  []
  [update]
    type = DensityUpdateTwoConstraints
    # This is
    density_sensitivity = Dc
    cost_density_sensitivity = Cc
    cost = Cost
    cost_fraction = ${cost_frac}
    design_density = mat_den
    volume_fraction = ${vol_frac}

    bisection_lower_bound = 0
    bisection_upper_bound = 1.0e16 # 100

    relative_tolerance = 1.0e-3

    execute_on = TIMESTEP_BEGIN
  []
  # Provides Dc
  [calc_sense]
    type = SensitivityFilter
    density_sensitivity = Dc
    design_density = mat_den
    filter_UO = rad_avg
    execute_on = TIMESTEP_END
    force_postaux = true
  []
  # Provides Cc
  [calc_sense_cost]
    type = SensitivityFilter
    density_sensitivity = Cc
    design_density = mat_den
    filter_UO = rad_avg_cost
    execute_on = TIMESTEP_END
    force_postaux = true
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'
  nl_abs_tol = 1e-8
  dt = 1.0
  num_steps = 10 #50000
[]

[Outputs]
  [out]
    type = CSV
    execute_on = 'TIMESTEP_END'
  []
  print_linear_residuals = false
[]

[Postprocessors]
  [total_vol]
    type = ElementIntegralVariablePostprocessor
    variable = mat_den
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [sensitivity]
    type = ElementIntegralMaterialProperty
    mat_prop = sensitivity
  []
  [cost_sensitivity]
    type = ElementIntegralMaterialProperty
    mat_prop = cost_sensitivity
  []
  [cost]
    type = ElementIntegralVariablePostprocessor
    variable = Cost
  []
[]

(modules/solid_mechanics/test/tests/uel/tensile_umat_moose_umat.i)

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  volumetric_locking_correction = true
[]

[Mesh]
  [mesh]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 1
    ny = 1
    nz = 1
    elem_type = HEX8
  []
  [extra_nodeset]
    type = ExtraNodesetGenerator
    input = mesh
    new_boundary = 'master'
    coord = '1.0 1.0 1.0'
  []
[]

[AuxVariables]
  [temperature]
    initial_condition = 500
  []
  [state_var_one]
    family = MONOMIAL
    order = FIRST
  []
  [state_var_two]
    family = MONOMIAL
    order = FIRST
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    add_variables = true
    generate_output = 'vonmises_stress'
    strain = FINITE
  []
[]

[Functions]
  [function_pull]
    type = PiecewiseLinear
    x = '0 100'
    y = '0 0.1'
  []
[]

[AuxKernels]
  [state_ker_one]
    type = MaterialStdVectorAux
    variable = state_var_one
    property = 'state_var'
    index = 0
    execute_on = timestep_end
  []
  [state_ker_two]
    type = MaterialStdVectorAux
    variable = state_var_two
    property = 'state_var'
    index = 1
    execute_on = timestep_end
  []
[]

[Constraints]
  [one]
    type = LinearNodalConstraint
    variable = disp_x
    primary = '6'
    secondary_node_ids = '1 2 5'
    penalty = 1.0e8
    formulation = kinematic
    weights = '1'
  []
  [two]
    type = LinearNodalConstraint
    variable = disp_z
    primary = '6'
    secondary_node_ids = '4 5 7'
    penalty = 1.0e8
    formulation = kinematic
    weights = '1'
  []
[]

[BCs]
  [symmy]
    type = DirichletBC
    variable = disp_y
    boundary = bottom
    value = 0
  []
  [symmx]
    type = DirichletBC
    variable = disp_x
    boundary = left
    value = 0
  []
  [symmz]
    type = DirichletBC
    variable = disp_z
    boundary = back
    value = 0
  []
  # What's done below is to capture the weird constraints
  [axial_load]
    type = FunctionDirichletBC
    variable = disp_y
    boundary = 'top'
    function = function_pull
  []
[]

# Something wrong in the input?
[Materials]
  [umat]
    type = AbaqusUMATStress
    constant_properties = '190.0 28.0 3.0 1.0 6.0 0.0 0.0 23.0 25.0 26.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 '
                          '0.0 0.0 0.0 0.0 0.0 31700000.0 0.32 6.67e-06 1e-08 5000.0 4.0' # 27 properties
    plugin = '../../../../tensor_mechanics/test/plugins/umat_hc40'
    num_state_vars = 177 # 141 + 6*6
    temperature = temperature
    use_one_based_indexing = true
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient

  l_max_its = 100
  l_tol = 1e-8
  nl_max_its = 50
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-8

  dtmin = 1
  dt = 5
  end_time = 100
[]

[Outputs]
  exodus = true
[]

(modules/xfem/test/tests/moving_interface/moving_bimaterial.i)

# This test is for two layer materials with different youngs modulus
# The global stress is determined by switching the stress based on level set values
# The material interface is marked by a level set function
# The two layer materials are glued together
# This case is also meant to test for a bug in moving interfaces on displaced meshes
# It should fail during the healing step of the 2nd timestep if the bug is present.

[GlobalParams]
  order = FIRST
  family = LAGRANGE
[]

[XFEM]
  qrule = volfrac
  output_cut_plane = true
[]

[UserObjects]
  [./level_set_cut_uo]
    type = LevelSetCutUserObject
    level_set_var = ls
    heal_always = true
  [../]
[]

[Mesh]
  displacements = 'disp_x disp_y'
  [generated_mesh]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 5
    ny = 5
    xmin = 0.0
    xmax = 5.
    ymin = 0.0
    ymax = 5.
    elem_type = QUAD4
  []
  [./left_bottom]
    type = ExtraNodesetGenerator
    new_boundary = 'left_bottom'
    coord = '0.0 0.0'
    input = generated_mesh
  [../]
  [./left_top]
    type = ExtraNodesetGenerator
    new_boundary = 'left_top'
    coord = '0.0 5.'
    input = left_bottom
  [../]
[]

[AuxVariables]
  [./ls]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxKernels]
  [./ls_function]
    type = FunctionAux
    variable = ls
    function = ls_func
  [../]
[]

[Variables]
  [./disp_x]
  [../]
  [./disp_y]
  [../]
[]

[Functions]
  [./ls_func]
    type = ParsedFunction
    expression = 'y-3.153 + t'
  [../]
[]

[AuxVariables]
  [./stress_xx]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./stress_yy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./stress_xy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./a_strain_xx]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./a_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./a_strain_xy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./b_strain_xx]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./b_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./b_strain_xy]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[Kernels]
  [./TensorMechanics]
    displacements = 'disp_x disp_y'
  [../]
[]

[AuxKernels]
  [./stress_xx]
    type = RankTwoAux
    rank_two_tensor = stress
    index_i = 0
    index_j = 0
    variable = stress_xx
  [../]
  [./stress_yy]
    type = RankTwoAux
    rank_two_tensor = stress
    index_i = 1
    index_j = 1
    variable = stress_yy
  [../]
  [./stress_xy]
    type = RankTwoAux
    rank_two_tensor = stress
    index_i = 0
    index_j = 1
    variable = stress_xy
  [../]
  [./a_strain_xx]
    type = RankTwoAux
    rank_two_tensor = A_total_strain
    index_i = 0
    index_j = 0
    variable = a_strain_xx
  [../]
  [./a_strain_yy]
    type = RankTwoAux
    rank_two_tensor = A_total_strain
    index_i = 1
    index_j = 1
    variable = a_strain_yy
  [../]
  [./a_strain_xy]
    type = RankTwoAux
    rank_two_tensor = A_total_strain
    index_i = 0
    index_j = 1
    variable = a_strain_xy
  [../]
  [./b_strain_xx]
    type = RankTwoAux
    rank_two_tensor = B_total_strain
    index_i = 0
    index_j = 0
    variable = b_strain_xx
  [../]
  [./b_strain_yy]
    type = RankTwoAux
    rank_two_tensor = B_total_strain
    index_i = 1
    index_j = 1
    variable = b_strain_yy
  [../]
  [./b_strain_xy]
    type = RankTwoAux
    rank_two_tensor = B_total_strain
    index_i = 0
    index_j = 1
    variable = b_strain_xy
  [../]
[]

[Constraints]
  [./dispx_constraint]
    type = XFEMSingleVariableConstraint
    use_displaced_mesh = false
    variable = disp_x
    alpha = 1e8
    geometric_cut_userobject = 'level_set_cut_uo'
  [../]
  [./dispy_constraint]
    type = XFEMSingleVariableConstraint
    use_displaced_mesh = false
    variable = disp_y
    alpha = 1e8
    geometric_cut_userobject = 'level_set_cut_uo'
  [../]
[]

[BCs]
  [./bottomx]
    type = DirichletBC
    boundary = bottom
    variable = disp_x
    value = 0.0
  [../]
  [./bottomy]
    type = DirichletBC
    boundary = bottom
    variable = disp_y
    value = 0.0
  [../]
  [./topx]
    type = FunctionDirichletBC
    boundary = top
    variable = disp_x
    function = 0.03*t
  [../]
  [./topy]
    type = FunctionDirichletBC
    boundary = top
    variable = disp_y
    function = '0.03*t'
  [../]
[]

[Materials]
  [./elasticity_tensor_A]
    type = ComputeIsotropicElasticityTensor
    base_name = A
    youngs_modulus = 1e9
    poissons_ratio = 0.3
  [../]
  [./strain_A]
    type = ComputeSmallStrain
    base_name = A
    displacements = 'disp_x disp_y'
  [../]
  [./stress_A]
    type = ComputeLinearElasticStress
    base_name = A
  [../]
  [./elasticity_tensor_B]
    type = ComputeIsotropicElasticityTensor
    base_name = B
    youngs_modulus = 1e7
    poissons_ratio = 0.3
  [../]
  [./strain_B]
    type = ComputeSmallStrain
    base_name = B
    displacements = 'disp_x disp_y'
  [../]
  [./stress_B]
    type = ComputeLinearElasticStress
    base_name = B
  [../]
  [./combined_stress]
    type = LevelSetBiMaterialRankTwo
    levelset_positive_base = 'A'
    levelset_negative_base = 'B'
    level_set_var = ls
    prop_name = stress
  [../]
  [./combined_dstressdstrain]
    type = LevelSetBiMaterialRankFour
    levelset_positive_base = 'A'
    levelset_negative_base = 'B'
    level_set_var = ls
    prop_name = Jacobian_mult
  [../]
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'
  petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
  petsc_options_value = '201                hypre    boomeramg      8'

  line_search = 'bt'

# controls for linear iterations
  l_max_its = 20
  l_tol = 1e-3

# controls for nonlinear iterations
  nl_max_its = 15
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-12

# time control
  start_time = 0.0
  dt = 0.15
  num_steps = 3

  max_xfem_update = 1
[]

[Outputs]
  exodus = true
  execute_on = timestep_end
  [./console]
    type = Console
    output_linear = true
  [../]
[]

(modules/combined/examples/optimization/multi-load/single_subapp_two.i)

power = 2
E0 = 1.0
Emin = 1.0e-6

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  [Bottom]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 80
    ny = 40
    xmin = 0
    xmax = 150
    ymin = 0
    ymax = 75
  []
  [left_load]
    type = ExtraNodesetGenerator
    input = Bottom
    new_boundary = left_load
    coord = '37.5 75 0'
  []
  [right_load]
    type = ExtraNodesetGenerator
    input = left_load
    new_boundary = right_load
    coord = '112.5 75 0'
  []
  [left_support]
    type = ExtraNodesetGenerator
    input = right_load
    new_boundary = left_support
    coord = '0 0 0'
  []
  [right_support]
    type = ExtraNodesetGenerator
    input = left_support
    new_boundary = right_support
    coord = '150 0 0'
  []
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
[]

[AuxVariables]
  [Dc]
    family = MONOMIAL
    order = SECOND
    initial_condition = -1.0
  []
  [Cc]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = -1.0
  []
  [mat_den]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = 0.1
  []
  [sensitivity_var]
    family = MONOMIAL
    order = SECOND
    initial_condition = -1.0
  []
[]

[AuxKernels]
  [sensitivity_kernel]
    type = MaterialRealAux
    check_boundary_restricted = false
    property = sensitivity
    variable = sensitivity_var
    execute_on = 'TIMESTEP_END'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = SMALL
    add_variables = true
    incremental = false
  []
[]

[BCs]
  [no_y]
    type = DirichletBC
    variable = disp_y
    boundary = left_support
    value = 0.0
  []
  [no_x]
    type = DirichletBC
    variable = disp_x
    boundary = left_support
    value = 0.0
  []
  [no_y_right]
    type = DirichletBC
    variable = disp_y
    boundary = right_support
    value = 0.0
  []
[]

[NodalKernels]
  [push_right]
    type = NodalGravity
    variable = disp_y
    boundary = right_load
    gravity_value = -1e-3
    mass = 1
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeVariableIsotropicElasticityTensor
    youngs_modulus = E_phys
    poissons_ratio = poissons_ratio
    args = 'mat_den'
  []
  [E_phys]
    type = DerivativeParsedMaterial
    # Emin + (density^penal) * (E0 - Emin)
    expression = '${Emin} + (mat_den ^ ${power}) * (${E0}-${Emin})'
    coupled_variables = 'mat_den'
    property_name = E_phys
  []
  [poissons_ratio]
    type = GenericConstantMaterial
    prop_names = poissons_ratio
    prop_values = 0.0
  []
  [stress]
    type = ComputeLinearElasticStress
  []
  [dc]
    type = ComplianceSensitivity
    design_density = mat_den
    youngs_modulus = E_phys
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[UserObjects]
  [rad_avg]
    type = RadialAverage
    radius = 3
    weights = linear
    prop_name = sensitivity
    execute_on = TIMESTEP_END
    force_preaux = true
  []
  # No SIMP optimization in subapp
  [calc_sense]
    type = SensitivityFilter
    density_sensitivity = Dc
    design_density = mat_den
    filter_UO = rad_avg
    execute_on = TIMESTEP_END
    force_postaux = true
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'
  nl_abs_tol = 1e-10
  dt = 1.0
  num_steps = 25
[]

[Outputs]
  exodus = true
  [out]
    type = CSV
    execute_on = 'TIMESTEP_END'
  []
  print_linear_residuals = false
[]

[Postprocessors]
  [mesh_volume]
    type = VolumePostprocessor
    execute_on = 'initial timestep_end'
  []
  [total_vol]
    type = ElementIntegralVariablePostprocessor
    variable = mat_den
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [vol_frac]
    type = ParsedPostprocessor
    expression = 'total_vol / mesh_volume'
    pp_names = 'total_vol mesh_volume'
  []
  [sensitivity]
    type = ElementIntegralMaterialProperty
    mat_prop = sensitivity
    execute_on = 'TIMESTEP_BEGIN TIMESTEP_END NONLINEAR'
  []
  [objective]
    type = ElementIntegralMaterialProperty
    mat_prop = strain_energy_density
    execute_on = 'INITIAL TIMESTEP_END'
  []
[]

(modules/solid_mechanics/test/tests/ad_anisotropic_creep/ad_aniso_creep_temperature_coefficients_function.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 10
    ny = 2
    nz = 2
    xmin = 0.0
    ymin = 0.0
    zmin = 0.0

    xmax = 10.0
    ymax = 1.0
    zmax = 1.0
  []
  [corner_node]
    type = ExtraNodesetGenerator
    new_boundary = '100'
    nodes = '3 69'
    input = gen
  []
  [corner_node_2]
    type = ExtraNodesetGenerator
    new_boundary = '101'
    nodes = '4 47'
    input = corner_node
  []
[]

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  volumetric_locking_correction = true
[]

[AuxVariables]
  [temperature]
    order = CONSTANT
    family = MONOMIAL
  []
  [hydrostatic_stress]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_xx]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_xy]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_zz]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_xz]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_yz]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [temperature]
    type = ConstantAux
    variable = temperature
    value = 50
  []
  [hydrostatic_stress]
    type = ADRankTwoScalarAux
    variable = hydrostatic_stress
    rank_two_tensor = stress
    scalar_type = Hydrostatic
  []
  [creep_strain_xx]
    type = ADRankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_xx
    index_i = 0
    index_j = 0
  []
  [creep_strain_xy]
    type = ADRankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_xy
    index_i = 0
    index_j = 1
  []
  [creep_strain_yy]
    type = ADRankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_yy
    index_i = 1
    index_j = 1
  []
  [creep_strain_zz]
    type = ADRankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_zz
    index_i = 2
    index_j = 2
  []
  [creep_strain_xz]
    type = ADRankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_xz
    index_i = 0
    index_j = 2
  []
  [creep_strain_yz]
    type = ADRankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_yz
    index_i = 1
    index_j = 2
  []
  [sigma_xx]
    type = ADRankTwoAux
    rank_two_tensor = stress
    variable = stress_xx
    index_i = 1
    index_j = 1
  []
[]

[ICs]
  [temp]
    type = ConstantIC
    variable = temperature
    value = 50.0
  []
[]

[Functions]
  [pull]
    type = PiecewiseLinear
    x = '0 1.0e-9 1.0'
    y = '0 -4e1 -4e1'
  []
  [F]
    type = PiecewiseLinear
    x = '-1000 10000'
    y = '0.5 0.5'
  []
  [G]
    type = PiecewiseLinear
    x = '-1000 10000'
    y = '0.5 0.5'
  []
  [H]
    type = PiecewiseLinear
    x = '-1000 10000'
    y = '0.5 0.5'
  []
  [L]
    type = PiecewiseLinear
    x = '-1000 10000'
    y = '1.5 1.5'
  []
  [M]
    type = PiecewiseLinear
    x = '-1000 10000'
    y = '1.5 1.5'
  []
  [N]
    type = PiecewiseLinear
    x = '-1000 10000'
    y = '1.5 1.5'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = FINITE
    generate_output = 'elastic_strain_xx stress_xx'
    use_automatic_differentiation = true
    add_variables = true
  []
[]

[Materials]
  [elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    youngs_modulus = 700
    poissons_ratio = 0.0
  []

  [elastic_strain]
    type = ADComputeMultipleInelasticStress
    inelastic_models = 'trial_creep_aniso_iso'
    max_iterations = 50
  []
  [hill_constants]
    type = ADHillConstants
    # F G H L M N
    hill_constants = "0.5 0.5 0.5 1.5 1.5 1.5"
    function_names = 'F G H L M N'
    temperature = temperature
  []
  [trial_creep_aniso_iso]
    type = ADHillCreepStressUpdate
    coefficient = 1e-16
    n_exponent = 9
    m_exponent = 0
    activation_energy = 0
    max_inelastic_increment = 0.00003
    relative_tolerance = 1e-20
    absolute_tolerance = 1e-20
    internal_solve_output_on = never
    # Force it to not use integration error
    max_integration_error = 1.0
  []

[]

[BCs]
  [no_disp_x]
    type = ADDirichletBC
    variable = disp_x
    boundary = left
    value = 0.0
  []

  [no_disp_y]
    type = ADDirichletBC
    variable = disp_y
    boundary = 100
    value = 0.0
  []

  [no_disp_z]
    type = ADDirichletBC
    variable = disp_z
    boundary = 101
    value = 0.0
  []

  [Pressure]
    [Side1]
      boundary = right
      function = pull
    []
  []

[]

[Executioner]
  type = Transient

  solve_type = NEWTON
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu     superlu_dist'

  nl_rel_tol = 1e-13
  nl_abs_tol = 1.0e-14
  l_max_its = 90
  num_steps = 50
  dt = 5.0e-4
  start_time = 0
  automatic_scaling = true
[]

[Postprocessors]
  [matl_ts_min]
    type = MaterialTimeStepPostprocessor
  []
  [max_disp_x]
    type = ElementExtremeValue
    variable = disp_x
  []
  [max_disp_y]
    type = ElementExtremeValue
    variable = disp_y
  []
  [max_hydro]
    type = ElementAverageValue
    variable = hydrostatic_stress
  []
  [dt]
    type = TimestepSize
  []
  [num_lin]
    type = NumLinearIterations
    outputs = console
  []
  [num_nonlin]
    type = NumNonlinearIterations
    outputs = console
  []
  [creep_strain_xx]
    type = ElementalVariableValue
    variable = creep_strain_xx
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [creep_strain_yy]
    type = ElementalVariableValue
    variable = creep_strain_yy
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [creep_strain_zz]
    type = ElementalVariableValue
    variable = creep_strain_zz
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [creep_strain_xy]
    type = ElementalVariableValue
    variable = creep_strain_xy
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [creep_strain_yz]
    type = ElementalVariableValue
    variable = creep_strain_yz
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [creep_strain_xz]
    type = ElementalVariableValue
    variable = creep_strain_xz
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [elastic_strain_xx]
    type = ElementalVariableValue
    variable = elastic_strain_xx
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [sigma_xx]
    type = ElementalVariableValue
    variable = stress_xx
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
[]

[Outputs]
  csv = true
  exodus = true
  perf_graph = true
[]

(modules/combined/examples/periodic_strain/global_strain_pfm.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 50
    ny = 50
    xmin = -0.5
    xmax = 0.5
    ymin = -0.5
    ymax = 0.5
  []
  [./cnode]
    input = gen
    type = ExtraNodesetGenerator
    coord = '0.0 0.0'
    new_boundary = 100
  [../]
[]

[Variables]
  [./u_x]
  [../]
  [./u_y]
  [../]
  [./global_strain]
    order = THIRD
    family = SCALAR
  [../]
  [./c]
    [./InitialCondition]
      type = FunctionIC
      function = 'sin(2*x*pi)*sin(2*y*pi)*0.05+0.6'
    [../]
  [../]
  [./w]
  [../]
[]

[AuxVariables]
  [./local_energy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./disp_x]
  [../]
  [./disp_y]
  [../]
  [./s00]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./s01]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./s10]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./s11]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./e00]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./e01]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./e10]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./e11]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[AuxKernels]
  [./disp_x]
    type = GlobalDisplacementAux
    variable = disp_x
    scalar_global_strain = global_strain
    global_strain_uo = global_strain_uo
    component = 0
  [../]
  [./disp_y]
    type = GlobalDisplacementAux
    variable = disp_y
    scalar_global_strain = global_strain
    global_strain_uo = global_strain_uo
    component = 1
  [../]
  [./local_free_energy]
    type = TotalFreeEnergy
    execute_on = 'initial LINEAR'
    variable = local_energy
    interfacial_vars = 'c'
    kappa_names = 'kappa_c'
  [../]
  [./s00]
    type = RankTwoAux
    variable = s00
    rank_two_tensor = stress
    index_i = 0
    index_j = 0
  [../]
  [./s01]
    type = RankTwoAux
    variable = s01
    rank_two_tensor = stress
    index_i = 0
    index_j = 1
  [../]
  [./s10]
    type = RankTwoAux
    variable = s10
    rank_two_tensor = stress
    index_i = 1
    index_j = 0
  [../]
  [./s11]
    type = RankTwoAux
    variable = s11
    rank_two_tensor = stress
    index_i = 1
    index_j = 1
  [../]
  [./e00]
    type = RankTwoAux
    variable = e00
    rank_two_tensor = total_strain
    index_i = 0
    index_j = 0
  [../]
  [./e01]
    type = RankTwoAux
    variable = e01
    rank_two_tensor = total_strain
    index_i = 0
    index_j = 1
  [../]
  [./e10]
    type = RankTwoAux
    variable = e10
    rank_two_tensor = total_strain
    index_i = 1
    index_j = 0
  [../]
  [./e11]
    type = RankTwoAux
    variable = e11
    rank_two_tensor = total_strain
    index_i = 1
    index_j = 1
  [../]
[]

[GlobalParams]
  derivative_order = 2
  enable_jit = true
  displacements = 'u_x u_y'
  block = 0
[]

[Kernels]
  [./TensorMechanics]
  [../]

  # Cahn-Hilliard kernels
  [./c_dot]
    type = CoupledTimeDerivative
    variable = w
    v = c
    block = 0
  [../]
  [./c_res]
    type = SplitCHParsed
    variable = c
    f_name = F
    kappa_name = kappa_c
    w = w
    block = 0
  [../]
  [./w_res]
    type = SplitCHWRes
    variable = w
    mob_name = M
    block = 0
  [../]
[]

[ScalarKernels]
  [./global_strain]
    type = GlobalStrain
    variable = global_strain
    global_strain_uo = global_strain_uo
  [../]
[]

[BCs]
  [./Periodic]
    [./all]
      auto_direction = 'x y'
      variable = 'c w u_x u_y'
    [../]
  [../]

  # fix center point location
  [./centerfix_x]
    type = DirichletBC
    boundary = 100
    variable = u_x
    value = 0
  [../]
  [./centerfix_y]
    type = DirichletBC
    boundary = 100
    variable = u_y
    value = 0
  [../]
[]

[Materials]
  [./consts]
    type = GenericConstantMaterial
    prop_names  = 'M   kappa_c'
    prop_values = '0.2 0.01   '
  [../]

  [./shear1]
    type = GenericConstantRankTwoTensor
    tensor_values = '0 0 0 0 0 0.5'
    tensor_name = shear1
  [../]
  [./shear2]
    type = GenericConstantRankTwoTensor
    tensor_values = '0 0 0 0 0 -0.5'
    tensor_name = shear2
  [../]
  [./expand3]
    type = GenericConstantRankTwoTensor
    tensor_values = '1 1 0 0 0 0'
    tensor_name = expand3
  [../]

  [./weight1]
    type = DerivativeParsedMaterial
    expression = '0.3*c^2'
    property_name = weight1
    coupled_variables = c
  [../]
  [./weight2]
    type = DerivativeParsedMaterial
    expression = '0.3*(1-c)^2'
    property_name = weight2
    coupled_variables = c
  [../]
  [./weight3]
    type = DerivativeParsedMaterial
    expression = '4*(0.5-c)^2'
    property_name = weight3
    coupled_variables = c
  [../]

  [./elasticity_tensor]
    type = ComputeElasticityTensor
    C_ijkl = '1 1'
    fill_method = symmetric_isotropic
  [../]
  [./strain]
    type = ComputeSmallStrain
    global_strain = global_strain
    eigenstrain_names = eigenstrain
  [../]

  [./eigenstrain]
    type = CompositeEigenstrain
    tensors = 'shear1  shear2  expand3'
    weights = 'weight1 weight2 weight3'
    coupled_variables = c
    eigenstrain_name = eigenstrain
  [../]

  [./global_strain]
    type = ComputeGlobalStrain
    scalar_global_strain = global_strain
    global_strain_uo = global_strain_uo
  [../]

  [./stress]
    type = ComputeLinearElasticStress
  [../]

  # chemical free energies
  [./chemical_free_energy]
    type = DerivativeParsedMaterial
    property_name = Fc
    expression = '4*c^2*(1-c)^2'
    coupled_variables = 'c'
    outputs = exodus
    output_properties = Fc
  [../]

  # elastic free energies
  [./elastic_free_energy]
    type = ElasticEnergyMaterial
    f_name = Fe
    coupled_variables = 'c'
    outputs = exodus
    output_properties = Fe
  [../]

  # free energy (chemical + elastic)
  [./free_energy]
    type = DerivativeSumMaterial
    block = 0
    property_name = F
    sum_materials = 'Fc Fe'
    coupled_variables = 'c'
  [../]
[]

[UserObjects]
  [./global_strain_uo]
    type = GlobalStrainUserObject
    execute_on = 'Initial Linear Nonlinear'
  [../]
[]

[Postprocessors]
  [./total_free_energy]
    type = ElementIntegralVariablePostprocessor
    execute_on = 'initial TIMESTEP_END'
    variable = local_energy
  [../]
  [./total_solute]
    type = ElementIntegralVariablePostprocessor
    execute_on = 'initial TIMESTEP_END'
    variable = c
  [../]
  [./min]
    type = ElementExtremeValue
    execute_on = 'initial TIMESTEP_END'
    value_type = min
    variable = c
  [../]
  [./max]
    type = ElementExtremeValue
    execute_on = 'initial TIMESTEP_END'
    value_type = max
    variable = c
  [../]
[]

[Preconditioning]
  [./SMP]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = Transient
  scheme = bdf2
  solve_type = 'PJFNK'

  line_search = basic

  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_ksp_type -sub_pc_type -pc_asm_overlap'
  petsc_options_value = 'asm         31   preonly   lu      1'

  l_max_its = 30
  nl_max_its = 12

  l_tol = 1.0e-4

  nl_rel_tol = 1.0e-8
  nl_abs_tol = 1.0e-10

  start_time = 0.0
  end_time = 2.0

  [./TimeStepper]
    type = IterationAdaptiveDT
    dt = 0.01
    growth_factor = 1.5
    cutback_factor = 0.8
    optimal_iterations = 9
    iteration_window = 2
  [../]
[]

[Outputs]
  execute_on = 'timestep_end'
  print_linear_residuals = false
  exodus = true
  [./table]
    type = CSV
    delimiter = ' '
  [../]
[]

(modules/solid_mechanics/test/tests/ad_anisotropic_creep/aniso_creep_x_3d.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 10
    ny = 2
    nz = 2
    xmin = 0.0
    ymin = 0.0
    zmin = 0.0

    xmax = 10.0
    ymax = 1.0
    zmax = 1.0
  []
  [corner_node]
    type = ExtraNodesetGenerator
    new_boundary = '100'
    nodes = '3 69'
    input = gen
  []
  [corner_node_2]
    type = ExtraNodesetGenerator
    new_boundary = '101'
    nodes = '4 47'
    input = corner_node
  []
[]

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  volumetric_locking_correction = true
[]

[AuxVariables]
  [hydrostatic_stress]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_xx]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_xy]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [hydrostatic_stress]
    type = RankTwoScalarAux
    variable = hydrostatic_stress
    rank_two_tensor = stress
    scalar_type = Hydrostatic
  []
  [creep_strain_xx]
    type = RankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_xx
    index_i = 0
    index_j = 0
  []
  [creep_strain_xy]
    type = RankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_xy
    index_i = 0
    index_j = 1
  []
  [creep_strain_yy]
    type = RankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_yy
    index_i = 1
    index_j = 1
  []
  [sigma_xx]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_xx
    index_i = 1
    index_j = 1
  []
[]

[Functions]
  [pull]
    type = PiecewiseLinear
    x = '0 1.0e-9 1.0'
    y = '0 -4e1 -4e1'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = FINITE
    generate_output = 'elastic_strain_xx stress_xx'
    add_variables = true
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 700
    poissons_ratio = 0.0
  []

  [elastic_strain]
    type = ComputeMultipleInelasticStress
    inelastic_models = "trial_creep_two"
    max_iterations = 50
    absolute_tolerance = 1e-16
  []

  [hill_tensor]
    type = HillConstants
    # F G H L M N
    hill_constants = "0.5 0.25 0.3866 1.6413 1.6413 1.2731"
  []

  [trial_creep_two]
    type = HillCreepStressUpdate
    coefficient = 1e-16
    n_exponent = 9
    m_exponent = 0
    activation_energy = 0
    max_inelastic_increment = 0.00003
    absolute_tolerance = 1e-20
    relative_tolerance = 1e-20
    # Force it to not use integration error
    max_integration_error = 100.0
  []
[]

[BCs]
  [no_disp_x]
    type = DirichletBC
    variable = disp_x
    boundary = left
    value = 0.0
  []

  [no_disp_y]
    type = DirichletBC
    variable = disp_y
    boundary = 100
    value = 0.0
  []

  [no_disp_z]
    type = DirichletBC
    variable = disp_z
    boundary = 101
    value = 0.0
  []

  [Pressure]
    [Side1]
      boundary = right
      function = pull
    []
  []

[]

[Executioner]
  type = Transient

  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -mat_mffd_err'
  petsc_options_value = 'lu     superlu_dist                    1e-5'

  nl_rel_tol = 1.0e-14
  nl_abs_tol = 1.0e-14
  l_max_its = 10
  num_steps = 10
  dt = 1.0e-4
  start_time = 0
  automatic_scaling = true
[]

[Postprocessors]
  [matl_ts_min]
    type = MaterialTimeStepPostprocessor
  []
  [max_disp_x]
    type = ElementExtremeValue
    variable = disp_x
  []
  [max_disp_y]
    type = ElementExtremeValue
    variable = disp_y
  []
  [max_hydro]
    type = ElementAverageValue
    variable = hydrostatic_stress
  []
  [dt]
    type = TimestepSize
  []
  [num_lin]
    type = NumLinearIterations
    outputs = console
  []
  [num_nonlin]
    type = NumNonlinearIterations
    outputs = console
  []
  [creep_strain_xx]
    type = ElementalVariableValue
    variable = creep_strain_xx
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [elastic_strain_xx]
    type = ElementalVariableValue
    variable = elastic_strain_xx
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [sigma_xx]
    type = ElementalVariableValue
    variable = stress_xx
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
[]

[Outputs]
  csv = true
  exodus = true
  perf_graph = true
[]

(modules/combined/test/tests/optimization/optimization_density_update/top_opt_3d.i)

vol_frac = 0.5
E0 = 1e5
Emin = 1e-2
power = 2

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
[]

[Mesh]
  [MeshGenerator]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 24
    ny = 12
    nz = 12
    xmin = 0
    xmax = 20
    ymin = 0
    ymax = 10
    zmin = 0
    zmax = 10
  []
  [middle_bottom_left_edge]
    type = ExtraNodesetGenerator
    input = MeshGenerator
    new_boundary = pull
    coord = '0 0 5'
  []
[]

[AuxVariables]
  [compliance]
    family = MONOMIAL
    order = CONSTANT
  []
  [Dc]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = -1.0
  []
  [mat_den]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = ${vol_frac}
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = SMALL
    add_variables = true
    incremental = false
  []
[]

[BCs]
  [no_x]
    type = DirichletBC
    variable = disp_x
    boundary = right
    value = 0.0
  []
  [no_y]
    type = DirichletBC
    variable = disp_y
    boundary = right
    value = 0.0
  []
  [no_z]
    type = DirichletBC
    variable = disp_z
    boundary = right
    value = 0.0
  []
[]
[NodalKernels]
  [pull]
    type = NodalGravity
    variable = disp_y
    boundary = pull
    gravity_value = -1
    mass = 1
  []
[]
[Materials]
  [elasticity_tensor]
    type = ComputeVariableIsotropicElasticityTensor
    youngs_modulus = E_phys
    poissons_ratio = poissons_ratio
    args = 'mat_den'
  []
  [E_phys]
    type = DerivativeParsedMaterial
    # Emin + (density^penal) * (E0 - Emin)
    expression = '${Emin} + (mat_den ^ ${power}) * (${E0}-${Emin})'
    coupled_variables = 'mat_den'
    property_name = E_phys
  []
  [poissons_ratio]
    type = GenericConstantMaterial
    prop_names = poissons_ratio
    prop_values = 0.3
  []
  [stress]
    type = ComputeLinearElasticStress
  []
  [dc]
    type = ComplianceSensitivity
    design_density = mat_den
    youngs_modulus = E_phys
    incremental = false
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]
[UserObjects]
  [rad_avg]
    type = RadialAverage
    radius = 0.5
    weights = constant
    prop_name = sensitivity
    execute_on = TIMESTEP_END
    execution_order_group = -1
  []
  [update]
    type = DensityUpdate
    density_sensitivity = Dc
    design_density = mat_den
    volume_fraction = ${vol_frac}
    execute_on = TIMESTEP_BEGIN
  []
  [calc_sense]
    type = SensitivityFilter
    density_sensitivity = Dc
    design_density = mat_den
    filter_UO = rad_avg
    execute_on = TIMESTEP_END
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu '
  nl_abs_tol = 1e-10
  l_max_its = 200
  start_time = 0.0
  dt = 1.0
  num_steps = 10

[]

[Outputs]
  [out]
    type = Exodus
    time_step_interval = 10
  []
[]

(modules/solid_mechanics/test/tests/ad_anisotropic_creep/ad_aniso_creep_temperature_coefficients.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 10
    ny = 2
    nz = 2
    xmin = 0.0
    ymin = 0.0
    zmin = 0.0

    xmax = 10.0
    ymax = 1.0
    zmax = 1.0
  []
  [corner_node]
    type = ExtraNodesetGenerator
    new_boundary = '100'
    nodes = '3 69'
    input = gen
  []
  [corner_node_2]
    type = ExtraNodesetGenerator
    new_boundary = '101'
    nodes = '4 47'
    input = corner_node
  []
[]

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  volumetric_locking_correction = true
[]

[AuxVariables]
  [hydrostatic_stress]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_xx]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_xy]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_zz]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_xz]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_yz]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [hydrostatic_stress]
    type = ADRankTwoScalarAux
    variable = hydrostatic_stress
    rank_two_tensor = stress
    scalar_type = Hydrostatic
  []
  [creep_strain_xx]
    type = ADRankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_xx
    index_i = 0
    index_j = 0
  []
  [creep_strain_xy]
    type = ADRankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_xy
    index_i = 0
    index_j = 1
  []
  [creep_strain_yy]
    type = ADRankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_yy
    index_i = 1
    index_j = 1
  []
  [creep_strain_zz]
    type = ADRankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_zz
    index_i = 2
    index_j = 2
  []
  [creep_strain_xz]
    type = ADRankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_xz
    index_i = 0
    index_j = 2
  []
  [creep_strain_yz]
    type = ADRankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_yz
    index_i = 1
    index_j = 2
  []
  [sigma_xx]
    type = ADRankTwoAux
    rank_two_tensor = stress
    variable = stress_xx
    index_i = 1
    index_j = 1
  []
[]

[Functions]
  [pull]
    type = PiecewiseLinear
    x = '0 1.0e-9 1.0'
    y = '0 -4e1 -4e1'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = FINITE
    generate_output = 'elastic_strain_xx stress_xx'
    use_automatic_differentiation = true
    add_variables = true
  []
[]

[Materials]
  [elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    youngs_modulus = 700
    poissons_ratio = 0.0
  []

  [elastic_strain]
    type = ADComputeMultipleInelasticStress
    inelastic_models = 'trial_creep_aniso_iso'
    max_iterations = 50
  []
  [hill_constants]
    type = ADHillConstants
    # F G H L M N
    hill_constants = "0.5 0.5 0.5 1.5 1.5 1.5"
  []
  [trial_creep_aniso_iso]
    type = ADHillCreepStressUpdate
    coefficient = 1e-16
    n_exponent = 9
    m_exponent = 0
    activation_energy = 0
    max_inelastic_increment = 0.00003
    relative_tolerance = 1e-20
    absolute_tolerance = 1e-20
    internal_solve_output_on = never
    # Force it to not use integration error
    max_integration_error = 1.0
  []

[]

[BCs]
  [no_disp_x]
    type = ADDirichletBC
    variable = disp_x
    boundary = left
    value = 0.0
  []

  [no_disp_y]
    type = ADDirichletBC
    variable = disp_y
    boundary = 100
    value = 0.0
  []

  [no_disp_z]
    type = ADDirichletBC
    variable = disp_z
    boundary = 101
    value = 0.0
  []

  [Pressure]
    [Side1]
      boundary = right
      function = pull
    []
  []

[]

[Executioner]
  type = Transient

  solve_type = NEWTON
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu     superlu_dist'

  nl_rel_tol = 1e-13
  nl_abs_tol = 1.0e-14
  l_max_its = 90
  num_steps = 50
  dt = 5.0e-4
  start_time = 0
  automatic_scaling = true
[]

[Postprocessors]
  [matl_ts_min]
    type = MaterialTimeStepPostprocessor
  []
  [max_disp_x]
    type = ElementExtremeValue
    variable = disp_x
  []
  [max_disp_y]
    type = ElementExtremeValue
    variable = disp_y
  []
  [max_hydro]
    type = ElementAverageValue
    variable = hydrostatic_stress
  []
  [dt]
    type = TimestepSize
  []
  [num_lin]
    type = NumLinearIterations
    outputs = console
  []
  [num_nonlin]
    type = NumNonlinearIterations
    outputs = console
  []
  [creep_strain_xx]
    type = ElementalVariableValue
    variable = creep_strain_xx
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [creep_strain_yy]
    type = ElementalVariableValue
    variable = creep_strain_yy
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [creep_strain_zz]
    type = ElementalVariableValue
    variable = creep_strain_zz
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [creep_strain_xy]
    type = ElementalVariableValue
    variable = creep_strain_xy
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [creep_strain_yz]
    type = ElementalVariableValue
    variable = creep_strain_yz
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [creep_strain_xz]
    type = ElementalVariableValue
    variable = creep_strain_xz
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [elastic_strain_xx]
    type = ElementalVariableValue
    variable = elastic_strain_xx
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [sigma_xx]
    type = ElementalVariableValue
    variable = stress_xx
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
[]

[Outputs]
  csv = true
  exodus = true
  perf_graph = true
[]

(modules/navier_stokes/test/tests/finite_element/ins/cg-dg-hybrid/lid-driven/hybrid-cg-dg.i)

mu = 1
rho = 1
l = 200
U = 1

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = ${l}
    ymin = 0
    ymax = ${l}
    nx = 20
    ny = 20
  []
  [corner_node]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node'
    nodes = '0'
    input = gen
  []
[]

[Variables]
  [u]
    family = MONOMIAL
  []
  [v]
    family = MONOMIAL
  []
  [pressure][]
[]

[Kernels]
  [momentum_x_convection]
    type = ADConservativeAdvection
    variable = u
    velocity = 'velocity'
    advected_quantity = 'rhou'
  []
  [momentum_x_diffusion]
    type = MatDiffusion
    variable = u
    diffusivity = 'mu'
  []
  [momentum_x_pressure]
    type = PressureGradient
    integrate_p_by_parts = false
    variable = u
    pressure = pressure
    component = 0
  []
  [momentum_y_convection]
    type = ADConservativeAdvection
    variable = v
    velocity = 'velocity'
    advected_quantity = 'rhov'
  []
  [momentum_y_diffusion]
    type = MatDiffusion
    variable = v
    diffusivity = 'mu'
  []
  [momentum_y_pressure]
    type = PressureGradient
    integrate_p_by_parts = false
    variable = v
    pressure = pressure
    component = 1
  []
  [mass]
    type = ADConservativeAdvection
    variable = pressure
    velocity = velocity
    advected_quantity = -1
  []
[]

[DGKernels]
  [momentum_x_convection]
    type = ADDGAdvection
    variable = u
    velocity = 'velocity'
    advected_quantity = 'rhou'
  []
  [momentum_x_diffusion]
    type = DGDiffusion
    variable = u
    sigma = 6
    epsilon = -1
    diff = 'mu'
  []
  [momentum_y_convection]
    type = ADDGAdvection
    variable = v
    velocity = 'velocity'
    advected_quantity = 'rhov'
  []
  [momentum_y_diffusion]
    type = DGDiffusion
    variable = v
    sigma = 6
    epsilon = -1
    diff = 'mu'
  []
[]

[BCs]
  [u_walls]
    type = DGFunctionDiffusionDirichletBC
    boundary = 'left bottom right'
    variable = u
    sigma = 6
    epsilon = -1
    function = '0'
    diff = 'mu'
  []
  [v_walls]
    type = DGFunctionDiffusionDirichletBC
    boundary = 'left bottom right top'
    variable = v
    sigma = 6
    epsilon = -1
    function = '0'
    diff = 'mu'
  []
  [u_top]
    type = DGFunctionDiffusionDirichletBC
    boundary = 'top'
    variable = u
    sigma = 6
    epsilon = -1
    function = '${U}'
    diff = 'mu'
  []
  [pressure_pin]
    type = DirichletBC
    variable = pressure
    boundary = 'pinned_node'
    value = 0
  []
[]

[Materials]
  [const]
    type = ADGenericConstantMaterial
    prop_names = 'rho'
    prop_values = '${rho}'
  []
  [const_reg]
    type = GenericConstantMaterial
    prop_names = 'mu'
    prop_values = '${mu}'
  []
  [vel]
    type = ADVectorFromComponentVariablesMaterial
    vector_prop_name = 'velocity'
    u = u
    v = v
  []
  [rhou]
    type = ADParsedMaterial
    property_name = 'rhou'
    coupled_variables = 'u'
    material_property_names = 'rho'
    expression = 'rho*u'
  []
  [rhov]
    type = ADParsedMaterial
    property_name = 'rhov'
    coupled_variables = 'v'
    material_property_names = 'rho'
    expression = 'rho*v'
  []
[]

[AuxVariables]
  [vel_x]
    family = MONOMIAL
    order = CONSTANT
  []
  [vel_y]
    family = MONOMIAL
    order = CONSTANT
  []
  [p]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[AuxKernels]
  [vel_x]
    type = ProjectionAux
    variable = vel_x
    v = u
  []
  [vel_y]
    type = ProjectionAux
    variable = vel_y
    v = v
  []
  [p]
    type = ProjectionAux
    variable = p
    v = pressure
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -pc_factor_shift_type'
  petsc_options_value = 'lu       NONZERO'
  nl_rel_tol = 1e-12
[]

[Outputs]
  exodus = true
[]

[Postprocessors]
  [Re]
    type = ParsedPostprocessor
    expression = '${rho} * ${U} * ${l} / ${mu}'
  []
[]

(modules/navier_stokes/test/tests/finite_element/ins/coupled-force/steady-function.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 1.0
    ymin = 0
    ymax = 1.0
    nx = 16
    ny = 16
  []
  [./corner_node]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node'
    nodes = '0'
    input = gen
  [../]
[]

[Variables]
  [./velocity]
    family = LAGRANGE_VEC
  [../]
  [./p]
  [../]
  [u]
    family = LAGRANGE_VEC
  []
[]

[ICs]
  [velocity]
    type = VectorConstantIC
    x_value = 1e-15
    y_value = 1e-15
    variable = velocity
  []
[]

[Kernels]
  [./mass]
    type = INSADMass
    variable = p
  [../]
  [./mass_pspg]
    type = INSADMassPSPG
    variable = p
  [../]

  [./momentum_convection]
    type = INSADMomentumAdvection
    variable = velocity
  [../]

  [./momentum_viscous]
    type = INSADMomentumViscous
    variable = velocity
  [../]

  [./momentum_pressure]
    type = INSADMomentumPressure
    variable = velocity
    pressure = p
    integrate_p_by_parts = true
  [../]

  [momentum_coupled_force]
    type = INSADMomentumCoupledForce
    variable = velocity
    vector_function = 'vector_func'
  []

  [./momentum_supg]
    type = INSADMomentumSUPG
    variable = velocity
    velocity = velocity
  [../]

  [u_diff]
    type = VectorDiffusion
    variable = u
  []
[]

[BCs]
  [./no_slip]
    type = VectorFunctionDirichletBC
    variable = velocity
    boundary = 'bottom right left top'
  [../]

  [./pressure_pin]
    type = DirichletBC
    variable = p
    boundary = 'pinned_node'
    value = 0
  [../]

  [u_left]
    type = VectorFunctionDirichletBC
    variable = u
    boundary = 'left'
    function_x = 1
    function_y = 1
  []

  [u_right]
    type = VectorFunctionDirichletBC
    variable = u
    boundary = 'right'
    function_x = -1
    function_y = -1
  []
[]

[Materials]
  [./const]
    type = ADGenericConstantMaterial
    prop_names = 'rho mu'
    prop_values = '1  1'
  [../]
  [ins_mat]
    type = INSADTauMaterial
    velocity = velocity
    pressure = p
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -sub_pc_factor_levels -ksp_gmres_restart'
  petsc_options_value = 'asm      6                     200'
  line_search = 'none'
  nl_rel_tol = 1e-12
  nl_max_its = 6
[]

[Outputs]
  exodus = true
[]

[Functions]
  [vector_func]
    type = ParsedVectorFunction
    expression_x = '-2*x + 1'
    expression_y = '-2*x + 1'
  []
[]

(modules/solid_mechanics/test/tests/beam/static_vm/ansys_vm2.i)

# This is a reproduction of test number 2 of ANSYS apdl verification manual.

# This test checks for the deformation at the center of a beam with simply
# supported boundary conditions and a uniform load w = 10,000 lb/ft.

#    |||||||||      def.      ||||||||
#    *---*---*---*---*---*---*---*---*
#            /\              /\
#           ///              oo
#        a           l            a
#     <-----> <--------------> <----->
#

# l = 240 in, a = 120 in, A = 50.65 in^2, Iz = 7892 in^2
# E = 30e6 psi
# Solution deflection: 0.182 in. (dispz_5: -1.824633e-01)

[Mesh]
  [generated_mesh]
    type = GeneratedMeshGenerator
    dim = 1
    nx = 8
    xmin = 0.0
    xmax = 480.0
  []
  [cnode]
    type = ExtraNodesetGenerator
    coord = '0.0'
    new_boundary = 'one'
    input = generated_mesh
  []
  [cnode1]
    type = ExtraNodesetGenerator
    coord = '60.0'
    new_boundary = 'two'
    input = cnode
  []
  [cnode2]
    type = ExtraNodesetGenerator
    coord = '420.0'
    new_boundary = 'eight'
    input = cnode1
  []
  [cnode3]
    type = ExtraNodesetGenerator
    coord = '480.0'
    new_boundary = 'nine'
    input = cnode2
  []

  [cnode4]
    type = ExtraNodesetGenerator
    coord = '120.0'
    new_boundary = 'BC1'
    input = cnode3
  []

  [cnode5]
    type = ExtraNodesetGenerator
    coord = '360.0'
    new_boundary = 'BC2'
    input = cnode4
  []
[]

[Physics/SolidMechanics/LineElement/QuasiStatic]
  [./all]
    add_variables = true
    displacements = 'disp_x disp_y disp_z'
    rotations = 'rot_x rot_y rot_z'
    # Geometry parameters
    area = 50.65
    Ay = 0.0
    Az = 0.0
    Iy = 7892.0
    Iz = 7892.0
    y_orientation = '0 1.0 0.0'
  [../]
[]

[Materials]
  [./elasticity]
    type = ComputeElasticityBeam
    youngs_modulus = 30.0e6
    # poissons_ratio = -0.9998699638
      poissons_ratio = 0.33
    # poissons_ratio = 0.3
    shear_coefficient = 0.85
    block = 0
  [../]
  [./stress]
    type = ComputeBeamResultants
    block = 0
  [../]
[]

[BCs]
  [./fixx1]
    type = DirichletBC
    variable = disp_x
    boundary = 'BC1'
    value = 0.0
  [../]
  [./fixy1]
    type = DirichletBC
    variable = disp_y
    boundary = 'BC1'
    value = 0.0
  [../]
  [./fixz1]
    type = DirichletBC
    variable = disp_z
    boundary = 'BC1'
    value = 0.0
  [../]

  [./fixy2]
    type = DirichletBC
    variable = disp_y
    boundary = 'BC2'
    value = 0.0
  [../]
  [./fixz2]
    type = DirichletBC
    variable = disp_z
    boundary = 'BC2'
    value = 0.0
  [../]
[]

[Functions]
  [./force_50e3]
    type = PiecewiseLinear
    x = '0.0 10.0'
    y = '0.0 50000.0'
  [../]
  [./force_25e3]
    type = PiecewiseLinear
    x = '0.0 10.0'
    y = '0.0 25000.0'
  [../]
[]

[NodalKernels]
  [./force_z2]
    type = UserForcingFunctorNodalKernel
    variable = disp_z
    boundary = 'two'
    functor = force_50e3
  [../]
  [./force_z8]
    type = UserForcingFunctorNodalKernel
    variable = disp_z
    boundary = 'eight'
    functor = force_50e3
  [../]

  [./force_z1]
    type = UserForcingFunctorNodalKernel
    variable = disp_z
    boundary = 'one'
    functor = force_25e3
  [../]
  [./force_z9]
    type =  UserForcingFunctorNodalKernel
    variable = disp_z
    boundary = 'nine'
    functor = force_25e3
  [../]
[]

[Preconditioning]
  [./smp]
    type = SMP
    full = true
  [../]
[]
[Executioner]
  type = Transient
  solve_type = JFNK
  line_search = 'none'
  nl_max_its = 15
  nl_rel_tol = 1e-06
  nl_abs_tol = 1e-06

  dt = 1.0
  dtmin = 0.001
  end_time = 10
[]

[Postprocessors]
  [./disp_z1]
    type = PointValue
    point = '0.0 0.0 0.0'
    variable = disp_z
  [../]
  [./disp_x1]
    type = PointValue
    point = '0.0 0.0 0.0'
    variable = disp_x
  [../]
  [./disp_z2]
    type = PointValue
    point = '60.0 0.0 0.0'
    variable = disp_z
  [../]
  [./disp_zBC1]
    type = PointValue
    point = '120.0 0.0 0.0'
    variable = disp_z
  [../]
  [./disp_z5]
    type = PointValue
    point = '240.0 0.0 0.0'
    variable = disp_z
  [../]
  [./disp_zBC2]
    type = PointValue
    point = '360.0 0.0 0.0'
    variable = disp_z
  [../]
  [./disp_xBC2]
    type = PointValue
    point = '360.0 0.0 0.0'
    variable = disp_x
  [../]
  [./disp_z8]
    type = PointValue
    point = '420.0 0.0 0.0'
    variable = disp_z
  [../]
  [./disp_z9]
    type = PointValue
    point = '480.0 0.0 0.0'
    variable = disp_z
  [../]
[]
[Debug]
 show_var_residual_norms = true
[]

[Outputs]
  csv = true
  exodus = false
[]

(test/tests/meshgenerators/extra_nodeset_generator/generate_extra_nodeset.i)

[Mesh]
  [./square]
    type = GeneratedMeshGenerator
    nx = 2
    ny = 2
    dim = 2
  [../]

  [./extra_nodeset]
    type = ExtraNodesetGenerator
    input = square
    new_boundary = 'middle_node'
    nodes = '2'
  []
[]

[Outputs]
  exodus = true
[]

(modules/navier_stokes/test/tests/finite_element/ins/lid_driven/lid_driven.i)

[GlobalParams]
  gravity = '0 0 0'
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 1.0
    ymin = 0
    ymax = 1.0
    nx = 16
    ny = 16
    elem_type = QUAD9
  []
  [./corner_node]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node'
    nodes = '0'
    input = gen
  [../]
[]

[Variables]
  [./vel_x]
    order = SECOND
    family = LAGRANGE
  [../]

  [./vel_y]
    order = SECOND
    family = LAGRANGE
  [../]

  [./T]
    order = SECOND
    family = LAGRANGE

    [./InitialCondition]
      type = ConstantIC
      value = 1.0
    [../]
  [../]

  [./p]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  # mass
  [./mass]
    type = INSMass
    variable = p
    u = vel_x
    v = vel_y
    pressure = p
  [../]

  # x-momentum, time
  [./x_momentum_time]
    type = INSMomentumTimeDerivative
    variable = vel_x
  [../]

  # x-momentum, space
  [./x_momentum_space]
    type = INSMomentumLaplaceForm
    variable = vel_x
    u = vel_x
    v = vel_y
    pressure = p
    component = 0
  [../]

  # y-momentum, time
  [./y_momentum_time]
    type = INSMomentumTimeDerivative
    variable = vel_y
  [../]

  # y-momentum, space
  [./y_momentum_space]
    type = INSMomentumLaplaceForm
    variable = vel_y
    u = vel_x
    v = vel_y
    pressure = p
    component = 1
  [../]

 # temperature
 [./temperature_time]
   type = INSTemperatureTimeDerivative
   variable = T
 [../]

 [./temperature_space]
   type = INSTemperature
   variable = T
   u = vel_x
   v = vel_y
 [../]
[]

[BCs]
  [./x_no_slip]
    type = DirichletBC
    variable = vel_x
    boundary = 'bottom right left'
    value = 0.0
  [../]

  [./lid]
    type = FunctionDirichletBC
    variable = vel_x
    boundary = 'top'
    function = 'lid_function'
  [../]

  [./y_no_slip]
    type = DirichletBC
    variable = vel_y
    boundary = 'bottom right top left'
    value = 0.0
  [../]

  [./T_hot]
    type = DirichletBC
    variable = T
    boundary = 'bottom'
    value = 1
  [../]

  [./T_cold]
    type = DirichletBC
    variable = T
    boundary = 'top'
    value = 0
  [../]

  [./pressure_pin]
    type = DirichletBC
    variable = p
    boundary = 'pinned_node'
    value = 0
  [../]
[]

[Materials]
  [./const]
    type = GenericConstantMaterial
    block = 0
    prop_names = 'rho mu cp k'
    prop_values = '1  1  1  .01'
  [../]
[]

[Functions]
  [./lid_function]
    # We pick a function that is exactly represented in the velocity
    # space so that the Dirichlet conditions are the same regardless
    # of the mesh spacing.
    type = ParsedFunction
    expression = '4*x*(1-x)'
  [../]
[]

[Preconditioning]
  [./SMP]
    type = SMP
    full = true
    solve_type = 'NEWTON'
  [../]
[]

[Executioner]
  type = Transient
  # Run for 100+ timesteps to reach steady state.
  num_steps = 5
  dt = .5
  dtmin = .5
  petsc_options_iname = '-pc_type -pc_asm_overlap -sub_pc_type -sub_pc_factor_levels'
  petsc_options_value = 'asm      2               ilu          4'
  line_search = 'none'
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-13
  nl_max_its = 6
  l_tol = 1e-6
  l_max_its = 500
[]

[Outputs]
  file_base = lid_driven_out
  exodus = true
  perf_graph = true
[]

(modules/solid_mechanics/test/tests/ad_anisotropic_creep/ad_aniso_creep_z_3d.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 2
    ny = 2
    nz = 10

    xmin = 0.0
    ymin = 0.0
    zmin = 0.0

    xmax = 1.0
    ymax = 1.0
    zmax = 10.0
  []
  [corner_node]
    type = ExtraNodesetGenerator
    new_boundary = '100'
    nodes = '9 3'
    input = gen
  []
  [corner_node_2]
    type = ExtraNodesetGenerator
    new_boundary = '101'
    nodes = '12 1'
    input = corner_node
  []
[]

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  volumetric_locking_correction = true
[]

[AuxVariables]
  [hydrostatic_stress]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_xx]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_xy]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_zz]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [hydrostatic_stress]
    type = ADRankTwoScalarAux
    variable = hydrostatic_stress
    rank_two_tensor = stress
    scalar_type = Hydrostatic
  []
  [creep_strain_xx]
    type = ADRankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_xx
    index_i = 0
    index_j = 0
  []
  [creep_strain_xy]
    type = ADRankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_xy
    index_i = 0
    index_j = 1
  []
  [creep_strain_zz]
    type = ADRankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_zz
    index_i = 2
    index_j = 2
  []
  [sigma_zz]
    type = ADRankTwoAux
    rank_two_tensor = stress
    variable = stress_zz
    index_i = 2
    index_j = 2
  []
[]

[Functions]
  [pull]
    type = PiecewiseLinear
    x = '0 1.0'
    y = '-4e1 -4e1'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = FINITE
    generate_output = 'elastic_strain_zz stress_zz stress_xx stress_yy stress_xy stress_xz stress_yz'
    use_automatic_differentiation = true
    add_variables = true
  []
[]

[Materials]
  [elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    youngs_modulus = 700
    poissons_ratio = 0.0
  []

  [elastic_strain]
    type = ADComputeMultipleInelasticStress
    inelastic_models = "trial_creep_two"
    max_iterations = 50
    absolute_tolerance = 1e-16
  []

  [hill_tensor]
    type = ADHillConstants
    # F G H L M N
    hill_constants = "0.5 0.25 0.3866 1.6413 1.6413 1.2731"
  []

  [trial_creep_two]
    type = ADHillCreepStressUpdate
    coefficient = 1e-16
    n_exponent = 9
    m_exponent = 0
    activation_energy = 0
    # F G H L M N
    max_inelastic_increment = 0.00003
    absolute_tolerance = 1e-20
    relative_tolerance = 1e-20
    # Force it to not use integration error
    max_integration_error = 100.0
  []
[]

[BCs]
  [no_disp_x]
    type = ADDirichletBC
    variable = disp_y
    boundary = 100
    value = 0.0
  []

  [no_disp_y]
    type = ADDirichletBC
    variable = disp_x
    boundary = 101
    value = 0.0
  []

  [no_disp_z]
    type = ADDirichletBC
    variable = disp_z
    boundary = back
    value = 0.0
  []

  [pressure]
    type = ADPressure
    boundary = front
    function = pull
    variable = disp_z
    component = 2
  []
[]

[Executioner]
  type = Transient

  solve_type = NEWTON
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu     superlu_dist'

  nl_rel_tol = 1.0e-13
  nl_abs_tol = 1.0e-13
  l_max_its = 90
  num_steps = 10
  dt = 1.0e-4
  start_time = 0
  automatic_scaling = true
[]

[Postprocessors]
  [matl_ts_min]
    type = MaterialTimeStepPostprocessor
  []
  [max_disp_x]
    type = ElementExtremeValue
    variable = disp_x
  []
  [max_disp_y]
    type = ElementExtremeValue
    variable = disp_y
  []
  [max_hydro]
    type = ElementAverageValue
    variable = hydrostatic_stress
  []
  [dt]
    type = TimestepSize
  []
  [num_lin]
    type = NumLinearIterations
    outputs = console
  []
  [num_nonlin]
    type = NumNonlinearIterations
    outputs = console
  []
  [creep_strain_zz]
    type = ElementalVariableValue
    variable = creep_strain_zz
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [elastic_strain_zz]
    type = ElementalVariableValue
    variable = elastic_strain_zz
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [sigma_zz]
    type = ElementalVariableValue
    variable = stress_zz
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
[]

[Outputs]
  csv = true
  exodus = true
  perf_graph = true
[]

(modules/solid_mechanics/test/tests/uel/reference.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 20
    ny = 10
    xmax = 10
    ymax = 3
    elem_type = TRI3
  []
  [pin]
    type = ExtraNodesetGenerator
    nodes = 106
    new_boundary = pin
    input = gen
  []
[]

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = SMALL
    incremental = false
    add_variables = true
    extra_vector_tags = 'kernel_residual'
  []
[]

[BCs]
  [left_x]
    type = DirichletBC
    variable = disp_x
    boundary = left
    value = 0
  []
  [left_y]
    type = DirichletBC
    variable = disp_y
    boundary = pin
    value = 0
  []

  inactive = 'right_dirichlet'
  [right_neumann]
    type = FunctionNeumannBC
    variable = disp_x
    function = t
    boundary = right
  []
  [right_dirichlet]
    type = FunctionDirichletBC
    variable = disp_x
    function = t/10
    boundary = right
  []
[]

[Materials]
  [stress]
    type = ComputeLinearElasticStress
  []
  [elasticity]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 100
    poissons_ratio = 0.3
  []
[]

[Problem]
  extra_tag_vectors = 'kernel_residual'
[]

[AuxVariables]
  [res_x]
  []
  [res_y]
  []
[]

[AuxKernels]
  [res_x]
    type = TagVectorAux
    variable = res_x
    v = disp_x
    vector_tag = kernel_residual
  []
  [res_y]
    type = TagVectorAux
    variable = res_y
    v = disp_y
    vector_tag = kernel_residual
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  dt = 1
  num_steps = 15
[]

[Postprocessors]
  [delta_l]
    type = SideAverageValue
    variable = disp_x
    boundary = right
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [V]
    type = ElementIntegralMaterialProperty
    mat_prop = 1
    use_displaced_mesh = true
    execute_on = 'INITIAL TIMESTEP_END'
  []
[]

[Outputs]
  exodus = true
  csv = true
[]

(modules/navier_stokes/test/tests/finite_element/ins/coupled-force/steady.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 1.0
    ymin = 0
    ymax = 1.0
    nx = 16
    ny = 16
  []
  [./corner_node]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node'
    nodes = '0'
    input = gen
  [../]
[]

[Variables]
  [./velocity]
    family = LAGRANGE_VEC
  [../]
  [./p]
  [../]
  [u]
    family = LAGRANGE_VEC
  []
[]

[ICs]
  [velocity]
    type = VectorConstantIC
    x_value = 1e-15
    y_value = 1e-15
    variable = velocity
  []
[]

[Kernels]
  [./mass]
    type = INSADMass
    variable = p
  [../]
  [./mass_pspg]
    type = INSADMassPSPG
    variable = p
  [../]

  [./momentum_convection]
    type = INSADMomentumAdvection
    variable = velocity
  [../]

  [./momentum_viscous]
    type = INSADMomentumViscous
    variable = velocity
  [../]

  [./momentum_pressure]
    type = INSADMomentumPressure
    variable = velocity
    pressure = p
    integrate_p_by_parts = true
  [../]

  [momentum_coupled_force]
    type = INSADMomentumCoupledForce
    variable = velocity
    coupled_vector_var = u
  []

  [./momentum_supg]
    type = INSADMomentumSUPG
    variable = velocity
    velocity = velocity
  [../]

  [u_diff]
    type = VectorDiffusion
    variable = u
  []
[]

[BCs]
  [./no_slip]
    type = VectorFunctionDirichletBC
    variable = velocity
    boundary = 'bottom right left top'
  [../]

  [./pressure_pin]
    type = DirichletBC
    variable = p
    boundary = 'pinned_node'
    value = 0
  [../]

  [u_left]
    type = VectorFunctionDirichletBC
    variable = u
    boundary = 'left'
    function_x = 1
    function_y = 1
  []

  [u_right]
    type = VectorFunctionDirichletBC
    variable = u
    boundary = 'right'
    function_x = -1
    function_y = -1
  []
[]

[Materials]
  [./const]
    type = ADGenericConstantMaterial
    prop_names = 'rho mu'
    prop_values = '1  1'
  [../]
  [ins_mat]
    type = INSADTauMaterial
    velocity = velocity
    pressure = p
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -sub_pc_factor_levels -ksp_gmres_restart'
  petsc_options_value = 'asm      6                     200'
  line_search = 'none'
  nl_rel_tol = 1e-12
  nl_max_its = 6
[]

[Outputs]
  exodus = true
[]

(modules/solid_mechanics/test/tests/finite_strain_jacobian/bending_jacobian.i)

[Mesh]
  [generated_mesh]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 10
    ymin = 0
    ymax = 2
    nx = 10
    ny = 2
    elem_type = QUAD4
  []
  [corner]
    type = ExtraNodesetGenerator
    new_boundary = 101
    coord = '0 0'
    input = generated_mesh
  []
  [side]
    type = ExtraNodesetGenerator
    new_boundary = 102
    coord = '10 0'
    input = corner
  []
  [mid]
    type = ExtraNodesetGenerator
    new_boundary = 103
    coord = '5 2'
    input = side
  []
[]

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Physics/SolidMechanics/QuasiStatic]
  [./all]
    strain = FINITE
    add_variables = true
    use_finite_deform_jacobian = true
    volumetric_locking_correction = false
  [../]
[]

[Materials]
  [./stress]
    type = ComputeFiniteStrainElasticStress
  [../]
  [./elasticity_tensor]
    type = ComputeElasticityTensor
    fill_method = symmetric9
    C_ijkl = '1.684e5 0.176e5 0.176e5 1.684e5 0.176e5 1.684e5 0.754e5 0.754e5 0.754e5'
  [../]
[]

[BCs]
 [./fix_corner_x]
   type = DirichletBC
   variable = disp_x
   boundary = 101
   value = 0
 [../]
 [./fix_corner_y]
   type = DirichletBC
   variable = disp_y
   boundary = 101
   value = 0
 [../]
 [./fix_y]
   type = DirichletBC
   variable = disp_y
   boundary = 102
   value = 0
 [../]
 [./move_y]
   type = FunctionDirichletBC
   variable = disp_y
   boundary = 103
   function = '-t'
 [../]
[]

[Executioner]
  type = Transient

  solve_type = NEWTON
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'

  nl_rel_tol = 1e-10
  nl_max_its = 10

  l_tol  = 1e-4
  l_max_its = 50

  dt = 0.1
  dtmin = 0.1

  num_steps = 2
[]

[Preconditioning]
  [./smp]
    type = SMP
    full = true
  [../]
[]

[Outputs]
  exodus = true
[]

(test/tests/mortar/periodic_segmental_constraint/periodic_checker2d.i)

[Mesh]
  [left_block]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = -1.0
    xmax = 1.0
    ymin = -1.0
    ymax = 1.0
    nx = 16
    ny = 16
    elem_type = QUAD9
  []
  [left_block_sidesets]
    type = RenameBoundaryGenerator
    input = left_block
    old_boundary = '0 1 2 3'
    new_boundary = '10 11 12 13'
  []
  [left_block_id]
    type = SubdomainIDGenerator
    input = left_block_sidesets
    subdomain_id = 1
  []
  [lowrig]
    type = SubdomainBoundingBoxGenerator
    input = 'left_block_id'
    block_id = 2
    bottom_left = '0 -1 0'
    top_right = '1 0 0'
  []
  [upplef]
    type = SubdomainBoundingBoxGenerator
    input = 'lowrig'
    block_id = 3
    bottom_left = '-1 0 0'
    top_right = '0 1 0'
  []
  [upprig]
    type = SubdomainBoundingBoxGenerator
    input = 'upplef'
    block_id = 4
    bottom_left = '0 0 0'
    top_right = '1 1 0'
  []
  [left]
    type = LowerDBlockFromSidesetGenerator
    input = upprig
    sidesets = '13'
    new_block_id = '10003'
    new_block_name = 'secondary_left'
  []
  [right]
    type = LowerDBlockFromSidesetGenerator
    input = left
    sidesets = '11'
    new_block_id = '10001'
    new_block_name = 'primary_right'
  []
  [bottom]
    type = LowerDBlockFromSidesetGenerator
    input = right
    sidesets = '10'
    new_block_id = '10000'
    new_block_name = 'secondary_bottom'
  []
  [top]
    type = LowerDBlockFromSidesetGenerator
    input = bottom
    sidesets = '12'
    new_block_id = '10002'
    new_block_name = 'primary_top'
  []

  [corner_node]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node'
    nodes = '0'
    input = top
  []
[]

[Variables]
  [u]
    order = SECOND
    family = LAGRANGE
  []
  [epsilon]
    order = SECOND
    family = SCALAR
  []
  [lm1]
    order = FIRST
    family = LAGRANGE
    block = secondary_left
  []
  [lm2]
    order = FIRST
    family = LAGRANGE
    block = secondary_bottom
  []
[]

[AuxVariables]
  [sigma]
    order = SECOND
    family = SCALAR
  []
  [flux_x]
      order = FIRST
      family = MONOMIAL
  []
  [flux_y]
      order = FIRST
      family = MONOMIAL
  []
[]

[AuxScalarKernels]
  [sigma]
    type = FunctionScalarAux
    variable = sigma
    function = '1 3'
    execute_on = initial #timestep_end
  []
[]

[AuxKernels]
  [flux_x]
    type = DiffusionFluxAux
    diffusivity = 'conductivity'
    variable = flux_x
    diffusion_variable = u
    component = x
    block = '1 2 3 4'
  []
  [flux_y]
    type = DiffusionFluxAux
    diffusivity = 'conductivity'
    variable = flux_y
    diffusion_variable = u
    component = y
    block = '1 2 3 4'
  []
[]

[Kernels]
  [diff1]
    type = Diffusion
    variable = u
    block = '1 4'
  []
  [diff2]
    type = MatDiffusion
    variable = u
    block = '2 3'
    diffusivity = conductivity
  []
[]

[Materials]
  [k1]
    type = GenericConstantMaterial
    prop_names = 'conductivity'
    prop_values = 1.0
    block = '1 4'
  []
  [k2]
    type = GenericConstantMaterial
    prop_names = 'conductivity'
    prop_values = 10.0
    block = '2 3'
  []
[]

[Problem]
  kernel_coverage_check = false
  error_on_jacobian_nonzero_reallocation = true
[]

[BCs]
  [fix_right]
    type = DirichletBC
    variable = u
    boundary = pinned_node
    value = 0
  []
[]

[Constraints]
  [mortarlr]
    type = EqualValueConstraint
    primary_boundary = '11'
    secondary_boundary = '13'
    primary_subdomain = 'primary_right'
    secondary_subdomain = 'secondary_left'
    secondary_variable = u
    variable = lm1
    correct_edge_dropping = true
  []
  [periodiclr]
    type = PeriodicSegmentalConstraint
    primary_boundary = '11'
    secondary_boundary = '13'
    primary_subdomain = 'primary_right'
    secondary_subdomain = 'secondary_left'
    secondary_variable = u
    epsilon = epsilon
    sigma = sigma
    variable = lm1
    correct_edge_dropping = true
  []
  [mortarbt]
    type = EqualValueConstraint
    primary_boundary = '12'
    secondary_boundary = '10'
    primary_subdomain = 'primary_top'
    secondary_subdomain = 'secondary_bottom'
    secondary_variable = u
    variable = lm2
    correct_edge_dropping = true
  []
  [periodicbt]
    type = PeriodicSegmentalConstraint
    primary_boundary = '12'
    secondary_boundary = '10'
    primary_subdomain = 'primary_top'
    secondary_subdomain = 'secondary_bottom'
    secondary_variable = u
    epsilon = epsilon
    sigma = sigma
    variable = lm2
    correct_edge_dropping = true
  []
[]

[Preconditioning]
  [smp]
    full = true
    type = SMP
  []
[]

[Executioner]
  type = Steady
  petsc_options_iname = '-pc_type -pc_factor_shift_type -pc_factor_shift_amount -pc_factor_mat_solver_type'
  petsc_options_value = 'lu       NONZERO               1e-15                   strumpack'
  solve_type = NEWTON
[]

[Postprocessors]
  [max]
    type = ElementExtremeValue
    variable = 'flux_x'
  []
[]

[Outputs]
  csv = true
[]

(modules/solid_mechanics/test/tests/free_expansion_abs_ref/free_expansion_abs_ref.i)

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Problem]
  type = ReferenceResidualProblem
  reference_vector = 'ref'
  extra_tag_vectors = 'ref'
  group_variables = 'disp_x disp_y'
[]

[Mesh]
  [square]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 2
    ny = 2
  []
  [eng1]
    type = ExtraNodesetGenerator
    input = square
    new_boundary = 'lower_left'
    coord = '0 0'
  []
  [eng2]
    type = ExtraNodesetGenerator
    input = eng1
    new_boundary = 'lower_right'
    coord = '1 0'
  []
[]

[AuxVariables]
  [temp]
  []
  [ref_x]
  []
  [ref_y]
  []
[]

[AuxKernels]
  [tempfuncaux]
    type = FunctionAux
    variable = temp
    function = '(1-x)*t'
    use_displaced_mesh = false
  []
  [ref_x]
    type = ReactionForceAux
    variable = 'ref_x'
    vector_tag = 'ref'
    v = 'disp_x'
  []
  [ref_y]
    type = ReactionForceAux
    variable = 'ref_y'
    vector_tag = 'ref'
    v = 'disp_y'
  []
[]

[BCs]
  [fix_x]
    type = DirichletBC
    boundary = 'lower_left'
    variable = disp_x
    value = 0.0
  []
  [fix_y]
    type = DirichletBC
    boundary = 'lower_left lower_right'
    variable = disp_y
    value = 0.0
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = SMALL
    add_variables = true
    temperature = temp
    generate_output = 'stress_xx stress_xy stress_yy stress_zz strain_xx strain_xy strain_yy strain_zz'
    planar_formulation = PLANE_STRAIN
    eigenstrain_names = eigenstrain
    absolute_value_vector_tags = 'ref'
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 1e6
    poissons_ratio = 0.3
  []
  [elastic_stress]
    type = ComputeLinearElasticStress
  []
  [thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    thermal_expansion_coeff = 0.02
    temperature = temp
    stress_free_temperature = 0.5
    eigenstrain_name = eigenstrain
  []
[]

[Executioner]
  type = Transient

  solve_type = PJFNK
  line_search = none

  l_max_its = 100
  l_tol = 1e-8

  nl_max_its = 15
  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-12

  start_time = 0.0
  dt = 1.0
  dtmin = 1.0
  end_time = 2.0
[]

[Outputs]
  exodus = true
[]

(modules/navier_stokes/test/tests/finite_element/ins/cg-dg-hybrid/mms/lid-driven/hybrid-cg-dg-mms.i)

rho=1.1
mu=1.1
cp=1.1
k=1.1

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = -1
    xmax = 1.0
    ymin = -1
    ymax = 1.0
    nx = 2
    ny = 2
  []
  [corner_node]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node'
    nodes = '0'
    input = gen
  []
[]

[Variables]
  [u]
    family = MONOMIAL
  []
  [v]
    family = MONOMIAL
  []
  [pressure][]
  [T]
    family = MONOMIAL
  []
[]

[Kernels]
  [momentum_x_convection]
    type = ADConservativeAdvection
    variable = u
    velocity_material = 'velocity'
    advected_quantity = 'rhou'
  []
  [momentum_x_diffusion]
    type = MatDiffusion
    variable = u
    diffusivity = 'mu'
  []
  [momentum_x_pressure]
    type = PressureGradient
    integrate_p_by_parts = false
    variable = u
    pressure = pressure
    component = 0
  []
  [u_forcing]
    type = BodyForce
    variable = u
    function = forcing_u
  []
  [momentum_y_convection]
    type = ADConservativeAdvection
    variable = v
    velocity_material = 'velocity'
    advected_quantity = 'rhov'
  []
  [momentum_y_diffusion]
    type = MatDiffusion
    variable = v
    diffusivity = 'mu'
  []
  [momentum_y_pressure]
    type = PressureGradient
    integrate_p_by_parts = false
    variable = v
    pressure = pressure
    component = 1
  []
  [v_forcing]
    type = BodyForce
    variable = v
    function = forcing_v
  []
  [mass]
    type = ADConservativeAdvection
    variable = pressure
    velocity_material = velocity
    advected_quantity = -1
  []
  [p_forcing]
    type = BodyForce
    variable = pressure
    function = forcing_p
  []
  [T_convection]
    type = ADConservativeAdvection
    variable = T
    velocity_material = 'velocity'
    advected_quantity = 'rho_cp_temp'
  []
  [T_diffusion]
    type = MatDiffusion
    variable = T
    diffusivity = 'k'
  []
  [T_forcing]
    type = BodyForce
    variable = T
    function = forcing_T
  []
[]

[DGKernels]
  [momentum_x_convection]
    type = ADDGAdvection
    variable = u
    velocity = 'velocity'
    advected_quantity = 'rhou'
  []
  [momentum_x_diffusion]
    type = DGDiffusion
    variable = u
    sigma = 6
    epsilon = -1
    diff = 'mu'
  []
  [momentum_y_convection]
    type = ADDGAdvection
    variable = v
    velocity = 'velocity'
    advected_quantity = 'rhov'
  []
  [momentum_y_diffusion]
    type = DGDiffusion
    variable = v
    sigma = 6
    epsilon = -1
    diff = 'mu'
  []
  [T_convection]
    type = ADDGAdvection
    variable = T
    velocity = 'velocity'
    advected_quantity = 'rho_cp_temp'
  []
  [T_diffusion]
    type = DGDiffusion
    variable = T
    sigma = 6
    epsilon = -1
    diff = 'k'
  []
[]

[BCs]
  [u_walls]
    type = DGFunctionDiffusionDirichletBC
    boundary = 'left bottom right top'
    variable = u
    sigma = 6
    epsilon = -1
    function = exact_u
    diff = 'mu'
  []
  [v_walls]
    type = DGFunctionDiffusionDirichletBC
    boundary = 'left bottom right top'
    variable = v
    sigma = 6
    epsilon = -1
    function = exact_v
    diff = 'mu'
  []
  [pressure_pin]
    type = FunctionDirichletBC
    variable = pressure
    boundary = 'pinned_node'
    function = 'exact_p'
  []
  [T_walls]
    type = DGFunctionDiffusionDirichletBC
    boundary = 'left bottom right top'
    variable = T
    sigma = 6
    epsilon = -1
    function = exact_T
    diff = 'k'
  []
[]

[Materials]
  [const]
    type = ADGenericConstantMaterial
    prop_names = 'rho cp'
    prop_values = '${rho} ${cp}'
  []
  [const_reg]
    type = GenericConstantMaterial
    prop_names = 'mu k'
    prop_values = '${mu} ${k}'
  []
  [vel]
    type = ADVectorFromComponentVariablesMaterial
    vector_prop_name = 'velocity'
    u = u
    v = v
  []
  [rhou]
    type = ADParsedMaterial
    property_name = 'rhou'
    coupled_variables = 'u'
    material_property_names = 'rho'
    expression = 'rho*u'
  []
  [rhov]
    type = ADParsedMaterial
    property_name = 'rhov'
    coupled_variables = 'v'
    material_property_names = 'rho'
    expression = 'rho*v'
  []
  [rho_cp]
    type = ADParsedMaterial
    property_name = 'rho_cp'
    material_property_names = 'rho cp'
    expression = 'rho*cp'
  []
  [rho_cp_temp]
    type = ADParsedMaterial
    property_name = 'rho_cp_temp'
    material_property_names = 'rho cp'
    coupled_variables = 'T'
    expression = 'rho*cp*T'
  []
[]

[Functions]
  [exact_u]
    type = ParsedFunction
    expression = 'sin(y)*cos((1/2)*x*pi)'
  []
  [forcing_u]
    type = ParsedFunction
    expression = 'mu*sin(y)*cos((1/2)*x*pi) + (1/4)*pi^2*mu*sin(y)*cos((1/2)*x*pi) - 1/2*pi*rho*sin(x)*sin(y)*sin((1/2)*y*pi)*cos((1/2)*x*pi) + rho*sin(x)*cos(y)*cos((1/2)*x*pi)*cos((1/2)*y*pi) - pi*rho*sin(y)^2*sin((1/2)*x*pi)*cos((1/2)*x*pi) + sin(y)*cos(x)'
    symbol_names = 'mu rho'
    symbol_values = '${mu} ${rho}'
  []
  [exact_v]
    type = ParsedFunction
    expression = 'sin(x)*cos((1/2)*y*pi)'
  []
  [forcing_v]
    type = ParsedFunction
    expression = 'mu*sin(x)*cos((1/2)*y*pi) + (1/4)*pi^2*mu*sin(x)*cos((1/2)*y*pi) - pi*rho*sin(x)^2*sin((1/2)*y*pi)*cos((1/2)*y*pi) - 1/2*pi*rho*sin(x)*sin(y)*sin((1/2)*x*pi)*cos((1/2)*y*pi) + rho*sin(y)*cos(x)*cos((1/2)*x*pi)*cos((1/2)*y*pi) + sin(x)*cos(y)'
    symbol_names = 'mu rho'
    symbol_values = '${mu} ${rho}'
  []
  [exact_p]
    type = ParsedFunction
    expression = 'sin(x)*sin(y)'
  []
  [forcing_p]
    type = ParsedFunction
    expression = '(1/2)*pi*sin(x)*sin((1/2)*y*pi) + (1/2)*pi*sin(y)*sin((1/2)*x*pi)'
  []
  [exact_T]
    type = ParsedFunction
    expression = 'cos(x)*cos(y)'
  []
  [forcing_T]
    type = ParsedFunction
    expression = '-cp*rho*sin(x)*sin(y)*cos(x)*cos((1/2)*y*pi) - cp*rho*sin(x)*sin(y)*cos(y)*cos((1/2)*x*pi) - 1/2*pi*cp*rho*sin(x)*sin((1/2)*y*pi)*cos(x)*cos(y) - 1/2*pi*cp*rho*sin(y)*sin((1/2)*x*pi)*cos(x)*cos(y) + 2*k*cos(x)*cos(y)'
    symbol_names = 'rho cp k'
    symbol_values = '${rho} ${cp} ${k}'
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -pc_factor_shift_type -pc_factor_mat_solver_type -mat_mumps_icntl_14'
  petsc_options_value = 'lu       NONZERO               mumps                      300'
  nl_rel_tol = 1e-12
[]

[Outputs]
  exodus = true
  csv = true
[]

[Postprocessors]
  [h]
    type = AverageElementSize
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2u]
    type = ElementL2Error
    variable = u
    function = exact_u
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2v]
    variable = v
    function = exact_v
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2T]
    variable = T
    function = exact_T
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2p]
    variable = pressure
    function = exact_p
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
[]

(modules/navier_stokes/test/tests/finite_element/ins/boussinesq/benchmark/benchmark.i)

rayleigh=1e3
hot_temp=${rayleigh}
temp_ref=${fparse hot_temp / 2.}

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 100
    ny = 100
  []
  [./bottom_left]
    type = ExtraNodesetGenerator
    new_boundary = corner
    coord = '0 0'
    input = gen
  [../]
[]


[Preconditioning]
  [./Newton_SMP]
    type = SMP
    full = true
    solve_type = 'NEWTON'
  [../]
[]

[Executioner]
  type = Steady

  nl_rel_tol = 1e-12
  petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type -ksp_gmres_restart'
  petsc_options_value = 'bjacobi  lu           NONZERO                   200'
[]

[Debug]
  show_var_residual_norms = true
[]

[Outputs]
  [out]
    type = Exodus
  []
[]

[Variables]
  [velocity]
    family = LAGRANGE_VEC
  []
  [p][]
  [temp]
    initial_condition = 340
    scaling = 1e-4
  []
[]

[ICs]
  [velocity]
    type = VectorConstantIC
    x_value = 1e-15
    y_value = 1e-15
    variable = velocity
  []
[]

[BCs]
  [./velocity_dirichlet]
    type = VectorDirichletBC
    boundary = 'left right bottom top'
    variable = velocity
    # The third entry is to satisfy RealVectorValue
    values = '0 0 0'
  [../]
  # Even though we are integrating by parts, because there are no integrated
  # boundary conditions on the velocity p doesn't appear in the system of
  # equations. Thus we must pin the pressure somewhere in order to ensure a
  # unique solution
  [./p_zero]
    type = DirichletBC
    boundary = corner
    variable = p
    value = 0
  [../]
  [./hot]
    type = DirichletBC
    variable = temp
    boundary = left
    value = ${hot_temp}
  [../]
  [./cold]
    type = DirichletBC
    variable = temp
    boundary = right
    value = 0
  [../]
[]


[Kernels]
  [./mass]
    type = INSADMass
    variable = p
  [../]
  [mass_pspg]
    type = INSADMassPSPG
    variable = p
  []

  [./momentum_viscous]
    type = INSADMomentumViscous
    variable = velocity
  [../]
  [momentum_advection]
    type = INSADMomentumAdvection
    variable = velocity
  []
  [momentum_pressure]
    type = INSADMomentumPressure
    variable = velocity
    pressure = p
    integrate_p_by_parts = true
  []
  [./buoyancy]
    type = INSADBoussinesqBodyForce
    variable = velocity
    temperature = temp
    gravity = '0 -1 0'
  [../]
  [./gravity]
    type = INSADGravityForce
    variable = velocity
    gravity = '0 -1 0'
  [../]
  [supg]
    type = INSADMomentumSUPG
    variable = velocity
    velocity = velocity
  []

  [temp_advection]
    type = INSADEnergyAdvection
    variable = temp
  []
  [temp_conduction]
    type = ADHeatConduction
    variable = temp
    thermal_conductivity = 'k'
  [../]
  [temp_supg]
    type = INSADEnergySUPG
    variable = temp
    velocity = velocity
  []
[]

[Materials]
  [./ad_const]
    type = ADGenericConstantMaterial
    # alpha = coefficient of thermal expansion where rho  = rho0 -alpha * rho0 * delta T
    prop_names =  'mu        rho   alpha   k        cp'
    prop_values = '1         1     1       1        1'
  [../]
  [./const]
    type = GenericConstantMaterial
    prop_names =  'temp_ref'
    prop_values = '${temp_ref}'
  [../]
  [ins_mat]
    type = INSADStabilized3Eqn
    velocity = velocity
    pressure = p
    temperature = temp
  []
[]

(modules/solid_mechanics/test/tests/uel/tensile_uel_umat_moose.i)

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
[]

[Mesh]
  [mesh]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 1
    ny = 1
    nz = 1
    elem_type = HEX8
  []
  [extra_nodeset]
    type = ExtraNodesetGenerator
    input = mesh
    new_boundary = 'master'
    coord = '1.0 1.0 1.0'
  []
[]

# [AuxVariables]
#   [temperature]
#     initial_condition = 500
#   []
# []

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [disp_z]
  []
[]

[Functions]
  [function_pull]
    type = PiecewiseLinear
    x = '0 100'
    y = '0 0.1'
  []
[]

[Constraints]
  [one]
    type = LinearNodalConstraint
    variable = disp_x
    primary = '6'
    secondary_node_ids = '1 2 5'
    penalty = 1.0e8
    formulation = kinematic
    weights = '1'
  []
  [two]
    type = LinearNodalConstraint
    variable = disp_z
    primary = '6'
    secondary_node_ids = '4 5 7'
    penalty = 1.0e8
    formulation = kinematic
    weights = '1'
  []
[]

[BCs]
  [symmy]
    type = DirichletBC
    variable = disp_y
    boundary = bottom
    value = 0
  []
  [symmx]
    type = DirichletBC
    variable = disp_x
    boundary = left
    value = 0
  []
  [symmz]
    type = DirichletBC
    variable = disp_z
    boundary = back
    value = 0
  []
  # What's done below is to capture the weird constraints
  [axial_load]
    type = FunctionDirichletBC
    variable = disp_y
    boundary = 'top'
    function = function_pull
  []
[]

[UserObjects]
  [uel]
    type = AbaqusUserElement
    variables = 'disp_x disp_y'
    plugin = '../../../../solid_mechanics/examples/uel_build/uel'
    use_displaced_mesh = false

    #temperature = temperature # TODO
    #use_one_based_indexing = true # TODO

    jtype = 17
    num_state_vars = 177
    constant_properties = '190.0 28.0 3.0 1.0 6.0 0.0 0.0 23.0 25.0 26.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 '
                          '0.0 0.0 0.0 0.0 0.0 31700000.0 0.32 6.67e-06 1e-08 5000.0 4.0' # 27 properties
    extra_vector_tags = 'kernel_residual'
  []
[]

[Problem]
  kernel_coverage_check = false
  extra_tag_vectors = 'kernel_residual'
[]

[AuxVariables]
  [res_x]
  []
  [res_y]
  []
[]

[AuxKernels]
  [res_x]
    type = TagVectorAux
    variable = res_x
    v = disp_x
    vector_tag = kernel_residual
  []
  [res_y]
    type = TagVectorAux
    variable = res_y
    v = disp_y
    vector_tag = kernel_residual
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient

  l_max_its = 100
  l_tol = 1e-8
  nl_max_its = 50
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-8

  dtmin = 1
  dt = 5
  end_time = 100
[]

[Outputs]
  exodus = true
[]

(modules/combined/examples/effective_properties/effective_th_cond.i)

# This example calculates the effective thermal conductivity across a microstructure
# with circular second phase precipitates. Two methods are used to calculate the effective thermal conductivity,
# the direct method that applies a temperature to one side and a heat flux to the other,
# and the AEH method.
[Mesh] #Sets mesh size to 10 microns by 10 microns
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 100
    ny = 100
    xmax = 10
    ymax = 10
  []
  [new_nodeset]
    input = gen
    type = ExtraNodesetGenerator
    coord = '5 5'
    new_boundary = 100
  []
[]

[Variables] #Adds variables needed for two ways of calculating effective thermal cond.
  [T] #Temperature used for the direct calculation
    initial_condition = 800
  []
  [Tx_AEH] #Temperature used for the x-component of the AEH solve
    initial_condition = 800
    scaling = 1.0e4 #Scales residual to improve convergence
  []
  [Ty_AEH] #Temperature used for the y-component of the AEH solve
    initial_condition = 800
    scaling = 1.0e4  #Scales residual to improve convergence
  []
[]

[AuxVariables] #Creates second constant phase
  [phase2]
  []
[]

[ICs] #Sets the IC for the second constant phase
  [phase2_IC] #Creates circles with smooth interfaces at random locations
    variable = phase2
    type = MultiSmoothCircleIC
    int_width = 0.3
    numbub = 20
    bubspac = 1.5
    radius = 0.5
    outvalue = 0
    invalue = 1
    block = 0
  []
[]

[Kernels]
  [HtCond] #Kernel for direct calculation of thermal cond
    type = HeatConduction
    variable = T
  []
  [heat_x] #All other kernels are for AEH approach to calculate thermal cond.
    type = HeatConduction
    variable = Tx_AEH
  []
  [heat_rhs_x]
    type = HomogenizedHeatConduction
    variable = Tx_AEH
    component = 0
  []
  [heat_y]
    type = HeatConduction
    variable = Ty_AEH
  []
  [heat_rhs_y]
    type = HomogenizedHeatConduction
    variable = Ty_AEH
    component = 1
  []
[]

[BCs]
  [Periodic]
    [all]
      auto_direction = 'x y'
      variable = 'Tx_AEH Ty_AEH'
    []
  []
  [left_T] #Fix temperature on the left side
    type = DirichletBC
    variable = T
    boundary = left
    value = 800
  []
  [right_flux] #Set heat flux on the right side
    type = NeumannBC
    variable = T
    boundary = right
    value = 5e-6
  []
  [fix_x] #Fix Tx_AEH at a single point
    type = DirichletBC
    variable = Tx_AEH
    value = 800
    boundary = 100
  []
  [fix_y] #Fix Ty_AEH at a single point
    type = DirichletBC
    variable = Ty_AEH
    value = 800
    boundary = 100
  []
[]

[Materials]
  [thcond] #The equation defining the thermal conductivity is defined here, using two ifs
    # The k in the bulk is k_b, in the precipitate k_p2, and across the interaface k_int
    type = ParsedMaterial
    block = 0
    constant_names = 'length_scale k_b k_p2 k_int'
    constant_expressions = '1e-6 5 1 0.1'
    expression = 'sk_b:= length_scale*k_b; sk_p2:= length_scale*k_p2; sk_int:= k_int*length_scale; if(phase2>0.1,if(phase2>0.95,sk_p2,sk_int),sk_b)'
    outputs = exodus
    f_name = thermal_conductivity
    coupled_variables = phase2
  []
[]

[Postprocessors]
  [right_T]
    type = SideAverageValue
    variable = T
    boundary = right
  []
  [k_x_direct] #Effective thermal conductivity from direct method
    # This value is lower than the AEH value because it is impacted by second phase
    # on the right boundary
    type = ThermalConductivity
    variable = T
    flux = 5e-6
    length_scale = 1e-06
    T_hot = 800
    dx = 10
    boundary = right
  []
  [k_x_AEH] #Effective thermal conductivity in x-direction from AEH
    type = HomogenizedThermalConductivity
    chi = 'Tx_AEH Ty_AEH'
    row = 0
    col = 0
    scale_factor = 1e6 #Scale due to length scale of problem
  []
  [k_y_AEH] #Effective thermal conductivity in x-direction from AEH
    type = HomogenizedThermalConductivity
    chi = 'Tx_AEH Ty_AEH'
    row = 1
    col = 1
    scale_factor = 1e6 #Scale due to length scale of problem
  []
[]

[Preconditioning]
  [SMP]
    type = SMP
    off_diag_row = 'Tx_AEH Ty_AEH'
    off_diag_column = 'Ty_AEH Tx_AEH'
  []
[]

[Executioner]
  type = Steady
  l_max_its = 15
  solve_type = NEWTON
  petsc_options_iname = '-pc_type -pc_hypre_type -ksp_gmres_restart -pc_hypre_boomeramg_strong_threshold'
  petsc_options_value = 'hypre boomeramg 31 0.7'
  l_tol = 1e-04
[]

[Outputs]
  execute_on = 'timestep_end'
  exodus = true
  csv = true
[]

(modules/solid_mechanics/test/tests/ad_anisotropic_creep/ad_aniso_creep_x_3d.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 10
    ny = 2
    nz = 2
    xmin = 0.0
    ymin = 0.0
    zmin = 0.0

    xmax = 10.0
    ymax = 1.0
    zmax = 1.0
  []
  [corner_node]
    type = ExtraNodesetGenerator
    new_boundary = '100'
    nodes = '3 69'
    input = gen
  []
  [corner_node_2]
    type = ExtraNodesetGenerator
    new_boundary = '101'
    nodes = '4 47'
    input = corner_node
  []
[]

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  volumetric_locking_correction = true
[]

[AuxVariables]
  [hydrostatic_stress]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_xx]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_xy]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [hydrostatic_stress]
    type = ADRankTwoScalarAux
    variable = hydrostatic_stress
    rank_two_tensor = stress
    scalar_type = Hydrostatic
  []
  [creep_strain_xx]
    type = ADRankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_xx
    index_i = 0
    index_j = 0
  []
  [creep_strain_xy]
    type = ADRankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_xy
    index_i = 0
    index_j = 1
  []
  [creep_strain_yy]
    type = ADRankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_yy
    index_i = 1
    index_j = 1
  []
  [sigma_xx]
    type = ADRankTwoAux
    rank_two_tensor = stress
    variable = stress_xx
    index_i = 1
    index_j = 1
  []
[]

[Functions]
  [pull]
    type = PiecewiseLinear
    x = '0 1.0e-9 1.0'
    y = '0 -4e1 -4e1'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = FINITE
    generate_output = 'elastic_strain_xx stress_xx'
    use_automatic_differentiation = true
    add_variables = true
  []
[]

[Materials]
  [elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    youngs_modulus = 700
    poissons_ratio = 0.0
  []

  [elastic_strain]
    type = ADComputeMultipleInelasticStress
    inelastic_models = "trial_creep_two"
    max_iterations = 50
    absolute_tolerance = 1e-16
  []

  [hill_tensor]
    type = ADHillConstants
    # F G H L M N
    hill_constants = "0.5 0.25 0.3866 1.6413 1.6413 1.2731"
  []

  [trial_creep_two]
    type = ADHillCreepStressUpdate
    coefficient = 1e-16
    n_exponent = 9
    m_exponent = 0
    activation_energy = 0
    max_inelastic_increment = 0.00003
    absolute_tolerance = 1e-20
    relative_tolerance = 1e-20
    # Force it to not use integration error
    max_integration_error = 100.0
  []
[]

[BCs]
  [no_disp_x]
    type = ADDirichletBC
    variable = disp_x
    boundary = left
    value = 0.0
  []

  [no_disp_y]
    type = ADDirichletBC
    variable = disp_y
    boundary = 100
    value = 0.0
  []

  [no_disp_z]
    type = ADDirichletBC
    variable = disp_z
    boundary = 101
    value = 0.0
  []

  [Pressure]
    [Side1]
      boundary = right
      function = pull
    []
  []

[]

[Executioner]
  type = Transient

  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -mat_mffd_err'
  petsc_options_value = 'lu     superlu_dist                    1e-5'

  nl_rel_tol = 1.0e-14
  nl_abs_tol = 1.0e-14
  l_max_its = 10
  num_steps = 10
  dt = 1.0e-4
  start_time = 0
  automatic_scaling = true
[]

[Postprocessors]
  [matl_ts_min]
    type = MaterialTimeStepPostprocessor
  []
  [max_disp_x]
    type = ElementExtremeValue
    variable = disp_x
  []
  [max_disp_y]
    type = ElementExtremeValue
    variable = disp_y
  []
  [max_hydro]
    type = ElementAverageValue
    variable = hydrostatic_stress
  []
  [dt]
    type = TimestepSize
  []
  [num_lin]
    type = NumLinearIterations
    outputs = console
  []
  [num_nonlin]
    type = NumNonlinearIterations
    outputs = console
  []
  [creep_strain_xx]
    type = ElementalVariableValue
    variable = creep_strain_xx
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [elastic_strain_xx]
    type = ElementalVariableValue
    variable = elastic_strain_xx
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [sigma_xx]
    type = ElementalVariableValue
    variable = stress_xx
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
[]

[Outputs]
  csv = true
  exodus = true
  perf_graph = true
[]

(modules/navier_stokes/test/tests/finite_element/ins/cg-dg-hybrid/mms/lid-driven-skewed/hybrid-skewed-vortex.i)

rho=1
mu=1

[Mesh]
  [gen_mesh]
    type = FileMeshGenerator
    file = skewed.msh
  []
  [corner_node]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node'
    nodes = '0'
    input = gen_mesh
  []
[]

[Variables]
  [u]
    family = MONOMIAL
    order = SECOND
  []
  [v]
    family = MONOMIAL
    order = SECOND
  []
  [pressure][]
[]

[Kernels]
  [momentum_x_convection]
    type = ADConservativeAdvection
    variable = u
    velocity = 'velocity'
  []
  [momentum_x_diffusion]
    type = Diffusion
    variable = u
  []
  [momentum_x_pressure]
    type = PressureGradient
    integrate_p_by_parts = false
    variable = u
    pressure = pressure
    component = 0
  []
  [u_forcing]
    type = BodyForce
    variable = u
    function = forcing_u
  []
  [momentum_y_convection]
    type = ADConservativeAdvection
    variable = v
    velocity = 'velocity'
  []
  [momentum_y_diffusion]
    type = Diffusion
    variable = v
  []
  [momentum_y_pressure]
    type = PressureGradient
    integrate_p_by_parts = false
    variable = v
    pressure = pressure
    component = 1
  []
  [v_forcing]
    type = BodyForce
    variable = v
    function = forcing_v
  []
  [mass]
    type = ADConservativeAdvection
    variable = pressure
    velocity = velocity
    advected_quantity = -1
  []
[]

[DGKernels]
  [momentum_x_convection]
    type = ADDGAdvection
    variable = u
    velocity = 'velocity'
  []
  [momentum_x_diffusion]
    type = DGDiffusion
    variable = u
    sigma = 6
    epsilon = -1
  []
  [momentum_y_convection]
    type = ADDGAdvection
    variable = v
    velocity = 'velocity'
  []
  [momentum_y_diffusion]
    type = DGDiffusion
    variable = v
    sigma = 6
    epsilon = -1
  []
[]

[BCs]
  [u_walls]
    type = DGFunctionDiffusionDirichletBC
    boundary = 'left bottom right top'
    variable = u
    sigma = 6
    epsilon = -1
    function = exact_u
  []
  [v_walls]
    type = DGFunctionDiffusionDirichletBC
    boundary = 'left bottom right top'
    variable = v
    sigma = 6
    epsilon = -1
    function = exact_v
  []
  [pressure_pin]
    type = FunctionDirichletBC
    variable = pressure
    boundary = 'pinned_node'
    function = 'exact_p'
  []
[]

[Materials]
  [rho]
    type = ADGenericConstantMaterial
    prop_names = 'rho'
    prop_values = '${rho}'
  []
  [vel]
    type = ADVectorFromComponentVariablesMaterial
    vector_prop_name = 'velocity'
    u = u
    v = v
  []
  [rhou]
    type = ADParsedMaterial
    property_name = 'rhou'
    coupled_variables = 'u'
    material_property_names = 'rho'
    expression = 'rho*u'
  []
  [rhov]
    type = ADParsedMaterial
    property_name = 'rhov'
    coupled_variables = 'v'
    material_property_names = 'rho'
    expression = 'rho*v'
  []
[]

[Functions]
  [exact_u]
    type = ParsedFunction
    expression = 'x^2*(1-x)^2*(2*y-6*y^2+4*y^3)'
  []
  [exact_v]
    type = ParsedFunction
    expression = '-y^2*(1-y)^2*(2*x-6*x^2+4*x^3)'
  []
  [exact_p]
    type = ParsedFunction
    expression = 'x*(1-x)-2/12'
  []
  [forcing_u]
    type = ParsedFunction
    expression = '-4*mu/rho*(-1+2*y)*(y^2-6*x*y^2+6*x^2*y^2-y+6*x*y-6*x^2*y+3*x^2-6*x^3+3*x^4)+1-2*x+4*x^3'
            '*y^2*(2*y^2-2*y+1)*(y-1)^2*(-1+2*x)*(x-1)^3'
    symbol_names = 'mu rho'
    symbol_values = '${mu} ${rho}'
  []
  [forcing_v]
    type = ParsedFunction
    expression = '4*mu/rho*(-1+2*x)*(x^2-6*y*x^2+6*x^2*y^2-x+6*x*y-6*x*y^2+3*y^2-6*y^3+3*y^4)+4*y^3*x^2*(2'
            '*x^2-2*x+1)*(x-1)^2*(-1+2*y)*(y-1)^3'
    symbol_names = 'mu rho'
    symbol_values = '${mu} ${rho}'
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -pc_factor_shift_type -pc_factor_mat_solver_type'
  petsc_options_value = 'lu       NONZERO               mumps'
  nl_rel_tol = 1e-12
[]

[Outputs]
  exodus = true
  csv = true
[]

[Postprocessors]
  [h]
    type = AverageElementSize
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2u]
    type = ElementL2Error
    variable = u
    function = exact_u
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2v]
    variable = v
    function = exact_v
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
  [L2p]
    variable = pressure
    function = exact_p
    type = ElementL2Error
    outputs = 'console csv'
    execute_on = 'timestep_end'
  []
[]

(test/tests/mortar/ad_periodic_segmental_constraint/penalty_periodic_checker2d.i)

[Mesh]
  [left_block]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = -1.0
    xmax = 1.0
    ymin = -1.0
    ymax = 1.0
    nx = 16
    ny = 16
    elem_type = QUAD4
  []
  [left_block_sidesets]
    type = RenameBoundaryGenerator
    input = left_block
    old_boundary = '0 1 2 3'
    new_boundary = '10 11 12 13'
  []
  [left_block_id]
    type = SubdomainIDGenerator
    input = left_block_sidesets
    subdomain_id = 1
  []
  [./lowrig]
    type = SubdomainBoundingBoxGenerator
    input = 'left_block_id'
    block_id = 2
    bottom_left = '0 -1 0'
    top_right = '1 0 0'
  [../]
  [./upplef]
    type = SubdomainBoundingBoxGenerator
    input = 'lowrig'
    block_id = 3
    bottom_left = '-1 0 0'
    top_right = '0 1 0'
  [../]
  [./upprig]
    type = SubdomainBoundingBoxGenerator
    input = 'upplef'
    block_id = 4
    bottom_left = '0 0 0'
    top_right = '1 1 0'
  [../]
  [left]
    type = LowerDBlockFromSidesetGenerator
    input = upprig
    sidesets = '13'
    new_block_id = '10003'
    new_block_name = 'secondary_left'
  []
  [right]
    type = LowerDBlockFromSidesetGenerator
    input = left
    sidesets = '11'
    new_block_id = '10001'
    new_block_name = 'primary_right'
  []
  [bottom]
    type = LowerDBlockFromSidesetGenerator
    input = right
    sidesets = '10'
    new_block_id = '10000'
    new_block_name = 'secondary_bottom'
  []
  [top]
    type = LowerDBlockFromSidesetGenerator
    input = bottom
    sidesets = '12'
    new_block_id = '10002'
    new_block_name = 'primary_top'
  []

  [corner_node]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node'
    nodes = '0'
    input = top
  []
[]

[Variables]
  [u]
    order = FIRST
    family = LAGRANGE
  []
  [epsilon]
    order = SECOND
    family = SCALAR
  []
[]

[AuxVariables]
  [sigma]
    order = SECOND
    family = SCALAR
  []
  [./flux_x]
      order = FIRST
      family = MONOMIAL
  [../]
  [./flux_y]
      order = FIRST
      family = MONOMIAL
  [../]
[]

[AuxScalarKernels]
  [sigma]
    type = FunctionScalarAux
    variable = sigma
    function = '1 3'
    execute_on = initial #timestep_end
  []
[]

[AuxKernels]
  [./flux_x]
    type = DiffusionFluxAux
    diffusivity = 'conductivity'
    variable = flux_x
    diffusion_variable = u
    component = x
    block = '1 2 3 4'
  [../]
  [./flux_y]
    type = DiffusionFluxAux
    diffusivity = 'conductivity'
    variable = flux_y
    diffusion_variable = u
    component = y
    block = '1 2 3 4'
  [../]
[]

[Kernels]
  [diff1]
    type = ADDiffusion
    variable = u
    block = '1 4'
  []
  [diff2]
    type = ADMatDiffusion
    variable = u
    block = '2 3'
    diffusivity = conductivity
  []
[]

[Materials]
  [k1]
    type = ADGenericConstantMaterial
    prop_names = 'conductivity'
    prop_values = 1.0
    block = '1 4'
  []
  [k2]
    type = ADGenericConstantMaterial
    prop_names = 'conductivity'
    prop_values = 10.0
    block = '2 3'
  []
[]

[Problem]
  kernel_coverage_check = false
  error_on_jacobian_nonzero_reallocation = true
[]

[BCs]
  [fix_right]
    type = DirichletBC
    variable = u
    boundary = pinned_node
    value = 0
  []
[]

[Constraints]
  [mortarlr]
    type = ADPenaltyEqualValueConstraint
    primary_boundary = '11'
    secondary_boundary = '13'
    primary_subdomain = 'primary_right'
    secondary_subdomain = 'secondary_left'
    secondary_variable = u
    correct_edge_dropping = true
    penalty_value = 1.e2
  []
  [periodiclr]
    type = ADPenaltyPeriodicSegmentalConstraint
    primary_boundary = '11'
    secondary_boundary = '13'
    primary_subdomain = 'primary_right'
    secondary_subdomain = 'secondary_left'
    secondary_variable = u
    epsilon = epsilon
    sigma = sigma
    correct_edge_dropping = true
    penalty_value = 1.e2
  []
  [mortarbt]
    type = ADPenaltyEqualValueConstraint
    primary_boundary = '12'
    secondary_boundary = '10'
    primary_subdomain = 'primary_top'
    secondary_subdomain = 'secondary_bottom'
    secondary_variable = u
    correct_edge_dropping = true
    penalty_value = 1.e2
  []
  [periodicbt]
    type = ADPenaltyPeriodicSegmentalConstraint
    primary_boundary = '12'
    secondary_boundary = '10'
    primary_subdomain = 'primary_top'
    secondary_subdomain = 'secondary_bottom'
    secondary_variable = u
    epsilon = epsilon
    sigma = sigma
    correct_edge_dropping = true
    penalty_value = 1.e2
  []
[]

[Preconditioning]
  [smp]
    full = true
    type = SMP
  []
[]

[Executioner]
  type = Steady
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  solve_type = NEWTON
[]

[Postprocessors]
  [max]
    type = ElementExtremeValue
    variable = 'flux_x'
  []
[]

[Outputs]
  csv = true
[]

(modules/navier_stokes/test/tests/finite_element/ins/hydrostatic/gravity.i)

[GlobalParams]
  gravity = '0 -0.001 0'
  convective_term = false
  integrate_p_by_parts = false
  u = vel_x
  v = vel_y
  pressure = p
[]

[Mesh]
  second_order = true
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 1
    ny = 5
    ymax = 5
  [../]
  [./corner_node]
    type = ExtraNodesetGenerator
    new_boundary = top_right
    coord = '0 5'
    input = gen
  [../]
[]

[Variables]
  [./vel_x]
    order = SECOND
  [../]
  [./vel_y]
    order = SECOND
  [../]
  [./p]
  [../]
[]

[Kernels]
  [./mass]
    type = INSMass
    variable = p
  [../]
  [./x_momentum_space]
    type = INSMomentumLaplaceForm
    variable = vel_x
    component = 0
  [../]
  [./y_momentum_space]
    type = INSMomentumLaplaceForm
    variable = vel_y
    component = 1
  [../]
[]

[BCs]
  [./x_no_slip]
    type = DirichletBC
    variable = vel_x
    boundary = 'top bottom left right'
    value = 0.0
  [../]
  [./y_no_slip]
    type = DirichletBC
    variable = vel_y
    boundary = 'top bottom left right'
    value = 0.0
  [../]
  [./p_corner]
    type = DirichletBC
    boundary = top_right
    value = 0
    variable = p
  [../]
[]

[Materials]
  [./const]
    type = GenericConstantMaterial
    prop_names  = 'rho mu'
    prop_values = '100  1'
  [../]
[]

[Preconditioning]
  [./SMP_PJFNK]
    type = SMP
    full = true
    solve_type = NEWTON
  [../]
[]

[Executioner]
  type = Steady
  petsc_options_iname = '-ksp_gmres_restart -pc_type -sub_pc_type -sub_pc_factor_levels'
  petsc_options_value = '300                bjacobi  ilu          4'
  line_search = none
  nl_rel_tol = 1e-12
  nl_max_its = 6
  l_tol = 1e-6
  l_max_its = 300
[]

[Outputs]
  exodus = true
  execute_on = TIMESTEP_END
[]

(modules/combined/examples/optimization/helmholtz_multimat_strip.i)

vol_frac = 0.35

power = 1.1

Emin = 1.0e-6
Ess = 0.475 # ss
Et = 1.0 # w

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  # final_generator = 'MoveRight'
  [Bottom]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 320
    ny = 30
    xmin = 0
    xmax = 150
    ymin = 0
    ymax = 15
  []
  [RenameBottom]
    type = RenameBoundaryGenerator
    input = Bottom
    old_boundary = 'top bottom right left'
    new_boundary = 'top_bottom bottom_bottom right_bottom left_bottom'
  []
  [Middle]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 320
    ny = 6
    xmin = 0
    xmax = 150
    ymin = 0
    ymax = 3
  []
  [MoveMiddle]
    type = TransformGenerator
    input = Middle
    transform = TRANSLATE
    vector_value = '0 15 0'
  []
  [RenameMiddle]
    type = RenameBoundaryGenerator
    input = MoveMiddle
    old_boundary = 'top bottom right left'
    new_boundary = 'top_middle bottom_middle right_middle left_middle'
  []
  [Top]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 320
    ny = 30
    xmin = 0
    xmax = 150
    ymin = 0
    ymax = 15
  []
  [MoveTop]
    type = TransformGenerator
    input = Top
    transform = TRANSLATE
    vector_value = '0 18 0'
  []
  [RenameTop]
    type = RenameBoundaryGenerator
    input = MoveTop
    old_boundary = 'top bottom right left'
    new_boundary = 'top_top bottom_top right_top left_top'
  []
  [bottom_gen]
    type = ParsedSubdomainMeshGenerator
    input = RenameBottom
    combinatorial_geometry = 'y <= 15'
    block_id = 1
  []
  [middle_gen]
    type = ParsedSubdomainMeshGenerator
    input = RenameMiddle
    combinatorial_geometry = 'y <= 18 & y > 15'
    block_id = 2
  []
  [top_gen]
    type = ParsedSubdomainMeshGenerator
    input = RenameTop
    combinatorial_geometry = 'y > 18'
    block_id = 3
  []
  [stitch]
    type = StitchedMeshGenerator
    inputs = 'bottom_gen middle_gen top_gen'
    stitch_boundaries_pairs = 'top_bottom bottom_middle; top_middle bottom_top'
  []
  [left_load]
    type = ExtraNodesetGenerator
    input = stitch
    new_boundary = left_load
    coord = '37.5 33 0'
  []
  [right_load]
    type = ExtraNodesetGenerator
    input = left_load
    new_boundary = right_load
    coord = '112.5 33 0'
  []
  [left_support]
    type = ExtraNodesetGenerator
    input = right_load
    new_boundary = left_support
    coord = '0 0 0'
  []
  [right_support]
    type = ExtraNodesetGenerator
    input = left_support
    new_boundary = right_support
    coord = '150 0 0'
  []
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [Dc]
    initial_condition = -1.0
  []
[]

[AuxVariables]
  [Cc]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = -1.0
  []
  [mat_den]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = ${vol_frac}
  []

  [sensitivity]
    family = MONOMIAL
    order = FIRST
    initial_condition = -1.0
    [AuxKernel]
      type = MaterialRealAux
      variable = sensitivity
      property = sensitivity
      execute_on = LINEAR
    []
    block = '1 2 3'
  []
  [mat_den_nodal]
    family = L2_LAGRANGE
    order = FIRST
    initial_condition = ${vol_frac}
    [AuxKernel]
      type = SelfAux
      execute_on = TIMESTEP_END
      variable = mat_den_nodal
      v = mat_den
    []
  []
  [Dc_elem]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = -1.0
    [AuxKernel]
      type = SelfAux
      variable = Dc_elem
      v = Dc
      execute_on = 'TIMESTEP_END'
    []
  []
[]

[Kernels]
  [diffusion]
    type = FunctionDiffusion
    variable = Dc
    function = 4.0
  []
  [potential]
    type = Reaction
    variable = Dc
  []
  [source]
    type = CoupledForce
    variable = Dc
    v = sensitivity
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = SMALL
    add_variables = true
    incremental = false
  []
[]

[BCs]
  [no_y]
    type = DirichletBC
    variable = disp_y
    boundary = left_support
    value = 0.0
  []
  [no_x]
    type = DirichletBC
    variable = disp_x
    boundary = left_support
    value = 0.0
  []
  [no_y_right]
    type = DirichletBC
    variable = disp_y
    boundary = right_support
    value = 0.0
  []
  [boundary_penalty]
    type = ADRobinBC
    variable = Dc
    boundary = 'bottom_bottom right_bottom left_bottom top_top right_top left_top left_middle '
               'right_middle'
    coefficient = 10
  []
[]

[NodalKernels]
  [left_down]
    type = NodalGravity
    variable = disp_y
    boundary = left_load
    gravity_value = -1e-3
    mass = 1
  []
  [right_down]
    type = NodalGravity
    variable = disp_y
    boundary = right_load
    gravity_value = -1e-3
    mass = 1
  []
[]

[Materials]
  [sensitivity]
    type = ParsedMaterial
    property_name = 'sensitivity'
    block = '2'
    expression = '0'
  []
  [elasticity_tensor_one]
    type = ComputeVariableIsotropicElasticityTensor
    youngs_modulus = E_phys_one
    poissons_ratio = poissons_ratio
    args = 'mat_den'
    block = '1'
  []
  [elasticity_tensor_three]
    type = ComputeVariableIsotropicElasticityTensor
    youngs_modulus = E_phys_three
    poissons_ratio = poissons_ratio
    args = 'mat_den'
    block = '3'
  []
  [elasticity_tensor_two]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 1.0
    poissons_ratio = 0.3
    block = '2'
  []
  # One: Tungsten
  [E_phys_one]
    type = DerivativeParsedMaterial
    # Emin + (density^penal) * (E0 - Emin)
    expression = '${Emin} + (mat_den ^ ${power}) * (${Et}-${Emin})'
    coupled_variables = 'mat_den'
    property_name = E_phys_one
    block = '1'
    outputs = 'exodus'
  []
  # Three: SS316
  [E_phys_three]
    type = DerivativeParsedMaterial
    # Emin + (density^penal) * (E0 - Emin)
    expression = '${Emin} + (mat_den ^ ${power}) * (${Ess}-${Emin})'
    coupled_variables = 'mat_den'
    property_name = E_phys_three
    block = '3'
    outputs = 'exodus'
  []
  [poissons_ratio]
    type = GenericConstantMaterial
    prop_names = poissons_ratio
    prop_values = 0.3
  []
  [stress]
    type = ComputeLinearElasticStress
  []
  [dc_one]
    type = ComplianceSensitivity
    design_density = mat_den
    youngs_modulus = E_phys_one
    block = '1'
  []
  [dc_three]
    type = ComplianceSensitivity
    design_density = mat_den
    youngs_modulus = E_phys_three
    block = '3'
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[UserObjects]
  [update_one]
    type = DensityUpdate
    density_sensitivity = Dc_elem
    design_density = mat_den
    volume_fraction = ${vol_frac}
    execute_on = TIMESTEP_BEGIN
    block = '1'
  []
  [update_three]
    type = DensityUpdate
    density_sensitivity = Dc_elem
    design_density = mat_den
    volume_fraction = ${vol_frac}
    execute_on = TIMESTEP_BEGIN
    block = '3'
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'
  nl_abs_tol = 1e-10
  dt = 1.0
  num_steps = 90
[]

[Outputs]
  exodus = true
  [out]
    type = CSV
    execute_on = 'TIMESTEP_END'
  []
  print_linear_residuals = false
[]

[Postprocessors]
  [mesh_volume]
    type = VolumePostprocessor
    execute_on = 'initial timestep_end'
  []
  [total_vol]
    type = ElementIntegralVariablePostprocessor
    variable = mat_den
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [vol_frac]
    type = ParsedPostprocessor
    expression = 'total_vol / mesh_volume'
    pp_names = 'total_vol mesh_volume'
  []
  [sensitivity]
    type = ElementIntegralMaterialProperty
    mat_prop = sensitivity
    block = '1 3'
  []
  [objective_one]
    type = ElementIntegralMaterialProperty
    mat_prop = strain_energy_density
    execute_on = 'INITIAL TIMESTEP_END'
    block = '1'
  []
  [objective_three]
    type = ElementIntegralMaterialProperty
    mat_prop = strain_energy_density
    execute_on = 'INITIAL TIMESTEP_END'
    block = '3'
  []
[]

(modules/combined/test/tests/optimization/compliance_sensitivity/2d_mbb_pde.i)

vol_frac = 0.5
E0 = 1
Emin = 1e-8
power = 3
[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  [MeshGenerator]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 150
    ny = 50
    xmin = 0
    xmax = 30
    ymin = 0
    ymax = 10
  []
  [node]
    type = ExtraNodesetGenerator
    input = MeshGenerator
    new_boundary = hold_y
    nodes = 0
  []
  [push]
    type = ExtraNodesetGenerator
    input = node
    new_boundary = push
    coord = '30 10 0'
  []

[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [Dc]
    initial_condition = -1.0
  []
[]

[AuxVariables]

  [sensitivity]
    family = MONOMIAL
    order = FIRST
    initial_condition = -1.0
    [AuxKernel]
      type = MaterialRealAux
      variable = sensitivity
      property = sensitivity
      execute_on = LINEAR
    []
  []
  [mat_den]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = ${vol_frac}
  []
  [Dc_elem]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = -1.0
    [AuxKernel]
      type = SelfAux
      variable = Dc_elem
      v = Dc
      execute_on = 'TIMESTEP_END'
    []
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = SMALL
    add_variables = true
    incremental = false
  []
[]
[Kernels]
  [diffusion]
    type = FunctionDiffusion
    variable = Dc
    function = 0.15 # radius coeff
  []
  [potential]
    type = Reaction
    variable = Dc
  []
  [source]
    type = CoupledForce
    variable = Dc
    v = sensitivity
  []
[]
[BCs]
  [no_x]
    type = DirichletBC
    variable = disp_y
    boundary = hold_y
    value = 0.0
  []
  [no_y]
    type = DirichletBC
    variable = disp_x
    boundary = right
    value = 0.0
  []
  [boundary_penalty]
    type = ADRobinBC
    variable = Dc
    boundary = 'left top'
    coefficient = 10
  []
  [boundary_penalty_right]
    type = ADRobinBC
    variable = Dc
    boundary = 'right'
    coefficient = 10
  []
[]
[NodalKernels]
  [push]
    type = NodalGravity
    variable = disp_y
    boundary = push
    gravity_value = -1
    mass = 1
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeVariableIsotropicElasticityTensor
    youngs_modulus = E_phys
    poissons_ratio = poissons_ratio
    args = 'mat_den'
  []
  [E_phys]
    type = DerivativeParsedMaterial
    # Emin + (density^penal) * (E0 - Emin)
    expression = '${Emin} + (mat_den ^ ${power}) * (${E0}-${Emin})'
    coupled_variables = 'mat_den'
    property_name = E_phys
  []
  [poissons_ratio]
    type = GenericConstantMaterial
    prop_names = poissons_ratio
    prop_values = 0.3
  []
  [stress]
    type = ComputeLinearElasticStress
  []
  [dc]
    type = ComplianceSensitivity
    design_density = mat_den
    youngs_modulus = E_phys
    incremental = false
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]
[UserObjects]
  [update]
    type = DensityUpdate
    density_sensitivity = Dc_elem
    design_density = mat_den
    volume_fraction = ${vol_frac}
    execute_on = TIMESTEP_BEGIN
    force_postaux = true
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'
  line_search = none
  nl_abs_tol = 1e-4
  l_max_its = 200
  start_time = 0.0
  dt = 1.0
  num_steps = 70
[]

[Outputs]
  [out]
    type = CSV
    execute_on = 'INITIAL TIMESTEP_END'
  []
  print_linear_residuals = false
[]

[Postprocessors]
  [total_vol]
    type = ElementIntegralVariablePostprocessor
    variable = mat_den
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [sensitivity]
    type = ElementIntegralMaterialProperty
    mat_prop = sensitivity
  []
[]

[Controls]
  [first_period]
    type = TimePeriod
    start_time = 0.0
    end_time = 10
    enable_objects = 'BCs::boundary_penalty_right'
    execute_on = 'initial timestep_begin'
  []
[]

(modules/combined/examples/geochem-porous_flow/geotes_weber_tensleep/porous_flow.i)

#########################################
#                                       #
# File written by create_input_files.py #
#                                       #
#########################################
# PorousFlow simulation of injection and production in a simplified GeoTES aquifer
# Much of this file is standard porous-flow stuff.  The unusual aspects are:
# - transfer of the rates of changes of each species (kg.s) to the aquifer_geochemistry.i simulation.  This is achieved by saving these changes from the PorousFlowMassTimeDerivative residuals
# - transfer of the temperature field to the aquifer_geochemistry.i simulation
# Interesting behaviour can be simulated by this file without its 'parent' simulation, exchanger.i.  exchanger.i provides mass-fractions injected via the injection_rate_massfrac_* variables, but since these are more-or-less constant throughout the duration of the exchanger.i simulation, the initial_conditions specified below may be used.  Similar, exchanger.i provides injection_temperature, but that is also constant.
injection_rate = -0.02 # kg/s/m, negative because injection as a source
production_rate = 0.02 # kg/s/m, this is about the maximum that can be sustained by the aquifer, with its fairly low permeability, without porepressure becoming negative
[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 3
    xmin = -75
    xmax = 75
    ymin = 0
    ymax = 40
    zmin = -25
    zmax = 25
    nx = 15
    ny = 4
    nz = 5
  []
  [aquifer]
    type = ParsedSubdomainMeshGenerator
    input = gen
    block_id = 1
    block_name = aquifer
    combinatorial_geometry = 'z >= -5 & z <= 5'
  []
  [injection_nodes]
    input = aquifer
    type = ExtraNodesetGenerator
    new_boundary = injection_nodes
    coord = '-25 0 -5; -25 0 5'
  []
  [production_nodes]
    input = injection_nodes
    type = ExtraNodesetGenerator
    new_boundary = production_nodes
    coord = '25 0 -5; 25 0 5'
  []
[]

[GlobalParams]
  PorousFlowDictator = dictator
  gravity = '0 0 -10'
[]

[BCs]
  [injection_temperature]
    type = MatchedValueBC
    variable = temperature
    v = injection_temperature
    boundary = injection_nodes
  []
[]

[FluidProperties]
  [the_simple_fluid]
    type = SimpleFluidProperties
    thermal_expansion = 0
    bulk_modulus = 2E9
    viscosity = 1E-3
    density0 = 1000
    cv = 4000.0
    cp = 4000.0
  []
[]

[PorousFlowFullySaturated]
  coupling_type = ThermoHydro
  porepressure = porepressure
  temperature = temperature
  mass_fraction_vars = 'f_H f_Cl f_SO4 f_HCO3 f_SiO2aq f_Al f_Ca f_Mg f_Fe f_K f_Na f_Sr f_F f_BOH f_Br f_Ba f_Li f_NO3 f_O2aq '
  save_component_rate_in = 'rate_H rate_Cl rate_SO4 rate_HCO3 rate_SiO2aq rate_Al rate_Ca rate_Mg rate_Fe rate_K rate_Na rate_Sr rate_F rate_BOH rate_Br rate_Ba rate_Li rate_NO3 rate_O2aq rate_H2O' # change in kg at every node / dt
  fp = the_simple_fluid
  temperature_unit = Celsius
[]

[Materials]
  [porosity_caps]
    type = PorousFlowPorosityConst # this simulation has no porosity changes from dissolution
    block = 0
    porosity = 0.01
  []
  [porosity_aquifer]
    type = PorousFlowPorosityConst # this simulation has no porosity changes from dissolution
    block = aquifer
    porosity = 0.063
  []
  [permeability_caps]
    type = PorousFlowPermeabilityConst
    block = 0
    permeability = '1E-18 0 0   0 1E-18 0   0 0 1E-18'
  []
  [permeability_aquifer]
    type = PorousFlowPermeabilityConst
    block = aquifer
    permeability = '1.7E-15 0 0   0 1.7E-15 0   0 0 4.1E-16'
  []
  [thermal_conductivity]
    type = PorousFlowThermalConductivityIdeal
    dry_thermal_conductivity = '0 0 0  0 0 0  0 0 0'
  []
  [rock_heat]
    type = PorousFlowMatrixInternalEnergy
    density = 2500.0
    specific_heat_capacity = 1200.0
  []
[]

[Preconditioning]
  active = typically_efficient
  [typically_efficient]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -pc_hypre_type'
    petsc_options_value = ' hypre    boomeramg'
  []
  [strong]
    type = SMP
    full = true
    petsc_options = '-ksp_diagonal_scale -ksp_diagonal_scale_fix'
    petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type -pc_asm_overlap'
    petsc_options_value = ' asm      ilu           NONZERO                   2'
  []
  [probably_too_strong]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
    petsc_options_value = ' lu       mumps'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  end_time = 7.76E6 # 90 days
  [TimeStepper]
    type = FunctionDT
    function = 'min(3E4, max(1E4, 0.2 * t))'
  []
[]

[Outputs]
  exodus = true
[]

[Variables]
  [f_H]
    initial_condition = -2.952985071156e-06
  []
  [f_Cl]
    initial_condition = 0.04870664551708
  []
  [f_SO4]
    initial_condition = 0.0060359986852517
  []
  [f_HCO3]
    initial_condition = 5.0897287594019e-05
  []
  [f_SiO2aq]
    initial_condition = 3.0246609868421e-05
  []
  [f_Al]
    initial_condition = 3.268028901929e-08
  []
  [f_Ca]
    initial_condition = 0.00082159428184586
  []
  [f_Mg]
    initial_condition = 1.8546347062146e-05
  []
  [f_Fe]
    initial_condition = 4.3291908204093e-05
  []
  [f_K]
    initial_condition = 6.8434768308898e-05
  []
  [f_Na]
    initial_condition = 0.033298053919671
  []
  [f_Sr]
    initial_condition = 1.2771866652177e-05
  []
  [f_F]
    initial_condition = 5.5648860174073e-06
  []
  [f_BOH]
    initial_condition = 0.0003758574621917
  []
  [f_Br]
    initial_condition = 9.0315286107068e-05
  []
  [f_Ba]
    initial_condition = 1.5637460875161e-07
  []
  [f_Li]
    initial_condition = 8.3017067912701e-05
  []
  [f_NO3]
    initial_condition = 0.00010958455036169
  []
  [f_O2aq]
    initial_condition = -7.0806852373351e-05
  []
  [porepressure]
    initial_condition = 30E6
  []
  [temperature]
    initial_condition = 92
    scaling = 1E-6 # fluid enthalpy is roughly 1E6
  []
[]

[DiracKernels]
  [inject_H]
    type = PorousFlowPolyLineSink
    SumQuantityUO = injected_mass
    fluxes = ${injection_rate}
    p_or_t_vals = 0.0
    multiplying_var = injection_rate_massfrac_H
    point_file = injection.bh
    variable = f_H
  []
  [inject_Cl]
    type = PorousFlowPolyLineSink
    SumQuantityUO = injected_mass
    fluxes = ${injection_rate}
    p_or_t_vals = 0.0
    multiplying_var = injection_rate_massfrac_Cl
    point_file = injection.bh
    variable = f_Cl
  []
  [inject_SO4]
    type = PorousFlowPolyLineSink
    SumQuantityUO = injected_mass
    fluxes = ${injection_rate}
    p_or_t_vals = 0.0
    multiplying_var = injection_rate_massfrac_SO4
    point_file = injection.bh
    variable = f_SO4
  []
  [inject_HCO3]
    type = PorousFlowPolyLineSink
    SumQuantityUO = injected_mass
    fluxes = ${injection_rate}
    p_or_t_vals = 0.0
    multiplying_var = injection_rate_massfrac_HCO3
    point_file = injection.bh
    variable = f_HCO3
  []
  [inject_SiO2aq]
    type = PorousFlowPolyLineSink
    SumQuantityUO = injected_mass
    fluxes = ${injection_rate}
    p_or_t_vals = 0.0
    multiplying_var = injection_rate_massfrac_SiO2aq
    point_file = injection.bh
    variable = f_SiO2aq
  []
  [inject_Al]
    type = PorousFlowPolyLineSink
    SumQuantityUO = injected_mass
    fluxes = ${injection_rate}
    p_or_t_vals = 0.0
    multiplying_var = injection_rate_massfrac_Al
    point_file = injection.bh
    variable = f_Al
  []
  [inject_Ca]
    type = PorousFlowPolyLineSink
    SumQuantityUO = injected_mass
    fluxes = ${injection_rate}
    p_or_t_vals = 0.0
    multiplying_var = injection_rate_massfrac_Ca
    point_file = injection.bh
    variable = f_Ca
  []
  [inject_Mg]
    type = PorousFlowPolyLineSink
    SumQuantityUO = injected_mass
    fluxes = ${injection_rate}
    p_or_t_vals = 0.0
    multiplying_var = injection_rate_massfrac_Mg
    point_file = injection.bh
    variable = f_Mg
  []
  [inject_Fe]
    type = PorousFlowPolyLineSink
    SumQuantityUO = injected_mass
    fluxes = ${injection_rate}
    p_or_t_vals = 0.0
    multiplying_var = injection_rate_massfrac_Fe
    point_file = injection.bh
    variable = f_Fe
  []
  [inject_K]
    type = PorousFlowPolyLineSink
    SumQuantityUO = injected_mass
    fluxes = ${injection_rate}
    p_or_t_vals = 0.0
    multiplying_var = injection_rate_massfrac_K
    point_file = injection.bh
    variable = f_K
  []
  [inject_Na]
    type = PorousFlowPolyLineSink
    SumQuantityUO = injected_mass
    fluxes = ${injection_rate}
    p_or_t_vals = 0.0
    multiplying_var = injection_rate_massfrac_Na
    point_file = injection.bh
    variable = f_Na
  []
  [inject_Sr]
    type = PorousFlowPolyLineSink
    SumQuantityUO = injected_mass
    fluxes = ${injection_rate}
    p_or_t_vals = 0.0
    multiplying_var = injection_rate_massfrac_Sr
    point_file = injection.bh
    variable = f_Sr
  []
  [inject_F]
    type = PorousFlowPolyLineSink
    SumQuantityUO = injected_mass
    fluxes = ${injection_rate}
    p_or_t_vals = 0.0
    multiplying_var = injection_rate_massfrac_F
    point_file = injection.bh
    variable = f_F
  []
  [inject_BOH]
    type = PorousFlowPolyLineSink
    SumQuantityUO = injected_mass
    fluxes = ${injection_rate}
    p_or_t_vals = 0.0
    multiplying_var = injection_rate_massfrac_BOH
    point_file = injection.bh
    variable = f_BOH
  []
  [inject_Br]
    type = PorousFlowPolyLineSink
    SumQuantityUO = injected_mass
    fluxes = ${injection_rate}
    p_or_t_vals = 0.0
    multiplying_var = injection_rate_massfrac_Br
    point_file = injection.bh
    variable = f_Br
  []
  [inject_Ba]
    type = PorousFlowPolyLineSink
    SumQuantityUO = injected_mass
    fluxes = ${injection_rate}
    p_or_t_vals = 0.0
    multiplying_var = injection_rate_massfrac_Ba
    point_file = injection.bh
    variable = f_Ba
  []
  [inject_Li]
    type = PorousFlowPolyLineSink
    SumQuantityUO = injected_mass
    fluxes = ${injection_rate}
    p_or_t_vals = 0.0
    multiplying_var = injection_rate_massfrac_Li
    point_file = injection.bh
    variable = f_Li
  []
  [inject_NO3]
    type = PorousFlowPolyLineSink
    SumQuantityUO = injected_mass
    fluxes = ${injection_rate}
    p_or_t_vals = 0.0
    multiplying_var = injection_rate_massfrac_NO3
    point_file = injection.bh
    variable = f_NO3
  []
  [inject_O2aq]
    type = PorousFlowPolyLineSink
    SumQuantityUO = injected_mass
    fluxes = ${injection_rate}
    p_or_t_vals = 0.0
    multiplying_var = injection_rate_massfrac_O2aq
    point_file = injection.bh
    variable = f_O2aq
  []
  [inject_H2O]
    type = PorousFlowPolyLineSink
    SumQuantityUO = injected_mass
    fluxes = ${injection_rate}
    p_or_t_vals = 0.0
    multiplying_var = injection_rate_massfrac_H2O
    point_file = injection.bh
    variable = porepressure
  []

  [produce_H]
    type = PorousFlowPolyLineSink
    SumQuantityUO = produced_mass_H
    fluxes = ${production_rate}
    p_or_t_vals = 0.0
    mass_fraction_component = 0
    point_file = production.bh
    variable = f_H
  []
  [produce_Cl]
    type = PorousFlowPolyLineSink
    SumQuantityUO = produced_mass_Cl
    fluxes = ${production_rate}
    p_or_t_vals = 0.0
    mass_fraction_component = 1
    point_file = production.bh
    variable = f_Cl
  []
  [produce_SO4]
    type = PorousFlowPolyLineSink
    SumQuantityUO = produced_mass_SO4
    fluxes = ${production_rate}
    p_or_t_vals = 0.0
    mass_fraction_component = 2
    point_file = production.bh
    variable = f_SO4
  []
  [produce_HCO3]
    type = PorousFlowPolyLineSink
    SumQuantityUO = produced_mass_HCO3
    fluxes = ${production_rate}
    p_or_t_vals = 0.0
    mass_fraction_component = 3
    point_file = production.bh
    variable = f_HCO3
  []
  [produce_SiO2aq]
    type = PorousFlowPolyLineSink
    SumQuantityUO = produced_mass_SiO2aq
    fluxes = ${production_rate}
    p_or_t_vals = 0.0
    mass_fraction_component = 4
    point_file = production.bh
    variable = f_SiO2aq
  []
  [produce_Al]
    type = PorousFlowPolyLineSink
    SumQuantityUO = produced_mass_Al
    fluxes = ${production_rate}
    p_or_t_vals = 0.0
    mass_fraction_component = 5
    point_file = production.bh
    variable = f_Al
  []
  [produce_Ca]
    type = PorousFlowPolyLineSink
    SumQuantityUO = produced_mass_Ca
    fluxes = ${production_rate}
    p_or_t_vals = 0.0
    mass_fraction_component = 6
    point_file = production.bh
    variable = f_Ca
  []
  [produce_Mg]
    type = PorousFlowPolyLineSink
    SumQuantityUO = produced_mass_Mg
    fluxes = ${production_rate}
    p_or_t_vals = 0.0
    mass_fraction_component = 7
    point_file = production.bh
    variable = f_Mg
  []
  [produce_Fe]
    type = PorousFlowPolyLineSink
    SumQuantityUO = produced_mass_Fe
    fluxes = ${production_rate}
    p_or_t_vals = 0.0
    mass_fraction_component = 8
    point_file = production.bh
    variable = f_Fe
  []
  [produce_K]
    type = PorousFlowPolyLineSink
    SumQuantityUO = produced_mass_K
    fluxes = ${production_rate}
    p_or_t_vals = 0.0
    mass_fraction_component = 9
    point_file = production.bh
    variable = f_K
  []
  [produce_Na]
    type = PorousFlowPolyLineSink
    SumQuantityUO = produced_mass_Na
    fluxes = ${production_rate}
    p_or_t_vals = 0.0
    mass_fraction_component = 10
    point_file = production.bh
    variable = f_Na
  []
  [produce_Sr]
    type = PorousFlowPolyLineSink
    SumQuantityUO = produced_mass_Sr
    fluxes = ${production_rate}
    p_or_t_vals = 0.0
    mass_fraction_component = 11
    point_file = production.bh
    variable = f_Sr
  []
  [produce_F]
    type = PorousFlowPolyLineSink
    SumQuantityUO = produced_mass_F
    fluxes = ${production_rate}
    p_or_t_vals = 0.0
    mass_fraction_component = 12
    point_file = production.bh
    variable = f_F
  []
  [produce_BOH]
    type = PorousFlowPolyLineSink
    SumQuantityUO = produced_mass_BOH
    fluxes = ${production_rate}
    p_or_t_vals = 0.0
    mass_fraction_component = 13
    point_file = production.bh
    variable = f_BOH
  []
  [produce_Br]
    type = PorousFlowPolyLineSink
    SumQuantityUO = produced_mass_Br
    fluxes = ${production_rate}
    p_or_t_vals = 0.0
    mass_fraction_component = 14
    point_file = production.bh
    variable = f_Br
  []
  [produce_Ba]
    type = PorousFlowPolyLineSink
    SumQuantityUO = produced_mass_Ba
    fluxes = ${production_rate}
    p_or_t_vals = 0.0
    mass_fraction_component = 15
    point_file = production.bh
    variable = f_Ba
  []
  [produce_Li]
    type = PorousFlowPolyLineSink
    SumQuantityUO = produced_mass_Li
    fluxes = ${production_rate}
    p_or_t_vals = 0.0
    mass_fraction_component = 16
    point_file = production.bh
    variable = f_Li
  []
  [produce_NO3]
    type = PorousFlowPolyLineSink
    SumQuantityUO = produced_mass_NO3
    fluxes = ${production_rate}
    p_or_t_vals = 0.0
    mass_fraction_component = 17
    point_file = production.bh
    variable = f_NO3
  []
  [produce_O2aq]
    type = PorousFlowPolyLineSink
    SumQuantityUO = produced_mass_O2aq
    fluxes = ${production_rate}
    p_or_t_vals = 0.0
    mass_fraction_component = 18
    point_file = production.bh
    variable = f_O2aq
  []
  [produce_H2O]
    type = PorousFlowPolyLineSink
    SumQuantityUO = produced_mass_H2O
    fluxes = ${production_rate}
    p_or_t_vals = 0.0
    mass_fraction_component = 19
    point_file = production.bh
    variable = porepressure
  []
  [produce_heat]
    type = PorousFlowPolyLineSink
    SumQuantityUO = produced_heat
    fluxes = ${production_rate}
    p_or_t_vals = 0.0
    use_enthalpy = true
    point_file = production.bh
    variable = temperature
  []
[]

[UserObjects]
  [injected_mass]
    type = PorousFlowSumQuantity
  []
  [produced_mass_H]
    type = PorousFlowSumQuantity
  []
  [produced_mass_Cl]
    type = PorousFlowSumQuantity
  []
  [produced_mass_SO4]
    type = PorousFlowSumQuantity
  []
  [produced_mass_HCO3]
    type = PorousFlowSumQuantity
  []
  [produced_mass_SiO2aq]
    type = PorousFlowSumQuantity
  []
  [produced_mass_Al]
    type = PorousFlowSumQuantity
  []
  [produced_mass_Ca]
    type = PorousFlowSumQuantity
  []
  [produced_mass_Mg]
    type = PorousFlowSumQuantity
  []
  [produced_mass_Fe]
    type = PorousFlowSumQuantity
  []
  [produced_mass_K]
    type = PorousFlowSumQuantity
  []
  [produced_mass_Na]
    type = PorousFlowSumQuantity
  []
  [produced_mass_Sr]
    type = PorousFlowSumQuantity
  []
  [produced_mass_F]
    type = PorousFlowSumQuantity
  []
  [produced_mass_BOH]
    type = PorousFlowSumQuantity
  []
  [produced_mass_Br]
    type = PorousFlowSumQuantity
  []
  [produced_mass_Ba]
    type = PorousFlowSumQuantity
  []
  [produced_mass_Li]
    type = PorousFlowSumQuantity
  []
  [produced_mass_NO3]
    type = PorousFlowSumQuantity
  []
  [produced_mass_O2aq]
    type = PorousFlowSumQuantity
  []
  [produced_mass_H2O]
    type = PorousFlowSumQuantity
  []
  [produced_heat]
    type = PorousFlowSumQuantity
  []
[]

[Postprocessors]
  [dt]
    type = TimestepSize
    execute_on = TIMESTEP_BEGIN
  []
  [tot_kg_injected_this_timestep]
    type = PorousFlowPlotQuantity
    uo = injected_mass
  []
  [kg_H_produced_this_timestep]
    type = PorousFlowPlotQuantity
    uo = produced_mass_H
  []
  [kg_Cl_produced_this_timestep]
    type = PorousFlowPlotQuantity
    uo = produced_mass_Cl
  []
  [kg_SO4_produced_this_timestep]
    type = PorousFlowPlotQuantity
    uo = produced_mass_SO4
  []
  [kg_HCO3_produced_this_timestep]
    type = PorousFlowPlotQuantity
    uo = produced_mass_HCO3
  []
  [kg_SiO2aq_produced_this_timestep]
    type = PorousFlowPlotQuantity
    uo = produced_mass_SiO2aq
  []
  [kg_Al_produced_this_timestep]
    type = PorousFlowPlotQuantity
    uo = produced_mass_Al
  []
  [kg_Ca_produced_this_timestep]
    type = PorousFlowPlotQuantity
    uo = produced_mass_Ca
  []
  [kg_Mg_produced_this_timestep]
    type = PorousFlowPlotQuantity
    uo = produced_mass_Mg
  []
  [kg_Fe_produced_this_timestep]
    type = PorousFlowPlotQuantity
    uo = produced_mass_Fe
  []
  [kg_K_produced_this_timestep]
    type = PorousFlowPlotQuantity
    uo = produced_mass_K
  []
  [kg_Na_produced_this_timestep]
    type = PorousFlowPlotQuantity
    uo = produced_mass_Na
  []
  [kg_Sr_produced_this_timestep]
    type = PorousFlowPlotQuantity
    uo = produced_mass_Sr
  []
  [kg_F_produced_this_timestep]
    type = PorousFlowPlotQuantity
    uo = produced_mass_F
  []
  [kg_BOH_produced_this_timestep]
    type = PorousFlowPlotQuantity
    uo = produced_mass_BOH
  []
  [kg_Br_produced_this_timestep]
    type = PorousFlowPlotQuantity
    uo = produced_mass_Br
  []
  [kg_Ba_produced_this_timestep]
    type = PorousFlowPlotQuantity
    uo = produced_mass_Ba
  []
  [kg_Li_produced_this_timestep]
    type = PorousFlowPlotQuantity
    uo = produced_mass_Li
  []
  [kg_NO3_produced_this_timestep]
    type = PorousFlowPlotQuantity
    uo = produced_mass_NO3
  []
  [kg_O2aq_produced_this_timestep]
    type = PorousFlowPlotQuantity
    uo = produced_mass_O2aq
  []
  [kg_H2O_produced_this_timestep]
    type = PorousFlowPlotQuantity
    uo = produced_mass_H2O
  []
  [mole_rate_H_produced]
    type = FunctionValuePostprocessor
    function = moles_H
    indirect_dependencies = 'kg_H_produced_this_timestep dt'
  []
  [mole_rate_Cl_produced]
    type = FunctionValuePostprocessor
    function = moles_Cl
    indirect_dependencies = 'kg_Cl_produced_this_timestep dt'
  []
  [mole_rate_SO4_produced]
    type = FunctionValuePostprocessor
    function = moles_SO4
    indirect_dependencies = 'kg_SO4_produced_this_timestep dt'
  []
  [mole_rate_HCO3_produced]
    type = FunctionValuePostprocessor
    function = moles_HCO3
    indirect_dependencies = 'kg_HCO3_produced_this_timestep dt'
  []
  [mole_rate_SiO2aq_produced]
    type = FunctionValuePostprocessor
    function = moles_SiO2aq
    indirect_dependencies = 'kg_SiO2aq_produced_this_timestep dt'
  []
  [mole_rate_Al_produced]
    type = FunctionValuePostprocessor
    function = moles_Al
    indirect_dependencies = 'kg_Al_produced_this_timestep dt'
  []
  [mole_rate_Ca_produced]
    type = FunctionValuePostprocessor
    function = moles_Ca
    indirect_dependencies = 'kg_Ca_produced_this_timestep dt'
  []
  [mole_rate_Mg_produced]
    type = FunctionValuePostprocessor
    function = moles_Mg
    indirect_dependencies = 'kg_Mg_produced_this_timestep dt'
  []
  [mole_rate_Fe_produced]
    type = FunctionValuePostprocessor
    function = moles_Fe
    indirect_dependencies = 'kg_Fe_produced_this_timestep dt'
  []
  [mole_rate_K_produced]
    type = FunctionValuePostprocessor
    function = moles_K
    indirect_dependencies = 'kg_K_produced_this_timestep dt'
  []
  [mole_rate_Na_produced]
    type = FunctionValuePostprocessor
    function = moles_Na
    indirect_dependencies = 'kg_Na_produced_this_timestep dt'
  []
  [mole_rate_Sr_produced]
    type = FunctionValuePostprocessor
    function = moles_Sr
    indirect_dependencies = 'kg_Sr_produced_this_timestep dt'
  []
  [mole_rate_F_produced]
    type = FunctionValuePostprocessor
    function = moles_F
    indirect_dependencies = 'kg_F_produced_this_timestep dt'
  []
  [mole_rate_BOH_produced]
    type = FunctionValuePostprocessor
    function = moles_BOH
    indirect_dependencies = 'kg_BOH_produced_this_timestep dt'
  []
  [mole_rate_Br_produced]
    type = FunctionValuePostprocessor
    function = moles_Br
    indirect_dependencies = 'kg_Br_produced_this_timestep dt'
  []
  [mole_rate_Ba_produced]
    type = FunctionValuePostprocessor
    function = moles_Ba
    indirect_dependencies = 'kg_Ba_produced_this_timestep dt'
  []
  [mole_rate_Li_produced]
    type = FunctionValuePostprocessor
    function = moles_Li
    indirect_dependencies = 'kg_Li_produced_this_timestep dt'
  []
  [mole_rate_NO3_produced]
    type = FunctionValuePostprocessor
    function = moles_NO3
    indirect_dependencies = 'kg_NO3_produced_this_timestep dt'
  []
  [mole_rate_O2aq_produced]
    type = FunctionValuePostprocessor
    function = moles_O2aq
    indirect_dependencies = 'kg_O2aq_produced_this_timestep dt'
  []
  [mole_rate_H2O_produced]
    type = FunctionValuePostprocessor
    function = moles_H2O
    indirect_dependencies = 'kg_H2O_produced_this_timestep dt'
  []
  [heat_joules_extracted_this_timestep]
    type = PorousFlowPlotQuantity
    uo = produced_heat
  []
  [production_temperature]
    type = AverageNodalVariableValue
    boundary = production_nodes
    variable = temperature
  []
[]

[Functions]
  [moles_H]
    type = ParsedFunction
    symbol_names = 'kg_H dt'
    symbol_values = 'kg_H_produced_this_timestep dt'
    expression = 'kg_H * 1000 / 1.0079 / dt'
  []
  [moles_Cl]
    type = ParsedFunction
    symbol_names = 'kg_Cl dt'
    symbol_values = 'kg_Cl_produced_this_timestep dt'
    expression = 'kg_Cl * 1000 / 35.453 / dt'
  []
  [moles_SO4]
    type = ParsedFunction
    symbol_names = 'kg_SO4 dt'
    symbol_values = 'kg_SO4_produced_this_timestep dt'
    expression = 'kg_SO4 * 1000 / 96.0576 / dt'
  []
  [moles_HCO3]
    type = ParsedFunction
    symbol_names = 'kg_HCO3 dt'
    symbol_values = 'kg_HCO3_produced_this_timestep dt'
    expression = 'kg_HCO3 * 1000 / 61.0171 / dt'
  []
  [moles_SiO2aq]
    type = ParsedFunction
    symbol_names = 'kg_SiO2aq dt'
    symbol_values = 'kg_SiO2aq_produced_this_timestep dt'
    expression = 'kg_SiO2aq * 1000 / 60.0843 / dt'
  []
  [moles_Al]
    type = ParsedFunction
    symbol_names = 'kg_Al dt'
    symbol_values = 'kg_Al_produced_this_timestep dt'
    expression = 'kg_Al * 1000 / 26.9815 / dt'
  []
  [moles_Ca]
    type = ParsedFunction
    symbol_names = 'kg_Ca dt'
    symbol_values = 'kg_Ca_produced_this_timestep dt'
    expression = 'kg_Ca * 1000 / 40.08 / dt'
  []
  [moles_Mg]
    type = ParsedFunction
    symbol_names = 'kg_Mg dt'
    symbol_values = 'kg_Mg_produced_this_timestep dt'
    expression = 'kg_Mg * 1000 / 24.305 / dt'
  []
  [moles_Fe]
    type = ParsedFunction
    symbol_names = 'kg_Fe dt'
    symbol_values = 'kg_Fe_produced_this_timestep dt'
    expression = 'kg_Fe * 1000 / 55.847 / dt'
  []
  [moles_K]
    type = ParsedFunction
    symbol_names = 'kg_K dt'
    symbol_values = 'kg_K_produced_this_timestep dt'
    expression = 'kg_K * 1000 / 39.0983 / dt'
  []
  [moles_Na]
    type = ParsedFunction
    symbol_names = 'kg_Na dt'
    symbol_values = 'kg_Na_produced_this_timestep dt'
    expression = 'kg_Na * 1000 / 22.9898 / dt'
  []
  [moles_Sr]
    type = ParsedFunction
    symbol_names = 'kg_Sr dt'
    symbol_values = 'kg_Sr_produced_this_timestep dt'
    expression = 'kg_Sr * 1000 / 87.62 / dt'
  []
  [moles_F]
    type = ParsedFunction
    symbol_names = 'kg_F dt'
    symbol_values = 'kg_F_produced_this_timestep dt'
    expression = 'kg_F * 1000 / 18.9984 / dt'
  []
  [moles_BOH]
    type = ParsedFunction
    symbol_names = 'kg_BOH dt'
    symbol_values = 'kg_BOH_produced_this_timestep dt'
    expression = 'kg_BOH * 1000 / 61.8329 / dt'
  []
  [moles_Br]
    type = ParsedFunction
    symbol_names = 'kg_Br dt'
    symbol_values = 'kg_Br_produced_this_timestep dt'
    expression = 'kg_Br * 1000 / 79.904 / dt'
  []
  [moles_Ba]
    type = ParsedFunction
    symbol_names = 'kg_Ba dt'
    symbol_values = 'kg_Ba_produced_this_timestep dt'
    expression = 'kg_Ba * 1000 / 137.33 / dt'
  []
  [moles_Li]
    type = ParsedFunction
    symbol_names = 'kg_Li dt'
    symbol_values = 'kg_Li_produced_this_timestep dt'
    expression = 'kg_Li * 1000 / 6.941 / dt'
  []
  [moles_NO3]
    type = ParsedFunction
    symbol_names = 'kg_NO3 dt'
    symbol_values = 'kg_NO3_produced_this_timestep dt'
    expression = 'kg_NO3 * 1000 / 62.0049 / dt'
  []
  [moles_O2aq]
    type = ParsedFunction
    symbol_names = 'kg_O2aq dt'
    symbol_values = 'kg_O2aq_produced_this_timestep dt'
    expression = 'kg_O2aq * 1000 / 31.9988 / dt'
  []
  [moles_H2O]
    type = ParsedFunction
    symbol_names = 'kg_H2O dt'
    symbol_values = 'kg_H2O_produced_this_timestep dt'
    expression = 'kg_H2O * 1000 / 18.01801802 / dt'
  []
[]

[AuxVariables]
  [injection_temperature]
    initial_condition = 92
  []
  [injection_rate_massfrac_H]
    initial_condition = -2.952985071156e-06
  []
  [injection_rate_massfrac_Cl]
    initial_condition = 0.04870664551708
  []
  [injection_rate_massfrac_SO4]
    initial_condition = 0.0060359986852517
  []
  [injection_rate_massfrac_HCO3]
    initial_condition = 5.0897287594019e-05
  []
  [injection_rate_massfrac_SiO2aq]
    initial_condition = 3.0246609868421e-05
  []
  [injection_rate_massfrac_Al]
    initial_condition = 3.268028901929e-08
  []
  [injection_rate_massfrac_Ca]
    initial_condition = 0.00082159428184586
  []
  [injection_rate_massfrac_Mg]
    initial_condition = 1.8546347062146e-05
  []
  [injection_rate_massfrac_Fe]
    initial_condition = 4.3291908204093e-05
  []
  [injection_rate_massfrac_K]
    initial_condition = 6.8434768308898e-05
  []
  [injection_rate_massfrac_Na]
    initial_condition = 0.033298053919671
  []
  [injection_rate_massfrac_Sr]
    initial_condition = 1.2771866652177e-05
  []
  [injection_rate_massfrac_F]
    initial_condition = 5.5648860174073e-06
  []
  [injection_rate_massfrac_BOH]
    initial_condition = 0.0003758574621917
  []
  [injection_rate_massfrac_Br]
    initial_condition = 9.0315286107068e-05
  []
  [injection_rate_massfrac_Ba]
    initial_condition = 1.5637460875161e-07
  []
  [injection_rate_massfrac_Li]
    initial_condition = 8.3017067912701e-05
  []
  [injection_rate_massfrac_NO3]
    initial_condition = 0.00010958455036169
  []
  [injection_rate_massfrac_O2aq]
    initial_condition = -7.0806852373351e-05
  []
  [injection_rate_massfrac_H2O]
    initial_condition = 0.91032275033842
  []
  [rate_H]
  []
  [rate_Cl]
  []
  [rate_SO4]
  []
  [rate_HCO3]
  []
  [rate_SiO2aq]
  []
  [rate_Al]
  []
  [rate_Ca]
  []
  [rate_Mg]
  []
  [rate_Fe]
  []
  [rate_K]
  []
  [rate_Na]
  []
  [rate_Sr]
  []
  [rate_F]
  []
  [rate_BOH]
  []
  [rate_Br]
  []
  [rate_Ba]
  []
  [rate_Li]
  []
  [rate_NO3]
  []
  [rate_O2aq]
  []
  [rate_H2O]
  []
[]

[MultiApps]
  [react]
    type = TransientMultiApp
    input_files = aquifer_geochemistry.i
    clone_master_mesh = true
    execute_on = 'timestep_end'
  []
[]
[Transfers]
  [changes_due_to_flow]
    type = MultiAppCopyTransfer
    source_variable = 'rate_H rate_Cl rate_SO4 rate_HCO3 rate_SiO2aq rate_Al rate_Ca rate_Mg rate_Fe rate_K rate_Na rate_Sr rate_F rate_BOH rate_Br rate_Ba rate_Li rate_NO3 rate_O2aq rate_H2O temperature'
    variable = 'pf_rate_H pf_rate_Cl pf_rate_SO4 pf_rate_HCO3 pf_rate_SiO2aq pf_rate_Al pf_rate_Ca pf_rate_Mg pf_rate_Fe pf_rate_K pf_rate_Na pf_rate_Sr pf_rate_F pf_rate_BOH pf_rate_Br pf_rate_Ba pf_rate_Li pf_rate_NO3 pf_rate_O2aq pf_rate_H2O temperature'
    to_multi_app = react
  []
  [massfrac_from_geochem]
    type = MultiAppCopyTransfer
    source_variable = 'massfrac_H massfrac_Cl massfrac_SO4 massfrac_HCO3 massfrac_SiO2aq massfrac_Al massfrac_Ca massfrac_Mg massfrac_Fe massfrac_K massfrac_Na massfrac_Sr massfrac_F massfrac_BOH massfrac_Br massfrac_Ba massfrac_Li massfrac_NO3 massfrac_O2aq '
    variable = 'f_H f_Cl f_SO4 f_HCO3 f_SiO2aq f_Al f_Ca f_Mg f_Fe f_K f_Na f_Sr f_F f_BOH f_Br f_Ba f_Li f_NO3 f_O2aq '
    from_multi_app = react
  []
[]

(modules/solid_mechanics/test/tests/anisotropic_plasticity/ad_aniso_plasticity_x_rotate.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 10
    ny = 2
    nz = 2
    xmin = 0.0
    ymin = 0.0
    zmin = 0.0

    xmax = 10.0
    ymax = 1.0
    zmax = 1.0
  []
  [corner_node]
    type = ExtraNodesetGenerator
    new_boundary = '100'
    nodes = '3 69'
    input = gen
  []
  [corner_node_2]
    type = ExtraNodesetGenerator
    new_boundary = '101'
    nodes = '4 47'
    input = corner_node
  []
[]

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  volumetric_locking_correction = true
[]

[AuxVariables]
  [hydrostatic_stress]
    order = CONSTANT
    family = MONOMIAL
  []
  [plastic_strain_xx]
    order = CONSTANT
    family = MONOMIAL
  []
  [plastic_strain_xy]
    order = CONSTANT
    family = MONOMIAL
  []
  [plastic_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []
  [plastic_strain_zz]
    order = CONSTANT
    family = MONOMIAL
  []
  [stress_yy]
    order = CONSTANT
    family = MONOMIAL
  []
  [elastic_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [hydrostatic_stress]
    type = ADRankTwoScalarAux
    variable = hydrostatic_stress
    rank_two_tensor = stress
    scalar_type = Hydrostatic
  []
  [plasticity_strain_xx]
    type = ADRankTwoAux
    rank_two_tensor = trial_plasticity_plastic_strain
    variable = plastic_strain_xx
    index_i = 0
    index_j = 0
  []
  [plasticity_strain_xy]
    type = ADRankTwoAux
    rank_two_tensor = trial_plasticity_plastic_strain
    variable = plastic_strain_xy
    index_i = 0
    index_j = 1
  []
  [plasticity_strain_yy]
    type = ADRankTwoAux
    rank_two_tensor = trial_plasticity_plastic_strain
    variable = plastic_strain_yy
    index_i = 1
    index_j = 1
  []
  [plasticity_strain_zz]
    type = ADRankTwoAux
    rank_two_tensor = trial_plasticity_plastic_strain
    variable = plastic_strain_zz
    index_i = 2
    index_j = 2
  []
  [sigma_xx]
    type = ADRankTwoAux
    rank_two_tensor = stress
    variable = stress_xx
    index_i = 1
    index_j = 1
  []
  [elastic_strain_yy]
    type = ADRankTwoAux
    rank_two_tensor = elastic_strain
    variable = elastic_strain_yy
    index_i = 1
    index_j = 1
  []
  [sigma_yy]
    type = ADRankTwoAux
    rank_two_tensor = stress
    variable = stress_yy
    index_i = 1
    index_j = 1
  []
[]

[Functions]
  [pull]
    type = PiecewiseLinear
    x = '0 1e1 1e8'
    y = '0 -4e2 -4e2'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = FINITE
    generate_output = 'elastic_strain_xx stress_xx'
    use_automatic_differentiation = true
    add_variables = true
  []
[]

[Materials]

  [elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    youngs_modulus = 70000
    poissons_ratio = 0.25
  []

  [elastic_strain]
    type = ADComputeMultipleInelasticStress
    inelastic_models = "trial_plasticity"
    max_iterations = 50
    absolute_tolerance = 1e-16
  []

  [hill_tensor]
    type = ADHillConstants
    # F G H L M N
    hill_constants = "0.5829856 0.364424 0.6342174 2.0691375 2.3492325 1.814589"
    base_name = trial_plasticity
    rotation_angles =  '90 90 90'
  []

  [trial_plasticity]
    type = ADHillPlasticityStressUpdate
    hardening_constant = 2000.0
    yield_stress = 0.001 # was 200 for verification
    absolute_tolerance = 1e-14
    relative_tolerance = 1e-12
    base_name = trial_plasticity
    internal_solve_full_iteration_history = true
    max_inelastic_increment = 2.0e-6
    internal_solve_output_on = on_error
  []
[]

[BCs]
  [no_disp_x]
    type = ADDirichletBC
    variable = disp_x
    boundary = left
    value = 0.0
  []

  [no_disp_y]
    type = ADDirichletBC
    variable = disp_y
    boundary = 100
    value = 0.0
  []

  [no_disp_z]
    type = ADDirichletBC
    variable = disp_z
    boundary = 101
    value = 0.0
  []

  [Pressure]
    [Side1]
      boundary = right
      function = pull
    []
  []

[]

[Executioner]
  type = Transient

  solve_type = NEWTON
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu     superlu_dist'

  nl_rel_tol = 1e-11
  nl_abs_tol = 1.0e-14
  l_max_its = 90
  num_steps = 25
  [TimeStepper]
    type = IterationAdaptiveDT
    optimal_iterations = 30
    iteration_window = 9
    growth_factor = 1.05
    cutback_factor = 0.5
    timestep_limiting_postprocessor = matl_ts_min
    dt = 1.0e-5
    time_t = '0 3.4e-5 10'
    time_dt = '1.0e-5 1.0e-7 1.0e-7'
  []
  start_time = 0
  automatic_scaling = true
[]

[Postprocessors]
  [matl_ts_min]
    type = MaterialTimeStepPostprocessor
  []
  [max_disp_x]
    type = ElementExtremeValue
    variable = disp_x
  []
  [max_disp_y]
    type = ElementExtremeValue
    variable = disp_y
  []
  [max_hydro]
    type = ElementAverageValue
    variable = hydrostatic_stress
  []
  [dt]
    type = TimestepSize
  []
  [num_lin]
    type = NumLinearIterations
    outputs = console
  []
  [num_nonlin]
    type = NumNonlinearIterations
    outputs = console
  []
  [plasticity_strain_yy]
    type = ElementalVariableValue
    variable = plastic_strain_yy
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [elastic_strain_yy]
    type = ElementalVariableValue
    variable = elastic_strain_yy
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [sigma_yy]
    type = ElementalVariableValue
    variable = stress_yy
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [plasticity_strain_xx]
    type = ElementalVariableValue
    variable = plastic_strain_xx
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [elastic_strain_xx]
    type = ElementalVariableValue
    variable = elastic_strain_xx
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [sigma_xx]
    type = ElementalVariableValue
    variable = stress_xx
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [plasticity_strain_zz]
    type = ElementalVariableValue
    variable = plastic_strain_zz
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
[]

[Outputs]
  csv = true
  perf_graph = true
[]

(modules/solid_mechanics/test/tests/uel/small_test_uel_states_fields.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 20
    ny = 10
    # nx = 10
    # ny = 3
    xmax = 10
    ymax = 3
    elem_type = TRI3
  []
  [pin]
    type = ExtraNodesetGenerator
    nodes = 106
    new_boundary = pin
    input = gen
  []
  displacements = 'disp_x disp_y'
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
[]

[AuxVariables]
  [temperature]
    initial_condition = 1500
  []
  [voltage]
    initial_condition = 210
  []
[]

[AuxKernels]
  [temperature]
    type = FunctionAux
    function = temperature_function
    variable = temperature
  []
  [voltage]
    type = FunctionAux
    function = voltage_function
    variable = voltage
  []
[]

[Functions]
  [voltage_function]
    type = PiecewiseLinear
    x = '0 15'
    y = '210 450'
  []
  [temperature_function]
    type = PiecewiseLinear
    x = '0 15'
    y = '1500 800'
  []
[]

[BCs]
  [left_x]
    type = DirichletBC
    variable = disp_x
    boundary = left
    value = 0
  []
  [left_y]
    type = DirichletBC
    variable = disp_y
    boundary = pin
    value = 0
  []

  inactive = 'right_dirichlet'
  # inactive = 'right_neumann'
  [right_neumann]
    type = FunctionNeumannBC
    variable = disp_x
    function = t
    boundary = right
  []
  [right_dirichlet]
    type = FunctionDirichletBC
    variable = disp_x
    function = t/10
    boundary = right
  []
[]

[UserObjects]
  [uel]
    type = AbaqusUserElement
    variables = 'disp_x disp_y'
    plugin = ../../../examples/uel_tri_states_tests/uel
    use_displaced_mesh = false
    num_state_vars = 8
    constant_properties = '100 0.3' # E nu
    external_fields = 'temperature voltage'
    extra_vector_tags = 'kernel_residual'
  []
[]

[Problem]
  kernel_coverage_check = false
  extra_tag_vectors = 'kernel_residual'
[]

[AuxVariables]
  [res_x]
  []
  [res_y]
  []
[]

[AuxKernels]
  [res_x]
    type = TagVectorAux
    variable = res_x
    v = disp_x
    vector_tag = kernel_residual
  []
  [res_y]
    type = TagVectorAux
    variable = res_y
    v = disp_y
    vector_tag = kernel_residual
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  dt = 1
  num_steps = 15
[]

[Postprocessors]
  [delta_l]
    type = SideAverageValue
    variable = disp_x
    boundary = right
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [V]
    type = ElementIntegralMaterialProperty
    mat_prop = 1
    use_displaced_mesh = true
    execute_on = 'INITIAL TIMESTEP_END'
  []
[]

[Outputs]
  exodus = true
  csv = true
[]

(test/tests/mortar/periodic_segmental_constraint/periodic_aux2d.i)

[Mesh]
  [left_block]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = -1.0
    xmax = 1.0
    ymin = -1.0
    ymax = 1.0
    nx = 4
    ny = 4
    elem_type = QUAD9
  []
  [left_block_sidesets]
    type = RenameBoundaryGenerator
    input = left_block
    old_boundary = '0 1 2 3'
    new_boundary = '10 11 12 13'
  []
  [left_block_id]
    type = SubdomainIDGenerator
    input = left_block_sidesets
    subdomain_id = 1
  []
  [left]
    type = LowerDBlockFromSidesetGenerator
    input = left_block_id
    sidesets = '13'
    new_block_id = '10003'
    new_block_name = 'secondary_left'
  []
  [right]
    type = LowerDBlockFromSidesetGenerator
    input = left
    sidesets = '11'
    new_block_id = '10001'
    new_block_name = 'primary_right'
  []
  [bottom]
    type = LowerDBlockFromSidesetGenerator
    input = right
    sidesets = '10'
    new_block_id = '10000'
    new_block_name = 'secondary_bottom'
  []
  [top]
    type = LowerDBlockFromSidesetGenerator
    input = bottom
    sidesets = '12'
    new_block_id = '10002'
    new_block_name = 'primary_top'
  []

  [corner_node]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node'
    nodes = '0'
    input = top
  []
[]

[Variables]
  [u]
    order = SECOND
    family = LAGRANGE
  []
  [./lm1]
    order = FIRST
    family = LAGRANGE
    block = secondary_left
  [../]
  [./lm2]
    order = FIRST
    family = LAGRANGE
    block = secondary_bottom
  [../]
[]

[AuxVariables]
  [sigma]
    order = SECOND
    family = SCALAR
  []
  [epsilon]
    order = SECOND
    family = SCALAR
  []
[]

[AuxScalarKernels]
  [sigma]
    type = FunctionScalarAux
    variable = sigma
    function = '1 1'
    execute_on = initial #timestep_end
  []
  [epsilon]
    type = FunctionScalarAux
    variable = epsilon
    function = '-1 -1'
    execute_on = initial #timestep_end
  []
[]

[Kernels]
  [diff1]
    type = Diffusion
    variable = u
    block = 1
  []
[]

[Problem]
  kernel_coverage_check = false
  error_on_jacobian_nonzero_reallocation = true
[]

[BCs]
  [fix_right]
    type = DirichletBC
    variable = u
    boundary = pinned_node
    value = 0
  []
[]

[Constraints]
  [mortarlr]
    type = EqualValueConstraint
    primary_boundary = '11'
    secondary_boundary = '13'
    primary_subdomain = 'primary_right'
    secondary_subdomain = 'secondary_left'
    secondary_variable = u
    variable = lm1
    correct_edge_dropping = true
  []
  [periodiclr]
    type = PeriodicSegmentalConstraint
    primary_boundary = '11'
    secondary_boundary = '13'
    primary_subdomain = 'primary_right'
    secondary_subdomain = 'secondary_left'
    secondary_variable = u
    epsilon = epsilon
    sigma = sigma
    variable = lm1
    correct_edge_dropping = true
    compute_scalar_residuals = false
  []
  [mortarbt]
    type = EqualValueConstraint
    primary_boundary = '12'
    secondary_boundary = '10'
    primary_subdomain = 'primary_top'
    secondary_subdomain = 'secondary_bottom'
    secondary_variable = u
    variable = lm2
    correct_edge_dropping = true
  []
  [periodicbt]
    type = PeriodicSegmentalConstraint
    primary_boundary = '12'
    secondary_boundary = '10'
    primary_subdomain = 'primary_top'
    secondary_subdomain = 'secondary_bottom'
    secondary_variable = u
    epsilon = epsilon
    sigma = sigma
    variable = lm2
    correct_edge_dropping = true
    compute_scalar_residuals = false
  []
[]

[Preconditioning]
  [smp]
    full = true
    type = SMP
  []
[]

[Executioner]
  type = Steady
  petsc_options_iname = '-pc_type -pc_factor_shift_type -pc_factor_shift_amount'
  petsc_options_value = 'lu       NONZERO               1e-15'
  solve_type = NEWTON
[]

[Outputs]
  csv = true
[]

(modules/solid_mechanics/test/tests/ad_anisotropic_creep/ad_aniso_creep_integration_error.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 10
    ny = 2
    nz = 2
    xmin = 0.0
    ymin = 0.0
    zmin = 0.0

    xmax = 10.0
    ymax = 1.0
    zmax = 1.0
  []
  [corner_node]
    type = ExtraNodesetGenerator
    new_boundary = '100'
    nodes = '3 69'
    input = gen
  []
  [corner_node_2]
    type = ExtraNodesetGenerator
    new_boundary = '101'
    nodes = '4 47'
    input = corner_node
  []
[]

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  volumetric_locking_correction = true
[]

[AuxVariables]
  [hydrostatic_stress]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_xx]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_xy]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [hydrostatic_stress]
    type = ADRankTwoScalarAux
    variable = hydrostatic_stress
    rank_two_tensor = stress
    scalar_type = Hydrostatic
  []
  [creep_strain_xx]
    type = ADRankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_xx
    index_i = 0
    index_j = 0
  []
  [creep_strain_xy]
    type = ADRankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_xy
    index_i = 0
    index_j = 1
  []
  [creep_strain_yy]
    type = ADRankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_yy
    index_i = 1
    index_j = 1
  []
  [sigma_xx]
    type = ADRankTwoAux
    rank_two_tensor = stress
    variable = stress_xx
    index_i = 1
    index_j = 1
  []
[]

[Functions]
  [pull]
    type = PiecewiseLinear
    x = '0 1.0'
    y = '0 -4e1'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = FINITE
    generate_output = 'elastic_strain_xx stress_xx'
    use_automatic_differentiation = true
    add_variables = true
  []
[]

[Materials]
  [elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    youngs_modulus = 7000
    poissons_ratio = 0.0
  []

  [elastic_strain]
    type = ADComputeMultipleInelasticStress
    inelastic_models = "trial_creep_two"
    max_iterations = 50
    absolute_tolerance = 1e-16
  []

  [hill_tensor]
    type = ADHillConstants
    # F G H L M N
    hill_constants = "0.5 0.25 0.3866 1.6413 1.6413 1.2731"
  []

  [trial_creep_two]
    type = ADHillCreepStressUpdate
    coefficient = 1e-16
    n_exponent = 9
    m_exponent = 0
    activation_energy = 0
    max_inelastic_increment = 1.0e-4
    absolute_tolerance = 1e-20
    relative_tolerance = 1e-20
    max_integration_error = 1.0e-5
  []
[]

[BCs]
  [no_disp_x]
    type = ADDirichletBC
    variable = disp_x
    boundary = left
    value = 0.0
  []

  [no_disp_y]
    type = ADDirichletBC
    variable = disp_y
    boundary = 100
    value = 0.0
  []

  [no_disp_z]
    type = ADDirichletBC
    variable = disp_z
    boundary = 101
    value = 0.0
  []

  [Pressure]
    [Side1]
      boundary = right
      function = pull
    []
  []

[]

[Executioner]
  type = Transient

  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu     superlu_dist'

  nl_rel_tol = 1.0e-13
  nl_abs_tol = 1.0e-13
  l_max_its = 10
  end_time = 1.65e-1
  dt = 2.5e-2
  start_time = 0
  automatic_scaling = true

  [./TimeStepper]
  type = IterationAdaptiveDT
  dt = 2.5e-2
  time_t = '0.0  10.0'
  time_dt = '2.5e-2 2.5e-2 '
  optimal_iterations = 30
  iteration_window = 9
  growth_factor = 1.5
  cutback_factor = 0.5
  timestep_limiting_postprocessor = matl_ts_min
  reject_large_step = true
  reject_large_step_threshold = 0.999
[../]
[]

[Postprocessors]
  [time_step_size]
    type = TimestepSize
  []
  [matl_ts_min]
    type = MaterialTimeStepPostprocessor
  []
  [max_disp_x]
    type = ElementExtremeValue
    variable = disp_x
  []
  [max_disp_y]
    type = ElementExtremeValue
    variable = disp_y
  []
  [max_hydro]
    type = ElementAverageValue
    variable = hydrostatic_stress
  []
  [dt]
    type = TimestepSize
  []
  [num_lin]
    type = NumLinearIterations
    outputs = console
  []
  [num_nonlin]
    type = NumNonlinearIterations
    outputs = console
  []
  [creep_strain_xx]
    type = ElementalVariableValue
    variable = creep_strain_xx
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [elastic_strain_xx]
    type = ElementalVariableValue
    variable = elastic_strain_xx
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [sigma_xx]
    type = ElementalVariableValue
    variable = stress_xx
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
[]

[Outputs]
  csv = true
  exodus = true
  perf_graph = true
[]

(modules/navier_stokes/test/tests/finite_element/ins/lid_driven/lid_driven_stabilized.i)

[GlobalParams]
  gravity = '0 0 0'
  laplace = true
  integrate_p_by_parts = true
  family = LAGRANGE
  order = FIRST

  # There are multiple types of stabilization possible in incompressible
  # Navier Stokes. The user can specify supg = true to apply streamline
  # upwind petrov-galerkin stabilization to the momentum equations. This
  # is most useful for high Reynolds numbers, e.g. when inertial effects
  # dominate over viscous effects. The user can also specify pspg = true
  # to apply pressure stabilized petrov-galerkin stabilization to the mass
  # equation. PSPG is a form of Galerkin Least Squares. This stabilization
  # allows equal order interpolations to be used for pressure and velocity.
  # Finally, the alpha parameter controls the amount of stabilization.
  # For PSPG, decreasing alpha leads to increased accuracy but may induce
  # spurious oscillations in the pressure field. Some numerical experiments
  # suggest that alpha between .1 and 1 may be optimal for accuracy and
  # robustness.
  supg = true
  pspg = true
  alpha = 1e-1
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 1.0
    ymin = 0
    ymax = 1.0
    nx = 64
    ny = 64
    elem_type = QUAD4
  []
  [./corner_node]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node'
    nodes = '0'
    input = gen
  [../]
[]

[Variables]
  [./vel_x]
  [../]

  [./vel_y]
  [../]

  [./p]
  [../]
[]

[Kernels]
  # mass
  [./mass]
    type = INSMass
    variable = p
    u = vel_x
    v = vel_y
    pressure = p
  [../]

  # x-momentum, space
  [./x_momentum_space]
    type = INSMomentumLaplaceForm
    variable = vel_x
    u = vel_x
    v = vel_y
    pressure = p
    component = 0
  [../]

  # y-momentum, space
  [./y_momentum_space]
    type = INSMomentumLaplaceForm
    variable = vel_y
    u = vel_x
    v = vel_y
    pressure = p
    component = 1
  [../]
[]

[BCs]
  [./x_no_slip]
    type = DirichletBC
    variable = vel_x
    boundary = 'bottom right left'
    value = 0.0
  [../]

  [./lid]
    type = FunctionDirichletBC
    variable = vel_x
    boundary = 'top'
    function = 'lid_function'
  [../]

  [./y_no_slip]
    type = DirichletBC
    variable = vel_y
    boundary = 'bottom right top left'
    value = 0.0
  [../]

  [./pressure_pin]
    type = DirichletBC
    variable = p
    boundary = 'pinned_node'
    value = 0
  [../]
[]

[Materials]
  [./const]
    type = GenericConstantMaterial
    block = 0
    prop_names = 'rho mu'
    prop_values = '1  1'
  [../]
[]

[Functions]
  [./lid_function]
    # We pick a function that is exactly represented in the velocity
    # space so that the Dirichlet conditions are the same regardless
    # of the mesh spacing.
    type = ParsedFunction
    expression = '4*x*(1-x)'
  [../]
[]

[Preconditioning]
  [./SMP]
    type = SMP
    full = true
    solve_type = 'NEWTON'
  [../]
[]

[Executioner]
  type = Steady
  petsc_options_iname = '-pc_type -pc_asm_overlap -sub_pc_type -sub_pc_factor_levels'
  petsc_options_value = 'asm      2               ilu          4'
  line_search = 'none'
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-13
  nl_max_its = 6
  l_tol = 1e-6
  l_max_its = 500
[]

[Outputs]
  exodus = true
  print_linear_converged_reason = false
  print_nonlinear_converged_reason = false
[]

[Postprocessors]
  [lin]
    type = NumLinearIterations
  []
  [nl]
    type = NumNonlinearIterations
  []
  [lin_tot]
    type = CumulativeValuePostprocessor
    postprocessor = 'lin'
  []
  [nl_tot]
    type = CumulativeValuePostprocessor
    postprocessor = 'nl'
  []
[]

(test/tests/mortar/periodic_segmental_constraint/penalty_periodic_simple2d.i)

[Mesh]
  [left_block]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = -1.0
    xmax = 1.0
    ymin = -1.0
    ymax = 1.0
    nx = 2
    ny = 2
    elem_type = QUAD4
  []
  [left_block_sidesets]
    type = RenameBoundaryGenerator
    input = left_block
    old_boundary = '0 1 2 3'
    new_boundary = '10 11 12 13'
  []
  [left_block_id]
    type = SubdomainIDGenerator
    input = left_block_sidesets
    subdomain_id = 1
  []
  [left]
    type = LowerDBlockFromSidesetGenerator
    input = left_block_id
    sidesets = '13'
    new_block_id = '10003'
    new_block_name = 'secondary_left'
  []
  [right]
    type = LowerDBlockFromSidesetGenerator
    input = left
    sidesets = '11'
    new_block_id = '10001'
    new_block_name = 'primary_right'
  []
  [bottom]
    type = LowerDBlockFromSidesetGenerator
    input = right
    sidesets = '10'
    new_block_id = '10000'
    new_block_name = 'secondary_bottom'
  []
  [top]
    type = LowerDBlockFromSidesetGenerator
    input = bottom
    sidesets = '12'
    new_block_id = '10002'
    new_block_name = 'primary_top'
  []

  [corner_node]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node'
    nodes = '0'
    input = top
  []
[]

[Variables]
  [u]
    order = FIRST
    family = LAGRANGE
  []
  [epsilon]
    order = SECOND
    family = SCALAR
  []
[]

[AuxVariables]
  [sigma]
    order = SECOND
    family = SCALAR
  []
[]

[AuxScalarKernels]
  [sigma]
    type = FunctionScalarAux
    variable = sigma
    function = '1 2'
    execute_on = initial #timestep_end
  []
[]

[Kernels]
  [diff1]
    type = Diffusion
    variable = u
    block = 1
  []
[]

[Problem]
  kernel_coverage_check = false
  error_on_jacobian_nonzero_reallocation = true
[]

[BCs]
  [fix_right]
    type = DirichletBC
    variable = u
    boundary = pinned_node
    value = 0
  []
[]

[Constraints]
  [mortarlr]
    type = PenaltyEqualValueConstraint
    primary_boundary = '11'
    secondary_boundary = '13'
    primary_subdomain = 'primary_right'
    secondary_subdomain = 'secondary_left'
    secondary_variable = u
    correct_edge_dropping = true
    penalty_value = 1.e2
  []
  [periodiclr]
    type = PenaltyPeriodicSegmentalConstraint
    primary_boundary = '11'
    secondary_boundary = '13'
    primary_subdomain = 'primary_right'
    secondary_subdomain = 'secondary_left'
    secondary_variable = u
    epsilon = epsilon
    sigma = sigma
    correct_edge_dropping = true
    penalty_value = 1.e2
  []
  [mortarbt]
    type = PenaltyEqualValueConstraint
    primary_boundary = '12'
    secondary_boundary = '10'
    primary_subdomain = 'primary_top'
    secondary_subdomain = 'secondary_bottom'
    secondary_variable = u
    correct_edge_dropping = true
    penalty_value = 1.e2
  []
  [periodicbt]
    type = PenaltyPeriodicSegmentalConstraint
    primary_boundary = '12'
    secondary_boundary = '10'
    primary_subdomain = 'primary_top'
    secondary_subdomain = 'secondary_bottom'
    secondary_variable = u
    epsilon = epsilon
    sigma = sigma
    correct_edge_dropping = true
    penalty_value = 1.e2
  []
[]

[Executioner]
  type = Steady
  solve_type = 'PJFNK'
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  csv = true
[]

(modules/navier_stokes/test/tests/finite_element/ins/lid_driven/lid_driven_chorin.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 1.0
    ymin = 0
    ymax = 1.0
    nx = 40
    ny = 40
    elem_type = QUAD4
  []
  [corner_node]
    type = ExtraNodesetGenerator
    new_boundary = 99
    nodes = '0'
    input = gen
  []
[]

[Variables]
  # x-velocity
  [u]
    order = FIRST
    family = LAGRANGE

    [InitialCondition]
      type = ConstantIC
      value = 0.0
    []
  []

  # y-velocity
  [v]
    order = FIRST
    family = LAGRANGE

    [InitialCondition]
      type = ConstantIC
      value = 0.0
    []
  []

  # x-star velocity
  [u_star]
    order = FIRST
    family = LAGRANGE

    [InitialCondition]
      type = ConstantIC
      value = 0.0
    []
  []

  # y-star velocity
  [v_star]
    order = FIRST
    family = LAGRANGE

    [InitialCondition]
      type = ConstantIC
      value = 0.0
    []
  []

  # Pressure
  [p]
    order = FIRST
    family = LAGRANGE

    [InitialCondition]
      type = ConstantIC
      value = 0
    []
  []
[]

[Kernels]
  [x_chorin_predictor]
    type = INSChorinPredictor
    variable = u_star
    u = u
    v = v
    u_star = u_star
    v_star = v_star
    component = 0
    predictor_type = 'new'
  []

  [y_chorin_predictor]
    type = INSChorinPredictor
    variable = v_star
    u = u
    v = v
    u_star = u_star
    v_star = v_star
    component = 1
    predictor_type = 'new'
  []

  [x_chorin_corrector]
    type = INSChorinCorrector
    variable = u
    u_star = u_star
    v_star = v_star
    pressure = p
    component = 0
  []

  [y_chorin_corrector]
    type = INSChorinCorrector
    variable = v
    u_star = u_star
    v_star = v_star
    pressure = p
    component = 1
  []

  [chorin_pressure_poisson]
    type = INSChorinPressurePoisson
    variable = p
    u_star = u_star
    v_star = v_star
  []
[]

[BCs]
  [u_no_slip]
    type = DirichletBC
    variable = u
    preset = false
    boundary = 'bottom right left'
    value = 0.0
  []

  [u_lid]
    type = DirichletBC
    variable = u
    preset = false
    boundary = 'top'
    value = 100.0
  []

  [v_no_slip]
    type = DirichletBC
    variable = v
    preset = false
    boundary = 'bottom right top left'
    value = 0.0
  []

  # Make u_star satsify all the same variables as the real velocity.
  [u_star_no_slip]
    type = DirichletBC
    variable = u_star
    preset = false
    boundary = 'bottom right left'
    value = 0.0
  []

  [u_star_lid]
    type = DirichletBC
    variable = u_star
    preset = false
    boundary = 'top'
    value = 100.0
  []

  [v_star_no_slip]
    type = DirichletBC
    variable = v_star
    preset = false
    boundary = 'bottom right top left'
    value = 0.0
  []

  # With solid walls everywhere, we specify dp/dn=0, i.e the
  # "natural BC" for pressure.  Technically the problem still
  # solves without pinning the pressure somewhere, but the pressure
  # bounces around a lot during the solve, possibly because of
  # the addition of arbitrary constants.
  [pressure_pin]
    type = DirichletBC
    variable = p
    preset = false
    boundary = '99'
    value = 0
  []
[]

[Materials]
  [const]
    type = GenericConstantMaterial
    block = 0
    # rho = 1000    # kg/m^3
    # mu = 0.798e-3 # Pa-s at 30C
    # cp = 4.179e3  # J/kg-K at 30C
    # k = 0.58      # W/m-K at ?C

    # Dummy parameters
    prop_names = 'rho mu cp k'
    prop_values = '1  1  1  1'
  []
[]

[Preconditioning]
  #active = 'FDP_Newton'
  #active = 'SMP_PJFNK'
  active = 'SMP_Newton'

  [FDP_Newton]
    type = FDP
    full = true

    solve_type = 'NEWTON'

    #petsc_options_iname = '-mat_fd_coloring_err'
    #petsc_options_value = '1.e-10'
  []

  # For some reason, nonlinear convergence with JFNK is poor, but it
  # seems to be OK for SMP_Newton.  This may indicate a a scaling issue
  # in the JFNK case....
  [SMP_PJFNK]
    type = SMP
    full = true

    #Preconditioned JFNK (default)
    solve_type = 'PJFNK'

  []

  [SMP_Newton]
    type = SMP
    full = true

    solve_type = 'NEWTON'

  []
[]

[Executioner]
  type = Transient
  # Note: the explicit case with lid velocity = 100 and a 40x40 was unstable
  # for dt=1.e-4, even though the restriction should be dt < dx/|u| = 1/4000 = 2.5e-4
  #
  dt = 1.e-3
  dtmin = 1.e-6
  petsc_options_iname = '-ksp_gmres_restart '
  petsc_options_value = '300                '

  line_search = 'none'

  nl_rel_tol = 1e-12
  nl_max_its = 6
  l_max_its = 300
  start_time = 0.0
  num_steps = 5

  automatic_scaling = true
  verbose = true
  compute_scaling_once = false
[]

[Debug]
  show_var_residual_norms = true
[]

[Outputs]
  file_base = lid_driven_chorin_out
  exodus = true
[]

(modules/combined/test/tests/optimization/optimization_density_update/top_opt_2d.i)

vol_frac = 0.4
E0 = 1e5
Emin = 1e-4
power = 2
[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  [MeshGenerator]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 40
    ny = 20
    xmin = 0
    xmax = 20
    ymin = 0
    ymax = 10
  []
  [node]
    type = ExtraNodesetGenerator
    input = MeshGenerator
    new_boundary = pull
    nodes = 0
  []
[]

[AuxVariables]
  [sensitivity]
    family = MONOMIAL
    order = FIRST
    initial_condition = -1.0
    [AuxKernel]
      type = MaterialRealAux
      variable = sensitivity
      property = sensitivity
      execute_on = LINEAR
    []
  []
  [compliance]
    family = MONOMIAL
    order = CONSTANT
  []
  [Dc]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = -1.0
  []
  [mat_den]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = ${vol_frac}
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = SMALL
    add_variables = true
    incremental = false
  []
[]

[BCs]
  [no_x]
    type = DirichletBC
    variable = disp_x
    boundary = right
    value = 0.0
  []
  [no_y]
    type = DirichletBC
    variable = disp_y
    boundary = right
    value = 0.0
  []

[]
[NodalKernels]
  [pull]
    type = NodalGravity
    variable = disp_y
    boundary = pull
    gravity_value = -1
    mass = 1
  []
[]
[Materials]
  [elasticity_tensor]
    type = ComputeVariableIsotropicElasticityTensor
    youngs_modulus = E_phys
    poissons_ratio = poissons_ratio
    args = 'mat_den'
  []
  [E_phys]
    type = DerivativeParsedMaterial
    # Emin + (density^penal) * (E0 - Emin)
    expression = '${Emin} + (mat_den ^ ${power}) * (${E0}-${Emin})'
    coupled_variables = 'mat_den'
    property_name = E_phys
  []
  [poissons_ratio]
    type = GenericConstantMaterial
    prop_names = poissons_ratio
    prop_values = 0.3
  []
  [stress]
    type = ComputeLinearElasticStress
  []
  [dc]
    type = ComplianceSensitivity
    design_density = mat_den
    youngs_modulus = E_phys
    incremental = false
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]
[UserObjects]
  [rad_avg]
    type = RadialAverage
    radius = 0.5
    weights = constant
    prop_name = sensitivity
    execute_on = TIMESTEP_END
    force_preaux = true
    execution_order_group = -1
  []
  [update]
    type = DensityUpdate
    density_sensitivity = Dc
    design_density = mat_den
    volume_fraction = ${vol_frac}
    execute_on = TIMESTEP_BEGIN
  []
  [calc_sense]
    type = SensitivityFilter
    density_sensitivity = Dc
    design_density = mat_den
    filter_UO = rad_avg
    execute_on = TIMESTEP_END
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type '
  petsc_options_value = 'lu'
  nl_abs_tol = 1e-10

  start_time = 0.0
  dt = 1.0
  num_steps = 50
[]

[Outputs]
  [out]
    type = Exodus
    time_step_interval = 10
  []
[]

(modules/combined/test/tests/optimization/optimization_density_update/top_opt_2d_pde_filter.i)

vol_frac = 0.4
E0 = 1e5
Emin = 1e-4
power = 2
[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  [MeshGenerator]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 40
    ny = 20
    xmin = 0
    xmax = 20
    ymin = 0
    ymax = 10
  []
  [node]
    type = ExtraNodesetGenerator
    input = MeshGenerator
    new_boundary = pull
    nodes = 0
  []
[]

[Variables]
  [Dc]
    initial_condition = -1.0
  []
[]

[AuxVariables]
  [sensitivity]
    family = MONOMIAL
    order = FIRST
    initial_condition = -1.0
    [AuxKernel]
      type = MaterialRealAux
      variable = sensitivity
      property = sensitivity
      execute_on = LINEAR
    []
  []

  [compliance]
    family = MONOMIAL
    order = CONSTANT
  []

  [mat_den]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = ${vol_frac}
  []
  [Dc_elem]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = -1.0
    [AuxKernel]
      type = ProjectionAux
      variable = Dc_elem
      v = Dc
      execute_on = 'TIMESTEP_END'
    []
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = SMALL
    add_variables = true
    incremental = false
  []
[]

[Kernels]
  [diffusion]
    type = FunctionDiffusion
    variable = Dc
    function = 0.05
  []
  [potential]
    type = Reaction
    variable = Dc
  []
  [source]
    type = CoupledForce
    variable = Dc
    v = sensitivity
  []
[]

[BCs]
  [no_x]
    type = DirichletBC
    variable = disp_x
    boundary = right
    value = 0.0
  []
  [no_y]
    type = DirichletBC
    variable = disp_y
    boundary = right
    value = 0.0
  []
  [boundary_penalty]
    type = ADRobinBC
    variable = Dc
    boundary = 'left top'
    coefficient = 10
  []
[]
[NodalKernels]
  [pull]
    type = NodalGravity
    variable = disp_y
    boundary = pull
    gravity_value = -1
    mass = 1
  []
[]
[Materials]
  [elasticity_tensor]
    type = ComputeVariableIsotropicElasticityTensor
    youngs_modulus = E_phys
    poissons_ratio = poissons_ratio
    args = 'mat_den'
  []
  [E_phys]
    type = DerivativeParsedMaterial
    # Emin + (density^penal) * (E0 - Emin)
    expression = '${Emin} + (mat_den ^ ${power}) * (${E0}-${Emin})'
    coupled_variables = 'mat_den'
    property_name = E_phys
  []
  [poissons_ratio]
    type = GenericConstantMaterial
    prop_names = poissons_ratio
    prop_values = 0.3
  []
  [stress]
    type = ComputeLinearElasticStress
  []
  [dc]
    type = ComplianceSensitivity
    design_density = mat_den
    youngs_modulus = E_phys
    incremental = false
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[UserObjects]
  [update]
    type = DensityUpdate
    density_sensitivity = Dc_elem
    design_density = mat_den
    volume_fraction = ${vol_frac}
    execute_on = TIMESTEP_BEGIN
    force_postaux = true
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type '
  petsc_options_value = 'lu'
  nl_abs_tol = 1e-10
  line_search = none
  dt = 1.0
  num_steps = 30
[]

[Outputs]
  [out]
    type = Exodus
    time_step_interval = 10
  []
[]

(modules/solid_mechanics/test/tests/uel/small_test_umat_states_fields.i)

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 20
    ny = 10
    xmax = 10
    ymax = 3
    elem_type = TRI3
  []
  [pin]
    type = ExtraNodesetGenerator
    nodes = 106
    new_boundary = pin
    input = gen
  []
  displacements = 'disp_x disp_y'
[]

[AuxVariables]
  [temperature]
    initial_condition = 1500
  []
  [voltage]
    initial_condition = 210
  []
[]

[AuxKernels]
  [temperature]
    type = FunctionAux
    function = temperature_function
    variable = temperature
  []
  [voltage]
    type = FunctionAux
    function = voltage_function
    variable = voltage
  []
[]

[Functions]
  [voltage_function]
    type = PiecewiseLinear
    x = '0 15'
    y = '210 450'
  []
  [temperature_function]
    type = PiecewiseLinear
    x = '0 15'
    y = '1500 800'
  []
[]

[BCs]
  [left_x]
    type = DirichletBC
    variable = disp_x
    boundary = left
    value = 0
  []
  [left_y]
    type = DirichletBC
    variable = disp_y
    boundary = pin
    value = 0
  []

  inactive = 'right_dirichlet'
  [right_neumann]
    type = FunctionNeumannBC
    variable = disp_x
    function = t
    boundary = right
  []
  [right_dirichlet]
    type = FunctionDirichletBC
    variable = disp_x
    function = t/10
    boundary = right
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    add_variables = true
    strain = SMALL
    incremental = true
    extra_vector_tags = 'kernel_residual'
  []
[]

[Materials]
  [umat]
    type = AbaqusUMATStress
    constant_properties = '100 0.3'
    plugin = '../../plugins/small_elastic_tri_states'
    num_state_vars = 2
    use_one_based_indexing = false
    temperature = 'temperature'
    external_fields = 'voltage'
  []
[]

[Problem]
  kernel_coverage_check = false
  extra_tag_vectors = 'kernel_residual'
[]

[AuxVariables]
  [res_x]
  []
  [res_y]
  []
[]

[AuxKernels]
  [res_x]
    type = TagVectorAux
    variable = res_x
    v = disp_x
    vector_tag = kernel_residual
  []
  [res_y]
    type = TagVectorAux
    variable = res_y
    v = disp_y
    vector_tag = kernel_residual
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  dt = 1
  num_steps = 15
[]

[Postprocessors]
  [delta_l]
    type = SideAverageValue
    variable = disp_x
    boundary = right
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [V]
    type = ElementIntegralMaterialProperty
    mat_prop = 1
    use_displaced_mesh = true
    execute_on = 'INITIAL TIMESTEP_END'
  []
[]

[Outputs]
  exodus = true
  csv = true
[]

(modules/combined/examples/geochem-porous_flow/forge/porous_flow.i)

# Input file modified from RobPodgorney version
# - 2D instead of 3D with different resolution.  Effectively this means a 1m height of RobPodgorney aquifer is simulated.  RobPodgorney total mass flux is 2.5kg/s meaning 0.25kg/s is appropriate here
# - Celsius instead of Kelvin
# - no use of PorousFlowPointEnthalpySourceFromPostprocessor since that is not yet merged into MOOSE: a DirichletBC is used instead
# - Use of PorousFlowFullySaturated instead of PorousFlowUnsaturated, and the save_component_rate_in feature to record the change in kg of each species at each node for passing to the Geochem simulation
# - MultiApps and Transfers to transfer information between this simulation and the aquifer_geochemistry.i simulation
[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 225
    ny = 200
    xmin = -400
    xmax = 500
    ymin = -400
    ymax = 400
  []
  [injection_node]
    input = gen
    type = ExtraNodesetGenerator
    new_boundary = injection_node
    coord = '0 0 0'
  []
[]

[GlobalParams]
  PorousFlowDictator = dictator
  gravity = '0 0 0'
[]

[Variables]
  [f_H]
    initial_condition = 8.201229858451E-07
  []
  [f_Na]
    initial_condition = 2.281094143525E-03
  []
  [f_K]
    initial_condition = 2.305489507836E-04
  []
  [f_Ca]
    initial_condition = 5.818776782059E-04
  []
  [f_Mg]
    initial_condition = 1.539513498238E-07
  []
  [f_SiO2]
    initial_condition = 2.691822196469E-04
  []
  [f_Al]
    initial_condition = 4.457519474122E-08
  []
  [f_Cl]
    initial_condition = 4.744309776594E-03
  []
  [f_SO4]
    initial_condition = 9.516650880811E-06
  []
  [f_HCO3]
    initial_condition = 5.906126982324E-05
  []
  [porepressure]
    initial_condition = 20E6
  []
  [temperature]
    initial_condition = 220 # degC
    scaling = 1E-6 # fluid enthalpy is roughly 1E6
  []
[]

[BCs]
  [source_temperature]
    type = DirichletBC
    boundary = injection_node
    variable = temperature
    value = 70 # degC
  []
[]

[DiracKernels]
  [inject_H]
    type = PorousFlowPointSourceFromPostprocessor
    point = ' 0 0 0'
    mass_flux = 4.790385871045E-08
    variable = f_H
  []
  [inject_Na]
    type = PorousFlowPointSourceFromPostprocessor
    point = ' 0 0 0'
    mass_flux = 7.586252963780E-07
    variable = f_Na
  []
  [inject_K]
    type = PorousFlowPointSourceFromPostprocessor
    point = ' 0 0 0'
    mass_flux = 2.746517625125E-07
    variable = f_K
  []
  [inject_Ca]
    type = PorousFlowPointSourceFromPostprocessor
    point = ' 0 0 0'
    mass_flux = 7.775129478597E-07
    variable = f_Ca
  []
  [inject_Mg]
    type = PorousFlowPointSourceFromPostprocessor
    point = ' 0 0 0'
    mass_flux = 1.749872109005E-07
    variable = f_Mg
  []
  [inject_SiO2]
    type = PorousFlowPointSourceFromPostprocessor
    point = ' 0 0 0'
    mass_flux = 4.100547515915E-06
    variable = f_SiO2
  []
  [inject_Al]
    type = PorousFlowPointSourceFromPostprocessor
    point = ' 0 0 0'
    mass_flux = 2.502408592080E-08
    variable = f_Al
  []
  [inject_Cl]
    type = PorousFlowPointSourceFromPostprocessor
    point = ' 0 0 0'
    mass_flux = 1.997260386272E-06
    variable = f_Cl
  []
  [inject_SO4]
    type = PorousFlowPointSourceFromPostprocessor
    point = ' 0 0 0'
    mass_flux = 2.497372164191E-07
    variable = f_SO4
  []
  [inject_HCO3]
    type = PorousFlowPointSourceFromPostprocessor
    point = ' 0 0 0'
    mass_flux = 5.003150992902E-06
    variable = f_HCO3
  []
  [inject_H2O]
    type = PorousFlowPointSourceFromPostprocessor
    point = ' 0 0 0'
    mass_flux = 2.499865905987E-01
    variable = porepressure
  []

  [produce_H]
    type = PorousFlowPeacemanBorehole
    variable = f_H
    SumQuantityUO = produced_mass_H
    mass_fraction_component = 0
    point_file = production.bh
    line_length = 1
    bottom_p_or_t = 20E6
    unit_weight = '0 0 0'
    use_mobility = true
    character = 1
  []
  [produce_Na]
    type = PorousFlowPeacemanBorehole
    variable = f_Na
    SumQuantityUO = produced_mass_Na
    mass_fraction_component = 1
    point_file = production.bh
    line_length = 1
    bottom_p_or_t = 20E6
    unit_weight = '0 0 0'
    use_mobility = true
    character = 1
  []
  [produce_K]
    type = PorousFlowPeacemanBorehole
    variable = f_K
    SumQuantityUO = produced_mass_K
    mass_fraction_component = 2
    point_file = production.bh
    line_length = 1
    bottom_p_or_t = 20E6
    unit_weight = '0 0 0'
    use_mobility = true
    character = 1
  []
  [produce_Ca]
    type = PorousFlowPeacemanBorehole
    variable = f_Ca
    SumQuantityUO = produced_mass_Ca
    mass_fraction_component = 3
    point_file = production.bh
    line_length = 1
    bottom_p_or_t = 20E6
    unit_weight = '0 0 0'
    use_mobility = true
    character = 1
  []
  [produce_Mg]
    type = PorousFlowPeacemanBorehole
    variable = f_Mg
    SumQuantityUO = produced_mass_Mg
    mass_fraction_component = 4
    point_file = production.bh
    line_length = 1
    bottom_p_or_t = 20E6
    unit_weight = '0 0 0'
    use_mobility = true
    character = 1
  []
  [produce_SiO2]
    type = PorousFlowPeacemanBorehole
    variable = f_SiO2
    SumQuantityUO = produced_mass_SiO2
    mass_fraction_component = 5
    point_file = production.bh
    line_length = 1
    bottom_p_or_t = 20E6
    unit_weight = '0 0 0'
    use_mobility = true
    character = 1
  []
  [produce_Al]
    type = PorousFlowPeacemanBorehole
    variable = f_Al
    SumQuantityUO = produced_mass_Al
    mass_fraction_component = 6
    point_file = production.bh
    line_length = 1
    bottom_p_or_t = 20E6
    unit_weight = '0 0 0'
    use_mobility = true
    character = 1
  []
  [produce_Cl]
    type = PorousFlowPeacemanBorehole
    variable = f_Cl
    SumQuantityUO = produced_mass_Cl
    mass_fraction_component = 7
    point_file = production.bh
    line_length = 1
    bottom_p_or_t = 20E6
    unit_weight = '0 0 0'
    use_mobility = true
    character = 1
  []
  [produce_SO4]
    type = PorousFlowPeacemanBorehole
    variable = f_SO4
    SumQuantityUO = produced_mass_SO4
    mass_fraction_component = 8
    point_file = production.bh
    line_length = 1
    bottom_p_or_t = 20E6
    unit_weight = '0 0 0'
    use_mobility = true
    character = 1
  []
  [produce_HCO3]
    type = PorousFlowPeacemanBorehole
    variable = f_HCO3
    SumQuantityUO = produced_mass_HCO3
    mass_fraction_component = 9
    point_file = production.bh
    line_length = 1
    bottom_p_or_t = 20E6
    unit_weight = '0 0 0'
    use_mobility = true
    character = 1
  []
  [produce_H2O]
    type = PorousFlowPeacemanBorehole
    variable = porepressure
    SumQuantityUO = produced_mass_H2O
    mass_fraction_component = 10
    point_file = production.bh
    line_length = 1
    bottom_p_or_t = 20E6
    unit_weight = '0 0 0'
    use_mobility = true
    character = 1
  []
  [remove_heat_at_production_well]
    type = PorousFlowPeacemanBorehole
    variable = temperature
    SumQuantityUO = produced_heat
    point_file = production.bh
    line_length = 1
    bottom_p_or_t = 20E6
    unit_weight = '0 0 0'
    use_mobility = true
    use_enthalpy = true
    character = 1
  []
[]

[UserObjects]
  [produced_mass_H]
    type = PorousFlowSumQuantity
  []
  [produced_mass_Na]
    type = PorousFlowSumQuantity
  []
  [produced_mass_K]
    type = PorousFlowSumQuantity
  []
  [produced_mass_Ca]
    type = PorousFlowSumQuantity
  []
  [produced_mass_Mg]
    type = PorousFlowSumQuantity
  []
  [produced_mass_SiO2]
    type = PorousFlowSumQuantity
  []
  [produced_mass_Al]
    type = PorousFlowSumQuantity
  []
  [produced_mass_Cl]
    type = PorousFlowSumQuantity
  []
  [produced_mass_SO4]
    type = PorousFlowSumQuantity
  []
  [produced_mass_HCO3]
    type = PorousFlowSumQuantity
  []
  [produced_mass_H2O]
    type = PorousFlowSumQuantity
  []
  [produced_heat]
    type = PorousFlowSumQuantity
  []
[]

[Postprocessors]
  [heat_extracted]
    type = PorousFlowPlotQuantity
    uo = produced_heat
  []
  [approx_production_temperature]
    type = PointValue
    point = '100 0 0'
    variable = temperature
  []
  [mass_extracted_H]
    type = PorousFlowPlotQuantity
    uo = produced_mass_H
    execute_on = 'initial timestep_end'
  []
  [mass_extracted_Na]
    type = PorousFlowPlotQuantity
    uo = produced_mass_Na
    execute_on = 'initial timestep_end'
  []
  [mass_extracted_K]
    type = PorousFlowPlotQuantity
    uo = produced_mass_K
    execute_on = 'initial timestep_end'
  []
  [mass_extracted_Ca]
    type = PorousFlowPlotQuantity
    uo = produced_mass_Ca
    execute_on = 'initial timestep_end'
  []
  [mass_extracted_Mg]
    type = PorousFlowPlotQuantity
    uo = produced_mass_Mg
    execute_on = 'initial timestep_end'
  []
  [mass_extracted_SiO2]
    type = PorousFlowPlotQuantity
    uo = produced_mass_SiO2
    execute_on = 'initial timestep_end'
  []
  [mass_extracted_Al]
    type = PorousFlowPlotQuantity
    uo = produced_mass_Al
    execute_on = 'initial timestep_end'
  []
  [mass_extracted_Cl]
    type = PorousFlowPlotQuantity
    uo = produced_mass_Cl
    execute_on = 'initial timestep_end'
  []
  [mass_extracted_SO4]
    type = PorousFlowPlotQuantity
    uo = produced_mass_SO4
    execute_on = 'initial timestep_end'
  []
  [mass_extracted_HCO3]
    type = PorousFlowPlotQuantity
    uo = produced_mass_HCO3
    execute_on = 'initial timestep_end'
  []
  [mass_extracted_H2O]
    type = PorousFlowPlotQuantity
    uo = produced_mass_H2O
    execute_on = 'initial timestep_end'
  []
  [mass_extracted]
    type = LinearCombinationPostprocessor
    pp_names = 'mass_extracted_H mass_extracted_Na mass_extracted_K mass_extracted_Ca mass_extracted_Mg mass_extracted_SiO2 mass_extracted_Al mass_extracted_Cl mass_extracted_SO4 mass_extracted_HCO3 mass_extracted_H2O'
    pp_coefs = '1 1 1 1 1 1 1 1 1 1 1'
    execute_on = 'initial timestep_end'
  []
  [dt]
    type = TimestepSize
    execute_on = 'timestep_begin'
  []
[]

[FluidProperties]
  [the_simple_fluid]
    type = SimpleFluidProperties
    thermal_expansion = 2E-4
    bulk_modulus = 2E9
    viscosity = 1E-3
    density0 = 980
    cv = 4000.0
    cp = 4000.0
    porepressure_coefficient = 0
  []
[]

[PorousFlowFullySaturated]
  coupling_type = ThermoHydro
  porepressure = porepressure
  temperature = temperature
  mass_fraction_vars = 'f_H f_Na f_K f_Ca f_Mg f_SiO2 f_Al f_Cl f_SO4 f_HCO3'
  save_component_rate_in = 'rate_H rate_Na rate_K rate_Ca rate_Mg rate_SiO2 rate_Al rate_Cl rate_SO4 rate_HCO3 rate_H2O' # change in kg at every node / dt
  fp = the_simple_fluid
  temperature_unit = Celsius
[]

[AuxVariables]
  [rate_H]
  []
  [rate_Na]
  []
  [rate_K]
  []
  [rate_Ca]
  []
  [rate_Mg]
  []
  [rate_SiO2]
  []
  [rate_Al]
  []
  [rate_Cl]
  []
  [rate_SO4]
  []
  [rate_HCO3]
  []
  [rate_H2O]
  []
[]

[Materials]
  [porosity]
    type = PorousFlowPorosityConst
    porosity = 0.01
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1E-14 0 0   0 1E-14 0   0 0 1E-14'
  []
  [thermal_conductivity]
    type = PorousFlowThermalConductivityIdeal
    dry_thermal_conductivity = '2.5 0 0  0 2.5 0  0 0 2.5'
  []
  [rock_heat]
    type = PorousFlowMatrixInternalEnergy
    density = 2750.0
    specific_heat_capacity = 900.0
  []
[]

[Preconditioning]
  active = typically_efficient
  [typically_efficient]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -pc_hypre_type'
    petsc_options_value = ' hypre    boomeramg'
  []
  [strong]
    type = SMP
    full = true
    petsc_options = '-ksp_diagonal_scale -ksp_diagonal_scale_fix'
    petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type -pc_asm_overlap'
    petsc_options_value = ' asm      ilu           NONZERO                   2'
  []
  [probably_too_strong]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
    petsc_options_value = ' lu       mumps'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  end_time = 31536000 #1 year

  [TimeStepper]
    type = SolutionTimeAdaptiveDT
    dt = 500
  []
[]

[Outputs]
  exodus = true
  csv = true
[]

[MultiApps]
  [react]
    type = TransientMultiApp
    input_files = aquifer_geochemistry.i
    clone_master_mesh = true
    execute_on = 'timestep_end'
  []
[]
[Transfers]
  [changes_due_to_flow]
    type = MultiAppCopyTransfer
    source_variable = 'rate_H rate_Na rate_K rate_Ca rate_Mg rate_SiO2 rate_Al rate_Cl rate_SO4 rate_HCO3 rate_H2O temperature'
    variable = 'pf_rate_H pf_rate_Na pf_rate_K pf_rate_Ca pf_rate_Mg pf_rate_SiO2 pf_rate_Al pf_rate_Cl pf_rate_SO4 pf_rate_HCO3 pf_rate_H2O temperature'
    to_multi_app = react
  []
  [massfrac_from_geochem]
    type = MultiAppCopyTransfer
    source_variable = 'massfrac_H massfrac_Na massfrac_K massfrac_Ca massfrac_Mg massfrac_SiO2 massfrac_Al massfrac_Cl massfrac_SO4 massfrac_HCO3'
    variable = 'f_H f_Na f_K f_Ca f_Mg f_SiO2 f_Al f_Cl f_SO4 f_HCO3'
    from_multi_app = react
  []
[]

(modules/solid_mechanics/test/tests/ad_finite_strain_jacobian/bending_jacobian.i)

[Mesh]
  [generated_mesh]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 10
    ymin = 0
    ymax = 2
    nx = 10
    ny = 2
    elem_type = QUAD4
  []
  [corner]
    type = ExtraNodesetGenerator
    new_boundary = 101
    coord = '0 0'
    input = generated_mesh
  []
  [side]
    type = ExtraNodesetGenerator
    new_boundary = 102
    coord = '10 0'
    input = corner
  []
  [mid]
    type = ExtraNodesetGenerator
    new_boundary = 103
    coord = '5 2'
    input = side
  []
[]

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = FINITE
    add_variables = true
    use_finite_deform_jacobian = true
    volumetric_locking_correction = false
    use_automatic_differentiation = true
  []
[]

[Materials]
  [stress]
    type = ADComputeFiniteStrainElasticStress
  []
  [elasticity_tensor]
    type = ADComputeElasticityTensor
    fill_method = symmetric9
    C_ijkl = '1.684e5 0.176e5 0.176e5 1.684e5 0.176e5 1.684e5 0.754e5 0.754e5 0.754e5'
  []
[]

[BCs]
 [fix_corner_x]
   type = ADDirichletBC
   variable = disp_x
   boundary = 101
   value = 0
 []
 [fix_corner_y]
   type = ADDirichletBC
   variable = disp_y
   boundary = 101
   value = 0
 []
 [fix_y]
   type = ADDirichletBC
   variable = disp_y
   boundary = 102
   value = 0
 []
 [move_y]
   type = ADFunctionDirichletBC
   variable = disp_y
   boundary = 103
   function = '-t'
 []
[]

[Executioner]
  type = Transient

  solve_type = NEWTON
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'

  nl_rel_tol = 1e-10
  nl_max_its = 10

  l_tol  = 1e-4
  l_max_its = 50

  dt = 0.1
  dtmin = 0.1

  num_steps = 2
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Outputs]
  exodus = true
[]

(modules/contact/test/tests/cohesive_zone_model/mortar_czm_analysis.i)

[Mesh]
  [msh]
    type = GeneratedMeshGenerator
    dim = 2
    xmax = 1
    ymax = 1
    nx = 5
    ny = 5
    boundary_name_prefix = bottom
  []
  [msh_id]
    type = SubdomainIDGenerator
    input = msh
    subdomain_id = 1
  []
  [msh_two]
    type = GeneratedMeshGenerator
    dim = 2
    xmax = 1
    ymin = 1
    ymax = 2
    nx = 5
    ny = 5
    boundary_name_prefix = top
    boundary_id_offset = 10
  []
  [msh_two_id]
    type = SubdomainIDGenerator
    input = msh_two
    subdomain_id = 2
  []
  [combined]
    type = MeshCollectionGenerator
    inputs = 'msh_id msh_two_id'
  []
  [top_node]
    type = ExtraNodesetGenerator
    coord = '0 2 0'
    input = combined
    new_boundary = top_node
  []
  [bottom_node]
    type = ExtraNodesetGenerator
    coord = '0 0 0'
    input = top_node
    new_boundary = bottom_node
  []
  # Build subdomains
  [secondary]
    type = LowerDBlockFromSidesetGenerator
    new_block_id = 10001
    new_block_name = 'secondary_lower'
    sidesets = 'bottom_top'
    input = bottom_node
  []
  [primary]
    type = LowerDBlockFromSidesetGenerator
    new_block_id = 10000
    sidesets = 'top_bottom'
    new_block_name = 'primary_lower'
    input = secondary
  []
  allow_renumbering = false
[]

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Physics]
  [SolidMechanics]
    [QuasiStatic]
      generate_output = 'stress_yy'
      [all]
        strain = FINITE
        add_variables = true
        use_automatic_differentiation = true
        decomposition_method = TaylorExpansion
        block = '1 2'
      []
    []
  []
[]

[BCs]
  [fix_x]
    type = DirichletBC
    preset = true
    value = 0.0
    boundary = bottom_node
    variable = disp_x
  []
  [lateral_top]
    type = FunctionDirichletBC
    boundary = top_top
    variable = disp_x
    function = 'if(t<=0.3,t,if(t<=0.6,0.3-(t-0.3),0.6-t))'
    preset = true
  []
  [top]
    type = FunctionDirichletBC
    boundary = top_top
    variable = disp_y
    function = 'if(t<=0.3,t,if(t<=0.6,0.3-(t-0.3),0.6-t))'
    preset = true
  []
  [bottom]
    type = DirichletBC
    boundary = bottom_bottom
    variable = disp_y
    value = 0
    preset = true
  []
[]

[AuxVariables]
  [mode_mixity_ratio]
  []
  [damage]
  []
  [local_normal_jump]
  []
  [local_tangential_jump]
  []
[]

[AuxKernels]
  [mode_mixity_ratio]
    type = CohesiveZoneMortarUserObjectAux
    variable = mode_mixity_ratio
    user_object = czm_uo
    cohesive_zone_quantity = mode_mixity_ratio
    boundary = 'bottom_top'
  []
  [cohesive_damage]
    type = CohesiveZoneMortarUserObjectAux
    variable = damage
    user_object = czm_uo
    cohesive_zone_quantity = cohesive_damage
    boundary = 'bottom_top'
  []
  [local_normal_jump]
    type = CohesiveZoneMortarUserObjectAux
    variable = local_normal_jump
    user_object = czm_uo
    cohesive_zone_quantity = local_normal_jump
    boundary = 'bottom_top'
  []
  [local_tangential_jump]
    type = CohesiveZoneMortarUserObjectAux
    variable = local_tangential_jump
    user_object = czm_uo
    cohesive_zone_quantity = local_tangential_jump
    boundary = 'bottom_top'
  []
[]

[Materials]
  [stress]
    type = ADComputeFiniteStrainElasticStress
    block = '1 2'
  []
  [elasticity_tensor]
    type = ADComputeElasticityTensor
    fill_method = symmetric9
    C_ijkl = '1.684e5 0.176e5 0.176e5 1.684e5 0.176e5 1.684e5 0.754e5 0.754e5 0.754e5'
    block = '1 2'
  []
  [normal_strength]
    type = GenericFunctionMaterial
    prop_names = 'N'
    prop_values = 'if(x<0.5,1,100)*1e4'
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient
  solve_type = 'NEWTON'
  line_search = none

  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'

  automatic_scaling = true

  l_max_its = 2
  l_tol = 1e-14
  nl_max_its = 30
  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-10
  start_time = 0.0
  dt = 0.0005
  end_time = 0.01
  dtmin = 0.0001
[]

[Outputs]
  exodus = true
[]

[UserObjects]
  [czm_uo]
    type = BilinearMixedModeCohesiveZoneModel
    primary_boundary = 'top_bottom'
    secondary_boundary = 'bottom_top'
    primary_subdomain = 10000
    secondary_subdomain = 10001

    disp_x = disp_x
    disp_y = disp_y
    friction_coefficient = 0.1 # with 2.0 works
    secondary_variable = disp_x

    penalty = 0e6
    penalty_friction = 1e4
    use_physical_gap = true

    correct_edge_dropping = true
    normal_strength = N
    shear_strength = 1e3
    viscosity = 1e-3
    penalty_stiffness = 1e6
    mixed_mode_criterion = POWER_LAW

    power_law_parameter = 2.2
    GI_c = 1e3
    GII_c = 1e2
    displacements = 'disp_x disp_y'
  []
[]

[Constraints]
  [x]
    type = NormalMortarMechanicalContact
    primary_boundary = 'top_bottom'
    secondary_boundary = 'bottom_top'
    primary_subdomain = 10000
    secondary_subdomain = 10001
    secondary_variable = disp_x
    component = x
    use_displaced_mesh = true
    compute_lm_residuals = false
    weighted_gap_uo = czm_uo
    correct_edge_dropping = true
  []
  [y]
    type = NormalMortarMechanicalContact
    primary_boundary = 'top_bottom'
    secondary_boundary = 'bottom_top'
    primary_subdomain = 10000
    secondary_subdomain = 10001
    secondary_variable = disp_y
    component = y
    use_displaced_mesh = true
    compute_lm_residuals = false
    weighted_gap_uo = czm_uo
    correct_edge_dropping = true
  []
  [c_x]
    type = MortarGenericTraction
    primary_boundary = 'top_bottom'
    secondary_boundary = 'bottom_top'
    primary_subdomain = 10000
    secondary_subdomain = 10001
    secondary_variable = disp_x
    component = x
    use_displaced_mesh = true
    compute_lm_residuals = false
    cohesive_zone_uo = czm_uo
    correct_edge_dropping = true
  []
  [c_y]
    type = MortarGenericTraction
    primary_boundary = 'top_bottom'
    secondary_boundary = 'bottom_top'
    primary_subdomain = 10000
    secondary_subdomain = 10001
    secondary_variable = disp_y
    component = y
    use_displaced_mesh = true
    compute_lm_residuals = false
    cohesive_zone_uo = czm_uo
    correct_edge_dropping = true
  []
[]

(modules/navier_stokes/test/tests/finite_element/ins/mms/supg/supg_mms_test.i)

mu=1.5
rho=2.5

[GlobalParams]
  gravity = '0 0 0'
  supg = true
  convective_term = true
  integrate_p_by_parts = false
  laplace = true
  u = vel_x
  v = vel_y
  pressure = p
  alpha = 1
  order = SECOND
  family = LAGRANGE
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 1.0
    ymin = 0
    ymax = 1.0
    elem_type = QUAD9
    nx = 4
    ny = 4
  []
  [./corner_node]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node'
    nodes = '0'
    input = gen
  [../]
[]

[Variables]
  [./vel_x]
  [../]

  [./vel_y]
  [../]

  [./p]
    order = FIRST
  [../]
[]

[Kernels]
  # mass
  [./mass]
    type = INSMass
    variable = p
  [../]

  # x-momentum, space
  [./x_momentum_space]
    type = INSMomentumLaplaceForm
    variable = vel_x
    component = 0
    forcing_func = vel_x_source_func
  [../]

  # y-momentum, space
  [./y_momentum_space]
    type = INSMomentumLaplaceForm
    variable = vel_y
    component = 1
    forcing_func = vel_y_source_func
  [../]

  [./p_source]
    type = BodyForce
    function = p_source_func
    variable = p
  [../]
[]

[BCs]
  [./vel_x]
    type = FunctionDirichletBC
    preset = false
    boundary = 'left right top bottom'
    function = vel_x_func
    variable = vel_x
  [../]
  [./vel_y]
    type = FunctionDirichletBC
    preset = false
    boundary = 'left right top bottom'
    function = vel_y_func
    variable = vel_y
  [../]
  [./p]
    type = FunctionDirichletBC
    preset = false
    boundary = 'left right top bottom'
    function = p_func
    variable = p
  [../]
[]

[Functions]
  [./vel_x_source_func]
    type = ParsedFunction
    expression = '-${mu}*(-0.028*pi^2*x^2*sin(0.2*pi*x*y) - 0.028*pi^2*y^2*sin(0.2*pi*x*y) - 0.1*pi^2*sin(0.5*pi*x) - 0.4*pi^2*sin(pi*y)) + ${rho}*(0.14*pi*x*cos(0.2*pi*x*y) + 0.4*pi*cos(pi*y))*(0.6*sin(0.8*pi*x) + 0.3*sin(0.3*pi*y) + 0.2*sin(0.3*pi*x*y) + 0.3) + ${rho}*(0.14*pi*y*cos(0.2*pi*x*y) + 0.2*pi*cos(0.5*pi*x))*(0.4*sin(0.5*pi*x) + 0.4*sin(pi*y) + 0.7*sin(0.2*pi*x*y) + 0.5) + 0.1*pi*y*cos(0.2*pi*x*y) + 0.25*pi*cos(0.5*pi*x)'
  [../]
  [./vel_y_source_func]
    type = ParsedFunction
    expression = '-${mu}*(-0.018*pi^2*x^2*sin(0.3*pi*x*y) - 0.018*pi^2*y^2*sin(0.3*pi*x*y) - 0.384*pi^2*sin(0.8*pi*x) - 0.027*pi^2*sin(0.3*pi*y)) + ${rho}*(0.06*pi*x*cos(0.3*pi*x*y) + 0.09*pi*cos(0.3*pi*y))*(0.6*sin(0.8*pi*x) + 0.3*sin(0.3*pi*y) + 0.2*sin(0.3*pi*x*y) + 0.3) + ${rho}*(0.06*pi*y*cos(0.3*pi*x*y) + 0.48*pi*cos(0.8*pi*x))*(0.4*sin(0.5*pi*x) + 0.4*sin(pi*y) + 0.7*sin(0.2*pi*x*y) + 0.5) + 0.1*pi*x*cos(0.2*pi*x*y) + 0.3*pi*cos(0.3*pi*y)'
  [../]
  [./p_source_func]
    type = ParsedFunction
    expression = '-0.06*pi*x*cos(0.3*pi*x*y) - 0.14*pi*y*cos(0.2*pi*x*y) - 0.2*pi*cos(0.5*pi*x) - 0.09*pi*cos(0.3*pi*y)'
  [../]
  [./vel_x_func]
    type = ParsedFunction
    expression = '0.4*sin(0.5*pi*x) + 0.4*sin(pi*y) + 0.7*sin(0.2*pi*x*y) + 0.5'
  [../]
  [./vel_y_func]
    type = ParsedFunction
    expression = '0.6*sin(0.8*pi*x) + 0.3*sin(0.3*pi*y) + 0.2*sin(0.3*pi*x*y) + 0.3'
  [../]
  [./p_func]
    type = ParsedFunction
    expression = '0.5*sin(0.5*pi*x) + 1.0*sin(0.3*pi*y) + 0.5*sin(0.2*pi*x*y) + 0.5'
  [../]
  [./vxx_func]
    type = ParsedFunction
    expression = '0.14*pi*y*cos(0.2*pi*x*y) + 0.2*pi*cos(0.5*pi*x)'
  [../]
[]

[Materials]
  [./const]
    type = GenericConstantMaterial
    block = 0
    prop_names = 'rho mu'
    prop_values = '${rho}  ${mu}'
  [../]
[]

[Preconditioning]
  [./SMP]
    type = SMP
    full = true
    solve_type = 'NEWTON'
  [../]
[]

[Executioner]
  type = Steady
  petsc_options = '-snes_converged_reason -ksp_converged_reason'
  petsc_options_iname = '-pc_type -pc_factor_shift_type'
  petsc_options_value = 'lu NONZERO'
  line_search = 'none'
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-13
  nl_max_its = 6
  l_tol = 1e-6
  l_max_its = 500
[]

[Outputs]
  [./exodus]
    type = Exodus
  [../]
  [./csv]
    type = CSV
  [../]
[]

[Postprocessors]
  [./L2vel_x]
    type = ElementL2Error
    variable = vel_x
    function = vel_x_func
    outputs = 'console'    execute_on = 'timestep_end'
  [../]
  [./L2vel_y]
    variable = vel_y
    function = vel_y_func
    type = ElementL2Error
    outputs = 'console'    execute_on = 'timestep_end'
  [../]
  [./L2p]
    variable = p
    function = p_func
    type = ElementL2Error
    outputs = 'console'    execute_on = 'timestep_end'
  [../]
  [./L2vxx]
    variable = vxx
    function = vxx_func
    type = ElementL2Error
    outputs = 'console'    execute_on = 'timestep_end'
  [../]
[]

[AuxVariables]
  [./vxx]
    family = MONOMIAL
    order = FIRST
  [../]
[]

[AuxKernels]
  [./vxx]
    type = VariableGradientComponent
    component = x
    variable = vxx
    gradient_variable = vel_x
  [../]
[]

(modules/combined/examples/optimization/thermomechanical/structural_sub.i)

vol_frac = 0.4

power = 2.0

E0 = 1.0e-6
E1 = 1.0

rho0 = 0.0
rho1 = 1.0


[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  [MeshGenerator]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 40
    ny = 40
    xmin = 0
    xmax = 40
    ymin = 0
    ymax = 40
  []
  [node]
    type = ExtraNodesetGenerator
    input = MeshGenerator
    new_boundary = hold
    nodes = 0
  []
  [push_left]
    type = ExtraNodesetGenerator
    input = node
    new_boundary = push_left
    coord = '16 0 0'
  []
  [push_center]
    type = ExtraNodesetGenerator
    input = push_left
    new_boundary = push_center
    coord = '24 0 0'
  []
  [extra]
    type = SideSetsFromBoundingBoxGenerator
    input = push_center
    bottom_left = '-0.01 17.999  0'
    top_right = '5 22.001  0'
    boundary_new = n1
    included_boundaries = left
  []
  [dirichlet_bc]
    type = SideSetsFromNodeSetsGenerator
    input = extra
  []
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
[]

[AuxVariables]
  [Dc]
    family = MONOMIAL
    order = FIRST
    initial_condition = -1.0
  []
  [mat_den]
    family = MONOMIAL
    order = FIRST
    initial_condition = ${vol_frac}
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = SMALL
    add_variables = true
    incremental = false
  []
[]

[BCs]
  [no_y]
    type = DirichletBC
    variable = disp_y
    boundary = hold
    value = 0.0
  []
  [no_x_symm]
    type = DirichletBC
    variable = disp_x
    boundary = right
    value = 0.0
  []
[]

[NodalKernels]
  [push_left]
    type = NodalGravity
    variable = disp_y
    boundary = push_left
    gravity_value = -1.0e-3
    mass = 1
  []
  [push_center]
    type = NodalGravity
    variable = disp_y
    boundary = push_center
    gravity_value = -1.0e-3
    mass = 1
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeVariableIsotropicElasticityTensor
    youngs_modulus = E_phys
    poissons_ratio = poissons_ratio
    args = 'mat_den'
  []
  [E_phys]
    type = DerivativeParsedMaterial
    expression = "A1:=(${E0}-${E1})/(${rho0}^${power}-${rho1}^${power}); "
                 "B1:=${E0}-A1*${rho0}^${power}; E1:=A1*mat_den^${power}+B1; E1"
    coupled_variables = 'mat_den'
    property_name = E_phys
  []
  [poissons_ratio]
    type = GenericConstantMaterial
    prop_names = poissons_ratio
    prop_values = 0.3
  []
  [stress]
    type = ComputeLinearElasticStress
  []
  [dc]
    type = ComplianceSensitivity
    design_density = mat_den
    youngs_modulus = E_phys
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[UserObjects]
  [rad_avg]
    type = RadialAverage
    radius = 1.2
    weights = linear
    prop_name = sensitivity
    execute_on = TIMESTEP_END
    force_preaux = true
  []
  [calc_sense]
    type = SensitivityFilter
    density_sensitivity = Dc
    design_density = mat_den
    filter_UO = rad_avg
    execute_on = TIMESTEP_END
    force_postaux = true
  []
[]

[Executioner]
  type = Transient
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'
  nl_abs_tol = 1e-12
  dt = 1.0
  num_steps = 500
[]

[Outputs]
  exodus = true
  [out]
    type = CSV
    execute_on = 'TIMESTEP_END'
  []
  print_linear_residuals = false
[]

[Postprocessors]
  [mesh_volume]
    type = VolumePostprocessor
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [total_vol]
    type = ElementIntegralVariablePostprocessor
    variable = mat_den
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [vol_frac]
    type = ParsedPostprocessor
    expression = 'total_vol / mesh_volume'
    pp_names = 'total_vol mesh_volume'
  []
  [sensitivity]
    type = ElementIntegralMaterialProperty
    mat_prop = sensitivity
  []
  [objective]
    type = ElementIntegralMaterialProperty
    mat_prop = strain_energy_density
    execute_on = 'INITIAL TIMESTEP_END'
  []
[]

(modules/navier_stokes/test/tests/finite_element/ins/boussinesq/boussinesq_stabilized.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmax = .05
    ymax = .05
    nx = 20
    ny = 20
    elem_type = QUAD9
  []
  [./bottom_left]
    type = ExtraNodesetGenerator
    new_boundary = corner
    coord = '0 0'
    input = gen
  [../]
[]


[Preconditioning]
  [./Newton_SMP]
    type = SMP
    full = true
    solve_type = 'NEWTON'
  [../]
[]

[Executioner]
  type = Steady

  nl_rel_tol = 1e-12
  petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type -ksp_gmres_restart'
  petsc_options_value = 'bjacobi  lu           NONZERO                   200'
[]

[Debug]
  show_var_residual_norms = true
[]

[Outputs]
  [out]
    type = Exodus
    execute_on = 'final'
  []
[]

[Variables]
  [velocity]
    family = LAGRANGE_VEC
  []
  [p][]
  [temp]
    initial_condition = 340
    scaling = 1e-4
  []
[]

[ICs]
  [velocity]
    type = VectorConstantIC
    x_value = 1e-15
    y_value = 1e-15
    variable = velocity
  []
[]

[BCs]
  [./velocity_dirichlet]
    type = VectorDirichletBC
    boundary = 'left right bottom top'
    variable = velocity
    # The third entry is to satisfy RealVectorValue
    values = '0 0 0'
  [../]
  # Even though we are integrating by parts, because there are no integrated
  # boundary conditions on the velocity p doesn't appear in the system of
  # equations. Thus we must pin the pressure somewhere in order to ensure a
  # unique solution
  [./p_zero]
    type = DirichletBC
    boundary = corner
    variable = p
    value = 0
  [../]
  [./cold]
    type = DirichletBC
    variable = temp
    boundary = left
    value = 300
  [../]
  [./hot]
    type = DirichletBC
    variable = temp
    boundary = right
    value = 400
  [../]
[]


[Kernels]
  [./mass]
    type = INSADMass
    variable = p
  [../]
  [mass_pspg]
    type = INSADMassPSPG
    variable = p
  []

  [./momentum_viscous]
    type = INSADMomentumViscous
    variable = velocity
  [../]
  [momentum_advection]
    type = INSADMomentumAdvection
    variable = velocity
  []
  [momentum_pressure]
    type = INSADMomentumPressure
    variable = velocity
    pressure = p
    integrate_p_by_parts = true
  []
  [./buoyancy]
    type = INSADBoussinesqBodyForce
    variable = velocity
    temperature = temp
    gravity = '0 -9.81 0'
  [../]
  [./gravity]
    type = INSADGravityForce
    variable = velocity
    gravity = '0 -9.81 0'
  [../]
  [supg]
    type = INSADMomentumSUPG
    variable = velocity
    velocity = velocity
  []

  [temp_advection]
    type = INSADEnergyAdvection
    variable = temp
  []
  [temp_conduction]
    type = ADHeatConduction
    variable = temp
    thermal_conductivity = 'k'
  [../]
  [temp_supg]
    type = INSADEnergySUPG
    variable = temp
    velocity = velocity
  []
[]

[Materials]
  [./ad_const]
    type = ADGenericConstantMaterial
    # alpha = coefficient of thermal expansion where rho  = rho0 -alpha * rho0 * delta T
    prop_names =  'mu        rho   alpha   k        cp'
    prop_values = '30.74e-6  .5757 2.9e-3  46.38e-3 1054'
  [../]
  [./const]
    type = GenericConstantMaterial
    prop_names =  'temp_ref'
    prop_values = '900'
  [../]
  [ins_mat]
    type = INSADStabilized3Eqn
    velocity = velocity
    pressure = p
    temperature = temp
  []
[]

(modules/contact/test/tests/cohesive_zone_model/bilinear_mixed_compare.i)

[Mesh]
  [base]
    type = GeneratedMeshGenerator
    dim = 2
    xmax = 1.0
    ymax = 1
    xmin = -0.0
    nx = 1
    ny = 1
  []
  [rename_base]
    type = RenameBoundaryGenerator
    input = base
    old_boundary = 'top bottom left right'
    new_boundary = 'top_base bottom_base left_base right_base'
  []
  [base_id]
    type = SubdomainIDGenerator
    input = rename_base
    subdomain_id = 1
  []
  [top]
    type = GeneratedMeshGenerator
    dim = 2
    xmax = 1
    ymin = 1
    ymax = 2
    nx = 1
    ny = 1
  []
  [rename_top]
    type = RenameBoundaryGenerator
    input = top
    old_boundary = 'top bottom left right'
    new_boundary = '100 101 102 103'
  []
  [top_id]
    type = SubdomainIDGenerator
    input = rename_top
    subdomain_id = 2
  []
  [combined]
    type = MeshCollectionGenerator
    inputs = 'base_id top_id'
  []
  [top_node]
    type = ExtraNodesetGenerator
    coord = '0 2 0'
    input = combined
    new_boundary = top_node
  []
  [bottom_node]
    type = ExtraNodesetGenerator
    coord = '-0.0 0 0'
    input = top_node
    new_boundary = bottom_node
  []

  [secondary]
    type = LowerDBlockFromSidesetGenerator
    new_block_id = 10001
    new_block_name = 'secondary_lower'
    sidesets = 'top_base'
    input = bottom_node
  []
  [primary]
    type = LowerDBlockFromSidesetGenerator
    new_block_id = 10000
    sidesets = '101'
    new_block_name = 'primary_lower'
    input = secondary
  []

  patch_update_strategy = auto
  patch_size = 20
  allow_renumbering = false
[]

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Physics]
  [SolidMechanics]
    [QuasiStatic]
      generate_output = 'stress_yy vonmises_stress stress_xy'
      [all]
        strain = FINITE
        add_variables = true
        use_automatic_differentiation = true
        decomposition_method = TaylorExpansion
        generate_output = 'vonmises_stress stress_yy stress_xy'
        block = '1 2'
      []
    []
  []
[]

[BCs]
  [fix_x]
    type = DirichletBC
    preset = true
    value = 0.0
    boundary = bottom_node
    variable = disp_x
  []
  [fix_top]
    type = DirichletBC
    preset = true
    boundary = 100
    variable = disp_x
    value = 0
  []
  [top]
    type = FunctionDirichletBC
    boundary = 100
    variable = disp_y
    function = 'if(t<=0.3,t,if(t<=0.6,0.3-(t-0.3),0.6-t))'
    preset = true
  []
  [bottom]
    type = DirichletBC
    boundary = bottom_base
    variable = disp_y
    value = 0
    preset = true
  []
[]

[Materials]
  [stress]
    type = ADComputeFiniteStrainElasticStress
    block = '1 2'
  []
  [elasticity_tensor]
    type = ADComputeElasticityTensor
    fill_method = symmetric9
    C_ijkl = '1.684e5 0.176e5 0.176e5 1.684e5 0.176e5 1.684e5 0.754e5 0.754e5 0.754e5'
    block = '1 2'
  []
[]

[Postprocessors]
  [stress_yy]
    type = ElementExtremeValue
    variable = stress_yy
    value_type = max
    block = '1 2'
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'
  line_search = 'none'

#  petsc_options = '-pc_svd_monitor -ksp_monitor_singular_values'
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'svd        superlu_dist'

  automatic_scaling = true

  l_max_its = 2
  l_tol = 1e-14
  nl_max_its = 150
  nl_rel_tol = 1e-14
  nl_abs_tol = 1e-12
  start_time = 0.0
  dt = 0.01
  end_time = 0.85
  dtmin = 0.01
[]

[Outputs]
  exodus = true
  csv = true
[]

[UserObjects]
  [czm_uo]
    type = BilinearMixedModeCohesiveZoneModel
    primary_boundary = 101
    secondary_boundary = 'top_base'
    primary_subdomain = 10000
    secondary_subdomain = 10001

    correct_edge_dropping = true

    disp_x = disp_x
    disp_y = disp_y
    friction_coefficient = 0.0 # with 2.0 works
    secondary_variable = disp_x
    penalty = 0e6
    penalty_friction = 0e4
    use_physical_gap = true

    # bilinear parameters
    normal_strength = 1e4
    shear_strength = 1e3
    penalty_stiffness = 1e6
    power_law_parameter = 2.2
    viscosity = 1.0e-3
    GI_c = 1e3
    GII_c = 1e2
    displacements = 'disp_x disp_y'
  []
[]

[Constraints]
  [c_x]
    type = MortarGenericTraction
    primary_boundary = 101
    secondary_boundary = 'top_base'
    primary_subdomain = 10000
    secondary_subdomain = 10001
    secondary_variable = disp_x
    component = x
    use_displaced_mesh = true
    compute_lm_residuals = false
    cohesive_zone_uo = czm_uo
  []
  [c_y]
    type = MortarGenericTraction
    primary_boundary = 101
    secondary_boundary = 'top_base'
    primary_subdomain = 10000
    secondary_subdomain = 10001
    secondary_variable = disp_y
    component = y
    use_displaced_mesh = true
    compute_lm_residuals = false
    cohesive_zone_uo = czm_uo
  []
[]

(modules/navier_stokes/test/tests/finite_element/ins/block-restriction/two-mats-two-eqn-sets.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 2
    ymin = 0
    ymax = 1
    nx = 16
    ny = 8
    elem_type = QUAD9
  []
  [./corner_node_0]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node_0'
    coord = '0 0 0'
    input = gen
  [../]
  [./corner_node_1]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node_1'
    coord = '1 0 0'
    input = corner_node_0
  [../]
  [./subdomain1]
    input = corner_node_1
    type = SubdomainBoundingBoxGenerator
    bottom_left = '1 0 0'
    top_right = '2 1 0'
    block_id = 1
  [../]
  [./break_boundary]
    input = subdomain1
    type = BreakBoundaryOnSubdomainGenerator
  [../]
  [./interface0]
    type = SideSetsBetweenSubdomainsGenerator
    input = break_boundary
    primary_block = '0'
    paired_block = '1'
    new_boundary = 'interface0'
  [../]
  [./interface1]
    type = SideSetsBetweenSubdomainsGenerator
    input = interface0
    primary_block = '1'
    paired_block = '0'
    new_boundary = 'interface1'
  [../]
[]

[Variables]
  [velocity0]
    order = SECOND
    family = LAGRANGE_VEC
    block = 0
  []
  [T0]
    order = SECOND
    [InitialCondition]
      type = ConstantIC
      value = 1.0
    []
    block = 0
  []
  [p0]
    block = 0
  []

  [velocity1]
    order = SECOND
    family = LAGRANGE_VEC
    block = 1
  []
  [T1]
    order = SECOND
    [InitialCondition]
      type = ConstantIC
      value = 1.0
    []
    block = 1
  []
  [p1]
    block = 1
  []
[]

[Kernels]
  [./mass0]
    type = INSADMass
    variable = p0
    block = 0
  [../]
  [./momentum_time0]
    type = INSADMomentumTimeDerivative
    variable = velocity0
    block = 0
  [../]
  [./momentum_convection0]
    type = INSADMomentumAdvection
    variable = velocity0
    block = 0
  [../]
  [./momentum_viscous0]
    type = INSADMomentumViscous
    variable = velocity0
    block = 0
  [../]
  [./momentum_pressure0]
    type = INSADMomentumPressure
    variable = velocity0
    pressure = p0
    integrate_p_by_parts = true
    block = 0
  [../]
  [./temperature_time0]
    type = INSADHeatConductionTimeDerivative
    variable = T0
    block = 0
  [../]
  [./temperature_advection0]
    type = INSADEnergyAdvection
    variable = T0
    block = 0
  [../]
  [./temperature_conduction0]
    type = ADHeatConduction
    variable = T0
    thermal_conductivity = 'k'
    block = 0
  [../]

  [./mass1]
    type = INSADMass
    variable = p1
    block = 1
  [../]
  [./momentum_time1]
    type = INSADMomentumTimeDerivative
    variable = velocity1
    block = 1
  [../]
  [./momentum_convection1]
    type = INSADMomentumAdvection
    variable = velocity1
    block = 1
  [../]
  [./momentum_viscous1]
    type = INSADMomentumViscous
    variable = velocity1
    block = 1
  [../]
  [./momentum_pressure1]
    type = INSADMomentumPressure
    variable = velocity1
    pressure = p1
    integrate_p_by_parts = true
    block = 1
  [../]
  [./temperature_time1]
    type = INSADHeatConductionTimeDerivative
    variable = T1
    block = 1
  [../]
  [./temperature_advection1]
    type = INSADEnergyAdvection
    variable = T1
    block = 1
  [../]
  [./temperature_conduction1]
    type = ADHeatConduction
    variable = T1
    thermal_conductivity = 'k'
    block = 1
  [../]
[]

[BCs]
  [./no_slip0]
    type = VectorFunctionDirichletBC
    variable = velocity0
    boundary = 'bottom_to_0 interface0 left'
  [../]
  [./lid0]
    type = VectorFunctionDirichletBC
    variable = velocity0
    boundary = 'top_to_0'
    function_x = 'lid_function0'
  [../]
  [./T_hot0]
    type = DirichletBC
    variable = T0
    boundary = 'bottom_to_0'
    value = 1
  [../]
  [./T_cold0]
    type = DirichletBC
    variable = T0
    boundary = 'top_to_0'
    value = 0
  [../]
  [./pressure_pin0]
    type = DirichletBC
    variable = p0
    boundary = 'pinned_node_0'
    value = 0
  [../]

  [./no_slip1]
    type = VectorFunctionDirichletBC
    variable = velocity1
    boundary = 'bottom_to_1 interface1 right'
  [../]
  [./lid1]
    type = VectorFunctionDirichletBC
    variable = velocity1
    boundary = 'top_to_1'
    function_x = 'lid_function1'
  [../]
  [./T_hot1]
    type = DirichletBC
    variable = T1
    boundary = 'bottom_to_1'
    value = 1
  [../]
  [./T_cold1]
    type = DirichletBC
    variable = T1
    boundary = 'top_to_1'
    value = 0
  [../]
  [./pressure_pin1]
    type = DirichletBC
    variable = p1
    boundary = 'pinned_node_1'
    value = 0
  [../]
[]

[Materials]
  [./const]
    type = ADGenericConstantMaterial
    prop_names = 'rho mu cp k'
    prop_values = '1  1  1  .01'
  [../]
  [ins_mat0]
    type = INSAD3Eqn
    velocity = velocity0
    pressure = p0
    temperature = T0
    block = 0
  []
  [ins_mat1]
    type = INSAD3Eqn
    velocity = velocity1
    pressure = p1
    temperature = T1
    block = 1
  []
[]

[Functions]
    # We pick a function that is exactly represented in the velocity
    # space so that the Dirichlet conditions are the same regardless
    # of the mesh spacing.
  [./lid_function0]
    type = ParsedFunction
    expression = '4*x*(1-x)'
  [../]
  [./lid_function1]
    type = ParsedFunction
    expression = '4*(x-1)*(2-x)'
  [../]
[]

[Preconditioning]
  [./SMP]
    type = SMP
    full = true
    solve_type = 'NEWTON'
  [../]
[]

[Executioner]
  type = Transient
  # Run for 100+ timesteps to reach steady state.
  num_steps = 5
  dt = .5
  dtmin = .5
  petsc_options_iname = '-pc_type -pc_asm_overlap -sub_pc_type -sub_pc_factor_levels -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      2               ilu          4                     NONZERO'
  line_search = 'none'
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-13
  nl_max_its = 6
  l_tol = 1e-6
  l_max_its = 500
[]

[Outputs]
  exodus = true
[]

(modules/combined/test/tests/optimization/compliance_sensitivity/paper_three_materials_test.i)

vol_frac = 0.4
cost_frac = 0.2 #0.283 # Change back to 0.4

power = 4

E0 = 1.0e-6
E1 = 0.2
E2 = 0.6
E3 = 1.0

rho0 = 1.0e-6
rho1 = 0.4
rho2 = 0.7
rho3 = 1.0

C0 = 1.0e-6
C1 = 0.5
C2 = 0.8
C3 = 1.0

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  [MeshGenerator]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 50
    ny = 50
    xmin = 0
    xmax = 50
    ymin = 0
    ymax = 50
  []
  [node]
    type = ExtraNodesetGenerator
    input = MeshGenerator
    new_boundary = hold
    nodes = 0
  []
  [push_left]
    type = ExtraNodesetGenerator
    input = node
    new_boundary = push_left
    coord = '25 0 0'
  []
  [push_center]
    type = ExtraNodesetGenerator
    input = push_left
    new_boundary = push_center
    coord = '50 0 0'
  []
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
[]

[AuxVariables]
  [Dc]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = -1.0
  []
  [Cc]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = -1.0
  []
  [Cost]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = -1.0
  []
  [mat_den]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = ${vol_frac}
  []
[]

[AuxKernels]
  [Cost]
    type = MaterialRealAux
    variable = Cost
    property = Cost_mat
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = SMALL
    add_variables = true
    incremental = false
  []
[]

[BCs]
  [no_y]
    type = DirichletBC
    variable = disp_y
    boundary = hold
    value = 0.0
  []
  [no_x_symm]
    type = DirichletBC
    variable = disp_x
    boundary = right
    value = 0.0
  []

[]
[NodalKernels]
  [push_left]
    type = NodalGravity
    variable = disp_y
    boundary = push_left
    gravity_value = -1e-3
    mass = 1
  []
  [push_center]
    type = NodalGravity
    variable = disp_y
    boundary = push_center
    gravity_value = -1e-3
    mass = 1
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeVariableIsotropicElasticityTensor
    youngs_modulus = E_phys
    poissons_ratio = poissons_ratio
    args = 'mat_den'
  []
  [E_phys]
    type = DerivativeParsedMaterial
    # ordered multimaterial simp
    expression = "A1:=(${E0}-${E1})/(${rho0}^${power}-${rho1}^${power}); "
                 "B1:=${E0}-A1*${rho0}^${power}; E1:=A1*mat_den^${power}+B1; "
                 "A2:=(${E1}-${E2})/(${rho1}^${power}-${rho2}^${power}); "
                 "B2:=${E1}-A2*${rho1}^${power}; E2:=A2*mat_den^${power}+B2; "
                 "A3:=(${E2}-${E3})/(${rho2}^${power}-${rho3}^${power}); "
                 "B3:=${E2}-A3*${rho2}^${power}; E3:=A3*mat_den^${power}+B3; "
                 "if(mat_den<${rho1},E1,if(mat_den<${rho2},E2,E3))"
    coupled_variables = 'mat_den'
    property_name = E_phys
    epsilon = 1e-12
  []

  [Cost_mat]
    type = DerivativeParsedMaterial
    # ordered multimaterial simp
    expression = "A1:=(${C0}-${C1})/(${rho0}^(1/${power})-${rho1}^(1/${power})); "
                 "B1:=${C0}-A1*${rho0}^(1/${power}); C1:=A1*mat_den^(1/${power})+B1; "
                 "A2:=(${C1}-${C2})/(${rho1}^(1/${power})-${rho2}^(1/${power})); "
                 "B2:=${C1}-A2*${rho1}^(1/${power}); C2:=A2*mat_den^(1/${power})+B2; "
                 "A3:=(${C2}-${C3})/(${rho2}^(1/${power})-${rho3}^(1/${power})); "
                 "B3:=${C2}-A3*${rho2}^(1/${power}); C3:=A3*mat_den^(1/${power})+B3; "
                 "if(mat_den<${rho1},C1,if(mat_den<${rho2},C2,C3))"
    coupled_variables = 'mat_den'
    property_name = Cost_mat
    epsilon = 1e-12
  []
  [CostDensity]
    type = ParsedMaterial
    property_name = CostDensity
    coupled_variables = 'mat_den Cost'
    expression = 'mat_den*Cost'
  []
  [poissons_ratio]
    type = GenericConstantMaterial
    prop_names = poissons_ratio
    prop_values = 0.3
  []
  [stress]
    type = ComputeLinearElasticStress
  []
  [dc]
    type = ComplianceSensitivity
    design_density = mat_den
    youngs_modulus = E_phys
  []
  [cc]
    type = CostSensitivity
    design_density = mat_den
    cost = Cost_mat
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[UserObjects]
  [rad_avg]
    type = RadialAverage
    radius = 2
    weights = linear
    prop_name = sensitivity
    execute_on = TIMESTEP_END
    force_preaux = true
  []
  [rad_avg_cost]
    type = RadialAverage
    radius = 2
    weights = linear
    prop_name = cost_sensitivity
    execute_on = TIMESTEP_END
    force_preaux = true
  []
  [update]
    type = DensityUpdateTwoConstraints
    # This is
    density_sensitivity = Dc
    cost_density_sensitivity = Cc
    cost = Cost
    cost_fraction = ${cost_frac}
    design_density = mat_den
    volume_fraction = ${vol_frac}

    bisection_lower_bound = 0
    bisection_upper_bound = 1.0e16 # 100

    relative_tolerance = 1.0e-3
    bisection_move = 0.02
    execute_on = TIMESTEP_BEGIN
  []
  # Provides Dc
  [calc_sense]
    type = SensitivityFilter
    density_sensitivity = Dc
    design_density = mat_den
    filter_UO = rad_avg
    execute_on = TIMESTEP_END
    force_postaux = true
  []
  # Provides Cc
  [calc_sense_cost]
    type = SensitivityFilter
    density_sensitivity = Cc
    design_density = mat_den
    filter_UO = rad_avg_cost
    execute_on = TIMESTEP_END
    force_postaux = true
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'
  nl_abs_tol = 1e-10
  dt = 1.0
  num_steps = 25
[]

[Outputs]
  [out]
    type = CSV
    execute_on = 'TIMESTEP_END'
  []
  print_linear_residuals = false
[]

[Postprocessors]
  [mesh_volume]
    type = VolumePostprocessor
    execute_on = 'initial timestep_end'
  []
  [total_vol]
    type = ElementIntegralVariablePostprocessor
    variable = mat_den
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [vol_frac]
    type = ParsedPostprocessor
    expression = 'total_vol / mesh_volume'
    pp_names = 'total_vol mesh_volume'
  []
  [sensitivity]
    type = ElementIntegralMaterialProperty
    mat_prop = sensitivity
  []
  [cost_sensitivity]
    type = ElementIntegralMaterialProperty
    mat_prop = cost_sensitivity
  []
  [cost]
    type = ElementIntegralMaterialProperty
    mat_prop = CostDensity
  []
  [cost_frac]
    type = ParsedPostprocessor
    expression = 'cost / mesh_volume'
    pp_names = 'cost mesh_volume'
  []
  [objective]
    type = ElementIntegralMaterialProperty
    mat_prop = strain_energy_density
    execute_on = 'INITIAL TIMESTEP_END'
  []
[]

(modules/solid_mechanics/test/tests/global_strain/global_strain_hydrostat.i)

[Mesh]
  [generated_mesh]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 1
    ny = 1
    nz = 1
  []
  [cnode]
    type = ExtraNodesetGenerator
    coord = '0.0 0.0 0.0'
    new_boundary = 100
    input = generated_mesh
  []
[]

[Variables]
  [./u_x]
  [../]
  [./u_y]
  [../]
  [./u_z]
  [../]
  [./global_strain]
    order = SIXTH
    family = SCALAR
  [../]
[]

[AuxVariables]
  [./disp_x]
  [../]
  [./disp_y]
  [../]
  [./disp_z]
  [../]
[]

[AuxKernels]
  [./disp_x]
    type = GlobalDisplacementAux
    variable = disp_x
    scalar_global_strain = global_strain
    global_strain_uo = global_strain_uo
    component = 1
  [../]
  [./disp_y]
    type = GlobalDisplacementAux
    variable = disp_y
    scalar_global_strain = global_strain
    global_strain_uo = global_strain_uo
    component = 1
  [../]
  [./disp_z]
    type = GlobalDisplacementAux
    variable = disp_z
    scalar_global_strain = global_strain
    global_strain_uo = global_strain_uo
    component = 2
  [../]
[]

[GlobalParams]
  displacements = 'u_x u_y u_z'
  block = 0
[]

[Kernels]
  [SolidMechanics]
  [../]
[]

[ScalarKernels]
  [./global_strain]
    type = GlobalStrain
    variable = global_strain
    global_strain_uo = global_strain_uo
  [../]
[]

[BCs]
  [./Periodic]
    [./all]
      auto_direction = 'x y z'
      variable = ' u_x u_y u_z'
    [../]
  [../]

  # fix center point location
  [./centerfix_x]
    type = DirichletBC
    boundary = 100
    variable = u_x
    value = 0
  [../]
  [./centerfix_y]
    type = DirichletBC
    boundary = 100
    variable = u_y
    value = 0
  [../]
  [./centerfix_z]
    type = DirichletBC
    boundary = 100
    variable = u_z
    value = 0
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeElasticityTensor
    block = 0
    C_ijkl = '70e9 0.33'
    fill_method = symmetric_isotropic_E_nu
  [../]
  [./strain]
    type = ComputeSmallStrain
    global_strain = global_strain
  [../]
  [./global_strain]
    type = ComputeGlobalStrain
    scalar_global_strain = global_strain
    global_strain_uo = global_strain_uo
  [../]
  [./stress]
    type = ComputeLinearElasticStress
  [../]
[]

[UserObjects]
  [./global_strain_uo]
    type = GlobalStrainUserObject
    applied_stress_tensor = '-5e9 -5e9 -5e9 0 0 0'
    execute_on = 'Initial Linear Nonlinear'
  [../]
[]

[Postprocessors]
  [./l2err]
    type = ScalarL2Error
    variable = global_strain
    function = -0.02428571 #strain = E*(1-2*nu)/sigma
  [../]
[]

[Preconditioning]
  [./SMP]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = Transient
  scheme = bdf2
  solve_type = 'PJFNK'

  line_search = basic

  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_ksp_type -sub_pc_type -pc_asm_overlap'
  petsc_options_value = 'asm         31   preonly   lu      1'

  l_max_its = 30
  nl_max_its = 12

  l_tol = 1.0e-4

  nl_rel_tol = 1.0e-8
  nl_abs_tol = 1.0e-10

  start_time = 0.0
  num_steps = 2
[]

[Outputs]
  exodus = true
[]

(modules/navier_stokes/test/tests/finite_element/ins/lid_driven/lid_driven_split.i)

[GlobalParams]
  gravity = '0 0 0'
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 1.0
    ymin = 0
    ymax = 1.0
    nx = 40
    ny = 40
    elem_type = QUAD4
  []
  [./corner_node]
    type = ExtraNodesetGenerator
    boundary = 99
    nodes = '0'
    input = gen
  [../]
[]

[Variables]
  # x-velocity
  [./u]
    order = FIRST
    family = LAGRANGE

    [./InitialCondition]
      type = ConstantIC
      value = 0.0
    [../]
  [../]

  # y-velocity
  [./v]
    order = FIRST
    family = LAGRANGE

    [./InitialCondition]
      type = ConstantIC
      value = 0.0
    [../]
  [../]

  # x-acceleration
  [./a1]
    order = FIRST
    family = LAGRANGE

    [./InitialCondition]
      type = ConstantIC
      value = 0.0
    [../]
  [../]

  # y-acceleration
  [./a2]
    order = FIRST
    family = LAGRANGE

    [./InitialCondition]
      type = ConstantIC
      value = 0.0
    [../]
  [../]

  # Pressure
  [./p]
    order = FIRST
    family = LAGRANGE

    [./InitialCondition]
      type = ConstantIC
      value = 0
    [../]
  [../]
[]



[Kernels]
  # split-momentum, x
  [./x_split_momentum]
    type = INSSplitMomentum
    variable = a1
    u = u
    v = v
    a1 = a1
    a2 = a2
    component = 0
  [../]

  # split-momentum, y
  [./y_split_momentum]
    type = INSSplitMomentum
    variable = a2
    u = u
    v = v
    a1 = a1
    a2 = a2
    component = 1
  [../]

  # projection-x, space
  [./x_proj_space]
    type = INSProjection
    variable = u
    a1 = a1
    a2 = a2
    pressure = p
    component = 0
  [../]

  # projection-y, space
  [./y_proj_space]
    type = INSProjection
    variable = v
    a1 = a1
    a2 = a2
    pressure = p
    component = 1
  [../]

  # projection-x, time
  [./x_proj_time]
    type = TimeDerivative
    variable = u
  [../]

  # projection-y, time
  [./y_proj_time]
    type = TimeDerivative
    variable = v
  [../]

  # Pressure
  [./pressure_poisson]
    type = INSPressurePoisson
    variable = p
    a1 = a1
    a2 = a2
  [../]
[]




[BCs]
  [./x_no_slip]
    type = DirichletBC
    variable = u
    boundary = 'bottom right left'
    value = 0.0
  [../]

  [./lid]
    type = DirichletBC
    variable = u
    boundary = 'top'
    value = 100.0
  [../]

  [./y_no_slip]
    type = DirichletBC
    variable = v
    boundary = 'bottom right top left'
    value = 0.0
  [../]

  # Acceleration boundary conditions.  What should these
  # be on the lid?  What should they be in general?  I tried pinning
  # values of acceleration at one node but that didn't seem to work.
  # I also tried setting non-zero acceleration values on the lid but
  # that didn't converge.
  [./x_no_accel]
    type = DirichletBC
    variable = a1
    boundary = 'bottom right top left'
    value = 0.0
  [../]

  [./y_no_accel]
    type = DirichletBC
    variable = a2
    boundary = 'bottom right top left'
    value = 0.0
  [../]

  # With solid walls everywhere, we specify dp/dn=0, i.e the
  # "natural BC" for pressure.  Technically the problem still
  # solves without pinning the pressure somewhere, but the pressure
  # bounces around a lot during the solve, possibly because of
  # the addition of arbitrary constants.
  [./pressure_pin]
    type = DirichletBC
    variable = p
    boundary = '99'
    value = 0
  [../]
[]

[Materials]
  [./const]
    type = GenericConstantMaterial
    block = 0
    # rho = 1000    # kg/m^3
    # mu = 0.798e-3 # Pa-s at 30C
    # cp = 4.179e3  # J/kg-K at 30C
    # k = 0.58      # W/m-K at ?C

    # Dummy parameters
    prop_names = 'rho mu cp k'
    prop_values = '1  1  1  1'
  [../]
[]

[Preconditioning]
# [./FDP_Newton]
#   type = FDP
#   full = true
#   petsc_options = '-snes'
#   #petsc_options_iname = '-mat_fd_coloring_err'
#   #petsc_options_value = '1.e-10'
# [../]

[./SMP_PJFNK]
  type = SMP
  full = true

  #Preconditioned JFNK (default)
  solve_type = 'PJFNK'


[../]
[]


[Executioner]
  type = Transient
  dt = 1.e-4
  dtmin = 1.e-6
  petsc_options_iname = '-ksp_gmres_restart '
  petsc_options_value = '300                '

  line_search = 'none'

  nl_rel_tol = 1e-5
  nl_max_its = 6
  l_tol = 1e-6
  l_max_its = 100
  start_time = 0.0
  num_steps = 1000
[]




[Outputs]
  file_base = lid_driven_split_out
  exodus = true
[]

(modules/combined/examples/geochem-porous_flow/forge/aquifer_geochemistry.i)

# Simulates geochemistry in the aquifer.  This input file may be run in standalone fashion, which will study the natural kinetically-controlled mineral changes in the same way as natural_reservoir.i.  To simulate the FORGE injection scenario, run the porous_flow.i simulation which couples to this input file using MultiApps.
# This file receives pf_rate_H pf_rate_Na pf_rate_K pf_rate_Ca pf_rate_Mg pf_rate_SiO2 pf_rate_Al pf_rate_Cl pf_rate_SO4 pf_rate_HCO3 pf_rate_H2O and temperature as AuxVariables from porous_flow.i
# The pf_rate quantities are kg/s changes of fluid-component mass at each node, but the geochemistry module expects rates-of-changes of moles at every node.  Secondly, since this input file considers just 1 litre of aqueous solution at every node, the nodal_void_volume is used to convert pf_rate_* into rate_*_per_1l, which is measured in mol/s/1_litre_of_aqueous_solution.
# This file sends massfrac_H massfrac_Na massfrac_K massfrac_Ca massfrac_Mg massfrac_SiO2 massfrac_Al massfrac_Cl massfrac_SO4 massfrac_HCO3 to porous_flow.i.  These are computed from the corresponding transported_* quantities.
# The results depend on the kinetic rates used and these are recognised to be poorly constrained by experiment
[UserObjects]
  [rate_Albite]
    type = GeochemistryKineticRate
    kinetic_species_name = Albite
    intrinsic_rate_constant = 1E-17
    multiply_by_mass = true
    area_quantity = 10
    activation_energy = 69.8E3
    one_over_T0 = 0.003354
  []
  [rate_Anhydrite]
    type = GeochemistryKineticRate
    kinetic_species_name = Anhydrite
    intrinsic_rate_constant = 1.0E-7
    multiply_by_mass = true
    area_quantity = 10
    activation_energy = 14.3E3
    one_over_T0 = 0.003354
  []
  [rate_Anorthite]
    type = GeochemistryKineticRate
    kinetic_species_name = Anorthite
    intrinsic_rate_constant = 1.0E-13
    multiply_by_mass = true
    area_quantity = 10
    activation_energy = 17.8E3
    one_over_T0 = 0.003354
  []
  [rate_Calcite]
    type = GeochemistryKineticRate
    kinetic_species_name = Calcite
    intrinsic_rate_constant = 1.0E-10
    multiply_by_mass = true
    area_quantity = 10
    activation_energy = 23.5E3
    one_over_T0 = 0.003354
  []
  [rate_Chalcedony]
    type = GeochemistryKineticRate
    kinetic_species_name = Chalcedony
    intrinsic_rate_constant = 1.0E-18
    multiply_by_mass = true
    area_quantity = 10
    activation_energy = 90.1E3
    one_over_T0 = 0.003354
  []
  [rate_Clinochl-7A]
    type = GeochemistryKineticRate
    kinetic_species_name = Clinochl-7A
    intrinsic_rate_constant = 1.0E-17
    multiply_by_mass = true
    area_quantity = 10
    activation_energy = 88.0E3
    one_over_T0 = 0.003354
  []
  [rate_Illite]
    type = GeochemistryKineticRate
    kinetic_species_name = Illite
    intrinsic_rate_constant = 1E-17
    multiply_by_mass = true
    area_quantity = 10
    activation_energy = 29E3
    one_over_T0 = 0.003354
  []
  [rate_K-feldspar]
    type = GeochemistryKineticRate
    kinetic_species_name = K-feldspar
    intrinsic_rate_constant = 1E-17
    multiply_by_mass = true
    area_quantity = 10
    activation_energy = 38E3
    one_over_T0 = 0.003354
  []
  [rate_Kaolinite]
    type = GeochemistryKineticRate
    kinetic_species_name = Kaolinite
    intrinsic_rate_constant = 1E-18
    multiply_by_mass = true
    area_quantity = 10
    activation_energy = 22.2E3
    one_over_T0 = 0.003354
  []
  [rate_Quartz]
    type = GeochemistryKineticRate
    kinetic_species_name = Quartz
    intrinsic_rate_constant = 1E-18
    multiply_by_mass = true
    area_quantity = 10
    activation_energy = 90.1E3
    one_over_T0 = 0.003354
  []
  [rate_Paragonite]
    type = GeochemistryKineticRate
    kinetic_species_name = Paragonite
    intrinsic_rate_constant = 1E-17
    multiply_by_mass = true
    area_quantity = 10
    activation_energy = 22E3
    one_over_T0 = 0.003354
  []
  [rate_Phlogopite]
    type = GeochemistryKineticRate
    kinetic_species_name = Phlogopite
    intrinsic_rate_constant = 1E-17
    multiply_by_mass = true
    area_quantity = 10
    activation_energy = 22E3
    one_over_T0 = 0.003354
  []
  [rate_Laumontite]
    type = GeochemistryKineticRate
    kinetic_species_name = Laumontite
    intrinsic_rate_constant = 1.0E-15
    multiply_by_mass = true
    area_quantity = 10
    activation_energy = 17.8E3
    one_over_T0 = 0.003354
  []
  [rate_Zoisite]
    type = GeochemistryKineticRate
    kinetic_species_name = Zoisite
    intrinsic_rate_constant = 1E-16
    multiply_by_mass = true
    area_quantity = 10
    activation_energy = 66.1E3
    one_over_T0 = 0.003354
  []
  [definition]
    type = GeochemicalModelDefinition
    database_file = '../../../../geochemistry/database/moose_geochemdb.json'
    basis_species = 'H2O H+ Na+ K+ Ca++ Mg++ SiO2(aq) Al+++ Cl- SO4-- HCO3-'
    remove_all_extrapolated_secondary_species = true
    kinetic_minerals = 'Albite Anhydrite Anorthite Calcite Chalcedony Clinochl-7A Illite K-feldspar Kaolinite Quartz Paragonite Phlogopite Zoisite Laumontite'
    kinetic_rate_descriptions = 'rate_Albite rate_Anhydrite rate_Anorthite rate_Calcite rate_Chalcedony rate_Clinochl-7A rate_Illite rate_K-feldspar rate_Kaolinite rate_Quartz rate_Paragonite rate_Phlogopite rate_Zoisite rate_Laumontite'
  []
  [nodal_void_volume_uo]
    type = NodalVoidVolume
    porosity = porosity
    execute_on = 'initial timestep_end' # "initial" means this is evaluated properly for the first timestep
  []
[]

[SpatialReactionSolver]
  model_definition = definition
  geochemistry_reactor_name = reactor
  charge_balance_species = 'Cl-'
  constraint_species = 'H2O              H+                  Na+              K+                 Ca++              Mg++                SiO2(aq)           Al+++               Cl-                SO4--               HCO3-'
# Following numbers are from water_60_to_220degC_out.csv
  constraint_value = '  1.0006383866109  9.5165072498215e-07 0.100020379171   0.0059389061065    0.011570884507621 4.6626763057447e-06 0.0045110404925255 5.8096968688789e-17 0.13500708594394   6.6523540147676e-05 7.7361407898089e-05'
  constraint_meaning = 'kg_solvent_water free_concentration       free_concentration    free_concentration      free_concentration     free_concentration       free_concentration      free_concentration       bulk_composition free_concentration       free_concentration'
  constraint_unit = '   kg               molal               molal            molal              molal             molal               molal              molal               moles              molal               molal'
  initial_temperature = 220
  temperature = temperature
  kinetic_species_name = '         Albite             Anorthite          K-feldspar         Quartz             Phlogopite         Paragonite         Calcite            Anhydrite          Chalcedony         Illite             Kaolinite          Clinochl-7A        Zoisite            Laumontite'
  kinetic_species_initial_value = '4.324073236492E+02 4.631370307325E+01 2.685015418378E+02 7.720095013956E+02 1.235192062541E+01 7.545461404965E-01 4.234651808835E-04 4.000485907930E-04 4.407616361072E+00 1.342524904876E+01 1.004823151125E+00 4.728132387707E-01 7.326007326007E-01 4.818116116598E-01'
  kinetic_species_unit = '         moles              moles              moles              moles              moles              moles              moles              moles              moles              moles              moles              moles              moles              moles'
  evaluate_kinetic_rates_always = true # otherwise will easily "run out" of dissolving species
  source_species_names = 'H2O H+ Na+ K+ Ca++ Mg++ SiO2(aq) Al+++ Cl- SO4-- HCO3-'
  source_species_rates = 'rate_H2O_per_1l rate_H_per_1l rate_Na_per_1l rate_K_per_1l rate_Ca_per_1l rate_Mg_per_1l rate_SiO2_per_1l rate_Al_per_1l rate_Cl_per_1l rate_SO4_per_1l rate_HCO3_per_1l'
  ramp_max_ionic_strength_initial = 0 # max_ionic_strength in such a simple problem does not need ramping
  execute_console_output_on = ''
  add_aux_molal = false # save some memory and reduce variables in output exodus
  add_aux_mg_per_kg = false # save some memory and reduce variables in output exodus
  add_aux_free_mg = false # save some memory and reduce variables in output exodus
  add_aux_activity = false # save some memory and reduce variables in output exodus
  add_aux_bulk_moles = false # save some memory and reduce variables in output exodus
  adaptive_timestepping = true
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 15
    ny = 10
    xmin = -100
    xmax = 200
    ymin = -100
    ymax = 100
  []
  [injection_node]
    input = gen
    type = ExtraNodesetGenerator
    new_boundary = injection_node
    coord = '0 0 0'
  []
[]

[Executioner]
  type = Transient
  [TimeStepper]
    type = FunctionDT
    function = 'max(1E6, 0.3 * t)'
  []
  end_time = 4E12
[]

[AuxVariables]
  [temperature]
    initial_condition = 220.0
  []
  [porosity]
    initial_condition = 0.01
  []
  [nodal_void_volume]
  []
  [free_cm3_Kfeldspar] # necessary because of the minus sign in K-feldspar which does not parse correctly in the porosity AuxKernel
  []
  [free_cm3_Clinochl7A] # necessary because of the minus sign in Clinochl-7A which does not parse correctly in the porosity AuxKernel
  []
  [pf_rate_H] # change in H mass (kg/s) at each node provided by the porous-flow simulation
  []
  [pf_rate_Na]
  []
  [pf_rate_K]
  []
  [pf_rate_Ca]
  []
  [pf_rate_Mg]
  []
  [pf_rate_SiO2]
  []
  [pf_rate_Al]
  []
  [pf_rate_Cl]
  []
  [pf_rate_SO4]
  []
  [pf_rate_HCO3]
  []
  [pf_rate_H2O] # change in H2O mass (kg/s) at each node provided by the porous-flow simulation
  []
  [rate_H_per_1l]
  []
  [rate_Na_per_1l]
  []
  [rate_K_per_1l]
  []
  [rate_Ca_per_1l]
  []
  [rate_Mg_per_1l]
  []
  [rate_SiO2_per_1l]
  []
  [rate_Al_per_1l]
  []
  [rate_Cl_per_1l]
  []
  [rate_SO4_per_1l]
  []
  [rate_HCO3_per_1l]
  []
  [rate_H2O_per_1l]
  []
  [transported_H]
  []
  [transported_Na]
  []
  [transported_K]
  []
  [transported_Ca]
  []
  [transported_Mg]
  []
  [transported_SiO2]
  []
  [transported_Al]
  []
  [transported_Cl]
  []
  [transported_SO4]
  []
  [transported_HCO3]
  []
  [transported_H2O]
  []
  [transported_mass]
  []
  [massfrac_H]
  []
  [massfrac_Na]
  []
  [massfrac_K]
  []
  [massfrac_Ca]
  []
  [massfrac_Mg]
  []
  [massfrac_SiO2]
  []
  [massfrac_Al]
  []
  [massfrac_Cl]
  []
  [massfrac_SO4]
  []
  [massfrac_HCO3]
  []
  [massfrac_H2O]
  []
[]

[AuxKernels]
  [free_cm3_Kfeldspar]
    type = GeochemistryQuantityAux
    variable = free_cm3_Kfeldspar
    species = 'K-feldspar'
    quantity = free_cm3
    execute_on = 'timestep_begin timestep_end'
  []
  [free_cm3_Clinochl7A]
    type = GeochemistryQuantityAux
    variable = free_cm3_Clinochl7A
    species = 'Clinochl-7A'
    quantity = free_cm3
    execute_on = 'timestep_begin timestep_end'
  []
  [porosity_auxk]
    type = ParsedAux
    coupled_variables = 'free_cm3_Albite free_cm3_Anhydrite free_cm3_Anorthite free_cm3_Calcite free_cm3_Chalcedony free_cm3_Clinochl7A free_cm3_Illite free_cm3_Kfeldspar free_cm3_Kaolinite free_cm3_Quartz free_cm3_Paragonite free_cm3_Phlogopite free_cm3_Zoisite free_cm3_Laumontite'
    expression = '1000.0 / (1000.0 + free_cm3_Albite + free_cm3_Anhydrite + free_cm3_Anorthite + free_cm3_Calcite + free_cm3_Chalcedony + free_cm3_Clinochl7A + free_cm3_Illite + free_cm3_Kfeldspar + free_cm3_Kaolinite + free_cm3_Quartz + free_cm3_Paragonite + free_cm3_Phlogopite + free_cm3_Zoisite + free_cm3_Laumontite)'
    variable = porosity
    execute_on = 'timestep_end'
  []
  [nodal_void_volume_auxk]
    type = NodalVoidVolumeAux
    variable = nodal_void_volume
    nodal_void_volume_uo = nodal_void_volume_uo
    execute_on = 'initial timestep_end' # "initial" to ensure it is properly evaluated for the first timestep
  []
  [rate_H_per_1l_auxk]
    type = ParsedAux
    coupled_variables = 'pf_rate_H nodal_void_volume'
    variable = rate_H_per_1l
    expression = 'pf_rate_H / 1.0079 / nodal_void_volume'
    execute_on = 'timestep_begin'
  []
  [rate_Na_per_1l_auxk]
    type = ParsedAux
    coupled_variables = 'pf_rate_Na nodal_void_volume'
    variable = rate_Na_per_1l
    expression = 'pf_rate_Na / 22.9898 / nodal_void_volume'
    execute_on = 'timestep_begin'
  []
  [rate_K_per_1l_auxk]
    type = ParsedAux
    coupled_variables = 'pf_rate_K nodal_void_volume'
    variable = rate_K_per_1l
    expression = 'pf_rate_K / 39.0983 / nodal_void_volume'
    execute_on = 'timestep_begin'
  []
  [rate_Ca_per_1l_auxk]
    type = ParsedAux
    coupled_variables = 'pf_rate_Ca nodal_void_volume'
    variable = rate_Ca_per_1l
    expression = 'pf_rate_Ca / 40.08 / nodal_void_volume'
    execute_on = 'timestep_begin'
  []
  [rate_Mg_per_1l_auxk]
    type = ParsedAux
    coupled_variables = 'pf_rate_Mg nodal_void_volume'
    variable = rate_Mg_per_1l
    expression = 'pf_rate_Mg / 24.305 / nodal_void_volume'
    execute_on = 'timestep_begin'
  []
  [rate_SiO2_per_1l_auxk]
    type = ParsedAux
    coupled_variables = 'pf_rate_SiO2 nodal_void_volume'
    variable = rate_SiO2_per_1l
    expression = 'pf_rate_SiO2 / 60.0843 / nodal_void_volume'
    execute_on = 'timestep_begin'
  []
  [rate_Al_per_1l_auxk]
    type = ParsedAux
    coupled_variables = 'pf_rate_Al nodal_void_volume'
    variable = rate_Al_per_1l
    expression = 'pf_rate_Al / 26.9815 / nodal_void_volume'
    execute_on = 'timestep_begin'
  []
  [rate_Cl_per_1l_auxk]
    type = ParsedAux
    coupled_variables = 'pf_rate_Cl nodal_void_volume'
    variable = rate_Cl_per_1l
    expression = 'pf_rate_Cl / 35.453 / nodal_void_volume'
    execute_on = 'timestep_begin'
  []
  [rate_SO4_per_1l_auxk]
    type = ParsedAux
    coupled_variables = 'pf_rate_SO4 nodal_void_volume'
    variable = rate_SO4_per_1l
    expression = 'pf_rate_SO4 / 96.0576 / nodal_void_volume'
    execute_on = 'timestep_begin'
  []
  [rate_HCO3_per_1l_auxk]
    type = ParsedAux
    coupled_variables = 'pf_rate_HCO3 nodal_void_volume'
    variable = rate_HCO3_per_1l
    expression = 'pf_rate_HCO3 / 61.0171 / nodal_void_volume'
    execute_on = 'timestep_begin'
  []
  [rate_H2O_per_1l_auxk]
    type = ParsedAux
    coupled_variables = 'pf_rate_H2O nodal_void_volume'
    variable = rate_H2O_per_1l
    expression = 'pf_rate_H2O / 18.01801802 / nodal_void_volume'
    execute_on = 'timestep_begin'
  []
  [transported_H_auxk]
    type = GeochemistryQuantityAux
    variable = transported_H
    species = 'H+'
    quantity = transported_moles_in_original_basis
    execute_on = 'timestep_begin'
  []
  [transported_Na_auxk]
    type = GeochemistryQuantityAux
    variable = transported_Na
    species = 'Na+'
    quantity = transported_moles_in_original_basis
    execute_on = 'timestep_begin'
  []
  [transported_K_auxk]
    type = GeochemistryQuantityAux
    variable = transported_K
    species = 'K+'
    quantity = transported_moles_in_original_basis
    execute_on = 'timestep_begin'
  []
  [transported_Ca_auxk]
    type = GeochemistryQuantityAux
    variable = transported_Ca
    species = 'Ca++'
    quantity = transported_moles_in_original_basis
    execute_on = 'timestep_begin'
  []
  [transported_Mg_auxk]
    type = GeochemistryQuantityAux
    variable = transported_Mg
    species = 'Mg++'
    quantity = transported_moles_in_original_basis
    execute_on = 'timestep_begin'
  []
  [transported_SiO2_auxk]
    type = GeochemistryQuantityAux
    variable = transported_SiO2
    species = 'SiO2(aq)'
    quantity = transported_moles_in_original_basis
    execute_on = 'timestep_begin'
  []
  [transported_Al_auxk]
    type = GeochemistryQuantityAux
    variable = transported_Al
    species = 'Al+++'
    quantity = transported_moles_in_original_basis
    execute_on = 'timestep_begin'
  []
  [transported_Cl_auxk]
    type = GeochemistryQuantityAux
    variable = transported_Cl
    species = 'Cl-'
    quantity = transported_moles_in_original_basis
    execute_on = 'timestep_begin'
  []
  [transported_SO4_auxk]
    type = GeochemistryQuantityAux
    variable = transported_SO4
    species = 'SO4--'
    quantity = transported_moles_in_original_basis
    execute_on = 'timestep_begin'
  []
  [transported_HCO3_auxk]
    type = GeochemistryQuantityAux
    variable = transported_HCO3
    species = 'HCO3-'
    quantity = transported_moles_in_original_basis
    execute_on = 'timestep_begin'
  []
  [transported_H2O_auxk]
    type = GeochemistryQuantityAux
    variable = transported_H2O
    species = 'H2O'
    quantity = transported_moles_in_original_basis
    execute_on = 'timestep_begin'
  []
  [transported_mass_auxk]
    type = ParsedAux
    coupled_variables = ' transported_H transported_Na transported_K transported_Ca transported_Mg transported_SiO2 transported_Al transported_Cl transported_SO4 transported_HCO3 transported_H2O'
    variable = transported_mass
    expression = 'transported_H * 1.0079 + transported_Cl * 35.453 + transported_SO4 * 96.0576 + transported_HCO3 * 61.0171 + transported_SiO2 * 60.0843 + transported_Al * 26.9815 + transported_Ca * 40.08 + transported_Mg * 24.305 + transported_K * 39.0983 + transported_Na * 22.9898 + transported_H2O * 18.01801802'
    execute_on = 'timestep_end'
  []
  [massfrac_H_auxk]
    type = ParsedAux
    coupled_variables = 'transported_H transported_mass'
    variable = massfrac_H
    expression = 'transported_H * 1.0079 / transported_mass'
    execute_on = 'timestep_end'
  []
  [massfrac_Na_auxk]
    type = ParsedAux
    coupled_variables = 'transported_Na transported_mass'
    variable = massfrac_Na
    expression = 'transported_Na * 22.9898 / transported_mass'
    execute_on = 'timestep_end'
  []
  [massfrac_K_auxk]
    type = ParsedAux
    coupled_variables = 'transported_K transported_mass'
    variable = massfrac_K
    expression = 'transported_K * 39.0983 / transported_mass'
    execute_on = 'timestep_end'
  []
  [massfrac_Ca_auxk]
    type = ParsedAux
    coupled_variables = 'transported_Ca transported_mass'
    variable = massfrac_Ca
    expression = 'transported_Ca * 40.08 / transported_mass'
    execute_on = 'timestep_end'
  []
  [massfrac_Mg_auxk]
    type = ParsedAux
    coupled_variables = 'transported_Mg transported_mass'
    variable = massfrac_Mg
    expression = 'transported_Mg * 24.305 / transported_mass'
    execute_on = 'timestep_end'
  []
  [massfrac_SiO2_auxk]
    type = ParsedAux
    coupled_variables = 'transported_SiO2 transported_mass'
    variable = massfrac_SiO2
    expression = 'transported_SiO2 * 60.0843 / transported_mass'
    execute_on = 'timestep_end'
  []
  [massfrac_Al_auxk]
    type = ParsedAux
    coupled_variables = 'transported_Al transported_mass'
    variable = massfrac_Al
    expression = 'transported_Al * 26.9815 / transported_mass'
    execute_on = 'timestep_end'
  []
  [massfrac_Cl_auxk]
    type = ParsedAux
    coupled_variables = 'transported_Cl transported_mass'
    variable = massfrac_Cl
    expression = 'transported_Cl * 35.453 / transported_mass'
    execute_on = 'timestep_end'
  []
  [massfrac_SO4_auxk]
    type = ParsedAux
    coupled_variables = 'transported_SO4 transported_mass'
    variable = massfrac_SO4
    expression = 'transported_SO4 * 96.0576 / transported_mass'
    execute_on = 'timestep_end'
  []
  [massfrac_HCO3_auxk]
    type = ParsedAux
    coupled_variables = 'transported_HCO3 transported_mass'
    variable = massfrac_HCO3
    expression = 'transported_HCO3 * 61.0171 / transported_mass'
    execute_on = 'timestep_end'
  []
  [massfrac_H2O_auxk]
    type = ParsedAux
    coupled_variables = 'transported_H2O transported_mass'
    variable = massfrac_H2O
    expression = 'transported_H2O * 18.01801802 / transported_mass'
    execute_on = 'timestep_end'
  []
[]

[GlobalParams]
  point = '0 0 0'
  reactor = reactor
[]

[Postprocessors]
  [temperature]
    type = PointValue
    variable = 'solution_temperature'
  []
  [porosity]
    type = PointValue
    variable = porosity
  []
  [solution_temperature]
    type = PointValue
    variable = solution_temperature
  []
  [massfrac_H]
    type = PointValue
    variable = massfrac_H
  []
  [massfrac_Na]
    type = PointValue
    variable = massfrac_Na
  []
  [massfrac_K]
    type = PointValue
    variable = massfrac_K
  []
  [massfrac_Ca]
    type = PointValue
    variable = massfrac_Ca
  []
  [massfrac_Mg]
    type = PointValue
    variable = massfrac_Mg
  []
  [massfrac_SiO2]
    type = PointValue
    variable = massfrac_SiO2
  []
  [massfrac_Al]
    type = PointValue
    variable = massfrac_Al
  []
  [massfrac_Cl]
    type = PointValue
    variable = massfrac_Cl
  []
  [massfrac_SO4]
    type = PointValue
    variable = massfrac_SO4
  []
  [massfrac_HCO3]
    type = PointValue
    variable = massfrac_HCO3
  []
  [massfrac_H2O]
    type = PointValue
    variable = massfrac_H2O
  []
  [cm3_Albite]
    type = PointValue
    variable = 'free_cm3_Albite'
  []
  [cm3_Anhydrite]
    type = PointValue
    variable = 'free_cm3_Anhydrite'
  []
  [cm3_Anorthite]
    type = PointValue
    variable = 'free_cm3_Anorthite'
  []
  [cm3_Calcite]
    type = PointValue
    variable = 'free_cm3_Calcite'
  []
  [cm3_Chalcedony]
    type = PointValue
    variable = 'free_cm3_Chalcedony'
  []
  [cm3_Clinochl-7A]
    type = PointValue
    variable = 'free_cm3_Clinochl-7A'
  []
  [cm3_Illite]
    type = PointValue
    variable = 'free_cm3_Illite'
  []
  [cm3_K-feldspar]
    type = PointValue
    variable = 'free_cm3_K-feldspar'
  []
  [cm3_Kaolinite]
    type = PointValue
    variable = 'free_cm3_Kaolinite'
  []
  [cm3_Quartz]
    type = PointValue
    variable = 'free_cm3_Quartz'
  []
  [cm3_Paragonite]
    type = PointValue
    variable = 'free_cm3_Paragonite'
  []
  [cm3_Phlogopite]
    type = PointValue
    variable = 'free_cm3_Phlogopite'
  []
  [cm3_Zoisite]
    type = PointValue
    variable = 'free_cm3_Zoisite'
  []
  [cm3_Laumontite]
    type = PointValue
    variable = 'free_cm3_Laumontite'
  []
  [cm3_mineral]
    type = LinearCombinationPostprocessor
    pp_names = 'cm3_Albite cm3_Anhydrite cm3_Anorthite cm3_Calcite cm3_Chalcedony cm3_Clinochl-7A cm3_Illite cm3_K-feldspar cm3_Kaolinite cm3_Quartz cm3_Paragonite cm3_Phlogopite cm3_Zoisite cm3_Laumontite'
    pp_coefs = '1 1 1 1 1 1 1 1 1 1 1 1 1 1'
  []
  [pH]
    type = PointValue
    variable = 'pH'
  []
[]

[Outputs]
  [exo]
    type = Exodus
    execute_on = final
  []
  csv = true
[]

(modules/porous_flow/test/tests/dirackernels/injection_production.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 10
    ny = 10
    nz = 1
    xmin = -50
    xmax = 50
    ymin = -50
    ymax = 50
    zmin = 0
    zmax = 10
  []
  [central_nodes]
    input = gen
    type = ExtraNodesetGenerator
    new_boundary = central_nodes
    coord = '0 0 0; 0 0 10'
  []
[]

[GlobalParams]
  PorousFlowDictator = dictator
[]

[Variables]
  [porepressure]
    initial_condition = 20E6
  []
  [temperature]
    initial_condition = 400
    scaling = 1E-6 # fluid enthalpy is roughly 1E6
  []
[]

[BCs]
  [injection_temperature]
    type = DirichletBC
    variable = temperature
    value = 300
    boundary = central_nodes
  []
[]

[DiracKernels]
  [fluid_injection]
    type = PorousFlowPeacemanBorehole
    variable = porepressure
    SumQuantityUO = injected_mass
    point_file = injection.bh
    function_of = pressure
    fluid_phase = 0
    bottom_p_or_t = 21E6
    unit_weight = '0 0 0'
    use_mobility = true
    character = -1
  []
  [fluid_production]
    type = PorousFlowPeacemanBorehole
    variable = porepressure
    SumQuantityUO = produced_mass
    point_file = production.bh
    function_of = pressure
    fluid_phase = 0
    bottom_p_or_t = 20E6
    unit_weight = '0 0 0'
    use_mobility = true
    character = 1
  []
  [remove_heat_at_production_well]
    type = PorousFlowPeacemanBorehole
    variable = temperature
    SumQuantityUO = produced_heat
    point_file = production.bh
    function_of = pressure
    fluid_phase = 0
    bottom_p_or_t = 20E6
    unit_weight = '0 0 0'
    use_mobility = true
    use_enthalpy = true
    character = 1
  []
[]

[UserObjects]
  [injected_mass]
    type = PorousFlowSumQuantity
  []
  [produced_mass]
    type = PorousFlowSumQuantity
  []
  [produced_heat]
    type = PorousFlowSumQuantity
  []
[]

[Postprocessors]
  [heat_joules_extracted_this_timestep]
    type = PorousFlowPlotQuantity
    uo = produced_heat
  []
[]

[FluidProperties]
  [the_simple_fluid]
    type = SimpleFluidProperties
    thermal_expansion = 2E-4
    bulk_modulus = 2E9
    viscosity = 1E-3
    density0 = 1000
    cv = 4000.0
    cp = 4000.0
  []
[]

[PorousFlowUnsaturated]
  porepressure = porepressure
  temperature = temperature
  coupling_type = ThermoHydro
  gravity = '0 0 0'
  fp = the_simple_fluid
[]

[Materials]
  [porosity]
    type = PorousFlowPorosityConst # only the initial value of this is ever used
    porosity = 0.1
  []
  [biot_modulus]
    type = PorousFlowConstantBiotModulus
    solid_bulk_compliance = 1E-10
    fluid_bulk_modulus = 2E9
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1E-12 0 0   0 1E-12 0   0 0 1E-12'
  []
  [thermal_expansion]
    type = PorousFlowConstantThermalExpansionCoefficient
    fluid_coefficient = 5E-6
    drained_coefficient = 2E-4
  []
  [thermal_conductivity]
    type = PorousFlowThermalConductivityIdeal
    dry_thermal_conductivity = '1 0 0  0 1 0  0 0 1'
  []
  [rock_heat]
    type = PorousFlowMatrixInternalEnergy
    density = 2500.0
    specific_heat_capacity = 1200.0
  []
[]

[Preconditioning]
  active = basic
  [basic]
    type = SMP
    full = true
    petsc_options = '-ksp_diagonal_scale -ksp_diagonal_scale_fix'
    petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type -pc_asm_overlap'
    petsc_options_value = ' asm      lu           NONZERO                   2'
  []
  [preferred_but_might_not_be_installed]
    type = SMP
    full = true
    petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
    petsc_options_value = ' lu       mumps'
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  end_time = 2E6
  dt = 2E5
[]

[Outputs]
  exodus = true
[]

(modules/combined/examples/geochem-porous_flow/geotes_weber_tensleep/aquifer_geochemistry.i)

#########################################
#                                       #
# File written by create_input_files.py #
#                                       #
#########################################
# Simulates geochemistry in the aquifer.  This input file may be run in standalone fashion but it does not do anything of interest.  To simulate something interesting, run the porous_flow.i simulation which couples to this input file using MultiApps.
# This file receives pf_rate_H pf_rate_Cl pf_rate_SO4 pf_rate_HCO3 pf_rate_SiO2aq pf_rate_Al pf_rate_Ca pf_rate_Mg pf_rate_Fe pf_rate_K pf_rate_Na pf_rate_Sr pf_rate_F pf_rate_BOH pf_rate_Br pf_rate_Ba pf_rate_Li pf_rate_NO3 pf_rate_O2aq pf_rate_H2O and temperature as AuxVariables from porous_flow.i
# The pf_rate quantities are kg/s changes of fluid-component mass at each node, but the geochemistry module expects rates-of-changes of moles at every node.  Secondly, since this input file considers just 1 litre of aqueous solution at every node, the nodal_void_volume is used to convert pf_rate_* into rate_*_per_1l, which is measured in mol/s/1_litre_of_aqueous_solution.
# This file sends massfrac_H massfrac_Cl massfrac_SO4 massfrac_HCO3 massfrac_SiO2aq massfrac_Al massfrac_Ca massfrac_Mg massfrac_Fe massfrac_K massfrac_Na massfrac_Sr massfrac_F massfrac_BOH massfrac_Br massfrac_Ba massfrac_Li massfrac_NO3 massfrac_O2aq to porous_flow.i.  These are computed from the corresponding transported_* quantities.

[UserObjects]
  [definition]
    type = GeochemicalModelDefinition
    database_file = '../../../../geochemistry/database/moose_geochemdb.json'
    basis_species = 'H2O H+ Cl- SO4-- HCO3- SiO2(aq) Al+++ Ca++ Mg++ Fe++ K+ Na+ Sr++ F- B(OH)3 Br- Ba++ Li+ NO3- O2(aq)'
    equilibrium_minerals = 'Siderite Pyrrhotite Dolomite Illite Anhydrite Calcite Quartz K-feldspar Kaolinite Barite Celestite Fluorite Albite Chalcedony Goethite'
  []
  [nodal_void_volume_uo]
    type = NodalVoidVolume
    porosity = porosity
    execute_on = 'initial timestep_end' # initial means this is evaluated properly for the first timestep
  []
[]

[SpatialReactionSolver]
  model_definition = definition
  geochemistry_reactor_name = reactor
  charge_balance_species = 'Cl-'
  swap_out_of_basis = 'NO3- H+         Fe++       Ba++   SiO2(aq) Mg++     O2(aq)   Al+++   K+     Ca++      HCO3-'
  swap_into_basis = '  NH3  Pyrrhotite K-feldspar Barite Quartz   Dolomite Siderite Calcite Illite Anhydrite Kaolinite'
# ASSUME that 1 litre of solution contains:
  constraint_species = 'H2O        Quartz     Calcite   K-feldspar Siderite  Dolomite  Anhydrite Pyrrhotite Illite    Kaolinite  Barite       Na+       Cl-       SO4--       Li+         B(OH)3      Br-         F-         Sr++        NH3'
  constraint_value = '  0.99778351 322.177447 12.111108 6.8269499  6.2844304 2.8670301 1.1912027 0.51474767 0.3732507 0.20903322 0.0001865889 1.5876606 1.5059455 0.046792579 0.013110503 0.006663119 0.001238987 0.00032108 0.000159781 0.001937302'
  constraint_meaning = 'kg_solvent_water bulk_composition bulk_composition bulk_composition bulk_composition bulk_composition bulk_composition bulk_composition bulk_composition bulk_composition bulk_composition bulk_composition bulk_composition bulk_composition bulk_composition bulk_composition bulk_composition bulk_composition bulk_composition bulk_composition'
  constraint_unit = "kg moles moles moles moles moles moles moles moles moles moles moles moles moles moles moles moles moles moles moles"
  prevent_precipitation = 'Fluorite Albite Goethite'
  initial_temperature = 92
  temperature = temperature
  source_species_names = 'H+ Cl- SO4-- HCO3- SiO2(aq) Al+++ Ca++ Mg++ Fe++ K+ Na+ Sr++ F- B(OH)3 Br- Ba++ Li+ NO3- O2(aq) H2O'
  source_species_rates = ' rate_H_per_1l rate_Cl_per_1l rate_SO4_per_1l rate_HCO3_per_1l rate_SiO2aq_per_1l rate_Al_per_1l rate_Ca_per_1l rate_Mg_per_1l rate_Fe_per_1l rate_K_per_1l rate_Na_per_1l rate_Sr_per_1l rate_F_per_1l rate_BOH_per_1l rate_Br_per_1l rate_Ba_per_1l rate_Li_per_1l rate_NO3_per_1l rate_O2aq_per_1l rate_H2O_per_1l'
  ramp_max_ionic_strength_initial = 0 # max_ionic_strength in such a simple problem does not need ramping
  execute_console_output_on = '' # only CSV and exodus output for this simulation
  add_aux_molal = false # save some memory and reduce variables in output exodus
  add_aux_mg_per_kg = false # save some memory and reduce variables in output exodus
  add_aux_free_mg = false # save some memory and reduce variables in output exodus
  add_aux_activity = false # save some memory and reduce variables in output exodus
  add_aux_bulk_moles = false # save some memory and reduce variables in output exodus
  adaptive_timestepping = true
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 3
    xmin = -75
    xmax = 75
    ymin = 0
    ymax = 40
    zmin = -25
    zmax = 25
    nx = 15
    ny = 4
    nz = 5
  []
  [aquifer]
    type = ParsedSubdomainMeshGenerator
    input = gen
    block_id = 1
    block_name = aquifer
    combinatorial_geometry = 'z >= -5 & z <= 5'
  []
  [injection_nodes]
    input = aquifer
    type = ExtraNodesetGenerator
    new_boundary = injection_nodes
    coord = '-25 0 -5; -25 0 5'
  []
  [production_nodes]
    input = injection_nodes
    type = ExtraNodesetGenerator
    new_boundary = production_nodes
    coord = '25 0 -5; 25 0 5'
  []
[]
[GlobalParams]
  point = '-25 0 0'
  reactor = reactor
[]
[Executioner]
  type = Transient
  solve_type = Newton
  end_time = 7.76E6 # 90 days
  [TimeStepper]
    type = FunctionDT
    function = 'min(3E4, max(1E4, 0.2 * t))'
  []
[]
[AuxVariables]
  [temperature]
    initial_condition = 92.0
  []
  [porosity]
    initial_condition = 0.1
  []
  [nodal_void_volume]
  []
  [free_cm3_Kfeldspar] # necessary because of the minus sign in K-feldspar which does not parse correctly in the porosity AuxKernel
  []
  [pf_rate_H] # change in H mass (kg/s) at each node provided by the porous-flow simulation
  []
  [pf_rate_Cl] # change in Cl mass (kg/s) at each node provided by the porous-flow simulation
  []
  [pf_rate_SO4] # change in SO4 mass (kg/s) at each node provided by the porous-flow simulation
  []
  [pf_rate_HCO3] # change in HCO3 mass (kg/s) at each node provided by the porous-flow simulation
  []
  [pf_rate_SiO2aq] # change in SiO2aq mass (kg/s) at each node provided by the porous-flow simulation
  []
  [pf_rate_Al] # change in Al mass (kg/s) at each node provided by the porous-flow simulation
  []
  [pf_rate_Ca] # change in Ca mass (kg/s) at each node provided by the porous-flow simulation
  []
  [pf_rate_Mg] # change in Mg mass (kg/s) at each node provided by the porous-flow simulation
  []
  [pf_rate_Fe] # change in Fe mass (kg/s) at each node provided by the porous-flow simulation
  []
  [pf_rate_K] # change in K mass (kg/s) at each node provided by the porous-flow simulation
  []
  [pf_rate_Na] # change in Na mass (kg/s) at each node provided by the porous-flow simulation
  []
  [pf_rate_Sr] # change in Sr mass (kg/s) at each node provided by the porous-flow simulation
  []
  [pf_rate_F] # change in F mass (kg/s) at each node provided by the porous-flow simulation
  []
  [pf_rate_BOH] # change in BOH mass (kg/s) at each node provided by the porous-flow simulation
  []
  [pf_rate_Br] # change in Br mass (kg/s) at each node provided by the porous-flow simulation
  []
  [pf_rate_Ba] # change in Ba mass (kg/s) at each node provided by the porous-flow simulation
  []
  [pf_rate_Li] # change in Li mass (kg/s) at each node provided by the porous-flow simulation
  []
  [pf_rate_NO3] # change in NO3 mass (kg/s) at each node provided by the porous-flow simulation
  []
  [pf_rate_O2aq] # change in O2aq mass (kg/s) at each node provided by the porous-flow simulation
  []
  [pf_rate_H2O] # change in H2O mass (kg/s) at each node provided by the porous-flow simulation
  []
  [rate_H_per_1l]
  []
  [rate_Cl_per_1l]
  []
  [rate_SO4_per_1l]
  []
  [rate_HCO3_per_1l]
  []
  [rate_SiO2aq_per_1l]
  []
  [rate_Al_per_1l]
  []
  [rate_Ca_per_1l]
  []
  [rate_Mg_per_1l]
  []
  [rate_Fe_per_1l]
  []
  [rate_K_per_1l]
  []
  [rate_Na_per_1l]
  []
  [rate_Sr_per_1l]
  []
  [rate_F_per_1l]
  []
  [rate_BOH_per_1l]
  []
  [rate_Br_per_1l]
  []
  [rate_Ba_per_1l]
  []
  [rate_Li_per_1l]
  []
  [rate_NO3_per_1l]
  []
  [rate_O2aq_per_1l]
  []
  [rate_H2O_per_1l]
  []
  [transported_H]
  []
  [transported_Cl]
  []
  [transported_SO4]
  []
  [transported_HCO3]
  []
  [transported_SiO2aq]
  []
  [transported_Al]
  []
  [transported_Ca]
  []
  [transported_Mg]
  []
  [transported_Fe]
  []
  [transported_K]
  []
  [transported_Na]
  []
  [transported_Sr]
  []
  [transported_F]
  []
  [transported_BOH]
  []
  [transported_Br]
  []
  [transported_Ba]
  []
  [transported_Li]
  []
  [transported_NO3]
  []
  [transported_O2aq]
  []
  [transported_H2O]
  []
  [transported_mass]
  []
  [massfrac_H]
  []
  [massfrac_Cl]
  []
  [massfrac_SO4]
  []
  [massfrac_HCO3]
  []
  [massfrac_SiO2aq]
  []
  [massfrac_Al]
  []
  [massfrac_Ca]
  []
  [massfrac_Mg]
  []
  [massfrac_Fe]
  []
  [massfrac_K]
  []
  [massfrac_Na]
  []
  [massfrac_Sr]
  []
  [massfrac_F]
  []
  [massfrac_BOH]
  []
  [massfrac_Br]
  []
  [massfrac_Ba]
  []
  [massfrac_Li]
  []
  [massfrac_NO3]
  []
  [massfrac_O2aq]
  []
  [massfrac_H2O]
  []
[]

[AuxKernels]
  [free_cm3_Kfeldspar]
    type = GeochemistryQuantityAux
    variable = free_cm3_Kfeldspar
    species = 'K-feldspar'
    quantity = free_cm3
    execute_on = 'timestep_end'
  []
  [porosity_auxk]
    type = ParsedAux
    coupled_variables = 'free_cm3_Siderite free_cm3_Pyrrhotite free_cm3_Dolomite free_cm3_Illite free_cm3_Anhydrite free_cm3_Calcite free_cm3_Quartz free_cm3_Kfeldspar free_cm3_Kaolinite free_cm3_Barite free_cm3_Celestite free_cm3_Fluorite free_cm3_Albite free_cm3_Chalcedony free_cm3_Goethite'
    expression = '1000.0 / (1000.0 + free_cm3_Siderite + free_cm3_Pyrrhotite + free_cm3_Dolomite + free_cm3_Illite + free_cm3_Anhydrite + free_cm3_Calcite + free_cm3_Quartz + free_cm3_Kfeldspar + free_cm3_Kaolinite + free_cm3_Barite + free_cm3_Celestite + free_cm3_Fluorite + free_cm3_Albite + free_cm3_Chalcedony + free_cm3_Goethite)'
    variable = porosity
    execute_on = 'timestep_end'
  []
  [nodal_void_volume_auxk]
    type = NodalVoidVolumeAux
    variable = nodal_void_volume
    nodal_void_volume_uo = nodal_void_volume_uo
    execute_on = 'initial timestep_end' # initial to ensure it is properly evaluated for the first timestep
  []
  [rate_H_per_1l_auxk]
    type = ParsedAux
    coupled_variables = 'pf_rate_H nodal_void_volume'
    variable = rate_H_per_1l
    expression = 'pf_rate_H / 1.0079 / nodal_void_volume'
    execute_on = 'timestep_end'
  []
  [rate_Cl_per_1l_auxk]
    type = ParsedAux
    coupled_variables = 'pf_rate_Cl nodal_void_volume'
    variable = rate_Cl_per_1l
    expression = 'pf_rate_Cl / 35.453 / nodal_void_volume'
    execute_on = 'timestep_end'
  []
  [rate_SO4_per_1l_auxk]
    type = ParsedAux
    coupled_variables = 'pf_rate_SO4 nodal_void_volume'
    variable = rate_SO4_per_1l
    expression = 'pf_rate_SO4 / 96.0576 / nodal_void_volume'
    execute_on = 'timestep_end'
  []
  [rate_HCO3_per_1l_auxk]
    type = ParsedAux
    coupled_variables = 'pf_rate_HCO3 nodal_void_volume'
    variable = rate_HCO3_per_1l
    expression = 'pf_rate_HCO3 / 61.0171 / nodal_void_volume'
    execute_on = 'timestep_end'
  []
  [rate_SiO2aq_per_1l_auxk]
    type = ParsedAux
    coupled_variables = 'pf_rate_SiO2aq nodal_void_volume'
    variable = rate_SiO2aq_per_1l
    expression = 'pf_rate_SiO2aq / 60.0843 / nodal_void_volume'
    execute_on = 'timestep_end'
  []
  [rate_Al_per_1l_auxk]
    type = ParsedAux
    coupled_variables = 'pf_rate_Al nodal_void_volume'
    variable = rate_Al_per_1l
    expression = 'pf_rate_Al / 26.9815 / nodal_void_volume'
    execute_on = 'timestep_end'
  []
  [rate_Ca_per_1l_auxk]
    type = ParsedAux
    coupled_variables = 'pf_rate_Ca nodal_void_volume'
    variable = rate_Ca_per_1l
    expression = 'pf_rate_Ca / 40.08 / nodal_void_volume'
    execute_on = 'timestep_end'
  []
  [rate_Mg_per_1l_auxk]
    type = ParsedAux
    coupled_variables = 'pf_rate_Mg nodal_void_volume'
    variable = rate_Mg_per_1l
    expression = 'pf_rate_Mg / 24.305 / nodal_void_volume'
    execute_on = 'timestep_end'
  []
  [rate_Fe_per_1l_auxk]
    type = ParsedAux
    coupled_variables = 'pf_rate_Fe nodal_void_volume'
    variable = rate_Fe_per_1l
    expression = 'pf_rate_Fe / 55.847 / nodal_void_volume'
    execute_on = 'timestep_end'
  []
  [rate_K_per_1l_auxk]
    type = ParsedAux
    coupled_variables = 'pf_rate_K nodal_void_volume'
    variable = rate_K_per_1l
    expression = 'pf_rate_K / 39.0983 / nodal_void_volume'
    execute_on = 'timestep_end'
  []
  [rate_Na_per_1l_auxk]
    type = ParsedAux
    coupled_variables = 'pf_rate_Na nodal_void_volume'
    variable = rate_Na_per_1l
    expression = 'pf_rate_Na / 22.9898 / nodal_void_volume'
    execute_on = 'timestep_end'
  []
  [rate_Sr_per_1l_auxk]
    type = ParsedAux
    coupled_variables = 'pf_rate_Sr nodal_void_volume'
    variable = rate_Sr_per_1l
    expression = 'pf_rate_Sr / 87.62 / nodal_void_volume'
    execute_on = 'timestep_end'
  []
  [rate_F_per_1l_auxk]
    type = ParsedAux
    coupled_variables = 'pf_rate_F nodal_void_volume'
    variable = rate_F_per_1l
    expression = 'pf_rate_F / 18.9984 / nodal_void_volume'
    execute_on = 'timestep_end'
  []
  [rate_BOH_per_1l_auxk]
    type = ParsedAux
    coupled_variables = 'pf_rate_BOH nodal_void_volume'
    variable = rate_BOH_per_1l
    expression = 'pf_rate_BOH / 61.8329 / nodal_void_volume'
    execute_on = 'timestep_end'
  []
  [rate_Br_per_1l_auxk]
    type = ParsedAux
    coupled_variables = 'pf_rate_Br nodal_void_volume'
    variable = rate_Br_per_1l
    expression = 'pf_rate_Br / 79.904 / nodal_void_volume'
    execute_on = 'timestep_end'
  []
  [rate_Ba_per_1l_auxk]
    type = ParsedAux
    coupled_variables = 'pf_rate_Ba nodal_void_volume'
    variable = rate_Ba_per_1l
    expression = 'pf_rate_Ba / 137.33 / nodal_void_volume'
    execute_on = 'timestep_end'
  []
  [rate_Li_per_1l_auxk]
    type = ParsedAux
    coupled_variables = 'pf_rate_Li nodal_void_volume'
    variable = rate_Li_per_1l
    expression = 'pf_rate_Li / 6.941 / nodal_void_volume'
    execute_on = 'timestep_end'
  []
  [rate_NO3_per_1l_auxk]
    type = ParsedAux
    coupled_variables = 'pf_rate_NO3 nodal_void_volume'
    variable = rate_NO3_per_1l
    expression = 'pf_rate_NO3 / 62.0049 / nodal_void_volume'
    execute_on = 'timestep_end'
  []
  [rate_O2aq_per_1l_auxk]
    type = ParsedAux
    coupled_variables = 'pf_rate_O2aq nodal_void_volume'
    variable = rate_O2aq_per_1l
    expression = 'pf_rate_O2aq / 31.9988 / nodal_void_volume'
    execute_on = 'timestep_end'
  []
  [rate_H2O_per_1l_auxk]
    type = ParsedAux
    coupled_variables = 'pf_rate_H2O nodal_void_volume'
    variable = rate_H2O_per_1l
    expression = 'pf_rate_H2O / 18.01801802 / nodal_void_volume'
    execute_on = 'timestep_end'
  []
  [transported_H_auxk]
    type = GeochemistryQuantityAux
    variable = transported_H
    species = 'H+'
    quantity = transported_moles_in_original_basis
    execute_on = 'timestep_end'
  []
  [transported_Cl_auxk]
    type = GeochemistryQuantityAux
    variable = transported_Cl
    species = 'Cl-'
    quantity = transported_moles_in_original_basis
    execute_on = 'timestep_end'
  []
  [transported_SO4_auxk]
    type = GeochemistryQuantityAux
    variable = transported_SO4
    species = 'SO4--'
    quantity = transported_moles_in_original_basis
    execute_on = 'timestep_end'
  []
  [transported_HCO3_auxk]
    type = GeochemistryQuantityAux
    variable = transported_HCO3
    species = 'HCO3-'
    quantity = transported_moles_in_original_basis
    execute_on = 'timestep_end'
  []
  [transported_SiO2aq_auxk]
    type = GeochemistryQuantityAux
    variable = transported_SiO2aq
    species = 'SiO2(aq)'
    quantity = transported_moles_in_original_basis
    execute_on = 'timestep_end'
  []
  [transported_Al_auxk]
    type = GeochemistryQuantityAux
    variable = transported_Al
    species = 'Al+++'
    quantity = transported_moles_in_original_basis
    execute_on = 'timestep_end'
  []
  [transported_Ca_auxk]
    type = GeochemistryQuantityAux
    variable = transported_Ca
    species = 'Ca++'
    quantity = transported_moles_in_original_basis
    execute_on = 'timestep_end'
  []
  [transported_Mg_auxk]
    type = GeochemistryQuantityAux
    variable = transported_Mg
    species = 'Mg++'
    quantity = transported_moles_in_original_basis
    execute_on = 'timestep_end'
  []
  [transported_Fe_auxk]
    type = GeochemistryQuantityAux
    variable = transported_Fe
    species = 'Fe++'
    quantity = transported_moles_in_original_basis
    execute_on = 'timestep_end'
  []
  [transported_K_auxk]
    type = GeochemistryQuantityAux
    variable = transported_K
    species = 'K+'
    quantity = transported_moles_in_original_basis
    execute_on = 'timestep_end'
  []
  [transported_Na_auxk]
    type = GeochemistryQuantityAux
    variable = transported_Na
    species = 'Na+'
    quantity = transported_moles_in_original_basis
    execute_on = 'timestep_end'
  []
  [transported_Sr_auxk]
    type = GeochemistryQuantityAux
    variable = transported_Sr
    species = 'Sr++'
    quantity = transported_moles_in_original_basis
    execute_on = 'timestep_end'
  []
  [transported_F_auxk]
    type = GeochemistryQuantityAux
    variable = transported_F
    species = 'F-'
    quantity = transported_moles_in_original_basis
    execute_on = 'timestep_end'
  []
  [transported_BOH_auxk]
    type = GeochemistryQuantityAux
    variable = transported_BOH
    species = 'B(OH)3'
    quantity = transported_moles_in_original_basis
    execute_on = 'timestep_end'
  []
  [transported_Br_auxk]
    type = GeochemistryQuantityAux
    variable = transported_Br
    species = 'Br-'
    quantity = transported_moles_in_original_basis
    execute_on = 'timestep_end'
  []
  [transported_Ba_auxk]
    type = GeochemistryQuantityAux
    variable = transported_Ba
    species = 'Ba++'
    quantity = transported_moles_in_original_basis
    execute_on = 'timestep_end'
  []
  [transported_Li_auxk]
    type = GeochemistryQuantityAux
    variable = transported_Li
    species = 'Li+'
    quantity = transported_moles_in_original_basis
    execute_on = 'timestep_end'
  []
  [transported_NO3_auxk]
    type = GeochemistryQuantityAux
    variable = transported_NO3
    species = 'NO3-'
    quantity = transported_moles_in_original_basis
    execute_on = 'timestep_end'
  []
  [transported_O2aq_auxk]
    type = GeochemistryQuantityAux
    variable = transported_O2aq
    species = 'O2(aq)'
    quantity = transported_moles_in_original_basis
    execute_on = 'timestep_end'
  []
  [transported_H2O_auxk]
    type = GeochemistryQuantityAux
    variable = transported_H2O
    species = 'H2O'
    quantity = transported_moles_in_original_basis
    execute_on = 'timestep_end'
  []
  [transported_mass_auxk]
    type = ParsedAux
    coupled_variables = ' transported_H transported_Cl transported_SO4 transported_HCO3 transported_SiO2aq transported_Al transported_Ca transported_Mg transported_Fe transported_K transported_Na transported_Sr transported_F transported_BOH transported_Br transported_Ba transported_Li transported_NO3 transported_O2aq transported_H2O'
    variable = transported_mass
    expression = 'transported_H * 1.0079 + transported_Cl * 35.453 + transported_SO4 * 96.0576 + transported_HCO3 * 61.0171 + transported_SiO2aq * 60.0843 + transported_Al * 26.9815 + transported_Ca * 40.08 + transported_Mg * 24.305 + transported_Fe * 55.847 + transported_K * 39.0983 + transported_Na * 22.9898 + transported_Sr * 87.62 + transported_F * 18.9984 + transported_BOH * 61.8329 + transported_Br * 79.904 + transported_Ba * 137.33 + transported_Li * 6.941 + transported_NO3 * 62.0049 + transported_O2aq * 31.9988 + transported_H2O * 18.01801802'
    execute_on = 'timestep_end'
  []
  [massfrac_H_auxk]
    type = ParsedAux
    coupled_variables = 'transported_H transported_mass'
    variable = massfrac_H
    expression = 'transported_H * 1.0079 / transported_mass'
    execute_on = 'timestep_end'
  []
  [massfrac_Cl_auxk]
    type = ParsedAux
    coupled_variables = 'transported_Cl transported_mass'
    variable = massfrac_Cl
    expression = 'transported_Cl * 35.453 / transported_mass'
    execute_on = 'timestep_end'
  []
  [massfrac_SO4_auxk]
    type = ParsedAux
    coupled_variables = 'transported_SO4 transported_mass'
    variable = massfrac_SO4
    expression = 'transported_SO4 * 96.0576 / transported_mass'
    execute_on = 'timestep_end'
  []
  [massfrac_HCO3_auxk]
    type = ParsedAux
    coupled_variables = 'transported_HCO3 transported_mass'
    variable = massfrac_HCO3
    expression = 'transported_HCO3 * 61.0171 / transported_mass'
    execute_on = 'timestep_end'
  []
  [massfrac_SiO2aq_auxk]
    type = ParsedAux
    coupled_variables = 'transported_SiO2aq transported_mass'
    variable = massfrac_SiO2aq
    expression = 'transported_SiO2aq * 60.0843 / transported_mass'
    execute_on = 'timestep_end'
  []
  [massfrac_Al_auxk]
    type = ParsedAux
    coupled_variables = 'transported_Al transported_mass'
    variable = massfrac_Al
    expression = 'transported_Al * 26.9815 / transported_mass'
    execute_on = 'timestep_end'
  []
  [massfrac_Ca_auxk]
    type = ParsedAux
    coupled_variables = 'transported_Ca transported_mass'
    variable = massfrac_Ca
    expression = 'transported_Ca * 40.08 / transported_mass'
    execute_on = 'timestep_end'
  []
  [massfrac_Mg_auxk]
    type = ParsedAux
    coupled_variables = 'transported_Mg transported_mass'
    variable = massfrac_Mg
    expression = 'transported_Mg * 24.305 / transported_mass'
    execute_on = 'timestep_end'
  []
  [massfrac_Fe_auxk]
    type = ParsedAux
    coupled_variables = 'transported_Fe transported_mass'
    variable = massfrac_Fe
    expression = 'transported_Fe * 55.847 / transported_mass'
    execute_on = 'timestep_end'
  []
  [massfrac_K_auxk]
    type = ParsedAux
    coupled_variables = 'transported_K transported_mass'
    variable = massfrac_K
    expression = 'transported_K * 39.0983 / transported_mass'
    execute_on = 'timestep_end'
  []
  [massfrac_Na_auxk]
    type = ParsedAux
    coupled_variables = 'transported_Na transported_mass'
    variable = massfrac_Na
    expression = 'transported_Na * 22.9898 / transported_mass'
    execute_on = 'timestep_end'
  []
  [massfrac_Sr_auxk]
    type = ParsedAux
    coupled_variables = 'transported_Sr transported_mass'
    variable = massfrac_Sr
    expression = 'transported_Sr * 87.62 / transported_mass'
    execute_on = 'timestep_end'
  []
  [massfrac_F_auxk]
    type = ParsedAux
    coupled_variables = 'transported_F transported_mass'
    variable = massfrac_F
    expression = 'transported_F * 18.9984 / transported_mass'
    execute_on = 'timestep_end'
  []
  [massfrac_BOH_auxk]
    type = ParsedAux
    coupled_variables = 'transported_BOH transported_mass'
    variable = massfrac_BOH
    expression = 'transported_BOH * 61.8329 / transported_mass'
    execute_on = 'timestep_end'
  []
  [massfrac_Br_auxk]
    type = ParsedAux
    coupled_variables = 'transported_Br transported_mass'
    variable = massfrac_Br
    expression = 'transported_Br * 79.904 / transported_mass'
    execute_on = 'timestep_end'
  []
  [massfrac_Ba_auxk]
    type = ParsedAux
    coupled_variables = 'transported_Ba transported_mass'
    variable = massfrac_Ba
    expression = 'transported_Ba * 137.33 / transported_mass'
    execute_on = 'timestep_end'
  []
  [massfrac_Li_auxk]
    type = ParsedAux
    coupled_variables = 'transported_Li transported_mass'
    variable = massfrac_Li
    expression = 'transported_Li * 6.941 / transported_mass'
    execute_on = 'timestep_end'
  []
  [massfrac_NO3_auxk]
    type = ParsedAux
    coupled_variables = 'transported_NO3 transported_mass'
    variable = massfrac_NO3
    expression = 'transported_NO3 * 62.0049 / transported_mass'
    execute_on = 'timestep_end'
  []
  [massfrac_O2aq_auxk]
    type = ParsedAux
    coupled_variables = 'transported_O2aq transported_mass'
    variable = massfrac_O2aq
    expression = 'transported_O2aq * 31.9988 / transported_mass'
    execute_on = 'timestep_end'
  []
  [massfrac_H2O_auxk]
    type = ParsedAux
    coupled_variables = 'transported_H2O transported_mass'
    variable = massfrac_H2O
    expression = 'transported_H2O * 18.01801802 / transported_mass'
    execute_on = 'timestep_end'
  []
[]

[Postprocessors]
  [memory]
    type = MemoryUsage
    outputs = 'console'
  []
  [porosity]
    type = PointValue
    variable = porosity
  []
  [solution_temperature]
    type = PointValue
    variable = solution_temperature
  []
  [massfrac_H]
    type = PointValue
    variable = massfrac_H
  []
  [massfrac_Cl]
    type = PointValue
    variable = massfrac_Cl
  []
  [massfrac_SO4]
    type = PointValue
    variable = massfrac_SO4
  []
  [massfrac_HCO3]
    type = PointValue
    variable = massfrac_HCO3
  []
  [massfrac_SiO2aq]
    type = PointValue
    variable = massfrac_SiO2aq
  []
  [massfrac_Al]
    type = PointValue
    variable = massfrac_Al
  []
  [massfrac_Ca]
    type = PointValue
    variable = massfrac_Ca
  []
  [massfrac_Mg]
    type = PointValue
    variable = massfrac_Mg
  []
  [massfrac_Fe]
    type = PointValue
    variable = massfrac_Fe
  []
  [massfrac_K]
    type = PointValue
    variable = massfrac_K
  []
  [massfrac_Na]
    type = PointValue
    variable = massfrac_Na
  []
  [massfrac_Sr]
    type = PointValue
    variable = massfrac_Sr
  []
  [massfrac_F]
    type = PointValue
    variable = massfrac_F
  []
  [massfrac_BOH]
    type = PointValue
    variable = massfrac_BOH
  []
  [massfrac_Br]
    type = PointValue
    variable = massfrac_Br
  []
  [massfrac_Ba]
    type = PointValue
    variable = massfrac_Ba
  []
  [massfrac_Li]
    type = PointValue
    variable = massfrac_Li
  []
  [massfrac_NO3]
    type = PointValue
    variable = massfrac_NO3
  []
  [massfrac_O2aq]
    type = PointValue
    variable = massfrac_O2aq
  []
  [massfrac_H2O]
    type = PointValue
    variable = massfrac_H2O
  []
  [free_cm3_Siderite]
    type = PointValue
    variable = free_cm3_Siderite
  []
  [free_cm3_Pyrrhotite]
    type = PointValue
    variable = free_cm3_Pyrrhotite
  []
  [free_cm3_Dolomite]
    type = PointValue
    variable = free_cm3_Dolomite
  []
  [free_cm3_Illite]
    type = PointValue
    variable = free_cm3_Illite
  []
  [free_cm3_Anhydrite]
    type = PointValue
    variable = free_cm3_Anhydrite
  []
  [free_cm3_Calcite]
    type = PointValue
    variable = free_cm3_Calcite
  []
  [free_cm3_Quartz]
    type = PointValue
    variable = free_cm3_Quartz
  []
  [free_cm3_K-feldspar]
    type = PointValue
    variable = free_cm3_K-feldspar
  []
  [free_cm3_Kaolinite]
    type = PointValue
    variable = free_cm3_Kaolinite
  []
  [free_cm3_Barite]
    type = PointValue
    variable = free_cm3_Barite
  []
  [free_cm3_Celestite]
    type = PointValue
    variable = free_cm3_Celestite
  []
  [free_cm3_Fluorite]
    type = PointValue
    variable = free_cm3_Fluorite
  []
  [free_cm3_Albite]
    type = PointValue
    variable = free_cm3_Albite
  []
  [free_cm3_Chalcedony]
    type = PointValue
    variable = free_cm3_Chalcedony
  []
  [free_cm3_Goethite]
    type = PointValue
    variable = free_cm3_Goethite
  []
[]
[Outputs]
  exodus = true
  csv = true
[]

(test/tests/mortar/periodic_segmental_constraint/periodic_simple3d.i)

[Mesh]
  [left_block]
    type = GeneratedMeshGenerator
    dim = 3
    xmin = -3.0
    xmax = 3.0
    ymin = -3.0
    ymax = 3.0
    zmin = -3.0
    zmax = 3.0
    nx = 3
    ny = 3
    nz = 3
    elem_type = HEX27
  []
  [left_block_sidesets]
    type = RenameBoundaryGenerator
    input = left_block
    old_boundary = '0 1 2 3 4 5'
    new_boundary = '10 11 12 13 14 15'
  []
  [left_block_id]
    type = SubdomainIDGenerator
    input = left_block_sidesets
    subdomain_id = 1
  []
  [left]
    type = LowerDBlockFromSidesetGenerator
    input = left_block_id
    sidesets = '14'
    new_block_id = '10004'
    new_block_name = 'secondary_left'
  []
  [right]
    type = LowerDBlockFromSidesetGenerator
    input = left
    sidesets = '12'
    new_block_id = '10002'
    new_block_name = 'primary_right'
  []
  [bottom]
    type = LowerDBlockFromSidesetGenerator
    input = right
    sidesets = '10'
    new_block_id = '10000'
    new_block_name = 'secondary_bottom'
  []
  [top]
    type = LowerDBlockFromSidesetGenerator
    input = bottom
    sidesets = '15'
    new_block_id = '10005'
    new_block_name = 'primary_top'
  []
  [back]
    type = LowerDBlockFromSidesetGenerator
    input = top
    sidesets = '11'
    new_block_id = '10001'
    new_block_name = 'secondary_back'
  []
  [front]
    type = LowerDBlockFromSidesetGenerator
    input = back
    sidesets = '13'
    new_block_id = '10003'
    new_block_name = 'primary_front'
  []

  [corner_node]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node'
    nodes = '0'
    input = front
  []
[]

[Variables]
  [u]
    order = SECOND
    family = LAGRANGE
  []
  [epsilon]
    order = THIRD
    family = SCALAR
  []
  [./lm1]
    order = FIRST
    family = LAGRANGE
    block = secondary_left
  [../]
  [./lm2]
    order = FIRST
    family = LAGRANGE
    block = secondary_bottom
  [../]
  [./lm3]
    order = FIRST
    family = LAGRANGE
    block = secondary_back
  [../]
[]

[AuxVariables]
  [sigma]
    order = THIRD
    family = SCALAR
  []
[]

[AuxScalarKernels]
  [sigma]
    type = FunctionScalarAux
    variable = sigma
    function = '1 2 3'
    execute_on = initial #timestep_end
  []
[]

[Kernels]
  [diff1]
    type = Diffusion
    variable = u
    block = 1
  []
[]

[Problem]
  kernel_coverage_check = false
  error_on_jacobian_nonzero_reallocation = true
[]

[BCs]
  [fix_right]
    type = DirichletBC
    variable = u
    boundary = pinned_node
    value = 0
  []
[]

[Constraints]
  [mortarlr]
    type = EqualValueConstraint
    primary_boundary = '12'
    secondary_boundary = '14'
    primary_subdomain = 'primary_right'
    secondary_subdomain = 'secondary_left'
    secondary_variable = u
    variable = lm1
    correct_edge_dropping = true
  []
  [periodiclr]
    type = PeriodicSegmentalConstraint
    primary_boundary = '12'
    secondary_boundary = '14'
    primary_subdomain = 'primary_right'
    secondary_subdomain = 'secondary_left'
    secondary_variable = u
    epsilon = epsilon
    sigma = sigma
    variable = lm1
    correct_edge_dropping = true
  []
  [mortarbt]
    type = EqualValueConstraint
    primary_boundary = '15'
    secondary_boundary = '10'
    primary_subdomain = 'primary_top'
    secondary_subdomain = 'secondary_bottom'
    secondary_variable = u
    variable = lm2
    correct_edge_dropping = true
  []
  [periodicbt]
    type = PeriodicSegmentalConstraint
    primary_boundary = '15'
    secondary_boundary = '10'
    primary_subdomain = 'primary_top'
    secondary_subdomain = 'secondary_bottom'
    secondary_variable = u
    epsilon = epsilon
    sigma = sigma
    variable = lm2
    correct_edge_dropping = true
  []
  [mortarbf]
    type = EqualValueConstraint
    primary_boundary = '13'
    secondary_boundary = '11'
    primary_subdomain = 'primary_front'
    secondary_subdomain = 'secondary_back'
    secondary_variable = u
    variable = lm3
    correct_edge_dropping = true
  []
  [periodicbf]
    type = PeriodicSegmentalConstraint
    primary_boundary = '13'
    secondary_boundary = '11'
    primary_subdomain = 'primary_front'
    secondary_subdomain = 'secondary_back'
    secondary_variable = u
    epsilon = epsilon
    sigma = sigma
    variable = lm3
    correct_edge_dropping = true
  []
[]

[Preconditioning]
  [smp]
    full = true
    type = SMP
  []
[]

[Executioner]
  type = Steady
  petsc_options_iname = '-pc_type -pc_factor_shift_type -pc_factor_shift_amount'
  petsc_options_value = 'lu       NONZERO               1e-15'
  solve_type = NEWTON
[]

[Outputs]
  exodus = true
  csv = true
[]

(modules/solid_mechanics/test/tests/uel/small.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 20
    ny = 10
    xmax = 10
    ymax = 3
    elem_type = TRI3
  []
  [pin]
    type = ExtraNodesetGenerator
    nodes = 106
    new_boundary = pin
    input = gen
  []
  displacements = 'disp_x disp_y'
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
[]

[BCs]
  [left_x]
    type = DirichletBC
    variable = disp_x
    boundary = left
    value = 0
  []
  [left_y]
    type = DirichletBC
    variable = disp_y
    boundary = pin
    value = 0
  []

  inactive = 'right_dirichlet'
  [right_neumann]
    type = FunctionNeumannBC
    variable = disp_x
    function = t
    boundary = right
  []
  [right_dirichlet]
    type = FunctionDirichletBC
    variable = disp_x
    function = t/10
    boundary = right
  []
[]

[UserObjects]
  [uel]
    type = AbaqusUserElement
    variables = 'disp_x disp_y'
    plugin = ../../plugins/small_strain_tri_uel
    use_displaced_mesh = false
    num_state_vars = 8
    constant_properties = '100 0.3' # E nu
    extra_vector_tags = 'kernel_residual'
  []
[]

[Problem]
  kernel_coverage_check = false
  extra_tag_vectors = 'kernel_residual'
[]

[AuxVariables]
  [res_x]
  []
  [res_y]
  []
[]

[AuxKernels]
  [res_x]
    type = TagVectorAux
    variable = res_x
    v = disp_x
    vector_tag = kernel_residual
  []
  [res_y]
    type = TagVectorAux
    variable = res_y
    v = disp_y
    vector_tag = kernel_residual
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  dt = 1
  num_steps = 15
[]

[Postprocessors]
  [delta_l]
    type = SideAverageValue
    variable = disp_x
    boundary = right
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [V]
    type = ElementIntegralMaterialProperty
    mat_prop = 1
    use_displaced_mesh = true
    execute_on = 'INITIAL TIMESTEP_END'
  []
[]

[Outputs]
  exodus = true
  csv = true
[]

(modules/solid_mechanics/test/tests/ad_anisotropic_creep/ad_aniso_creep_y_3d.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 2
    ny = 10
    nz = 2

    xmin = 0.0
    ymin = 0.0
    zmin = 0.0

    xmax = 1.0
    ymax = 10.0
    zmax = 1.0
  []
  [corner_node]
    type = ExtraNodesetGenerator
    new_boundary = '100'
    nodes = '4 10'
    input = gen
  []
  [corner_node_2]
    type = ExtraNodesetGenerator
    new_boundary = '101'
    nodes = '1 67'
    input = corner_node
  []
[]

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  volumetric_locking_correction = true
[]

[AuxVariables]
  [hydrostatic_stress]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_xx]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_xy]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_zz]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [hydrostatic_stress]
    type = ADRankTwoScalarAux
    variable = hydrostatic_stress
    rank_two_tensor = stress
    scalar_type = Hydrostatic
  []
  [creep_strain_xx]
    type = ADRankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_xx
    index_i = 0
    index_j = 0
  []
  [creep_strain_xy]
    type = ADRankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_xy
    index_i = 0
    index_j = 1
  []
  [creep_strain_yy]
    type = ADRankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_yy
    index_i = 1
    index_j = 1
  []
  [creep_strain_zz]
    type = ADRankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_yy
    index_i = 1
    index_j = 1
  []
  [sigma_yy]
    type = ADRankTwoAux
    rank_two_tensor = stress
    variable = stress_yy
    index_i = 1
    index_j = 1
  []
[]

[Functions]
  [pull]
    type = PiecewiseLinear
    x = '0 1.0e-11 1.0'
    y = '0 -4e1 -4e1'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = FINITE
    generate_output = 'elastic_strain_yy stress_yy'
    use_automatic_differentiation = true
    add_variables = true
  []
[]

[Materials]
  [elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    youngs_modulus = 700
    poissons_ratio = 0.0
  []

  [elastic_strain]
    type = ADComputeMultipleInelasticStress
    inelastic_models = "trial_creep_two"
    max_iterations = 50
    absolute_tolerance = 1e-16
  []

  [hill_tensor]
    type = ADHillConstants
    # F G H L M N
    hill_constants = "0.5 0.25 0.3866 1.6413 1.6413 1.2731"
  []

  [trial_creep_two]
    type = ADHillCreepStressUpdate
    coefficient = 1e-16
    n_exponent = 9
    m_exponent = 0
    activation_energy = 0
    max_inelastic_increment = 0.00003
    absolute_tolerance = 1e-20
    relative_tolerance = 1e-20
    # Force it to not use integration error
    max_integration_error = 0.000001
  []
[]

[BCs]
  [no_disp_x]
    type = ADDirichletBC
    variable = disp_x
    boundary = 101
    value = 0.0
  []

  [no_disp_y]
    type = ADDirichletBC
    variable = disp_y
    boundary = bottom
    value = 0.0
  []

  [no_disp_z]
    type = ADDirichletBC
    variable = disp_z
    boundary = 100
    value = 0.0
  []

  [pressure]
    type = ADPressure
    boundary = top
    function = pull
    variable = disp_y
    component = 1
  []
[]

[Executioner]
  type = Transient

  solve_type = NEWTON
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu     superlu_dist'

  nl_rel_tol = 1.0e-13
  nl_abs_tol = 1.0e-13
  l_max_its = 90
  num_steps = 10
  dt = 1.0e-4
  start_time = 0
  automatic_scaling = true
[]

[Postprocessors]
  [matl_ts_min]
    type = MaterialTimeStepPostprocessor
  []
  [max_disp_x]
    type = ElementExtremeValue
    variable = disp_x
  []
  [max_disp_y]
    type = ElementExtremeValue
    variable = disp_y
  []
  [max_hydro]
    type = ElementAverageValue
    variable = hydrostatic_stress
  []
  [dt]
    type = TimestepSize
  []
  [num_lin]
    type = NumLinearIterations
    outputs = console
  []
  [num_nonlin]
    type = NumNonlinearIterations
    outputs = console
  []
  [creep_strain_yy]
    type = ElementalVariableValue
    variable = creep_strain_yy
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [elastic_strain_yy]
    type = ElementalVariableValue
    variable = elastic_strain_yy
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [sigma_yy]
    type = ElementalVariableValue
    variable = stress_yy
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
[]

[Outputs]
  csv = true
  exodus = true
  perf_graph = true
[]

(modules/solid_mechanics/test/tests/anisotropic_plasticity/ad_aniso_plasticity_y.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 3

    # Original verification nx = 2, ny = 10, nz = 2
    nx = 2
    ny = 10
    nz = 2

    xmin = 0.0
    ymin = 0.0
    zmin = 0.0

    xmax = 1.0
    ymax = 10.0
    zmax = 1.0
  []
  [corner_node]
    type = ExtraNodesetGenerator
    new_boundary = '100'
    nodes = '4 10'
    input = gen
  []
  [corner_node_2]
    type = ExtraNodesetGenerator
    new_boundary = '101'
    nodes = '1 67'
    input = corner_node
  []
[]

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  volumetric_locking_correction = true
[]

[AuxVariables]
  [hydrostatic_stress]
    order = CONSTANT
    family = MONOMIAL
  []
  [plastic_strain_xx]
    order = CONSTANT
    family = MONOMIAL
  []
  [plastic_strain_xy]
    order = CONSTANT
    family = MONOMIAL
  []
  [plastic_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []
  [stress_yy]
    order = CONSTANT
    family = MONOMIAL
  []
  [elastic_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [hydrostatic_stress]
    type = ADRankTwoScalarAux
    variable = hydrostatic_stress
    rank_two_tensor = stress
    scalar_type = Hydrostatic
  []
  [plasticity_strain_xx]
    type = ADRankTwoAux
    rank_two_tensor = trial_plasticity_plastic_strain
    variable = plastic_strain_xx
    index_i = 0
    index_j = 0
  []
  [plasticity_strain_xy]
    type = ADRankTwoAux
    rank_two_tensor = trial_plasticity_plastic_strain
    variable = plastic_strain_xy
    index_i = 0
    index_j = 1
  []
  [plasticity_strain_yy]
    type = ADRankTwoAux
    rank_two_tensor = trial_plasticity_plastic_strain
    variable = plastic_strain_yy
    index_i = 1
    index_j = 1
  []
  [elastic_strain_yy]
    type = ADRankTwoAux
    rank_two_tensor = elastic_strain
    variable = elastic_strain_yy
    index_i = 1
    index_j = 1
  []
  [sigma_yy]
    type = ADRankTwoAux
    rank_two_tensor = stress
    variable = stress_yy
    index_i = 1
    index_j = 1
  []
[]

[Functions]
  [pull]
    type = PiecewiseLinear
    x = '0 1e1 1e8'
    y = '0 -4e2 -4e2'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = FINITE
    use_automatic_differentiation = true
    add_variables = true
  []
[]

[Materials]

  [elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    youngs_modulus = 70000
    poissons_ratio = 0.25
  []

  [elastic_strain]
    type = ADComputeMultipleInelasticStress
    inelastic_models = "trial_plasticity"
    max_iterations = 50
    absolute_tolerance = 1e-16
  []

  [hill_tensor]
    type = ADHillConstants
    # F G H L M N
    hill_constants = "0.5829856 0.364424 0.6342174 2.0691375 2.3492325 1.814589"
    base_name = trial_plasticity
  []

  [trial_plasticity]
    type = ADHillPlasticityStressUpdate
    hardening_constant = 2000.0
    yield_stress = 0.001
    absolute_tolerance = 1e-14
    relative_tolerance = 1e-12
    base_name = trial_plasticity
    internal_solve_full_iteration_history = true
    max_inelastic_increment = 2.0e-6
    internal_solve_output_on = on_error
  []
[]

[BCs]
  [no_disp_x]
    type = ADDirichletBC
    variable = disp_x
    boundary = 101
    value = 0.0
  []

  [no_disp_y]
    type = ADDirichletBC
    variable = disp_y
    boundary = bottom
    value = 0.0
  []

  [no_disp_z]
    type = ADDirichletBC
    variable = disp_z
    boundary = 100
    value = 0.0
  []

  [Pressure]
    [Side1]
      boundary = top
      function = pull
    []
  []
[]

[Executioner]
  type = Transient

  solve_type = NEWTON
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu     superlu_dist'

  nl_rel_tol = 1e-11
  nl_abs_tol = 1.0e-14
  l_max_its = 90
  num_steps = 25
  [TimeStepper]
    type = IterationAdaptiveDT
    optimal_iterations = 30
    iteration_window = 9
    growth_factor = 1.05
    cutback_factor = 0.5
    timestep_limiting_postprocessor = matl_ts_min
    dt = 1e-5
    time_t = '0 3.2e-5 10'
    time_dt = '1e-5 1.0e-7 1.0e-7'
  []
  start_time = 0
  automatic_scaling = true
[]

[Postprocessors]
  [matl_ts_min]
    type = MaterialTimeStepPostprocessor
  []
  [max_disp_x]
    type = ElementExtremeValue
    variable = disp_x
  []
  [max_disp_y]
    type = ElementExtremeValue
    variable = disp_y
  []
  [max_hydro]
    type = ElementAverageValue
    variable = hydrostatic_stress
  []
  [dt]
    type = TimestepSize
  []
  [num_lin]
    type = NumLinearIterations
    outputs = console
  []
  [num_nonlin]
    type = NumNonlinearIterations
    outputs = console
  []
  [plasticity_strain_yy]
    type = ElementalVariableValue
    variable = plastic_strain_yy
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [elastic_strain_yy]
    type = ElementalVariableValue
    variable = elastic_strain_yy
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [sigma_yy]
    type = ElementalVariableValue
    variable = stress_yy
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
[]

[Outputs]
  csv = true
  perf_graph = true
[]

(modules/solid_mechanics/test/tests/ad_anisotropic_creep/ad_aniso_creep_temperature_coefficients_function_variation.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 10
    ny = 2
    nz = 2
    xmin = 0.0
    ymin = 0.0
    zmin = 0.0

    xmax = 10.0
    ymax = 1.0
    zmax = 1.0
  []
  [corner_node]
    type = ExtraNodesetGenerator
    new_boundary = '100'
    nodes = '3 69'
    input = gen
  []
  [corner_node_2]
    type = ExtraNodesetGenerator
    new_boundary = '101'
    nodes = '4 47'
    input = corner_node
  []
[]

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  volumetric_locking_correction = true
[]

[AuxVariables]
  [temperature]
    order = CONSTANT
    family = MONOMIAL
  []
  [hydrostatic_stress]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_xx]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_xy]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_zz]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_xz]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_yz]
    order = CONSTANT
    family = MONOMIAL
  []
  [hill_constants_f]
    order = CONSTANT
    family = MONOMIAL
  []
  [hill_constants_g]
    order = CONSTANT
    family = MONOMIAL
  []
  [hill_constants_h]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [temperature]
    type = FunctionAux
    variable = temperature
    function = time_temperature
  []
  [hydrostatic_stress]
    type = ADRankTwoScalarAux
    variable = hydrostatic_stress
    rank_two_tensor = stress
    scalar_type = Hydrostatic
  []
  [creep_strain_xx]
    type = ADRankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_xx
    index_i = 0
    index_j = 0
  []
  [creep_strain_xy]
    type = ADRankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_xy
    index_i = 0
    index_j = 1
  []
  [creep_strain_yy]
    type = ADRankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_yy
    index_i = 1
    index_j = 1
  []
  [creep_strain_zz]
    type = ADRankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_zz
    index_i = 2
    index_j = 2
  []
  [creep_strain_xz]
    type = ADRankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_xz
    index_i = 0
    index_j = 2
  []
  [creep_strain_yz]
    type = ADRankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_yz
    index_i = 1
    index_j = 2
  []
  [sigma_xx]
    type = ADRankTwoAux
    rank_two_tensor = stress
    variable = stress_xx
    index_i = 1
    index_j = 1
  []
  [hill_constant_f]
    type = MaterialStdVectorAux
    property = hill_constants
    variable = hill_constants_f
    index = 0
  []
  [hill_constant_g]
    type = MaterialStdVectorAux
    property = hill_constants
    variable = hill_constants_g
    index = 1
  []
  [hill_constant_h]
    type = MaterialStdVectorAux
    property = hill_constants
    variable = hill_constants_h
    index = 2
  []
[]

[ICs]
  [temp]
    type = ConstantIC
    variable = temperature
    value = 50.0
  []
[]

[Functions]
  [pull]
    type = PiecewiseLinear
    x = '0 1.0e-9 1.0'
    y = '0 -4e1 -4e1'
  []
  [F]
    type = PiecewiseLinear
    x = '50 200'
    y = '0.2 0.5'
  []
  [G]
    type = PiecewiseLinear
    x = '50 200'
    y = '0.9 0.6'
  []
  [H]
    type = PiecewiseLinear
    x = '50 200'
    y = '0.5 0.3'
  []
  [L]
    type = PiecewiseLinear
    x = '50 200'
    y = '1.5 1.5'
  []
  [M]
    type = PiecewiseLinear
    x = '50 200'
    y = '1.5 1.5'
  []
  [N]
    type = PiecewiseLinear
    x = '50 200'
    y = '1.5 1.5'
  []
  [time_temperature]
    type = PiecewiseLinear
    x = '0 1.0e-2'
    y = '50 200'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = FINITE
    generate_output = 'elastic_strain_xx stress_xx'
    use_automatic_differentiation = true
    add_variables = true
  []
[]

[Materials]
  [elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    youngs_modulus = 700
    poissons_ratio = 0.0
  []

  [elastic_strain]
    type = ADComputeMultipleInelasticStress
    inelastic_models = 'trial_creep_aniso_iso'
    max_iterations = 50
  []
  [hill_constants]
    type = ADHillConstants
    # F G H L M N
    hill_constants = "0.5 0.5 0.5 1.5 1.5 1.5"
    function_names = 'F G H L M N'
    temperature = temperature
  []
  [trial_creep_aniso_iso]
    type = ADHillCreepStressUpdate
    coefficient = 1e-16
    n_exponent = 9
    m_exponent = 0
    activation_energy = 0
    max_inelastic_increment = 0.00003
    relative_tolerance = 1e-20
    absolute_tolerance = 1e-20
    internal_solve_output_on = never
    # Force it to not use integration error
    max_integration_error = 1.0
  []

[]

[BCs]
  [no_disp_x]
    type = ADDirichletBC
    variable = disp_x
    boundary = left
    value = 0.0
  []

  [no_disp_y]
    type = ADDirichletBC
    variable = disp_y
    boundary = 100
    value = 0.0
  []

  [no_disp_z]
    type = ADDirichletBC
    variable = disp_z
    boundary = 101
    value = 0.0
  []

  [Pressure]
    [Side1]
      boundary = right
      function = pull
    []
  []

[]

[Executioner]
  type = Transient

  solve_type = NEWTON
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu     superlu_dist'

  nl_rel_tol = 1e-13
  nl_abs_tol = 1.0e-14
  l_max_its = 90
  num_steps = 20
  dt = 5.0e-4
  start_time = 0
  automatic_scaling = true
[]

[Postprocessors]
  [matl_ts_min]
    type = MaterialTimeStepPostprocessor
  []
  [max_disp_x]
    type = ElementExtremeValue
    variable = disp_x
  []
  [max_disp_y]
    type = ElementExtremeValue
    variable = disp_y
  []
  [max_hydro]
    type = ElementAverageValue
    variable = hydrostatic_stress
  []
  [dt]
    type = TimestepSize
  []
  [num_lin]
    type = NumLinearIterations
    outputs = console
  []
  [num_nonlin]
    type = NumNonlinearIterations
    outputs = console
  []
  [creep_strain_xx]
    type = ElementalVariableValue
    variable = creep_strain_xx
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [creep_strain_yy]
    type = ElementalVariableValue
    variable = creep_strain_yy
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [creep_strain_zz]
    type = ElementalVariableValue
    variable = creep_strain_zz
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [creep_strain_xy]
    type = ElementalVariableValue
    variable = creep_strain_xy
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [creep_strain_yz]
    type = ElementalVariableValue
    variable = creep_strain_yz
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [creep_strain_xz]
    type = ElementalVariableValue
    variable = creep_strain_xz
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [elastic_strain_xx]
    type = ElementalVariableValue
    variable = elastic_strain_xx
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [sigma_xx]
    type = ElementalVariableValue
    variable = stress_xx
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
[]

[Outputs]
  csv = true
  exodus = true
  perf_graph = true
[]

(test/tests/mortar/periodic_segmental_constraint/testperiodicsole.i)

[Mesh]
  [left_block]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = -1.0
    xmax = 1.0
    ymin = -1.0
    ymax = 1.0
    nx = 2
    ny = 2
    elem_type = QUAD4
  []
  [left_block_sidesets]
    type = RenameBoundaryGenerator
    input = left_block
    old_boundary = '0 1 2 3'
    new_boundary = '10 11 12 13'
  []
  [left_block_id]
    type = SubdomainIDGenerator
    input = left_block_sidesets
    subdomain_id = 1
  []
  [left]
    type = LowerDBlockFromSidesetGenerator
    input = left_block_id
    sidesets = '13'
    new_block_id = '10003'
    new_block_name = 'secondary_left'
  []
  [right]
    type = LowerDBlockFromSidesetGenerator
    input = left
    sidesets = '11'
    new_block_id = '10001'
    new_block_name = 'primary_right'
  []
  [bottom]
    type = LowerDBlockFromSidesetGenerator
    input = right
    sidesets = '10'
    new_block_id = '10000'
    new_block_name = 'secondary_bottom'
  []
  [top]
    type = LowerDBlockFromSidesetGenerator
    input = bottom
    sidesets = '12'
    new_block_id = '10002'
    new_block_name = 'primary_top'
  []

  [corner_node]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node'
    nodes = '0'
    input = top
  []
[]

[Variables]
  [u]
    order = FIRST
    family = LAGRANGE
  []
  [kappa_x]
    order = FIRST
    family = SCALAR
  []
  [kappa_y]
    order = FIRST
    family = SCALAR
  []
[]

[AuxVariables]
  [kappa_aux]
    order = SECOND
    family = SCALAR
  []
  [./flux_x]
      order = FIRST
      family = MONOMIAL
  [../]
  [./flux_y]
      order = FIRST
      family = MONOMIAL
  [../]
[]

[AuxScalarKernels]
  [kappa]
    type = FunctionScalarAux
    variable = kappa_aux
    function = '1 3'
    execute_on = initial #timestep_end
  []
[]

[AuxKernels]
  [./flux_x]
    type = DiffusionFluxAux
    diffusivity = 'conductivity'
    variable = flux_x
    diffusion_variable = u
    component = x
    block = 1
  [../]
  [./flux_y]
    type = DiffusionFluxAux
    diffusivity = 'conductivity'
    variable = flux_y
    diffusion_variable = u
    component = y
    block = 1
  [../]
[]

[Kernels]
  [diff1]
    type = Diffusion
    variable = u
    block = 1
  []
[]

[Materials]
  [k1]
    type = GenericConstantMaterial
    prop_names = 'conductivity'
    prop_values = 1.0
    block = 1
  []
[]

[Problem]
  kernel_coverage_check = false
  error_on_jacobian_nonzero_reallocation = true
[]

[BCs]
  [fix_right]
    type = DirichletBC
    variable = u
    boundary = pinned_node
    value = 0
  []
[]

[Constraints]
  [mortarlr]
    type = PenaltyEqualValueConstraint
    primary_boundary = '11'
    secondary_boundary = '13'
    primary_subdomain = 'primary_right'
    secondary_subdomain = 'secondary_left'
    secondary_variable = u
    correct_edge_dropping = true
    penalty_value = 1.e3
  []
  [periodiclrx]
    type = TestPeriodicSole
    primary_boundary = '11'
    secondary_boundary = '13'
    primary_subdomain = 'primary_right'
    secondary_subdomain = 'secondary_left'
    secondary_variable = u
    kappa = kappa_x
    kappa_aux = kappa_aux
    component = 0
    kappa_other = kappa_y
    correct_edge_dropping = true
    penalty_value = 1.e3
  []
  [periodiclry]
    type = TestPeriodicSole
    primary_boundary = '11'
    secondary_boundary = '13'
    primary_subdomain = 'primary_right'
    secondary_subdomain = 'secondary_left'
    secondary_variable = u
    kappa = kappa_y
    kappa_aux = kappa_aux
    component = 1
    kappa_other = kappa_x
    correct_edge_dropping = true
    penalty_value = 1.e3
  []
  [mortarbt]
    type = PenaltyEqualValueConstraint
    primary_boundary = '12'
    secondary_boundary = '10'
    primary_subdomain = 'primary_top'
    secondary_subdomain = 'secondary_bottom'
    secondary_variable = u
    correct_edge_dropping = true
    penalty_value = 1.e3
  []
  [periodicbtx]
    type = TestPeriodicSole
    primary_boundary = '12'
    secondary_boundary = '10'
    primary_subdomain = 'primary_top'
    secondary_subdomain = 'secondary_bottom'
    secondary_variable = u
    kappa = kappa_x
    kappa_aux = kappa_aux
    component = 0
    kappa_other = kappa_y
    correct_edge_dropping = true
    penalty_value = 1.e3
  []
  [periodicbty]
    type = TestPeriodicSole
    primary_boundary = '12'
    secondary_boundary = '10'
    primary_subdomain = 'primary_top'
    secondary_subdomain = 'secondary_bottom'
    secondary_variable = u
    kappa = kappa_y
    kappa_aux = kappa_aux
    component = 1
    kappa_other = kappa_x
    correct_edge_dropping = true
    compute_scalar_residuals = true
    penalty_value = 1.e3
  []
[]

[Preconditioning]
  [smp]
    full = true
    type = SMP
  []
[]

[Executioner]
  type = Steady
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  solve_type = NEWTON
[]

[Postprocessors]
  [max]
    type = ElementExtremeValue
    variable = 'flux_x'
  []
[]

[Outputs]
  csv = true
[]

(modules/solid_mechanics/test/tests/finite_strain_elastic_anisotropy/3d_bar_orthotropic_90deg_rotation.i)

[Mesh]
  [generated_mesh]
    type = GeneratedMeshGenerator
    dim = 3
    xmin = 0
    xmax = 2
    ymin = 0
    ymax = 10
    zmin = 0
    zmax = 2
    nx = 1
    ny = 1
    nz = 1
    elem_type = HEX8
  []
  [corner]
    type = ExtraNodesetGenerator
    new_boundary = 101
    coord = '0 0 0'
    input = generated_mesh
  []
  [side]
    type = ExtraNodesetGenerator
    new_boundary = 102
    coord = '2 0 0'
    input = corner
  []
[]

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = FINITE
    add_variables = true
    use_finite_deform_jacobian = true
    volumetric_locking_correction = false
    generate_output = 'stress_xx stress_yy stress_zz stress_xy stress_xz'
  []
[]

[Materials]
  [stress]
    type = ComputeFiniteStrainElasticStress
  []
  [elasticity_tensor]
    type = ComputeElasticityTensor
    fill_method = orthotropic
    C_ijkl = '2.0e3 2.0e5 2.0e3 0.71428571e3 0.71428571e3 0.71428571e3 0.4 0.2 0.004 0.004 0.2 0.4'
  []
[]

[BCs]
  [fix_z]
    type = DirichletBC
    variable = disp_z
    boundary = bottom
    value = 0
  []

  [rot_y]
    type = DisplacementAboutAxis
    boundary = bottom
    function = t
    angle_units = degrees
    axis_origin = '0. 0. 0.'
    axis_direction = '0. 0. 1.'
    component = 1
    variable = disp_y
  []
  #
  [rot_x]
    type = DisplacementAboutAxis
    boundary = bottom
    function = t
    angle_units = degrees
    axis_origin = '0. 0. 0.'
    axis_direction = '0. 0. 1.'
    component = 0
    variable = disp_x
  []

  [rot_y90]
    type = DisplacementAboutAxis
    boundary = bottom
    function = 90
    angle_units = degrees
    axis_origin = '0. 0. 0.'
    axis_direction = '0. 0. 1.'
    component = 1
    variable = disp_y
  []
  #
  [rot_x90]
    type = DisplacementAboutAxis
    boundary = bottom
    function = 90
    angle_units = degrees
    axis_origin = '0. 0. 0.'
    axis_direction = '0. 0. 1.'
    component = 0
    variable = disp_x
  []

  [press]
    boundary = top
    function = '-1.0*(t-90)*10.0'
    use_displaced_mesh = true
    displacements = 'disp_x disp_y disp_z'
    type = Pressure
    variable = disp_x
  []

[]

[Controls]
  [c1]
    type = TimePeriod
    enable_objects = 'BCs::rot_x BCs::rot_y'
    disable_objects = 'BCs::rot_x90 BCs::rot_y90 BCs::press'
    start_time = '0'
    end_time = '90'
  []
  [c190plus]
    type = TimePeriod
    enable_objects = 'BCs::rot_x90 BCs::rot_y90 BCs::press'
    disable_objects = 'BCs::rot_x BCs::rot_y '
    start_time = '90'
    end_time = '390'
  []
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-ksp_gmres_restart'
  petsc_options_value = '101'

  line_search = 'none'

  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-08
  nl_max_its = 50

  l_tol = 1e-4
  l_max_its = 50
  start_time = 0.0

  dt = 5
  dtmin = 5

  num_steps = 78
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Outputs]
  exodus = true
[]

(modules/solid_mechanics/test/tests/anisotropic_plasticity/ad_aniso_plasticity_x.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 10
    ny = 2
    nz = 2
    xmin = 0.0
    ymin = 0.0
    zmin = 0.0

    xmax = 10.0
    ymax = 1.0
    zmax = 1.0
  []
  [corner_node]
    type = ExtraNodesetGenerator
    new_boundary = '100'
    nodes = '3 69'
    input = gen
  []
  [corner_node_2]
    type = ExtraNodesetGenerator
    new_boundary = '101'
    nodes = '4 47'
    input = corner_node
  []
[]

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  volumetric_locking_correction = true
[]

[AuxVariables]
  [hydrostatic_stress]
    order = CONSTANT
    family = MONOMIAL
  []
  [plastic_strain_xx]
    order = CONSTANT
    family = MONOMIAL
  []
  [plastic_strain_xy]
    order = CONSTANT
    family = MONOMIAL
  []
  [plastic_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []
  [plastic_strain_zz]
    order = CONSTANT
    family = MONOMIAL
  []
  [stress_yy]
    order = CONSTANT
    family = MONOMIAL
  []
  [elastic_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [hydrostatic_stress]
    type = ADRankTwoScalarAux
    variable = hydrostatic_stress
    rank_two_tensor = stress
    scalar_type = Hydrostatic
  []
  [plasticity_strain_xx]
    type = ADRankTwoAux
    rank_two_tensor = trial_plasticity_plastic_strain
    variable = plastic_strain_xx
    index_i = 0
    index_j = 0
  []
  [plasticity_strain_xy]
    type = ADRankTwoAux
    rank_two_tensor = trial_plasticity_plastic_strain
    variable = plastic_strain_xy
    index_i = 0
    index_j = 1
  []
  [plasticity_strain_yy]
    type = ADRankTwoAux
    rank_two_tensor = trial_plasticity_plastic_strain
    variable = plastic_strain_yy
    index_i = 1
    index_j = 1
  []
  [plasticity_strain_zz]
    type = ADRankTwoAux
    rank_two_tensor = trial_plasticity_plastic_strain
    variable = plastic_strain_zz
    index_i = 2
    index_j = 2
  []
  [sigma_xx]
    type = ADRankTwoAux
    rank_two_tensor = stress
    variable = stress_xx
    index_i = 1
    index_j = 1
  []
  [elastic_strain_yy]
    type = ADRankTwoAux
    rank_two_tensor = elastic_strain
    variable = elastic_strain_yy
    index_i = 1
    index_j = 1
  []
  [sigma_yy]
    type = ADRankTwoAux
    rank_two_tensor = stress
    variable = stress_yy
    index_i = 1
    index_j = 1
  []
[]

[Functions]
  [pull]
    type = PiecewiseLinear
    x = '0 1e1 1e8'
    y = '0 -4e2 -4e2'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = FINITE
    generate_output = 'elastic_strain_xx stress_xx'
    use_automatic_differentiation = true
    add_variables = true
  []
[]

[Materials]

  [elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    youngs_modulus = 70000
    poissons_ratio = 0.25
  []

  [elastic_strain]
    type = ADComputeMultipleInelasticStress
    inelastic_models = "trial_plasticity"
    max_iterations = 50
    absolute_tolerance = 1e-16
  []

  [hill_tensor]
    type = ADHillConstants
    # F G H L M N
    hill_constants = "0.5829856 0.364424 0.6342174 2.0691375 2.3492325 1.814589"
    base_name = trial_plasticity
  []

  [trial_plasticity]
    type = ADHillPlasticityStressUpdate
    hardening_constant = 2000.0
    yield_stress = 0.001 # was 200 for verification
    absolute_tolerance = 1e-14
    relative_tolerance = 1e-12
    base_name = trial_plasticity
    internal_solve_full_iteration_history = true
    max_inelastic_increment = 2.0e-6
    internal_solve_output_on = on_error
  []
[]

[BCs]
  [no_disp_x]
    type = ADDirichletBC
    variable = disp_x
    boundary = left
    value = 0.0
  []

  [no_disp_y]
    type = ADDirichletBC
    variable = disp_y
    boundary = 100
    value = 0.0
  []

  [no_disp_z]
    type = ADDirichletBC
    variable = disp_z
    boundary = 101
    value = 0.0
  []

  [Pressure]
    [Side1]
      boundary = right
      function = pull
    []
  []

[]

[Executioner]
  type = Transient

  solve_type = NEWTON
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu     superlu_dist'

  nl_rel_tol = 1e-11
  nl_abs_tol = 1.0e-14
  l_max_its = 90
  num_steps = 25
  [TimeStepper]
    type = IterationAdaptiveDT
    optimal_iterations = 30
    iteration_window = 9
    growth_factor = 1.05
    cutback_factor = 0.5
    timestep_limiting_postprocessor = matl_ts_min
    dt = 1.0e-5
    time_t = '0 3.4e-5 10'
    time_dt = '1.0e-5 1.0e-7 1.0e-7'
  []
  start_time = 0
  automatic_scaling = true
[]

[Postprocessors]
  [matl_ts_min]
    type = MaterialTimeStepPostprocessor
  []
  [max_disp_x]
    type = ElementExtremeValue
    variable = disp_x
  []
  [max_disp_y]
    type = ElementExtremeValue
    variable = disp_y
  []
  [max_hydro]
    type = ElementAverageValue
    variable = hydrostatic_stress
  []
  [dt]
    type = TimestepSize
  []
  [num_lin]
    type = NumLinearIterations
    outputs = console
  []
  [num_nonlin]
    type = NumNonlinearIterations
    outputs = console
  []
  [plasticity_strain_yy]
    type = ElementalVariableValue
    variable = plastic_strain_yy
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [elastic_strain_yy]
    type = ElementalVariableValue
    variable = elastic_strain_yy
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [sigma_yy]
    type = ElementalVariableValue
    variable = stress_yy
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [plasticity_strain_xx]
    type = ElementalVariableValue
    variable = plastic_strain_xx
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [elastic_strain_xx]
    type = ElementalVariableValue
    variable = elastic_strain_xx
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [sigma_xx]
    type = ElementalVariableValue
    variable = stress_xx
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [plasticity_strain_zz]
    type = ElementalVariableValue
    variable = plastic_strain_zz
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
[]

[Outputs]
  csv = true
  perf_graph = true
[]

(modules/contact/test/tests/cohesive_zone_model/bilinear_mixed_mortar_only_czm.i)

[Mesh]
  [base]
    type = GeneratedMeshGenerator
    dim = 2
    xmax = 1.1
    ymax = 1
    xmin = -0.1
    nx = 1
    ny = 1
  []
  [rename_base]
    type = RenameBoundaryGenerator
    input = base
    old_boundary = 'top bottom left right'
    new_boundary = 'top_base bottom_base left_base right_base'
  []
  [base_id]
    type = SubdomainIDGenerator
    input = rename_base
    subdomain_id = 1
  []

  [top]
    type = GeneratedMeshGenerator
    dim = 2
    xmax = 1
    ymin = 1
    ymax = 2
    nx = 1
    ny = 1
  []
  [rename_top]
    type = RenameBoundaryGenerator
    input = top
    old_boundary = 'top bottom left right'
    new_boundary = '100 101 102 103'
  []
  [top_id]
    type = SubdomainIDGenerator
    input = rename_top
    subdomain_id = 2
  []
  [combined]
    type = MeshCollectionGenerator
    inputs = 'base_id top_id'
  []
  [top_node]
    type = ExtraNodesetGenerator
    coord = '0 2 0'
    input = combined
    new_boundary = top_node
  []
  [bottom_node]
    type = ExtraNodesetGenerator
    coord = '-0.1 0 0'
    input = top_node
    new_boundary = bottom_node
  []

  [secondary]
    type = LowerDBlockFromSidesetGenerator
    new_block_id = 10001
    new_block_name = 'secondary_lower'
    sidesets = 'top_base'
    input = bottom_node
  []
  [primary]
    type = LowerDBlockFromSidesetGenerator
    new_block_id = 10000
    sidesets = '101'
    new_block_name = 'primary_lower'
    input = secondary
  []

  patch_update_strategy = auto
  patch_size = 20
  allow_renumbering = false
[]

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Physics]
  [SolidMechanics]
    [QuasiStatic]
      generate_output = 'stress_yy'
      [all]
        strain = FINITE
        add_variables = true
        use_automatic_differentiation = true
        decomposition_method = TaylorExpansion
        generate_output = 'vonmises_stress'
        block = '1 2'
      []
    []
  []
[]

[BCs]
  [fix_x]
    type = DirichletBC
    preset = true
    value = 0.0
    boundary = bottom_node
    variable = disp_x
  []

  [fix_top]
    type = DirichletBC
    preset = true
    boundary = 100
    variable = disp_x
    value = 0
  []

  [top]
    type = FunctionDirichletBC
    boundary = 100
    variable = disp_y
    function = 'if(t<=0.3,t,if(t<=0.6,0.3-(t-0.3),0.6-t))'
    preset = true
  []

  [bottom]
    type = DirichletBC
    boundary = bottom_base
    variable = disp_y
    value = 0
    preset = true
  []
[]

[Materials]
  [normal_strength]
    type = GenericConstantMaterial
    prop_names = 'normal_strength'
    prop_values = '1e3'
  []
  [shear_strength]
    type = GenericConstantMaterial
    prop_names = 'shear_strength'
    prop_values = '7.5e2'
  []
  [stress]
    type = ADComputeFiniteStrainElasticStress
    block = '1 2'
  []
  [elasticity_tensor]
    type = ADComputeElasticityTensor
    fill_method = symmetric9
    C_ijkl = '1.684e5 0.176e5 0.176e5 1.684e5 0.176e5 1.684e5 0.754e5 0.754e5 0.754e5'
    block = '1 2'
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'
  line_search = none

  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'

  automatic_scaling = true
  compute_scaling_once = false
  off_diagonals_in_auto_scaling = true

  l_max_its = 2
  l_tol = 1e-14
  nl_max_its = 150
  nl_rel_tol = 1e-14
  nl_abs_tol = 1e-12
  start_time = 0.0
  dt = 0.1
  end_time = 1.0
  dtmin = 0.1
[]

[Outputs]
  exodus = true
[]

[UserObjects]
  [czm_uo]
    type = BilinearMixedModeCohesiveZoneModel
    primary_boundary = 101
    secondary_boundary = 'top_base'
    primary_subdomain = 10000
    secondary_subdomain = 10001

    correct_edge_dropping = true

    disp_x = disp_x
    disp_y = disp_y
    friction_coefficient = 0.0 # with 2.0 works
    secondary_variable = disp_x
    penalty = 0e6
    penalty_friction = 0e4
    use_physical_gap = true

    # bilinear model parameters
    normal_strength = 'normal_strength'
    shear_strength = 'shear_strength'
    penalty_stiffness = 200
    power_law_parameter = 0.1
    GI_c = 123
    GII_c = 54
    displacements = 'disp_x disp_y'

  []
[]

[Constraints]
  [x]
    type = NormalMortarMechanicalContact
    primary_boundary = 101
    secondary_boundary = 'top_base'
    primary_subdomain = 10000
    secondary_subdomain = 10001
    secondary_variable = disp_x
    component = x
    use_displaced_mesh = true
    compute_lm_residuals = false
    weighted_gap_uo = czm_uo
  []
  [y]
    type = NormalMortarMechanicalContact
    primary_boundary = 101
    secondary_boundary = 'top_base'
    primary_subdomain = 10000
    secondary_subdomain = 10001
    secondary_variable = disp_y
    component = y
    use_displaced_mesh = true
    compute_lm_residuals = false
    weighted_gap_uo = czm_uo
  []
  [c_x]
    type = MortarGenericTraction
    primary_boundary = 101
    secondary_boundary = 'top_base'
    primary_subdomain = 10000
    secondary_subdomain = 10001
    secondary_variable = disp_x
    component = x
    use_displaced_mesh = true
    compute_lm_residuals = false
    cohesive_zone_uo = czm_uo
  []
  [c_y]
    type = MortarGenericTraction
    primary_boundary = 101
    secondary_boundary = 'top_base'
    primary_subdomain = 10000
    secondary_subdomain = 10001
    secondary_variable = disp_y
    component = y
    use_displaced_mesh = true
    compute_lm_residuals = false
    cohesive_zone_uo = czm_uo
  []
[]

(modules/solid_mechanics/test/tests/finite_strain_jacobian/3d_bar.i)

[Mesh]
  [generated_mesh]
    type = GeneratedMeshGenerator
    dim = 3
    xmin = 0
    xmax = 2
    ymin = 0
    ymax = 2
    zmin = 0
    zmax = 10
    nx = 10
    ny = 2
    nz = 2
    elem_type = HEX8
  []
  [corner]
    type = ExtraNodesetGenerator
    new_boundary = 101
    coord = '0 0 0'
    input = generated_mesh
  []
  [side]
    type = ExtraNodesetGenerator
    new_boundary = 102
    coord = '2 0 0'
    input = corner
  []
[]

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
[]

[Physics/SolidMechanics/QuasiStatic]
  [./all]
    strain = FINITE
    add_variables = true
    use_finite_deform_jacobian = true
    volumetric_locking_correction = false
  [../]
[]

[Materials]
  [./stress]
    type = ComputeFiniteStrainElasticStress
  [../]
  [./elasticity_tensor]
    type = ComputeElasticityTensor
    fill_method = symmetric9
    C_ijkl = '1.684e5 0.176e5 0.176e5 1.684e5 0.176e5 1.684e5 0.754e5 0.754e5 0.754e5'
  [../]
[]

[BCs]
 [./fix_corner_x]
   type = DirichletBC
   variable = disp_x
   boundary = 101
   value = 0
 [../]
 [./fix_corner_y]
   type = DirichletBC
   variable = disp_y
   boundary = 101
   value = 0
 [../]
 [./fix_side_y]
   type = DirichletBC
   variable = disp_y
   boundary = 102
   value = 0
 [../]
 [./fix_z]
   type = DirichletBC
   variable = disp_z
   boundary = back
   value = 0
 [../]
 [./move_z]
   type = FunctionDirichletBC
   variable = disp_z
   boundary = front
   function = 't'
 [../]
[]

[Executioner]
  type = Transient

  solve_type = NEWTON
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'

  nl_rel_tol = 1e-10
  nl_max_its = 10

  l_tol  = 1e-4
  l_max_its = 50

  dt = 0.2
  dtmin = 0.2

  num_steps = 2
[]

[Preconditioning]
  [./smp]
    type = SMP
    full = true
  [../]
[]

[Outputs]
  exodus = true
[]

(modules/combined/examples/optimization/multi-load/square_subapp_two.i)

power = 1.0
E0 = 1.0
Emin = 1.0e-6

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  [Bottom]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 100
    ny = 100
    xmin = 0
    xmax = 150
    ymin = 0
    ymax = 150
  []
  [left_load]
    type = ExtraNodesetGenerator
    input = Bottom
    new_boundary = left_load
    coord = '0 150 0'
  []
  [right_load]
    type = ExtraNodesetGenerator
    input = left_load
    new_boundary = right_load
    coord = '150 150 0'
  []
  [left_support]
    type = ExtraNodesetGenerator
    input = right_load
    new_boundary = left_support
    coord = '0 0 0'
  []
  [right_support]
    type = ExtraNodesetGenerator
    input = left_support
    new_boundary = right_support
    coord = '150 0 0'
  []
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
[]

[AuxVariables]
  [Dc]
    family = MONOMIAL
    order = SECOND
    initial_condition = -1.0
  []
  [Cc]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = -1.0
  []
  [mat_den]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = 0.25
  []
  [sensitivity_var]
    family = MONOMIAL
    order = SECOND
    initial_condition = -1.0
  []
[]

[AuxKernels]
  [sensitivity_kernel]
    type = MaterialRealAux
    check_boundary_restricted = false
    property = sensitivity
    variable = sensitivity_var
    execute_on = 'TIMESTEP_END'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = SMALL
    add_variables = true
    incremental = false
  []
[]

[BCs]
  [no_y]
    type = DirichletBC
    variable = disp_y
    boundary = left_support
    value = 0.0
  []
  [no_x]
    type = DirichletBC
    variable = disp_x
    boundary = left_support
    value = 0.0
  []
  [no_y_right]
    type = DirichletBC
    variable = disp_y
    boundary = right_support
    value = 0.0
  []
  [no_x_right]
    type = DirichletBC
    variable = disp_x
    boundary = right_support
    value = 0.0
  []
[]

[NodalKernels]
  [push_right]
    type = NodalGravity
    variable = disp_y
    boundary = right_load
    gravity_value = 1e-3
    mass = 1
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeVariableIsotropicElasticityTensor
    youngs_modulus = E_phys
    poissons_ratio = poissons_ratio
    args = 'mat_den'
  []
  [E_phys]
    type = DerivativeParsedMaterial
    # Emin + (density^penal) * (E0 - Emin)
    expression = '${Emin} + (mat_den ^ ${power}) * (${E0}-${Emin})'
    coupled_variables = 'mat_den'
    property_name = E_phys
  []
  [poissons_ratio]
    type = GenericConstantMaterial
    prop_names = poissons_ratio
    prop_values = 0.3
  []
  [stress]
    type = ComputeLinearElasticStress
  []
  [dc]
    type = ComplianceSensitivity
    design_density = mat_den
    youngs_modulus = E_phys
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[UserObjects]
  # We do averaging in subapps
  [rad_avg]
    type = RadialAverage
    radius = 8
    weights = linear
    prop_name = sensitivity
    execute_on = TIMESTEP_END
    force_preaux = true
  []
  [calc_sense]
    type = SensitivityFilter
    density_sensitivity = Dc
    design_density = mat_den
    filter_UO = rad_avg
    execute_on = TIMESTEP_END
    force_postaux = true
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'
  nl_abs_tol = 1e-10
  dt = 1.0
  num_steps = 10
[]

[Outputs]
  exodus = true
  [out]
    type = CSV
    execute_on = 'TIMESTEP_END'
  []
  print_linear_residuals = false
[]

[Postprocessors]
  [mesh_volume]
    type = VolumePostprocessor
    execute_on = 'initial timestep_end'
  []
  [total_vol]
    type = ElementIntegralVariablePostprocessor
    variable = mat_den
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [vol_frac]
    type = ParsedPostprocessor
    expression = 'total_vol / mesh_volume'
    pp_names = 'total_vol mesh_volume'
  []
  [sensitivity]
    type = ElementIntegralMaterialProperty
    mat_prop = sensitivity
    execute_on = 'TIMESTEP_BEGIN TIMESTEP_END NONLINEAR'
  []
  [objective]
    type = ElementIntegralMaterialProperty
    mat_prop = strain_energy_density
    execute_on = 'INITIAL TIMESTEP_END'
  []
[]

(modules/solid_mechanics/test/tests/global_strain/global_strain_action.i)

[Mesh]
  [generated_mesh]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 2
    ny = 2
    nz = 2
    xmin = -0.5
    xmax = 0.5
    ymin = -0.5
    ymax = 0.5
    zmin = -0.5
    zmax = 0.5
  []
  [cnode]
    type = ExtraNodesetGenerator
    coord = '0 -0.5 0'
    new_boundary = 100
    input = generated_mesh
  []
[]

[GlobalParams]
  displacements = 'u_x u_y u_z'
  block = 0
[]

[Variables]
  [./global_strain]
    order = SIXTH
    family = SCALAR
  [../]
[]

[Physics]
  [SolidMechanics]
    # QuasiStatic action for generating the tensor mechanics kernels, variables,
    # strain calculation material, and the auxilliary system for visualization
    [QuasiStatic]
      [./stress_div]
        strain = SMALL
        add_variables = true
        global_strain = global_strain #global strain contribution
        generate_output = 'strain_xx strain_xy strain_yy stress_xx stress_xy
                           stress_yy vonmises_stress'
      [../]
    [../]
    # GlobalStrain action for generating the objects associated with the global
    # strain calculation and associated displacement visualization
    [./GlobalStrain]
      [./global_strain]
        scalar_global_strain = global_strain
        displacements = 'u_x u_y u_z'
        auxiliary_displacements = 'disp_x disp_y disp_z'
        global_displacements = 'ug_x ug_y ug_z'
      [../]
    [../]
  [../]
[]

[BCs]
  [./Periodic]
    [./all]
      auto_direction = 'z'
      variable = 'u_x u_y u_z'
    [../]
  [../]

  # fix center point location
  [./centerfix_x]
    type = DirichletBC
    boundary = 100
    variable = u_x
    value = 0
  [../]
  [./centerfix_z]
    type = DirichletBC
    boundary = 100
    variable = u_z
    value = 0
  [../]
  # applied displacement
  [./appl_y]
    type = DirichletBC
    boundary = top
    variable = u_y
    value = 0.033
  [../]
  [./fix_y]
    type = DirichletBC
    boundary = bottom
    variable = u_y
    value = 0
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeElasticityTensor
    block = 0
    C_ijkl = '7 0.33'
    fill_method = symmetric_isotropic_E_nu
  [../]
  [./stress]
    type = ComputeLinearElasticStress
  [../]
[]

[Preconditioning]
  [./SMP]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = Transient
  scheme = bdf2
  solve_type = 'PJFNK'

  line_search = basic

  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_ksp_type -sub_pc_type -pc_asm_overlap'
  petsc_options_value = 'asm         31   preonly   lu      1'

  l_max_its = 30
  nl_max_its = 12

  l_tol = 1.0e-4

  nl_rel_tol = 1.0e-6
  nl_abs_tol = 1.0e-10

  start_time = 0.0
  num_steps = 2
[]

[Outputs]
  exodus = true
[]

(modules/navier_stokes/test/tests/finite_element/ins/mms/pspg/pspg_mms_test.i)

mu=1.5
rho=2.5

[GlobalParams]
  gravity = '0 0 0'
  pspg = true
  convective_term = true
  integrate_p_by_parts = true
  laplace = true
  u = vel_x
  v = vel_y
  pressure = p
  alpha = 1e-6
  order = FIRST
  family = LAGRANGE
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 1.0
    ymin = 0
    ymax = 1.0
    elem_type = QUAD9
    nx = 4
    ny = 4
  []
  [./corner_node]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node'
    nodes = '0'
    input = gen
  [../]
[]

[Variables]
  [./vel_x]
  [../]

  [./vel_y]
  [../]

  [./p]
  [../]
[]

[Kernels]
  # mass
  [./mass]
    type = INSMass
    variable = p
    x_vel_forcing_func = vel_x_source_func
    y_vel_forcing_func = vel_y_source_func
  [../]

  # x-momentum, space
  [./x_momentum_space]
    type = INSMomentumLaplaceForm
    variable = vel_x
    component = 0
    forcing_func = vel_x_source_func
  [../]

  # y-momentum, space
  [./y_momentum_space]
    type = INSMomentumLaplaceForm
    variable = vel_y
    component = 1
    forcing_func = vel_y_source_func
  [../]

  [./p_source]
    type = BodyForce
    function = p_source_func
    variable = p
  [../]
[]

[BCs]
  [./vel_x]
    type = FunctionDirichletBC
    boundary = 'left right top bottom'
    function = vel_x_func
    variable = vel_x
  [../]
  [./vel_y]
    type = FunctionDirichletBC
    boundary = 'left right top bottom'
    function = vel_y_func
    variable = vel_y
  [../]
  [./p]
    type = FunctionDirichletBC
    boundary = 'left right top bottom'
    function = p_func
    variable = p
  [../]
[]

[Functions]
  [./vel_x_source_func]
    type = ParsedFunction
    expression = '-${mu}*(-0.028*pi^2*x^2*sin(0.2*pi*x*y) - 0.028*pi^2*y^2*sin(0.2*pi*x*y) - 0.1*pi^2*sin(0.5*pi*x) - 0.4*pi^2*sin(pi*y)) + ${rho}*(0.14*pi*x*cos(0.2*pi*x*y) + 0.4*pi*cos(pi*y))*(0.6*sin(0.8*pi*x) + 0.3*sin(0.3*pi*y) + 0.2*sin(0.3*pi*x*y) + 0.3) + ${rho}*(0.14*pi*y*cos(0.2*pi*x*y) + 0.2*pi*cos(0.5*pi*x))*(0.4*sin(0.5*pi*x) + 0.4*sin(pi*y) + 0.7*sin(0.2*pi*x*y) + 0.5) + 0.1*pi*y*cos(0.2*pi*x*y) + 0.25*pi*cos(0.5*pi*x)'
  [../]
  [./vel_y_source_func]
    type = ParsedFunction
    expression = '-${mu}*(-0.018*pi^2*x^2*sin(0.3*pi*x*y) - 0.018*pi^2*y^2*sin(0.3*pi*x*y) - 0.384*pi^2*sin(0.8*pi*x) - 0.027*pi^2*sin(0.3*pi*y)) + ${rho}*(0.06*pi*x*cos(0.3*pi*x*y) + 0.09*pi*cos(0.3*pi*y))*(0.6*sin(0.8*pi*x) + 0.3*sin(0.3*pi*y) + 0.2*sin(0.3*pi*x*y) + 0.3) + ${rho}*(0.06*pi*y*cos(0.3*pi*x*y) + 0.48*pi*cos(0.8*pi*x))*(0.4*sin(0.5*pi*x) + 0.4*sin(pi*y) + 0.7*sin(0.2*pi*x*y) + 0.5) + 0.1*pi*x*cos(0.2*pi*x*y) + 0.3*pi*cos(0.3*pi*y)'
  [../]
  [./p_source_func]
    type = ParsedFunction
    expression = '-0.06*pi*x*cos(0.3*pi*x*y) - 0.14*pi*y*cos(0.2*pi*x*y) - 0.2*pi*cos(0.5*pi*x) - 0.09*pi*cos(0.3*pi*y)'
  [../]
  [./vel_x_func]
    type = ParsedFunction
    expression = '0.4*sin(0.5*pi*x) + 0.4*sin(pi*y) + 0.7*sin(0.2*pi*x*y) + 0.5'
  [../]
  [./vel_y_func]
    type = ParsedFunction
    expression = '0.6*sin(0.8*pi*x) + 0.3*sin(0.3*pi*y) + 0.2*sin(0.3*pi*x*y) + 0.3'
  [../]
  [./p_func]
    type = ParsedFunction
    expression = '0.5*sin(0.5*pi*x) + 1.0*sin(0.3*pi*y) + 0.5*sin(0.2*pi*x*y) + 0.5'
  [../]
  [./vxx_func]
    type = ParsedFunction
    expression = '0.14*pi*y*cos(0.2*pi*x*y) + 0.2*pi*cos(0.5*pi*x)'
  [../]
  [./px_func]
    type = ParsedFunction
    expression = '0.1*pi*y*cos(0.2*pi*x*y) + 0.25*pi*cos(0.5*pi*x)'
  [../]
[]

[Materials]
  [./const]
    type = GenericConstantMaterial
    block = 0
    prop_names = 'rho mu'
    prop_values = '${rho}  ${mu}'
  [../]
[]

[Preconditioning]
  [./SMP]
    type = SMP
    full = true
    solve_type = 'NEWTON'
  [../]
[]

[Executioner]
  type = Steady
  petsc_options = '-snes_converged_reason -ksp_converged_reason'
  petsc_options_iname = '-pc_type -pc_factor_shift_type'
  petsc_options_value = 'lu NONZERO'
  line_search = 'none'
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-13
  nl_max_its = 6
  l_tol = 1e-6
  l_max_its = 500
[]

[Outputs]
  [./exodus]
    type = Exodus
  [../]
  [./csv]
    type = CSV
  [../]
[]

[Postprocessors]
  [./L2vel_x]
    type = ElementL2Error
    variable = vel_x
    function = vel_x_func
    outputs = 'console'    execute_on = 'timestep_end'
  [../]
  [./L2vel_y]
    variable = vel_y
    function = vel_y_func
    type = ElementL2Error
    outputs = 'console'    execute_on = 'timestep_end'
  [../]
  [./L2p]
    variable = p
    function = p_func
    type = ElementL2Error
    outputs = 'console'    execute_on = 'timestep_end'
  [../]
  [./L2vxx]
    variable = vxx
    function = vxx_func
    type = ElementL2Error
    outputs = 'console'    execute_on = 'timestep_end'
  [../]
  [./L2px]
    variable = px
    function = px_func
    type = ElementL2Error
    outputs = 'console'    execute_on = 'timestep_end'
  [../]
[]

[AuxVariables]
  [./vxx]
    family = MONOMIAL
    order = FIRST
  [../]
  [./px]
    family = MONOMIAL
    order = FIRST
  [../]
[]

[AuxKernels]
  [./vxx]
    type = VariableGradientComponent
    component = x
    variable = vxx
    gradient_variable = vel_x
  [../]
  [./px]
    type = VariableGradientComponent
    component = x
    variable = px
    gradient_variable = p
  [../]
[]

(modules/solid_mechanics/test/tests/finite_strain_elastic_anisotropy/3d_bar_orthotropic.i)

[Mesh]
  [generated_mesh]
    type = GeneratedMeshGenerator
    dim = 3
    xmin = 0
    xmax = 2
    ymin = 0
    ymax = 2
    zmin = 0
    zmax = 10
    nx = 6
    ny = 2
    nz = 2
    elem_type = HEX8
  []
  [corner]
    type = ExtraNodesetGenerator
    new_boundary = 101
    coord = '0 0 0'
    input = generated_mesh
  []
  [side]
    type = ExtraNodesetGenerator
    new_boundary = 102
    coord = '2 0 0'
    input = corner
  []
[]

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = FINITE
    add_variables = true
    use_finite_deform_jacobian = true
    volumetric_locking_correction = false
    generate_output = 'stress_xx stress_yy stress_zz stress_xy stress_xz'
  []
[]

[Materials]
  [stress]
    type = ComputeFiniteStrainElasticStress
  []
  [elasticity_tensor]
    type = ComputeElasticityTensor
    fill_method = orthotropic
    C_ijkl = '2.0e5 2.0e5 2.0e5 0.71428571e5 0.71428571e5 0.71428571e5 0.4 0.4 0.4 0.4 0.4 0.4' # Isotropic
  []
[]

[BCs]
  [fix_corner_x]
    type = DirichletBC
    variable = disp_x
    boundary = 101
    value = 0
  []
  [fix_corner_y]
    type = DirichletBC
    variable = disp_y
    boundary = 101
    value = 0
  []
  [fix_side_y]
    type = DirichletBC
    variable = disp_y
    boundary = 102
    value = 0
  []
  [fix_z]
    type = DirichletBC
    variable = disp_z
    boundary = back
    value = 0
  []
  [move_z]
    type = FunctionDirichletBC
    variable = disp_z
    boundary = front
    function = 't'
  []
  [move_y]
    type = FunctionDirichletBC
    variable = disp_y
    boundary = front
    function = 't*1.4'
  []
[]

[Executioner]
  type = Transient

  solve_type = NEWTON
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'

  nl_rel_tol = 1e-12
  nl_max_its = 50

  l_tol = 1e-4
  l_max_its = 50

  dt = 0.4
  dtmin = 0.4

  num_steps = 1
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Outputs]
  exodus = true
[]

(modules/solid_mechanics/test/tests/ad_finite_strain_jacobian/3d_bar.i)

[Mesh]
  [generated_mesh]
    type = GeneratedMeshGenerator
    dim = 3
    xmin = 0
    xmax = 2
    ymin = 0
    ymax = 2
    zmin = 0
    zmax = 10
    nx = 10
    ny = 2
    nz = 2
    elem_type = HEX8
  []
  [corner]
    type = ExtraNodesetGenerator
    new_boundary = 101
    coord = '0 0 0'
    input = generated_mesh
  []
  [side]
    type = ExtraNodesetGenerator
    new_boundary = 102
    coord = '2 0 0'
    input = corner
  []
[]

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = FINITE
    add_variables = true
    use_finite_deform_jacobian = true
    volumetric_locking_correction = false
    use_automatic_differentiation = true
  []
[]

[Materials]
  [stress]
    type = ADComputeFiniteStrainElasticStress
  []
  [elasticity_tensor]
    type = ADComputeElasticityTensor
    fill_method = symmetric9
    C_ijkl = '1.684e5 0.176e5 0.176e5 1.684e5 0.176e5 1.684e5 0.754e5 0.754e5 0.754e5'
  []
[]

[BCs]
 [fix_corner_x]
   type = ADDirichletBC
   variable = disp_x
   boundary = 101
   value = 0
 []
 [fix_corner_y]
   type = ADDirichletBC
   variable = disp_y
   boundary = 101
   value = 0
 []
 [fix_side_y]
   type = ADDirichletBC
   variable = disp_y
   boundary = 102
   value = 0
 []
 [fix_z]
   type = ADDirichletBC
   variable = disp_z
   boundary = back
   value = 0
 []
 [move_z]
   type = ADFunctionDirichletBC
   variable = disp_z
   boundary = front
   function = 't'
 []
[]

[Executioner]
  type = Transient

  solve_type = NEWTON
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'

  nl_rel_tol = 1e-10
  nl_max_its = 10

  l_tol  = 1e-4
  l_max_its = 50

  dt = 0.2
  dtmin = 0.2

  num_steps = 2
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Outputs]
  exodus = true
[]

(modules/xfem/test/tests/moving_interface/moving_ad_bimaterial.i)

# This test is for two layer materials with different youngs modulus with AD
# The global stress is determined by switching the stress based on level set values
# The material interface is marked by a level set function
# The two layer materials are glued together
# This case is also meant to test for a bug in moving interfaces on displaced meshes
# It should fail during the healing step of the 2nd timestep if the bug is present.

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[XFEM]
  qrule = volfrac
  output_cut_plane = true
[]

[UserObjects]
  [./level_set_cut_uo]
    type = LevelSetCutUserObject
    level_set_var = ls
    heal_always = true
  [../]
[]

[Mesh]
  displacements = 'disp_x disp_y'
  [generated_mesh]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 5
    ny = 5
    xmin = 0.0
    xmax = 5.
    ymin = 0.0
    ymax = 5.
    elem_type = QUAD4
  []
  [./left_bottom]
    type = ExtraNodesetGenerator
    new_boundary = 'left_bottom'
    coord = '0.0 0.0'
    input = generated_mesh
  [../]
  [./left_top]
    type = ExtraNodesetGenerator
    new_boundary = 'left_top'
    coord = '0.0 5.'
    input = left_bottom
  [../]
[]

[AuxVariables]
  [./ls]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxKernels]
  [./ls_function]
    type = FunctionAux
    variable = ls
    function = ls_func
  [../]
[]

[Functions]
  [./ls_func]
    type = ParsedFunction
    expression = 'y-3.153 + t'
  [../]
[]

[AuxVariables]
  [./a_strain_xx]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./a_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./a_strain_xy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./b_strain_xx]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./b_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./b_strain_xy]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[Physics/SolidMechanics/QuasiStatic]
  [./all]
    strain = SMALL
    use_automatic_differentiation = true
    add_variables = true
    generate_output = 'stress_xx stress_yy stress_xy'
  [../]
[]

[AuxKernels]
  [./a_strain_xx]
    type = ADRankTwoAux
    rank_two_tensor = A_total_strain
    index_i = 0
    index_j = 0
    variable = a_strain_xx
  [../]
  [./a_strain_yy]
    type = ADRankTwoAux
    rank_two_tensor = A_total_strain
    index_i = 1
    index_j = 1
    variable = a_strain_yy
  [../]
  [./a_strain_xy]
    type = ADRankTwoAux
    rank_two_tensor = A_total_strain
    index_i = 0
    index_j = 1
    variable = a_strain_xy
  [../]
  [./b_strain_xx]
    type = ADRankTwoAux
    rank_two_tensor = B_total_strain
    index_i = 0
    index_j = 0
    variable = b_strain_xx
  [../]
  [./b_strain_yy]
    type = ADRankTwoAux
    rank_two_tensor = B_total_strain
    index_i = 1
    index_j = 1
    variable = b_strain_yy
  [../]
  [./b_strain_xy]
    type = ADRankTwoAux
    rank_two_tensor = B_total_strain
    index_i = 0
    index_j = 1
    variable = b_strain_xy
  [../]
[]

[Constraints]
  [./dispx_constraint]
    type = XFEMSingleVariableConstraint
    use_displaced_mesh = false
    variable = disp_x
    alpha = 1e8
    geometric_cut_userobject = 'level_set_cut_uo'
  [../]
  [./dispy_constraint]
    type = XFEMSingleVariableConstraint
    use_displaced_mesh = false
    variable = disp_y
    alpha = 1e8
    geometric_cut_userobject = 'level_set_cut_uo'
  [../]
[]

[BCs]
  [./bottomx]
    type = ADDirichletBC
    boundary = bottom
    variable = disp_x
    value = 0.0
  [../]
  [./bottomy]
    type = ADDirichletBC
    boundary = bottom
    variable = disp_y
    value = 0.0
  [../]
  [./topx]
    type = ADFunctionDirichletBC
    boundary = top
    variable = disp_x
    function = 0.03*t
  [../]
  [./topy]
    type = ADFunctionDirichletBC
    boundary = top
    variable = disp_y
    function = '0.03*t'
  [../]
[]

[Materials]
  [./elasticity_tensor_A]
    type = ADComputeIsotropicElasticityTensor
    base_name = A
    youngs_modulus = 1e9
    poissons_ratio = 0.3
  [../]
  [./strain_A]
    type = ADComputeSmallStrain
    base_name = A
    displacements = 'disp_x disp_y'
  [../]
  [./stress_A]
    type = ADComputeLinearElasticStress
    base_name = A
  [../]
  [./elasticity_tensor_B]
    type = ADComputeIsotropicElasticityTensor
    base_name = B
    youngs_modulus = 1e7
    poissons_ratio = 0.3
  [../]
  [./strain_B]
    type = ADComputeSmallStrain
    base_name = B
    displacements = 'disp_x disp_y'
  [../]
  [./stress_B]
    type = ADComputeLinearElasticStress
    base_name = B
  [../]
  [./combined_stress]
    type = ADLevelSetBiMaterialRankTwo
    levelset_positive_base = 'A'
    levelset_negative_base = 'B'
    level_set_var = ls
    prop_name = stress
  [../]
  [./combined_elasticity_tensor]
    type = ADLevelSetBiMaterialRankFour
    levelset_positive_base = 'A'
    levelset_negative_base = 'B'
    level_set_var = ls
    prop_name = elasticity_tensor
  [../]
[]

[Executioner]
  type = Transient

  solve_type = NEWTON
  petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
  petsc_options_value = '201                hypre    boomeramg      8'

  line_search = 'bt'

# controls for linear iterations
  l_max_its = 20
  l_tol = 1e-8

# controls for nonlinear iterations
  nl_max_its = 15
  nl_rel_tol = 1e-14
  nl_abs_tol = 1e-50

# time control
  start_time = 0.0
  dt = 0.15
  num_steps = 3

  max_xfem_update = 1
[]

[Outputs]
  exodus = true
  execute_on = timestep_end
  file_base = moving_bimaterial_out
  perf_graph = true
  [./console]
    type = Console
    output_linear = true
  [../]
[]

(modules/xfem/test/tests/moving_interface/moving_bimaterial_finite_strain.i)

# This test is for two layer materials with different youngs modulus with AD
# The global stress is determined by switching the stress based on level set values
# The material interface is marked by a level set function
# The two layer materials are glued together

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[XFEM]
  output_cut_plane = true
[]

[UserObjects]
  [level_set_cut_uo]
    type = LevelSetCutUserObject
    level_set_var = ls
    heal_always = true
  []
[]

[Mesh]
  use_displaced_mesh = true
  [generated_mesh]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 10
    xmin = 0
    xmax = 5
    ymin = 0
    ymax = 5
    elem_type = QUAD4
  []
  [left_bottom]
    type = ExtraNodesetGenerator
    new_boundary = 'left_bottom'
    coord = '0 0'
    input = generated_mesh
  []
  [left_top]
    type = ExtraNodesetGenerator
    new_boundary = 'left_top'
    coord = '0 5'
    input = left_bottom
  []
[]

[Functions]
  [ls_func]
    type = ParsedFunction
    expression = 'y-2.73+t'
  []
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
[]

[AuxVariables]
  [ls]
  []
  [a_strain_xx]
    order = CONSTANT
    family = MONOMIAL
  []
  [a_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []
  [a_strain_xy]
    order = CONSTANT
    family = MONOMIAL
  []
  [b_strain_xx]
    order = CONSTANT
    family = MONOMIAL
  []
  [b_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []
  [b_strain_xy]
    order = CONSTANT
    family = MONOMIAL
  []
  [stress_xx]
    order = CONSTANT
    family = MONOMIAL
  []
  [stress_yy]
    order = CONSTANT
    family = MONOMIAL
  []
  [stress_xy]
    order = CONSTANT
    family = MONOMIAL
  []

[]

[AuxKernels]
  [ls_function]
    type = FunctionAux
    variable = ls
    function = ls_func
  []
  [a_strain_xx]
    type = RankTwoAux
    variable = a_strain_xx
    rank_two_tensor = A_total_strain
    index_i = 0
    index_j = 0
  []
  [a_strain_yy]
    type = RankTwoAux
    variable = a_strain_yy
    rank_two_tensor = A_total_strain
    index_i = 1
    index_j = 1
  []
  [a_strain_xy]
    type = RankTwoAux
    variable = a_strain_xy
    rank_two_tensor = A_total_strain
    index_i = 0
    index_j = 1
  []
  [b_strain_xx]
    type = RankTwoAux
    variable = b_strain_xx
    rank_two_tensor = B_total_strain
    index_i = 0
    index_j = 0
  []
  [b_strain_yy]
    type = RankTwoAux
    variable = b_strain_yy
    rank_two_tensor = B_total_strain
    index_i = 1
    index_j = 1
  []
  [b_strain_xy]
    type = RankTwoAux
    variable = b_strain_xy
    rank_two_tensor = B_total_strain
    index_i = 0
    index_j = 1
  []
  [stress_xx]
    type = RankTwoAux
    variable = stress_xx
    rank_two_tensor = stress
    index_i = 0
    index_j = 0
  []
  [stress_xy]
    type = RankTwoAux
    variable = stress_xy
    rank_two_tensor = stress
    index_i = 0
    index_j = 1
  []
  [stress_yy]
    type = RankTwoAux
    variable = stress_yy
    rank_two_tensor = stress
    index_i = 1
    index_j = 1
  []
[]

[Kernels]
  [solid_x]
    type = StressDivergenceTensors
    variable = disp_x
    component = 0
    use_displaced_mesh = true
  []
  [solid_y]
    type = StressDivergenceTensors
    variable = disp_y
    component = 1
    use_displaced_mesh = true
  []
[]

[Constraints]
  [dispx_constraint]
    type = XFEMSingleVariableConstraint
    use_displaced_mesh = false
    variable = disp_x
    alpha = 1e8
    geometric_cut_userobject = 'level_set_cut_uo'
  []
  [dispy_constraint]
    type = XFEMSingleVariableConstraint
    use_displaced_mesh = false
    variable = disp_y
    alpha = 1e8
    geometric_cut_userobject = 'level_set_cut_uo'
  []
[]

[BCs]
  [bottomx]
    type = DirichletBC
    boundary = bottom
    variable = disp_x
    value = 0.0
  []
  [bottomy]
    type = DirichletBC
    boundary = bottom
    variable = disp_y
    value = 0.0
  []
  [topx]
    type = FunctionDirichletBC
    boundary = top
    variable = disp_x
    function = 0.03*t
  []
  [topy]
    type = FunctionDirichletBC
    boundary = top
    variable = disp_y
    function = '0.03*t'
  []
[]

[Materials]
  [elasticity_tensor_A]
    type = ComputeIsotropicElasticityTensor
    base_name = A
    youngs_modulus = 1e9
    poissons_ratio = 0.3
  []
  [strain_A]
    type = ComputeFiniteStrain
    base_name = A
  []
  [stress_A]
    type = ComputeFiniteStrainElasticStress
    base_name = A
  []
  [elasticity_tensor_B]
    type = ComputeIsotropicElasticityTensor
    base_name = B
    youngs_modulus = 1e7
    poissons_ratio = 0.3
  []
  [strain_B]
    type = ComputeFiniteStrain
    base_name = B
  []
  [stress_B]
    type = ComputeFiniteStrainElasticStress
    base_name = B
  []
  [combined_stress]
    type = LevelSetBiMaterialRankTwo
    levelset_positive_base = 'A'
    levelset_negative_base = 'B'
    level_set_var = ls
    prop_name = stress
  []
  [combined_jacob_mult]
    type = LevelSetBiMaterialRankFour
    levelset_positive_base = 'A'
    levelset_negative_base = 'B'
    level_set_var = ls
    prop_name = Jacobian_mult
  []
[]

[Postprocessors]
  [disp_x_norm]
    type = ElementL2Norm
    variable = disp_x
  []
  [disp_y_norm]
    type = ElementL2Norm
    variable = disp_y
  []
[]

[Executioner]
  type = Transient

  solve_type = NEWTON
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  automatic_scaling = true

  # controls for nonlinear iterations
  nl_max_its = 15
  nl_rel_tol = 1e-13
  nl_abs_tol = 1e-50

  # time control
  start_time = 0.0
  dt = 0.1
  num_steps = 4

  max_xfem_update = 1
[]

[Outputs]
  print_linear_residuals = false
  exodus = true
[]

(modules/solid_mechanics/test/tests/static_deformations/cosserat_tension.i)

[Mesh]
  [generated_mesh]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 2
    ny = 2
    nz = 2
    zmax = 0.2
  []
  [bottom_xline1]
    type = ExtraNodesetGenerator
    new_boundary = 101
    coord = '0 0 0'
    input = generated_mesh
  []
  [bottom_xline2]
    type = ExtraNodesetGenerator
    new_boundary = 101
    coord = '0.5 0 0'
    input = bottom_xline1
  []
  [bottom_xline3]
    type = ExtraNodesetGenerator
    new_boundary = 101
    coord = '1 0 0'
    input = bottom_xline2
  []
  [bottom_zline1]
    type = ExtraNodesetGenerator
    new_boundary = 102
    coord = '0 0 0.0'
    input = bottom_xline3
  []
  [bottom_zline2]
    type = ExtraNodesetGenerator
    new_boundary = 102
    coord = '0 0 0.1'
    input = bottom_zline1
  []
  [bottom_zline3]
    type = ExtraNodesetGenerator
    new_boundary = 102
    coord = '0 0 0.2'
    input = bottom_zline2
  []
[]

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  Cosserat_rotations = 'wc_x wc_y wc_z'
[]

[Postprocessors]
  [./disp_y_top]
    type = PointValue
    point = '0.5 1 0.1'
    variable = disp_y
  [../]
  [./wc_z_top]
    type = PointValue
    point = '0.5 1 0.1'
    variable = wc_z
  [../]
[]

[Variables]
  [./disp_x]
  [../]
  [./disp_y]
  [../]
  [./disp_z]
  [../]
  [./wc_x]
  [../]
  [./wc_y]
  [../]
  [./wc_z]
  [../]
[]

[Kernels]
  [./cx_elastic]
    type = CosseratStressDivergenceTensors
    variable = disp_x
    component = 0
  [../]
  [./cy_elastic]
    type = CosseratStressDivergenceTensors
    variable = disp_y
    component = 1
  [../]
  [./cz_elastic]
    type = CosseratStressDivergenceTensors
    variable = disp_z
    component = 2
  [../]
  [./x_couple]
    type = StressDivergenceTensors
    variable = wc_x
    displacements = 'wc_x wc_y wc_z'
    component = 0
    base_name = couple
  [../]
  [./y_couple]
    type = StressDivergenceTensors
    variable = wc_y
    displacements = 'wc_x wc_y wc_z'
    component = 1
    base_name = couple
  [../]
  [./z_couple]
    type = StressDivergenceTensors
    variable = wc_z
    displacements = 'wc_x wc_y wc_z'
    component = 2
    base_name = couple
  [../]
  [./x_moment]
    type = MomentBalancing
    variable = wc_x
    component = 0
  [../]
  [./y_moment]
    type = MomentBalancing
    variable = wc_y
    component = 1
  [../]
  [./z_moment]
    type = MomentBalancing
    variable = wc_z
    component = 2
  [../]
[]

[BCs]
  [./y_bottom]
    type = DirichletBC
    variable = disp_y
    boundary = bottom
    value = 0
  [../]

  [./x_line]
    type = DirichletBC
    variable = disp_z
    boundary = 101
    value = 0
  [../]
  [./z_line]
    type = DirichletBC
    variable = disp_x
    boundary = 102
    value = 0
  [../]

  [./wc_x_bottom]
    type = DirichletBC
    variable = wc_x
    boundary = bottom
    value = 0
  [../]
  [./wc_y_bottom]
    type = DirichletBC
    variable = wc_y
    boundary = bottom
    value = 0
  [../]
  [./wc_z_bottom]
    type = DirichletBC
    variable = wc_z
    boundary = bottom
    value = 0
  [../]
  [./top_force]
    type = NeumannBC
    variable = disp_y
    boundary = top
    value = 1
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeCosseratElasticityTensor
    B_ijkl = 0.5
    E_ijkl = '1 2 1.3333'
    fill_method = 'general_isotropic'
  [../]
  [./strain]
    type = ComputeCosseratSmallStrain
  [../]
  [./stress]
    type = ComputeCosseratLinearElasticStress
  [../]
[]

[Preconditioning]
  [./andy]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -snes_atol -snes_rtol -snes_max_it -ksp_atol -ksp_rtol'
    petsc_options_value = 'gmres bjacobi 1E-10 1E-10 10 1E-15 1E-10'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = Newton
  num_steps = 1
[]

[Outputs]
  execute_on = 'timestep_end'
  file_base = cosserat_tension_out
  exodus = true
[]

(modules/combined/test/tests/optimization/compliance_sensitivity/thermal_test.i)

vol_frac = 0.4
cost_frac = 10.0

power = 2.0

E0 = 1.0e-6
E1 = 1.0

rho0 = 0.0
rho1 = 1.0

C0 = 1.0e-6
C1 = 1.0

TC0 = 1.0e-16
TC1 = 1.0

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  [MeshGenerator]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 10
    xmin = 0
    xmax = 40
    ymin = 0
    ymax = 40
  []
  [node]
    type = ExtraNodesetGenerator
    input = MeshGenerator
    new_boundary = hold
    nodes = 0
  []
  [push_left]
    type = ExtraNodesetGenerator
    input = node
    new_boundary = push_left
    coord = '16 0 0'
  []
  [push_center]
    type = ExtraNodesetGenerator
    input = push_left
    new_boundary = push_center
    coord = '24 0 0'
  []
  [extra]
    type = SideSetsFromBoundingBoxGenerator
    input = push_center
    bottom_left = '-0.01 17.999  0'
    top_right = '5 22.001  0'
    boundary_new = n1
    included_boundaries = left
  []
  [dirichlet_bc]
    type = SideSetsFromNodeSetsGenerator
    input = extra
  []
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [temp]
    initial_condition = 100.0
  []
[]

[AuxVariables]
  [Dc]
    family = MONOMIAL
    order = FIRST
    initial_condition = -1.0
  []
  [Cc]
    family = MONOMIAL
    order = FIRST
    initial_condition = -1.0
  []
  [Tc]
    family = MONOMIAL
    order = FIRST
    initial_condition = -1.0
  []
  [Cost]
    family = MONOMIAL
    order = FIRST
    initial_condition = -1.0
  []
  [mat_den]
    family = MONOMIAL
    order = FIRST
    initial_condition = ${vol_frac}
  []
[]

[AuxKernels]
  [Cost]
    type = MaterialRealAux
    variable = Cost
    property = Cost_mat
  []
[]

[Kernels]
  [heat_conduction]
    type = HeatConduction
    variable = temp
    diffusion_coefficient = thermal_cond
  []
  [heat_source]
    type = HeatSource
    value = 1e-2 # W/m^3
    variable = temp
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = SMALL
    add_variables = true
    incremental = false
  []
[]

[BCs]
  [no_y]
    type = DirichletBC
    variable = disp_y
    boundary = hold
    value = 0.0
  []
  [no_x_symm]
    type = DirichletBC
    variable = disp_x
    boundary = right
    value = 0.0
  []
  [left_n1]
    type = DirichletBC
    variable = temp
    boundary = n1
    value = 0.0
  []
  [top]
    type = NeumannBC
    variable = temp
    boundary = top
    value = 0
  []
  [bottom]
    type = NeumannBC
    variable = temp
    boundary = bottom
    value = 0
  []
  [right]
    type = NeumannBC
    variable = temp
    boundary = right
    value = 0
  []
  [left]
    type = NeumannBC
    variable = temp
    boundary = left
    value = 0
  []
[]

[NodalKernels]
  [push_left]
    type = NodalGravity
    variable = disp_y
    boundary = push_left
    gravity_value = 0.0 # -1e-8
    mass = 1
  []
  [push_center]
    type = NodalGravity
    variable = disp_y
    boundary = push_center
    gravity_value = 0.0 # -1e-8
    mass = 1
  []
[]

[Materials]
  [thermal_cond]
    type = DerivativeParsedMaterial
    # ordered multimaterial simp
    expression = "A1:=(${TC0}-${TC1})/(${rho0}^${power}-${rho1}^${power}); "
                 "B1:=${TC0}-A1*${rho0}^${power}; TC1:=A1*mat_den^${power}+B1; TC1"
    coupled_variables = 'mat_den'
    property_name = thermal_cond
    outputs = 'exodus'
  []
  [thermal_compliance]
    type = ThermalCompliance
    temperature = temp
    thermal_conductivity = thermal_cond
    outputs = 'exodus'
  []
  [elasticity_tensor]
    type = ComputeVariableIsotropicElasticityTensor
    youngs_modulus = E_phys
    poissons_ratio = poissons_ratio
    args = 'mat_den'
  []
  [E_phys]
    type = DerivativeParsedMaterial
    # ordered multimaterial simp
    expression = "A1:=(${E0}-${E1})/(${rho0}^${power}-${rho1}^${power}); "
                 "B1:=${E0}-A1*${rho0}^${power}; E1:=A1*mat_den^${power}+B1; E1"
    coupled_variables = 'mat_den'
    property_name = E_phys
  []
  [Cost_mat]
    type = DerivativeParsedMaterial
    # ordered multimaterial simp
    expression = "A1:=(${C0}-${C1})/(${rho0}^(1/${power})-${rho1}^(1/${power})); "
                 "B1:=${C0}-A1*${rho0}^(1/${power}); C1:=A1*mat_den^(1/${power})+B1; C1"
    coupled_variables = 'mat_den'
    property_name = Cost_mat
  []
  [CostDensity]
    type = ParsedMaterial
    property_name = CostDensity
    coupled_variables = 'mat_den Cost'
    expression = 'mat_den*Cost'
  []
  [poissons_ratio]
    type = GenericConstantMaterial
    prop_names = poissons_ratio
    prop_values = 0.3
  []
  [stress]
    type = ComputeLinearElasticStress
  []
  [dc]
    type = ComplianceSensitivity
    design_density = mat_den
    youngs_modulus = E_phys
  []
  [cc]
    type = CostSensitivity
    design_density = mat_den
    cost = Cost_mat
    outputs = 'exodus'
  []
  [tc]
    type = ThermalSensitivity
    design_density = mat_den
    thermal_conductivity = thermal_cond
    temperature = temp
    outputs = 'exodus'
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[UserObjects]
  [rad_avg]
    type = RadialAverage
    radius = 0.1
    weights = linear
    prop_name = sensitivity
    execute_on = TIMESTEP_END
    force_preaux = true
  []
  [rad_avg_cost]
    type = RadialAverage
    radius = 0.1
    weights = linear
    prop_name = cost_sensitivity
    execute_on = TIMESTEP_END
    force_preaux = true
  []
  [rad_avg_thermal]
    type = RadialAverage
    radius = 0.1
    weights = linear
    prop_name = thermal_sensitivity
    execute_on = TIMESTEP_END
    force_preaux = true
  []
  [update]
    type = DensityUpdateTwoConstraints
    density_sensitivity = Dc
    cost_density_sensitivity = Cc
    cost = Cost
    cost_fraction = ${cost_frac}
    design_density = mat_den
    volume_fraction = ${vol_frac}

    bisection_lower_bound = 0
    bisection_upper_bound = 1.0e12 # 100

    use_thermal_compliance = true
    thermal_sensitivity = Tc
    weight_mechanical_thermal = '0 1'

    relative_tolerance = 1.0e-12
    bisection_move = 0.015
    adaptive_move = false
    execute_on = TIMESTEP_BEGIN
  []
  # Provides Dc
  [calc_sense]
    type = SensitivityFilter
    density_sensitivity = Dc
    design_density = mat_den
    filter_UO = rad_avg
    execute_on = TIMESTEP_END
    force_postaux = true
  []
  # Provides Cc
  [calc_sense_cost]
    type = SensitivityFilter
    density_sensitivity = Cc
    design_density = mat_den
    filter_UO = rad_avg_cost
    execute_on = TIMESTEP_END
    force_postaux = true
  []
  # Provides Tc
  [calc_sense_thermal]
    type = SensitivityFilter
    density_sensitivity = Tc
    design_density = mat_den
    filter_UO = rad_avg_thermal
    execute_on = TIMESTEP_END
    force_postaux = true
  []
[]

[Executioner]
  type = Transient
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'
  nl_abs_tol = 1e-12
  dt = 1.0
  num_steps = 5
[]

[Outputs]
  exodus = true
  [out]
    type = CSV
    execute_on = 'TIMESTEP_END'
  []
  print_linear_residuals = false
[]

[Postprocessors]
  [right_flux]
    type = SideDiffusiveFluxAverage
    variable = temp
    boundary = right
    diffusivity = 10
  []
  [mesh_volume]
    type = VolumePostprocessor
    execute_on = 'initial timestep_end'
  []
  [total_vol]
    type = ElementIntegralVariablePostprocessor
    variable = mat_den
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [vol_frac]
    type = ParsedPostprocessor
    expression = 'total_vol / mesh_volume'
    pp_names = 'total_vol mesh_volume'
  []
  [sensitivity]
    type = ElementIntegralMaterialProperty
    mat_prop = sensitivity
  []
  [cost_sensitivity]
    type = ElementIntegralMaterialProperty
    mat_prop = cost_sensitivity
  []
  [cost]
    type = ElementIntegralMaterialProperty
    mat_prop = CostDensity
  []
  [cost_frac]
    type = ParsedPostprocessor
    expression = 'cost / mesh_volume'
    pp_names = 'cost mesh_volume'
  []
  [objective]
    type = ElementIntegralMaterialProperty
    mat_prop = strain_energy_density
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [objective_thermal]
    type = ElementIntegralMaterialProperty
    mat_prop = thermal_compliance
    execute_on = 'INITIAL TIMESTEP_END'
  []
[]

(modules/solid_mechanics/test/tests/uel/small_test.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 20
    ny = 10
    xmax = 10
    ymax = 3
    elem_type = TRI3
  []
  [pin]
    type = ExtraNodesetGenerator
    nodes = 106
    new_boundary = pin
    input = gen
  []
  displacements = 'disp_x disp_y'
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
[]

[BCs]
  [left_x]
    type = DirichletBC
    variable = disp_x
    boundary = left
    value = 0
  []
  [left_y]
    type = DirichletBC
    variable = disp_y
    boundary = pin
    value = 0
  []

  inactive = 'right_dirichlet'
  [right_neumann]
    type = FunctionNeumannBC
    variable = disp_x
    function = t
    boundary = right
  []
  [right_dirichlet]
    type = FunctionDirichletBC
    variable = disp_x
    function = t/10
    boundary = right
  []
[]

[UserObjects]
  [uel]
    type = AbaqusUserElement
    variables = 'disp_x disp_y'
    plugin = ../../../examples/uel_tri_tests/uel
    use_displaced_mesh = false
    num_state_vars = 6
    constant_properties = '100 0.3' # E nu
    extra_vector_tags = 'kernel_residual'
  []
[]

[Problem]
  kernel_coverage_check = false
  extra_tag_vectors = 'kernel_residual'
[]

[AuxVariables]
  [res_x]
  []
  [res_y]
  []
[]

[AuxKernels]
  [res_x]
    type = TagVectorAux
    variable = res_x
    v = disp_x
    vector_tag = kernel_residual
  []
  [res_y]
    type = TagVectorAux
    variable = res_y
    v = disp_y
    vector_tag = kernel_residual
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  dt = 1
  num_steps = 15
[]

[Postprocessors]
  [delta_l]
    type = SideAverageValue
    variable = disp_x
    boundary = right
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [V]
    type = ElementIntegralMaterialProperty
    mat_prop = 1
    use_displaced_mesh = true
    execute_on = 'INITIAL TIMESTEP_END'
  []
[]

[Outputs]
  exodus = true
  csv = true
[]

(test/tests/mortar/periodic_segmental_constraint/periodic_simple2d.i)

[Mesh]
  [left_block]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = -1.0
    xmax = 1.0
    ymin = -1.0
    ymax = 1.0
    nx = 2
    ny = 2
    elem_type = QUAD9
  []
  [left_block_sidesets]
    type = RenameBoundaryGenerator
    input = left_block
    old_boundary = '0 1 2 3'
    new_boundary = '10 11 12 13'
  []
  [left_block_id]
    type = SubdomainIDGenerator
    input = left_block_sidesets
    subdomain_id = 1
  []
  [left]
    type = LowerDBlockFromSidesetGenerator
    input = left_block_id
    sidesets = '13'
    new_block_id = '10003'
    new_block_name = 'secondary_left'
  []
  [right]
    type = LowerDBlockFromSidesetGenerator
    input = left
    sidesets = '11'
    new_block_id = '10001'
    new_block_name = 'primary_right'
  []
  [bottom]
    type = LowerDBlockFromSidesetGenerator
    input = right
    sidesets = '10'
    new_block_id = '10000'
    new_block_name = 'secondary_bottom'
  []
  [top]
    type = LowerDBlockFromSidesetGenerator
    input = bottom
    sidesets = '12'
    new_block_id = '10002'
    new_block_name = 'primary_top'
  []

  [corner_node]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node'
    nodes = '0'
    input = top
  []
[]

[Variables]
  [u]
    order = SECOND
    family = LAGRANGE
  []
  [epsilon]
    order = SECOND
    family = SCALAR
  []
  [./lm1]
    order = FIRST
    family = LAGRANGE
    block = secondary_left
  [../]
  [./lm2]
    order = FIRST
    family = LAGRANGE
    block = secondary_bottom
  [../]
[]

[AuxVariables]
  [sigma]
    order = SECOND
    family = SCALAR
  []
[]

[AuxScalarKernels]
  [sigma]
    type = FunctionScalarAux
    variable = sigma
    function = '1 2'
    execute_on = initial #timestep_end
  []
[]

[Kernels]
  [diff1]
    type = Diffusion
    variable = u
    block = 1
  []
[]

[Problem]
  kernel_coverage_check = false
  error_on_jacobian_nonzero_reallocation = true
[]

[BCs]
  [fix_right]
    type = DirichletBC
    variable = u
    boundary = pinned_node
    value = 0
  []
[]

[Constraints]
  [mortarlr]
    type = EqualValueConstraint
    primary_boundary = '11'
    secondary_boundary = '13'
    primary_subdomain = 'primary_right'
    secondary_subdomain = 'secondary_left'
    secondary_variable = u
    variable = lm1
    correct_edge_dropping = true
  []
  [periodiclr]
    type = PeriodicSegmentalConstraint
    primary_boundary = '11'
    secondary_boundary = '13'
    primary_subdomain = 'primary_right'
    secondary_subdomain = 'secondary_left'
    secondary_variable = u
    epsilon = epsilon
    sigma = sigma
    variable = lm1
    correct_edge_dropping = true
  []
  [mortarbt]
    type = EqualValueConstraint
    primary_boundary = '12'
    secondary_boundary = '10'
    primary_subdomain = 'primary_top'
    secondary_subdomain = 'secondary_bottom'
    secondary_variable = u
    variable = lm2
    correct_edge_dropping = true
  []
  [periodicbt]
    type = PeriodicSegmentalConstraint
    primary_boundary = '12'
    secondary_boundary = '10'
    primary_subdomain = 'primary_top'
    secondary_subdomain = 'secondary_bottom'
    secondary_variable = u
    epsilon = epsilon
    sigma = sigma
    variable = lm2
    correct_edge_dropping = true
  []
[]

[Preconditioning]
  [smp]
    full = true
    type = SMP
  []
[]

[Executioner]
  type = Steady
  petsc_options_iname = '-pc_type -pc_factor_shift_type -pc_factor_shift_amount'
  petsc_options_value = 'lu       NONZERO               1e-15'
  solve_type = NEWTON
[]

[Outputs]
  exodus = true
  csv = true
[]

(test/tests/mortar/periodic_segmental_constraint/penalty_periodic_simple2d_flip.i)

[Mesh]
  [left_block]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = -1.0
    xmax = 1.0
    ymin = -1.0
    ymax = 1.0
    nx = 2
    ny = 2
    elem_type = QUAD4
  []
  [left_block_sidesets]
    type = RenameBoundaryGenerator
    input = left_block
    old_boundary = '0 1 2 3'
    new_boundary = '10 11 12 13'
  []
  [left_block_id]
    type = SubdomainIDGenerator
    input = left_block_sidesets
    subdomain_id = 1
  []
  [left]
    type = LowerDBlockFromSidesetGenerator
    input = left_block_id
    sidesets = '13'
    new_block_id = '10003'
    new_block_name = 'secondary_left'
  []
  [right]
    type = LowerDBlockFromSidesetGenerator
    input = left
    sidesets = '11'
    new_block_id = '10001'
    new_block_name = 'primary_right'
  []
  [bottom]
    type = LowerDBlockFromSidesetGenerator
    input = right
    sidesets = '10'
    new_block_id = '10000'
    new_block_name = 'secondary_bottom'
  []
  [top]
    type = LowerDBlockFromSidesetGenerator
    input = bottom
    sidesets = '12'
    new_block_id = '10002'
    new_block_name = 'primary_top'
  []

  [corner_node]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node'
    nodes = '0'
    input = top
  []
[]

[Variables]
  [u]
    order = FIRST
    family = LAGRANGE
  []
  [epsilon]
    order = SECOND
    family = SCALAR
  []
[]

[AuxVariables]
  [sigma]
    order = SECOND
    family = SCALAR
  []
[]

[AuxScalarKernels]
  [sigma]
    type = FunctionScalarAux
    variable = sigma
    function = '1 2'
    execute_on = initial #timestep_end
  []
[]

[Kernels]
  [diff1]
    type = Diffusion
    variable = u
    block = 1
  []
[]

[Problem]
  kernel_coverage_check = false
  error_on_jacobian_nonzero_reallocation = true
[]

[BCs]
  [fix_right]
    type = DirichletBC
    variable = u
    boundary = pinned_node
    value = 0
  []
[]

[Constraints]
  [mortarlr]
    type = PenaltyEqualValueConstraint
    secondary_boundary = '11'
    primary_boundary = '13'
    secondary_subdomain = 'primary_right'
    primary_subdomain = 'secondary_left'
    secondary_variable = u
    correct_edge_dropping = true
    penalty_value = 1.e2
  []
  [periodiclr]
    type = PenaltyPeriodicSegmentalConstraint
    secondary_boundary = '11'
    primary_boundary = '13'
    secondary_subdomain = 'primary_right'
    primary_subdomain = 'secondary_left'
    secondary_variable = u
    epsilon = epsilon
    sigma = sigma
    correct_edge_dropping = true
    penalty_value = 1.e2
  []
  [mortarbt]
    type = PenaltyEqualValueConstraint
    secondary_boundary = '12'
    primary_boundary = '10'
    secondary_subdomain = 'primary_top'
    primary_subdomain = 'secondary_bottom'
    secondary_variable = u
    correct_edge_dropping = true
    penalty_value = 1.e2
  []
  [periodicbt]
    type = PenaltyPeriodicSegmentalConstraint
    secondary_boundary = '12'
    primary_boundary = '10'
    secondary_subdomain = 'primary_top'
    primary_subdomain = 'secondary_bottom'
    secondary_variable = u
    epsilon = epsilon
    sigma = sigma
    correct_edge_dropping = true
    penalty_value = 1.e2
  []
[]

[Executioner]
  type = Steady
  solve_type = 'PJFNK'
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
  csv = true
[]

(modules/navier_stokes/test/tests/finite_element/ins/RZ_cone/ad_rz_cone_stab_jac_test.i)

[GlobalParams]
  order = SECOND
  integrate_p_by_parts = true
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 2
    ny = 2
    xmin = 0
    xmax = 1.1
    ymin = -1.1
    ymax = 1.1
    elem_type = QUAD9
  []
  [./corner_node]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node'
    nodes = '0'
    input = gen
  [../]
  coord_type = RZ
[]

[Preconditioning]
  [./SMP_PJFNK]
    type = SMP
    full = true
    solve_type = NEWTON
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 1
  dt = 1.1
[]

[Variables]
  [./velocity]
    family = LAGRANGE_VEC
  [../]
  [./p]
    order = FIRST
  [../]
[]


# Need to set a non-zero initial condition because we have a velocity norm in
# the denominator for the tau coefficient of the stabilization term
[ICs]
  [velocity]
    type = VectorConstantIC
    x_value = 1e-15
    y_value = 1e-15
    variable = velocity
  []
[]

[Kernels]
  [./mass]
    type = INSADMass
    variable = p
  [../]
  [mass_pspg]
    type = INSADMassPSPG
    variable = p
  []

  [momentum_time]
    type = INSADMomentumTimeDerivative
    variable = velocity
  []
  [momentum_advection]
    type = INSADMomentumAdvection
    variable = velocity
  []
  [./momentum_viscous]
    type = INSADMomentumViscous
    variable = velocity
  [../]

  [./momentum_pressure]
    type = INSADMomentumPressure
    variable = velocity
    pressure = p
  [../]
  [momentum_supg]
    type = INSADMomentumSUPG
    variable = velocity
    velocity = velocity
  []
[]

[BCs]
  [inlet]
    type = VectorFunctionDirichletBC
    variable = velocity
    boundary = 'bottom'
    function_x = 0
    function_y = 1
  [../]
  [wall]
    type = VectorFunctionDirichletBC
    variable = velocity
    boundary = 'right'
    function_x = 0
    function_y = 0
  []
  [axis]
    type = ADVectorFunctionDirichletBC
    variable = velocity
    boundary = 'left'
    set_y_comp = false
    function_x = 0
  []
  [outlet]
    type = INSADMomentumNoBCBC
    variable = velocity
    pressure = p
    boundary = 'top'
  []
  # When the NoBCBC is applied on the outlet boundary then there is nothing
  # constraining the pressure. Thus we must pin the pressure somewhere to ensure
  # that the problem is not singular. If the below BC is not applied then
  # -pc_type svd -pc_svd_monitor reveals a singular value
  [p_corner]
    type = DirichletBC
    boundary = pinned_node
    value = 0
    variable = p
  []
[]

[Materials]
  [./const]
    type = ADGenericConstantMaterial
    prop_names = 'rho mu'
    prop_values = '1.1 1.1'
  [../]
  [ins_mat]
    type = INSADTauMaterial
    velocity = velocity
    pressure = p
  []
[]

(modules/navier_stokes/test/tests/finite_element/ins/lid_driven/ad_lid_driven_stabilized_with_temp.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 1.0
    ymin = 0
    ymax = 1.0
    nx = 16
    ny = 16
  []
  [./corner_node]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node'
    nodes = '0'
    input = gen
  [../]
[]

[Variables]
  [./velocity]
    family = LAGRANGE_VEC
  [../]
  [./p]
  [../]
  [temperature][]
[]

[ICs]
  [velocity]
    type = VectorConstantIC
    x_value = 1e-15
    y_value = 1e-15
    variable = velocity
  []
[]

[Kernels]
  [./mass]
    type = INSADMass
    variable = p
  [../]
  [./mass_pspg]
    type = INSADMassPSPG
    variable = p
  [../]

  [./momentum_convection]
    type = INSADMomentumAdvection
    variable = velocity
  [../]

  [./momentum_viscous]
    type = INSADMomentumViscous
    variable = velocity
  [../]

  [./momentum_pressure]
    type = INSADMomentumPressure
    variable = velocity
    pressure = p
    integrate_p_by_parts = true
  [../]

  [./momentum_supg]
    type = INSADMomentumSUPG
    variable = velocity
    velocity = velocity
  [../]

 [./temperature_advection]
   type = INSADEnergyAdvection
   variable = temperature
 [../]

 [./temperature_conduction]
   type = ADHeatConduction
   variable = temperature
   thermal_conductivity = 'k'
 [../]

  [temperature_supg]
    type = INSADEnergySUPG
    variable = temperature
    velocity = velocity
  []
[]

[BCs]
  [./no_slip]
    type = VectorFunctionDirichletBC
    variable = velocity
    boundary = 'bottom right left'
  [../]

  [./lid]
    type = VectorFunctionDirichletBC
    variable = velocity
    boundary = 'top'
    function_x = 'lid_function'
  [../]

  [./pressure_pin]
    type = DirichletBC
    variable = p
    boundary = 'pinned_node'
    value = 0
  [../]

  [./temperature_hot]
    type = DirichletBC
    variable = temperature
    boundary = 'bottom'
    value = 1
  [../]

  [./temperature_cold]
    type = DirichletBC
    variable = temperature
    boundary = 'top'
    value = 0
  [../]
[]

[Materials]
  [./const]
    type = ADGenericConstantMaterial
    prop_names = 'rho mu cp k'
    prop_values = '1  1  1  .01'
  [../]
  [ins_mat]
    type = INSADStabilized3Eqn
    velocity = velocity
    pressure = p
    temperature = temperature
  []
[]

[Functions]
  [./lid_function]
    # We pick a function that is exactly represented in the velocity
    # space so that the Dirichlet conditions are the same regardless
    # of the mesh spacing.
    type = ParsedFunction
    expression = '4*x*(1-x)'
  [../]
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -sub_pc_factor_levels -ksp_gmres_restart'
  petsc_options_value = 'asm      6                     200'
  line_search = 'none'
  nl_rel_tol = 1e-12
  nl_max_its = 6
[]

[Outputs]
  exodus = true
[]

(modules/solid_mechanics/test/tests/finite_strain_elastic_anisotropy/3d_bar_orthotropic_full_rotation.i)

[Mesh]
  [generated_mesh]
    type = GeneratedMeshGenerator
    dim = 3
    xmin = 0
    xmax = 2
    ymin = 0
    ymax = 10
    zmin = 0
    zmax = 2
    nx = 1
    ny = 1
    nz = 1
    elem_type = HEX8
  []
  [corner]
    type = ExtraNodesetGenerator
    new_boundary = 101
    coord = '0 0 0'
    input = generated_mesh
  []
  [side]
    type = ExtraNodesetGenerator
    new_boundary = 102
    coord = '2 0 0'
    input = corner
  []
[]

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = FINITE
    add_variables = true
    use_finite_deform_jacobian = true
    volumetric_locking_correction = false
    generate_output = 'stress_xx stress_yy stress_zz stress_xy stress_xz'
  []
[]

[Materials]
  [stress]
    type = ComputeFiniteStrainElasticStress
  []
  [elasticity_tensor]
    type = ComputeElasticityTensor
    fill_method = orthotropic
    C_ijkl = '2.0e3 2.0e5 2.0e3 0.71428571e3 0.71428571e3 0.71428571e3 0.4 0.2 0.004 0.004 0.2 0.4'
  []
[]

[BCs]
  [fix_z]
    type = DirichletBC
    variable = disp_z
    boundary = bottom
    value = 0
  []

  [rot_y]
    type = DisplacementAboutAxis
    boundary = bottom
    function = t
    angle_units = degrees
    axis_origin = '0. 0. 0.'
    axis_direction = '0. 0. 1.'
    component = 1
    variable = disp_y
  []
  #
  [rot_x]
    type = DisplacementAboutAxis
    boundary = bottom
    function = t
    angle_units = degrees
    axis_origin = '0. 0. 0.'
    axis_direction = '0. 0. 1.'
    component = 0
    variable = disp_x
  []

  [rot_y90]
    type = DisplacementAboutAxis
    boundary = bottom
    function = 360
    angle_units = degrees
    axis_origin = '0. 0. 0.'
    axis_direction = '0. 0. 1.'
    component = 1
    variable = disp_y
  []
  #
  [rot_x90]
    type = DisplacementAboutAxis
    boundary = bottom
    function = 360
    angle_units = degrees
    axis_origin = '0. 0. 0.'
    axis_direction = '0. 0. 1.'
    component = 0
    variable = disp_x
  []

  [press]
    boundary = top
    function = '-1.0*(t-360)*10.0'
    use_displaced_mesh = true
    displacements = 'disp_x disp_y disp_z'
    type = Pressure
    variable = disp_y
  []

[]

[Controls]
  [c1]
    type = TimePeriod
    enable_objects = 'BCs::rot_x BCs::rot_y'
    disable_objects = 'BCs::rot_x90 BCs::rot_y90 BCs::press'
    start_time = '0'
    end_time = '360'
  []
  [c190plus]
    type = TimePeriod
    enable_objects = 'BCs::rot_x90 BCs::rot_y90 BCs::press'
    disable_objects = 'BCs::rot_x BCs::rot_y '
    start_time = '360'
    end_time = '660'
  []
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-ksp_gmres_restart'
  petsc_options_value = '101'

  line_search = 'none'

  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-08
  nl_max_its = 50

  l_tol = 1e-4
  l_max_its = 50
  start_time = 0.0

  dt = 5
  dtmin = 5

  num_steps = 132
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Outputs]
  exodus = true
[]

(modules/solid_mechanics/tutorials/introduction/mech_step03a.i)

#
# Added subdomains and subdomain-specific properties
# https://mooseframework.inl.gov/modules/solid_mechanics/tutorials/introduction/step03.html
#

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  [generated]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 20
    xmin = -0.25
    xmax = 0.25
    ymax = 5
  []
  [block1]
    type = SubdomainBoundingBoxGenerator
    input = generated
    block_id = 1
    bottom_left = '-0.25 0 0'
    top_right = '0 5 0'
  []
  [block2]
    type = SubdomainBoundingBoxGenerator
    input = block1
    block_id = 2
    bottom_left = '0 0 0'
    top_right = '0.25 5 0'
  []

  # select a single node in the center of the bottom boundary
  [pin]
    type = ExtraNodesetGenerator
    input = block2
    new_boundary = pin
    coord = '0 0 0'
  []
[]

[AuxVariables]
  [T]
  []
[]

[AuxKernels]
  [temperature_ramp]
    type = FunctionAux
    execute_on = TIMESTEP_BEGIN
    variable = T
    function = 300+5*t
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    add_variables = true
    automatic_eigenstrain_names = true
    generate_output = 'vonmises_stress'
  []
[]

[BCs]
  [pin_x]
    type = DirichletBC
    variable = disp_x
    boundary = pin
    value = 0
  []
  [bottom_y]
    type = DirichletBC
    variable = disp_y
    boundary = bottom
    value = 0
  []
[]

[Materials]
  [elasticity]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 1e9
    poissons_ratio = 0.3
  []
  [expansion1]
    type = ComputeThermalExpansionEigenstrain
    temperature = T
    thermal_expansion_coeff = 0.001
    stress_free_temperature = 300
    eigenstrain_name = thermal_expansion
    block = 1
  []
  [expansion2]
    type = ComputeThermalExpansionEigenstrain
    temperature = T
    thermal_expansion_coeff = 0.002
    stress_free_temperature = 300
    eigenstrain_name = thermal_expansion
    block = 2
  []
  [stress]
    type = ComputeLinearElasticStress
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  end_time = 5
  dt = 1
[]

[Outputs]
  exodus = true
[]

(modules/combined/examples/mortar/eigenstrain_action.i)

#
# Eigenstrain with Mortar gradient periodicity
#

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 50
    ny = 50
    xmin = -0.5
    xmax = 0.5
    ymin = -0.5
    ymax = 0.5
  []
  [./cnode]
    input = gen
    type = ExtraNodesetGenerator
    coord = '0.0 0.0'
    new_boundary = 100
  [../]
  [./anode]
    input = cnode
    type = ExtraNodesetGenerator
    coord = '0.0 0.5'
    new_boundary = 101
  [../]
[]

[Modules/PhaseField/MortarPeriodicity]
  [./strain]
    variable = 'disp_x disp_y'
    periodicity = gradient
    periodic_directions = 'x y'
  [../]
[]

[GlobalParams]
  derivative_order = 2
  enable_jit = true
  displacements = 'disp_x disp_y'
[]

# AuxVars to compute the free energy density for outputting
[AuxVariables]
  [./local_energy]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[AuxKernels]
  [./local_free_energy]
    type = TotalFreeEnergy
    block = 0
    execute_on = 'initial LINEAR'
    variable = local_energy
    interfacial_vars = 'c'
    kappa_names = 'kappa_c'
  [../]
[]

[Variables]
  # Solute concentration variable
  [./c]
    [./InitialCondition]
      type = RandomIC
      min = 0.49
      max = 0.51
    [../]
    block = 0
  [../]
  [./w]
    block = 0
  [../]

  # Mesh displacement
  [./disp_x]
    block = 0
  [../]
  [./disp_y]
    block = 0
  [../]
[]

[Kernels]
  # Set up stress divergence kernels
  [./TensorMechanics]
  [../]

  # Cahn-Hilliard kernels
  [./c_dot]
    type = CoupledTimeDerivative
    variable = w
    v = c
  [../]
  [./c_res]
    type = SplitCHParsed
    variable = c
    f_name = F
    kappa_name = kappa_c
    w = w
  [../]
  [./w_res]
    type = SplitCHWRes
    variable = w
    mob_name = M
  [../]
[]

[Materials]
  # declare a few constants, such as mobilities (L,M) and interface gradient prefactors (kappa*)
  [./consts]
    type = GenericConstantMaterial
    block = '0'
    prop_names  = 'M   kappa_c'
    prop_values = '0.2 0.01   '
  [../]

  [./shear1]
    type = GenericConstantRankTwoTensor
    block = 0
    tensor_values = '0 0 0 0 0 0.5'
    tensor_name = shear1
  [../]
  [./shear2]
    type = GenericConstantRankTwoTensor
    block = 0
    tensor_values = '0 0 0 0 0 -0.5'
    tensor_name = shear2
  [../]
  [./expand3]
    type = GenericConstantRankTwoTensor
    block = 0
    tensor_values = '1 1 0 0 0 0'
    tensor_name = expand3
  [../]

  [./weight1]
    type = DerivativeParsedMaterial
    block = 0
    expression = '0.3*c^2'
    property_name = weight1
    coupled_variables = c
  [../]
  [./weight2]
    type = DerivativeParsedMaterial
    block = 0
    expression = '0.3*(1-c)^2'
    property_name = weight2
    coupled_variables = c
  [../]
  [./weight3]
    type = DerivativeParsedMaterial
    block = 0
    expression = '4*(0.5-c)^2'
    property_name = weight3
    coupled_variables = c
  [../]

  # matrix phase
  [./elasticity_tensor]
    type = ComputeElasticityTensor
    block = 0
    C_ijkl = '1 1'
    fill_method = symmetric_isotropic
  [../]
  [./strain]
    type = ComputeSmallStrain
    block = 0
    displacements = 'disp_x disp_y'
  [../]

  [./eigenstrain]
    type = CompositeEigenstrain
    block = 0
    tensors = 'shear1  shear2  expand3'
    weights = 'weight1 weight2 weight3'
    coupled_variables = c
    eigenstrain_name = eigenstrain
  [../]

  [./stress]
    type = ComputeLinearElasticStress
    block = 0
  [../]

  # chemical free energies
  [./chemical_free_energy]
    type = DerivativeParsedMaterial
    block = 0
    property_name = Fc
    expression = '4*c^2*(1-c)^2'
    coupled_variables = 'c'
    outputs = exodus
    output_properties = Fc
  [../]

  # elastic free energies
  [./elastic_free_energy]
    type = ElasticEnergyMaterial
    f_name = Fe
    block = 0
    coupled_variables = 'c'
    outputs = exodus
    output_properties = Fe
  [../]

  # free energy (chemical + elastic)
  [./free_energy]
    type = DerivativeSumMaterial
    block = 0
    property_name = F
    sum_materials = 'Fc Fe'
    coupled_variables = 'c'
  [../]
[]

[BCs]
  [./Periodic]
    [./up_down]
      primary = top
      secondary = bottom
      translation = '0 -1 0'
      variable = 'c w'
    [../]
    [./left_right]
      primary = left
      secondary = right
      translation = '1 0 0'
      variable = 'c w'
    [../]
  [../]

  # fix center point location
  [./centerfix_x]
    type = DirichletBC
    boundary = 100
    variable = disp_x
    value = 0
  [../]
  [./centerfix_y]
    type = DirichletBC
    boundary = 100
    variable = disp_y
    value = 0
  [../]

  # fix side point x coordinate to inhibit rotation
  [./angularfix]
    type = DirichletBC
    boundary = 101
    variable = disp_x
    value = 0
  [../]
[]

[Preconditioning]
  [./SMP]
    type = SMP
    full = true
  [../]
[]

# We monitor the total free energy and the total solute concentration (should be constant)
[Postprocessors]
  [./total_free_energy]
    type = ElementIntegralVariablePostprocessor
    block = 0
    execute_on = 'initial TIMESTEP_END'
    variable = local_energy
  [../]
  [./total_solute]
    type = ElementIntegralVariablePostprocessor
    block = 0
    execute_on = 'initial TIMESTEP_END'
    variable = c
  [../]
  [./min]
    type = ElementExtremeValue
    block = 0
    execute_on = 'initial TIMESTEP_END'
    value_type = min
    variable = c
  [../]
  [./max]
    type = ElementExtremeValue
    block = 0
    execute_on = 'initial TIMESTEP_END'
    value_type = max
    variable = c
  [../]
[]

[Executioner]
  type = Transient
  scheme = bdf2
  solve_type = 'PJFNK'

  line_search = basic

  # mortar currently does not support MPI parallelization
  petsc_options_iname = '-pc_type -pc_factor_shift_type -pc_factor_shift_amount'
  petsc_options_value = ' lu       NONZERO               1e-10'

  l_max_its = 30
  nl_max_its = 12

  l_tol = 1.0e-4

  nl_rel_tol = 1.0e-8
  nl_abs_tol = 1.0e-10

  start_time = 0.0
  num_steps = 200

  [./TimeStepper]
    type = SolutionTimeAdaptiveDT
    dt = 0.01
  [../]
[]

[Outputs]
  execute_on = 'timestep_end'
  print_linear_residuals = false
  exodus = true
  [./table]
    type = CSV
    delimiter = ' '
  [../]
[]

(modules/combined/examples/optimization/helmholtz_multimat_nostrip.i)

vol_frac = 0.35

power = 1.1

Emin = 1.0e-6
Ess = 0.475 # ss
Et = 1.0 # w

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  # final_generator = 'MoveRight'
  [Bottom]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 320
    ny = 30
    xmin = 0
    xmax = 150
    ymin = 0
    ymax = 15
  []
  [RenameBottom]
    type = RenameBoundaryGenerator
    input = Bottom
    old_boundary = 'top bottom right left'
    new_boundary = 'top_bottom bottom_bottom right_bottom left_bottom'
  []
  [Top]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 320
    ny = 30
    xmin = 0
    xmax = 150
    ymin = 0
    ymax = 15
  []
  [MoveTop]
    type = TransformGenerator
    input = Top
    transform = TRANSLATE
    vector_value = '0 15 0'
  []
  [RenameTop]
    type = RenameBoundaryGenerator
    input = MoveTop
    old_boundary = 'top bottom right left'
    new_boundary = 'top_top bottom_top right_top left_top'
  []
  [bottom_gen]
    type = ParsedSubdomainMeshGenerator
    input = RenameBottom
    combinatorial_geometry = 'y <= 15'
    block_id = 1
  []
  [top_gen]
    type = ParsedSubdomainMeshGenerator
    input = RenameTop
    combinatorial_geometry = 'y > 15'
    block_id = 3
  []
  [stitch]
    type = StitchedMeshGenerator
    inputs = 'bottom_gen top_gen'
    stitch_boundaries_pairs = 'top_bottom bottom_top'
  []
  [left_load]
    type = ExtraNodesetGenerator
    input = stitch
    new_boundary = left_load
    coord = '37.5 30 0'
  []
  [right_load]
    type = ExtraNodesetGenerator
    input = left_load
    new_boundary = right_load
    coord = '112.5 30 0'
  []
  [left_support]
    type = ExtraNodesetGenerator
    input = right_load
    new_boundary = left_support
    coord = '0 0 0'
  []
  [right_support]
    type = ExtraNodesetGenerator
    input = left_support
    new_boundary = right_support
    coord = '150 0 0'
  []
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [Dc]
    initial_condition = -1.0
  []
[]

[AuxVariables]
  [Cc]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = -1.0
  []
  [mat_den]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = ${vol_frac}
  []
  [sensitivity]
    family = MONOMIAL
    order = FIRST
    initial_condition = -1.0
    [AuxKernel]
      type = MaterialRealAux
      variable = sensitivity
      property = sensitivity
      execute_on = LINEAR
    []
  []
  [mat_den_nodal]
    family = L2_LAGRANGE
    order = FIRST
    initial_condition = ${vol_frac}
    [AuxKernel]
      type = SelfAux
      execute_on = TIMESTEP_END
      variable = mat_den_nodal
      v = mat_den
    []
  []
  [Dc_elem]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = -1.0
    [AuxKernel]
      type = SelfAux
      variable = Dc_elem
      v = Dc
      execute_on = 'TIMESTEP_END'
    []
  []
[]

[Kernels]
  [diffusion]
    type = FunctionDiffusion
    variable = Dc
    function = 4.0
  []
  [potential]
    type = Reaction
    variable = Dc
  []
  [source]
    type = CoupledForce
    variable = Dc
    v = sensitivity
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = SMALL
    add_variables = true
    incremental = false
  []
[]

[BCs]
  [no_y]
    type = DirichletBC
    variable = disp_y
    boundary = left_support
    value = 0.0
  []
  [no_x]
    type = DirichletBC
    variable = disp_x
    boundary = left_support
    value = 0.0
  []
  [no_y_right]
    type = DirichletBC
    variable = disp_y
    boundary = right_support
    value = 0.0
  []
  [boundary_penalty]
    type = ADRobinBC
    variable = Dc
    boundary = 'bottom_bottom right_bottom left_bottom top_top right_top left_top'
    coefficient = 10
  []
[]

[NodalKernels]
  [left_down]
    type = NodalGravity
    variable = disp_y
    boundary = left_load
    gravity_value = -1e-3
    mass = 1
  []
  [right_down]
    type = NodalGravity
    variable = disp_y
    boundary = right_load
    gravity_value = -1e-3
    mass = 1
  []
[]

[Materials]
  [elasticity_tensor_one]
    type = ComputeVariableIsotropicElasticityTensor
    youngs_modulus = E_phys_one
    poissons_ratio = poissons_ratio
    args = 'mat_den'
    block = '1'
  []
  [elasticity_tensor_three]
    type = ComputeVariableIsotropicElasticityTensor
    youngs_modulus = E_phys_three
    poissons_ratio = poissons_ratio
    args = 'mat_den'
    block = '3'
  []
  # One: Tungsten
  [E_phys_one]
    type = DerivativeParsedMaterial
    # Emin + (density^penal) * (E0 - Emin)
    expression = '${Emin} + (mat_den ^ ${power}) * (${Et}-${Emin})'
    coupled_variables = 'mat_den'
    property_name = E_phys_one
    block = '1'
    outputs = 'exodus'
  []
  # Three: SS316
  [E_phys_three]
    type = DerivativeParsedMaterial
    # Emin + (density^penal) * (E0 - Emin)
    expression = '${Emin} + (mat_den ^ ${power}) * (${Ess}-${Emin})'
    coupled_variables = 'mat_den'
    property_name = E_phys_three
    block = '3'
    outputs = 'exodus'
  []
  [poissons_ratio]
    type = GenericConstantMaterial
    prop_names = poissons_ratio
    prop_values = 0.3
  []
  [stress]
    type = ComputeLinearElasticStress
  []
  [dc_one]
    type = ComplianceSensitivity
    design_density = mat_den
    youngs_modulus = E_phys_one
    block = '1'
  []
  [dc_three]
    type = ComplianceSensitivity
    design_density = mat_den
    youngs_modulus = E_phys_three
    block = '3'
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[UserObjects]
  [update_one]
    type = DensityUpdate
    density_sensitivity = Dc_elem
    design_density = mat_den
    volume_fraction = ${vol_frac}
    execute_on = TIMESTEP_BEGIN
    block = '1'
  []
  [update_three]
    type = DensityUpdate
    density_sensitivity = Dc_elem
    design_density = mat_den
    volume_fraction = ${vol_frac}
    execute_on = TIMESTEP_BEGIN
    block = '3'
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'
  nl_abs_tol = 1e-10
  dt = 1.0
  num_steps = 90
[]

[Outputs]
  exodus = true
  [out]
    type = CSV
    execute_on = 'TIMESTEP_END'
  []
  print_linear_residuals = false
[]

[Postprocessors]
  [mesh_volume]
    type = VolumePostprocessor
    execute_on = 'initial timestep_end'
  []
  [total_vol]
    type = ElementIntegralVariablePostprocessor
    variable = mat_den
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [vol_frac]
    type = ParsedPostprocessor
    expression = 'total_vol / mesh_volume'
    pp_names = 'total_vol mesh_volume'
  []
  [sensitivity]
    type = ElementIntegralMaterialProperty
    mat_prop = sensitivity
    block = '1 3'
  []
  [objective_one]
    type = ElementIntegralMaterialProperty
    mat_prop = strain_energy_density
    execute_on = 'INITIAL TIMESTEP_END'
    block = '1'
  []
  [objective_three]
    type = ElementIntegralMaterialProperty
    mat_prop = strain_energy_density
    execute_on = 'INITIAL TIMESTEP_END'
    block = '3'
  []
[]

(modules/xfem/test/tests/bimaterials/glued_ad_bimaterials_2d.i)

# This test is for two layer materials with different youngs modulus using AD
# The global stress is determined by switching the stress based on level set values
# The material interface is marked by a level set function
# The two layer materials are glued together

[GlobalParams]
  order = FIRST
  family = LAGRANGE
  displacements = 'disp_x disp_y'
[]

[XFEM]
  qrule = volfrac
  output_cut_plane = true
[]

[UserObjects]
  [./level_set_cut_uo]
    type = LevelSetCutUserObject
    level_set_var = ls
  [../]
[]

[Mesh]
  displacements = 'disp_x disp_y'
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 5
    ny = 5
    xmin = 0.0
    xmax = 5.
    ymin = 0.0
    ymax = 5.
    elem_type = QUAD4
  []
  [./left_bottom]
    type = ExtraNodesetGenerator
    new_boundary = 'left_bottom'
    coord = '0.0 0.0'
    input = gen
  [../]
  [./left_top]
    type = ExtraNodesetGenerator
    new_boundary = 'left_top'
    coord = '0.0 5.'
    input = left_bottom
  [../]
[]

[AuxVariables]
  [./ls]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxKernels]
  [./ls_function]
    type = FunctionAux
    variable = ls
    function = ls_func
  [../]
[]

[Variables]
  [./disp_x]
  [../]
  [./disp_y]
  [../]
[]

[Functions]
  [./ls_func]
    type = ParsedFunction
    expression = 'y-2.5'
  [../]
[]

[AuxVariables]
  [./a_strain_xx]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./a_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./a_strain_xy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./b_strain_xx]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./b_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./b_strain_xy]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[Physics/SolidMechanics/QuasiStatic]
  [./all]
    strain = SMALL
    use_automatic_differentiation = true
    add_variables = true
    generate_output = 'stress_xx stress_yy stress_xy'
  [../]
[]

[AuxKernels]
  [./a_strain_xx]
    type = ADRankTwoAux
    rank_two_tensor = A_total_strain
    index_i = 0
    index_j = 0
    variable = a_strain_xx
  [../]
  [./a_strain_yy]
    type = ADRankTwoAux
    rank_two_tensor = A_total_strain
    index_i = 1
    index_j = 1
    variable = a_strain_yy
  [../]
  [./a_strain_xy]
    type = ADRankTwoAux
    rank_two_tensor = A_total_strain
    index_i = 0
    index_j = 1
    variable = a_strain_xy
  [../]
  [./b_strain_xx]
    type = ADRankTwoAux
    rank_two_tensor = B_total_strain
    index_i = 0
    index_j = 0
    variable = b_strain_xx
  [../]
  [./b_strain_yy]
    type = ADRankTwoAux
    rank_two_tensor = B_total_strain
    index_i = 1
    index_j = 1
    variable = b_strain_yy
  [../]
  [./b_strain_xy]
    type = ADRankTwoAux
    rank_two_tensor = B_total_strain
    index_i = 0
    index_j = 1
    variable = b_strain_xy
  [../]
[]

[Constraints]
  [./dispx_constraint]
    type = XFEMSingleVariableConstraint
    use_displaced_mesh = false
    variable = disp_x
    alpha = 1e8
    geometric_cut_userobject = 'level_set_cut_uo'
  [../]
  [./dispy_constraint]
    type = XFEMSingleVariableConstraint
    use_displaced_mesh = false
    variable = disp_y
    alpha = 1e8
    geometric_cut_userobject = 'level_set_cut_uo'
  [../]
[]

[BCs]
  [./bottomx]
    type = ADDirichletBC
    boundary = bottom
    variable = disp_x
    value = 0.0
  [../]
  [./bottomy]
    type = ADDirichletBC
    boundary = bottom
    variable = disp_y
    value = 0.0
  [../]
  [./topx]
    type = ADFunctionDirichletBC
    boundary = top
    variable = disp_x
    function = 0.03*t
  [../]
  [./topy]
    type = ADFunctionDirichletBC
    boundary = top
    variable = disp_y
    function = '0.03*t'
  [../]
[]

[Materials]
  [./elasticity_tensor_A]
    type = ADComputeIsotropicElasticityTensor
    base_name = A
    youngs_modulus = 1e9
    poissons_ratio = 0.3
  [../]
  [./strain_A]
    type = ADComputeSmallStrain
    base_name = A
  [../]
  [./stress_A]
    type = ADComputeLinearElasticStress
    base_name = A
  [../]
  [./elasticity_tensor_B]
    type = ADComputeIsotropicElasticityTensor
    base_name = B
    youngs_modulus = 1e5
    poissons_ratio = 0.3
  [../]
  [./strain_B]
    type = ADComputeSmallStrain
    base_name = B
  [../]
  [./stress_B]
    type = ADComputeLinearElasticStress
    base_name = B
  [../]
  [./combined_stress]
    type = ADLevelSetBiMaterialRankTwo
    levelset_positive_base = 'A'
    levelset_negative_base = 'B'
    level_set_var = ls
    prop_name = stress
  [../]
  [./combined_elasticity_tensor]
    type = ADLevelSetBiMaterialRankFour
    levelset_positive_base = 'A'
    levelset_negative_base = 'B'
    level_set_var = ls
    prop_name = elasticity_tensor
  [../]
[]

[Executioner]
  type = Transient

  solve_type = NEWTON
  petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
  petsc_options_value = '201                hypre    boomeramg      8'

  line_search = 'bt'

# controls for linear iterations
  l_max_its = 20
  l_tol = 1e-8

# controls for nonlinear iterations
  nl_max_its = 15
  nl_rel_tol = 1e-14
  nl_abs_tol = 1e-50

# time control
  start_time = 0.0
  dt = 0.1
  num_steps = 2

  max_xfem_update = 1
[]

[Outputs]
  exodus = true
  file_base = glued_bimaterials_2d_out
  execute_on = timestep_end
  [./console]
    type = Console
    output_linear = true
  [../]
[]

(modules/solid_mechanics/test/tests/uel/small_test_expanded.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 20
    ny = 10
    xmax = 10
    ymax = 3
    elem_type = TRI3
  []
  [pin]
    type = ExtraNodesetGenerator
    nodes = 106
    new_boundary = pin
    input = gen
  []
  displacements = 'disp_x disp_y'
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
[]

[BCs]
  [left_x]
    type = DirichletBC
    variable = disp_x
    boundary = left
    value = 0
  []
  [left_y]
    type = DirichletBC
    variable = disp_y
    boundary = pin
    value = 0
  []

  inactive = 'right_dirichlet'
  [right_neumann]
    type = FunctionNeumannBC
    variable = disp_x
    function = t
    boundary = right
  []
  [right_dirichlet]
    type = FunctionDirichletBC
    variable = disp_x
    function = t/10
    boundary = right
  []
[]

[UserObjects]
  [uel]
    type = AbaqusUserElement
    variables = 'disp_x disp_y'
    plugin = ../../../examples/uel_tri_tests/uel
    use_displaced_mesh = false
    num_state_vars = 18
    constant_properties = '100 0.3' # E nu
    extra_vector_tags = 'kernel_residual'
  []
[]

[Problem]
  kernel_coverage_check = false
  extra_tag_vectors = 'kernel_residual'
[]

[AuxVariables]
  [res_x]
  []
  [res_y]
  []
[]

[AuxKernels]
  [res_x]
    type = TagVectorAux
    variable = res_x
    v = disp_x
    vector_tag = kernel_residual
  []
  [res_y]
    type = TagVectorAux
    variable = res_y
    v = disp_y
    vector_tag = kernel_residual
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  dt = 1
  num_steps = 15
[]

[Postprocessors]
  [delta_l]
    type = SideAverageValue
    variable = disp_x
    boundary = right
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [V]
    type = ElementIntegralMaterialProperty
    mat_prop = 1
    use_displaced_mesh = true
    execute_on = 'INITIAL TIMESTEP_END'
  []
[]

[Outputs]
  exodus = true
  csv = true
[]

(modules/solid_mechanics/test/tests/ad_anisotropic_creep/aniso_iso_creep_x_3d.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 10
    ny = 2
    nz = 2
    xmin = 0.0
    ymin = 0.0
    zmin = 0.0

    xmax = 10.0
    ymax = 1.0
    zmax = 1.0
  []
  [corner_node]
    type = ExtraNodesetGenerator
    new_boundary = '100'
    nodes = '3 69'
    input = gen
  []
  [corner_node_2]
    type = ExtraNodesetGenerator
    new_boundary = '101'
    nodes = '4 47'
    input = corner_node
  []
[]

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  volumetric_locking_correction = true
[]

[AuxVariables]
  [hydrostatic_stress]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_xx]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_xy]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_zz]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_xz]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_yz]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [hydrostatic_stress]
    type = RankTwoScalarAux
    variable = hydrostatic_stress
    rank_two_tensor = stress
    scalar_type = Hydrostatic
  []
  [creep_strain_xx]
    type = RankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_xx
    index_i = 0
    index_j = 0
  []
  [creep_strain_xy]
    type = RankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_xy
    index_i = 0
    index_j = 1
  []
  [creep_strain_yy]
    type = RankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_yy
    index_i = 1
    index_j = 1
  []
  [creep_strain_zz]
    type = RankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_zz
    index_i = 2
    index_j = 2
  []
  [creep_strain_xz]
    type = RankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_xz
    index_i = 0
    index_j = 2
  []
  [creep_strain_yz]
    type = RankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_yz
    index_i = 1
    index_j = 2
  []
  [sigma_xx]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_xx
    index_i = 1
    index_j = 1
  []
[]

[Functions]
  [pull]
    type = PiecewiseLinear
    x = '0 1.0e-9 1.0'
    y = '0 -4e1 -4e1'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = FINITE
    generate_output = 'elastic_strain_xx stress_xx'
    add_variables = true
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 700
    poissons_ratio = 0.0
  []

  [elastic_strain]
    type = ComputeMultipleInelasticStress
    # inelastic_models = 'trial_creep_iso'
    max_iterations = 50
  []

  [hill_tensor]
    type = HillConstants
    # F G H L M N
    hill_constants = "0.5 0.5 0.5 1.5 1.5 1.5"
  []

  [trial_creep_aniso_iso]
    type = HillCreepStressUpdate
    coefficient = 1e-16
    n_exponent = 9
    m_exponent = 0
    activation_energy = 0
    max_inelastic_increment = 0.00003
    relative_tolerance = 1e-20
    absolute_tolerance = 1e-20
    internal_solve_output_on = never
    # Force it to not use integration error
    max_integration_error = 1.0
  []

  [trial_creep_iso]
    type = PowerLawCreepStressUpdate
    coefficient = 1e-16
    n_exponent = 9
    m_exponent = 0
    activation_energy = 0
    # F G H L M N
    max_inelastic_increment = 0.00003
    relative_tolerance = 1e-16
    absolute_tolerance = 1e-16
    internal_solve_output_on = never
  []
[]

[BCs]
  [no_disp_x]
    type = DirichletBC
    variable = disp_x
    boundary = left
    value = 0.0
  []

  [no_disp_y]
    type = DirichletBC
    variable = disp_y
    boundary = 100
    value = 0.0
  []

  [no_disp_z]
    type = DirichletBC
    variable = disp_z
    boundary = 101
    value = 0.0
  []

  [Pressure]
    [Side1]
      boundary = right
      function = pull
    []
  []

[]

[Executioner]
  type = Transient

  solve_type = NEWTON
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu     superlu_dist'

  nl_rel_tol = 1e-13
  nl_abs_tol = 1.0e-14
  l_max_its = 90
  num_steps = 10
  dt = 5.0e-4
  start_time = 0
  automatic_scaling = true
[]

[Postprocessors]
  [matl_ts_min]
    type = MaterialTimeStepPostprocessor
  []
  [max_disp_x]
    type = ElementExtremeValue
    variable = disp_x
  []
  [max_disp_y]
    type = ElementExtremeValue
    variable = disp_y
  []
  [max_hydro]
    type = ElementAverageValue
    variable = hydrostatic_stress
  []
  [dt]
    type = TimestepSize
  []
  [num_lin]
    type = NumLinearIterations
    outputs = console
  []
  [num_nonlin]
    type = NumNonlinearIterations
    outputs = console
  []
  [creep_strain_xx]
    type = ElementalVariableValue
    variable = creep_strain_xx
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [creep_strain_yy]
    type = ElementalVariableValue
    variable = creep_strain_yy
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [creep_strain_zz]
    type = ElementalVariableValue
    variable = creep_strain_zz
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [creep_strain_xy]
    type = ElementalVariableValue
    variable = creep_strain_xy
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [creep_strain_yz]
    type = ElementalVariableValue
    variable = creep_strain_yz
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [creep_strain_xz]
    type = ElementalVariableValue
    variable = creep_strain_xz
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [elastic_strain_xx]
    type = ElementalVariableValue
    variable = elastic_strain_xx
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [sigma_xx]
    type = ElementalVariableValue
    variable = stress_xx
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
[]

[Outputs]
  csv = true
  exodus = true
  perf_graph = true
[]

(modules/solid_mechanics/test/tests/uel/small_test_expanded_umat.i)

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 20
    ny = 10
    xmax = 10
    ymax = 3
    elem_type = TRI3
  []
  [pin]
    type = ExtraNodesetGenerator
    nodes = 106
    new_boundary = pin
    input = gen
  []
  displacements = 'disp_x disp_y'
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
[]

[BCs]
  [left_x]
    type = DirichletBC
    variable = disp_x
    boundary = left
    value = 0
  []
  [left_y]
    type = DirichletBC
    variable = disp_y
    boundary = pin
    value = 0
  []

  inactive = 'right_dirichlet'
  [right_neumann]
    type = FunctionNeumannBC
    variable = disp_x
    function = t
    boundary = right
  []
  [right_dirichlet]
    type = FunctionDirichletBC
    variable = disp_x
    function = t/10
    boundary = right
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    add_variables = true
    strain = SMALL
    incremental = true
    extra_vector_tags = 'kernel_residual'
  []
[]

[Materials]
  [umat]
    type = AbaqusUMATStress
    constant_properties = '100 0.3'
    plugin = '../../plugins/small_elastic_tri'
    num_state_vars = 8
    use_one_based_indexing = false
  []
[]

[Problem]
  kernel_coverage_check = false
  extra_tag_vectors = 'kernel_residual'
[]

[AuxVariables]
  [res_x]
  []
  [res_y]
  []
[]

[AuxKernels]
  [res_x]
    type = TagVectorAux
    variable = res_x
    v = disp_x
    vector_tag = kernel_residual
  []
  [res_y]
    type = TagVectorAux
    variable = res_y
    v = disp_y
    vector_tag = kernel_residual
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  dt = 1
  num_steps = 15
[]

[Postprocessors]
  [delta_l]
    type = SideAverageValue
    variable = disp_x
    boundary = right
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [V]
    type = ElementIntegralMaterialProperty
    mat_prop = 1
    use_displaced_mesh = true
    execute_on = 'INITIAL TIMESTEP_END'
  []
[]

[Outputs]
  exodus = true
  csv = true
[]

(test/tests/mortar/ad_periodic_segmental_constraint/periodic_simple2d.i)

[Mesh]
  [left_block]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = -1.0
    xmax = 1.0
    ymin = -1.0
    ymax = 1.0
    nx = 2
    ny = 2
    elem_type = QUAD9
  []
  [left_block_sidesets]
    type = RenameBoundaryGenerator
    input = left_block
    old_boundary = '0 1 2 3'
    new_boundary = '10 11 12 13'
  []
  [left_block_id]
    type = SubdomainIDGenerator
    input = left_block_sidesets
    subdomain_id = 1
  []
  [left]
    type = LowerDBlockFromSidesetGenerator
    input = left_block_id
    sidesets = '13'
    new_block_id = '10003'
    new_block_name = 'secondary_left'
  []
  [right]
    type = LowerDBlockFromSidesetGenerator
    input = left
    sidesets = '11'
    new_block_id = '10001'
    new_block_name = 'primary_right'
  []
  [bottom]
    type = LowerDBlockFromSidesetGenerator
    input = right
    sidesets = '10'
    new_block_id = '10000'
    new_block_name = 'secondary_bottom'
  []
  [top]
    type = LowerDBlockFromSidesetGenerator
    input = bottom
    sidesets = '12'
    new_block_id = '10002'
    new_block_name = 'primary_top'
  []

  [corner_node]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node'
    nodes = '0'
    input = top
  []
[]

[Variables]
  [u]
    order = SECOND
    family = LAGRANGE
  []
  [epsilon]
    order = SECOND
    family = SCALAR
  []
  [./lm1]
    order = FIRST
    family = LAGRANGE
    block = secondary_left
  [../]
  [./lm2]
    order = FIRST
    family = LAGRANGE
    block = secondary_bottom
  [../]
[]

[AuxVariables]
  [sigma]
    order = SECOND
    family = SCALAR
  []
[]

[AuxScalarKernels]
  [sigma]
    type = FunctionScalarAux
    variable = sigma
    function = '1 2'
    execute_on = initial #timestep_end
  []
[]

[Kernels]
  [diff1]
    type = Diffusion
    variable = u
    block = 1
  []
[]

[Problem]
  kernel_coverage_check = false
  error_on_jacobian_nonzero_reallocation = true
[]

[BCs]
  [fix_right]
    type = DirichletBC
    variable = u
    boundary = pinned_node
    value = 0
  []
[]

[Constraints]
  [mortarlr]
    type = EqualValueConstraint
    primary_boundary = '11'
    secondary_boundary = '13'
    primary_subdomain = 'primary_right'
    secondary_subdomain = 'secondary_left'
    secondary_variable = u
    variable = lm1
    correct_edge_dropping = true
  []
  [periodiclr]
    type = ADPeriodicSegmentalConstraint
    primary_boundary = '11'
    secondary_boundary = '13'
    primary_subdomain = 'primary_right'
    secondary_subdomain = 'secondary_left'
    secondary_variable = u
    epsilon = epsilon
    sigma = sigma
    variable = lm1
    correct_edge_dropping = true
  []
  [mortarbt]
    type = EqualValueConstraint
    primary_boundary = '12'
    secondary_boundary = '10'
    primary_subdomain = 'primary_top'
    secondary_subdomain = 'secondary_bottom'
    secondary_variable = u
    variable = lm2
    correct_edge_dropping = true
  []
  [periodicbt]
    type = ADPeriodicSegmentalConstraint
    primary_boundary = '12'
    secondary_boundary = '10'
    primary_subdomain = 'primary_top'
    secondary_subdomain = 'secondary_bottom'
    secondary_variable = u
    epsilon = epsilon
    sigma = sigma
    variable = lm2
    correct_edge_dropping = true
  []
[]

[Preconditioning]
  [smp]
    full = true
    type = SMP
  []
[]

[Executioner]
  type = Steady
  petsc_options_iname = '-pc_type -pc_factor_shift_type'
  petsc_options_value = 'lu       NONZERO'
  solve_type = NEWTON
[]

[Outputs]
#  exodus = true
  csv = true
[]

(modules/combined/test/tests/optimization/compliance_sensitivity/2d_mmb_2material.i)

vol_frac = 0.5

power = 1

E0 = 1e-5
E1 = 0.6
E2 = 1.0

rho0 = 0.0
rho1 = 0.4
rho2 = 1.0

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  [MeshGenerator]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 150
    ny = 50
    xmin = 0
    xmax = 30
    ymin = 0
    ymax = 10
  []
  [node]
    type = ExtraNodesetGenerator
    input = MeshGenerator
    new_boundary = hold
    nodes = 0
  []
  [push]
    type = ExtraNodesetGenerator
    input = node
    new_boundary = push
    coord = '30 10 0'
  []
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
[]

[AuxVariables]
  [Dc]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = -1.0
  []
  [mat_den]
    family = MONOMIAL
    order = CONSTANT
    # initial_condition = ${vol_frac}
  []
[]
[ICs]
  [mat_den]
    type = RandomIC
    seed = 5
    variable = mat_den
    max = '${fparse vol_frac+0.15}'
    min = '${fparse vol_frac-0.15}'
  []
[]
[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = SMALL
    add_variables = true
    incremental = false
  []
[]

[BCs]
  [no_x]
    type = DirichletBC
    variable = disp_y
    boundary = hold
    value = 0.0
  []
  [no_y]
    type = DirichletBC
    variable = disp_x
    boundary = right
    value = 0.0
  []

[]
[NodalKernels]
  [push]
    type = NodalGravity
    variable = disp_y
    boundary = push
    gravity_value = -1
    mass = 1
  []
[]
[Materials]
  [elasticity_tensor]
    type = ComputeVariableIsotropicElasticityTensor
    youngs_modulus = E_phys
    poissons_ratio = poissons_ratio
    args = 'mat_den'
  []
  [E_phys]
    type = DerivativeParsedMaterial
    # ordered multimaterial simp
    expression = "A1:=(${E0}-${E1})/(${rho0}^${power}-${rho1}^${power}); "
                 "B1:=${E0}-A1*${rho0}^${power}; E1:=A1*mat_den^${power}+B1; "
                 "A2:=(${E1}-${E2})/(${rho1}^${power}-${rho2}^${power}); "
                 "B2:=${E1}-A2*${rho1}^${power}; E2:=A2*mat_den^${power}+B2; "
                 "if(mat_den<${rho1},E1,E2)"
    coupled_variables = 'mat_den'
    property_name = E_phys
  []
  [poissons_ratio]
    type = GenericConstantMaterial
    prop_names = poissons_ratio
    prop_values = 0.3
  []
  [stress]
    type = ComputeLinearElasticStress
  []
  [dc]
    type = ComplianceSensitivity2
    design_density = mat_den
    youngs_modulus = E_phys
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]
[UserObjects]
  [rad_avg]
    type = RadialAverage
    radius = 1.2
    weights = linear
    prop_name = sensitivity
    execute_on = TIMESTEP_END
    force_preaux = true
  []
  [update]
    type = DensityUpdate
    density_sensitivity = Dc
    design_density = mat_den
    volume_fraction = ${vol_frac}
    execute_on = TIMESTEP_BEGIN
  []
  [calc_sense]
    type = SensitivityFilter
    density_sensitivity = Dc
    design_density = mat_den
    filter_UO = rad_avg
    execute_on = TIMESTEP_END
    force_postaux = true
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'
  nl_abs_tol = 1e-8
  dt = 1.0
  num_steps = 70
[]

[Outputs]
  exodus = true
  [out]
    type = CSV
    execute_on = 'TIMESTEP_END'
  []
  print_linear_residuals = false
[]

[Postprocessors]
  [total_vol]
    type = ElementIntegralVariablePostprocessor
    variable = mat_den
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [sensitivity]
    type = ElementIntegralMaterialProperty
    mat_prop = sensitivity
  []
[]

(modules/navier_stokes/test/tests/finite_element/ins/nonzero-malloc/test.i)

[GlobalParams]
  gravity = '0 0 0'
  pspg = true
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 1.0
    ymin = 0
    ymax = 1.0
    nx = 5
    ny = 5
  []
  [./corner_node]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node'
    nodes = '0'
    input = gen
  [../]
[]

[Variables]
  [./vel_x]
  [../]

  [./vel_y]
  [../]

  [./T]
    [./InitialCondition]
      type = ConstantIC
      value = 1.0
    [../]
  [../]

  [./p]
  [../]
[]

[Kernels]
  # mass
  [./mass]
    type = INSMass
    variable = p
    u = vel_x
    v = vel_y
    pressure = p
  [../]

  # x-momentum, time
  [./x_momentum_time]
    type = INSMomentumTimeDerivative
    variable = vel_x
  [../]

  # x-momentum, space
  [./x_momentum_space]
    type = INSMomentumLaplaceForm
    variable = vel_x
    u = vel_x
    v = vel_y
    pressure = p
    component = 0
  [../]

  # y-momentum, time
  [./y_momentum_time]
    type = INSMomentumTimeDerivative
    variable = vel_y
  [../]

  # y-momentum, space
  [./y_momentum_space]
    type = INSMomentumLaplaceForm
    variable = vel_y
    u = vel_x
    v = vel_y
    pressure = p
    component = 1
  [../]

 # temperature
 [./temperature_time]
   type = INSTemperatureTimeDerivative
   variable = T
 [../]

 [./temperature_space]
   type = INSTemperature
   variable = T
   u = vel_x
   v = vel_y
 [../]

  [malloc]
    type = MallocKernel
    # Variable choice doesn't matter
    variable = vel_x
  []
[]

[BCs]
  [./x_no_slip]
    type = DirichletBC
    variable = vel_x
    boundary = 'bottom right left'
    value = 0.0
  [../]

  [./lid]
    type = FunctionDirichletBC
    variable = vel_x
    boundary = 'top'
    function = 'lid_function'
  [../]

  [./y_no_slip]
    type = DirichletBC
    variable = vel_y
    boundary = 'bottom right top left'
    value = 0.0
  [../]

  [./T_hot]
    type = DirichletBC
    variable = T
    boundary = 'bottom'
    value = 1
  [../]

  [./T_cold]
    type = DirichletBC
    variable = T
    boundary = 'top'
    value = 0
  [../]

  [./pressure_pin]
    type = DirichletBC
    variable = p
    boundary = 'pinned_node'
    value = 0
  [../]
[]

[Materials]
  [./const]
    type = GenericConstantMaterial
    block = 0
    prop_names = 'rho mu cp k'
    prop_values = '1  1  1  .01'
  [../]
[]

[Functions]
  [./lid_function]
    # We pick a function that is exactly represented in the velocity
    # space so that the Dirichlet conditions are the same regardless
    # of the mesh spacing.
    type = ParsedFunction
    expression = '4*x*(1-x)'
  [../]
[]

[Executioner]
  type = Transient
  num_steps = 5
  dt = .5
  dtmin = .5
  petsc_options_iname = '-pc_type -pc_asm_overlap -sub_pc_type -sub_pc_factor_levels'
  petsc_options_value = 'asm      2               ilu          4'
  line_search = 'none'
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-13
  nl_max_its = 6
  l_tol = 1e-6
  l_max_its = 500
[]

[Outputs]
  file_base = lid_driven_out
  perf_graph = true
[]

(test/tests/mortar/ad_periodic_segmental_constraint/penalty_periodic_simple2d.i)

[Mesh]
  [left_block]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = -1.0
    xmax = 1.0
    ymin = -1.0
    ymax = 1.0
    nx = 2
    ny = 2
    elem_type = QUAD4
  []
  [left_block_sidesets]
    type = RenameBoundaryGenerator
    input = left_block
    old_boundary = '0 1 2 3'
    new_boundary = '10 11 12 13'
  []
  [left_block_id]
    type = SubdomainIDGenerator
    input = left_block_sidesets
    subdomain_id = 1
  []
  [left]
    type = LowerDBlockFromSidesetGenerator
    input = left_block_id
    sidesets = '13'
    new_block_id = '10003'
    new_block_name = 'secondary_left'
  []
  [right]
    type = LowerDBlockFromSidesetGenerator
    input = left
    sidesets = '11'
    new_block_id = '10001'
    new_block_name = 'primary_right'
  []
  [bottom]
    type = LowerDBlockFromSidesetGenerator
    input = right
    sidesets = '10'
    new_block_id = '10000'
    new_block_name = 'secondary_bottom'
  []
  [top]
    type = LowerDBlockFromSidesetGenerator
    input = bottom
    sidesets = '12'
    new_block_id = '10002'
    new_block_name = 'primary_top'
  []

  [corner_node]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node'
    nodes = '0'
    input = top
  []
[]

[Variables]
  [u]
    order = FIRST
    family = LAGRANGE
  []
  [epsilon]
    order = SECOND
    family = SCALAR
  []
[]

[AuxVariables]
  [sigma]
    order = SECOND
    family = SCALAR
  []
[]

[AuxScalarKernels]
  [sigma]
    type = FunctionScalarAux
    variable = sigma
    function = '1 2'
    execute_on = initial #timestep_end
  []
[]

[Kernels]
  [diff1]
    type = ADDiffusion
    variable = u
    block = 1
  []
[]

[Problem]
  kernel_coverage_check = false
  error_on_jacobian_nonzero_reallocation = true
[]

[BCs]
  [fix_right]
    type = DirichletBC
    variable = u
    boundary = pinned_node
    value = 0
  []
[]

[Constraints]
  [mortarlr]
    type = ADPenaltyEqualValueConstraint
    primary_boundary = '11'
    secondary_boundary = '13'
    primary_subdomain = 'primary_right'
    secondary_subdomain = 'secondary_left'
    secondary_variable = u
    correct_edge_dropping = true
    penalty_value = 1.e2
  []
  [periodiclr]
    type = ADPenaltyPeriodicSegmentalConstraint
    primary_boundary = '11'
    secondary_boundary = '13'
    primary_subdomain = 'primary_right'
    secondary_subdomain = 'secondary_left'
    secondary_variable = u
    epsilon = epsilon
    sigma = sigma
    correct_edge_dropping = true
    penalty_value = 1.e2
  []
  [mortarbt]
    type = ADPenaltyEqualValueConstraint
    primary_boundary = '12'
    secondary_boundary = '10'
    primary_subdomain = 'primary_top'
    secondary_subdomain = 'secondary_bottom'
    secondary_variable = u
    correct_edge_dropping = true
    penalty_value = 1.e2
  []
  [periodicbt]
    type = ADPenaltyPeriodicSegmentalConstraint
    primary_boundary = '12'
    secondary_boundary = '10'
    primary_subdomain = 'primary_top'
    secondary_subdomain = 'secondary_bottom'
    secondary_variable = u
    epsilon = epsilon
    sigma = sigma
    correct_edge_dropping = true
    penalty_value = 1.e2
  []
[]

[Executioner]
  type = Steady
  solve_type = 'PJFNK'
  petsc_options_iname = '-pc_type -pc_hypre_type'
  petsc_options_value = 'hypre boomeramg'
[]

[Outputs]
#  exodus = true
  csv = true
[]

(modules/solid_mechanics/test/tests/uel/small_test_uel_states_fields_gradient.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 20
    ny = 10
    xmax = 10
    ymax = 3
    elem_type = TRI3
  []
  [pin]
    type = ExtraNodesetGenerator
    nodes = 106
    new_boundary = pin
    input = gen
  []
  displacements = 'disp_x disp_y'
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
[]

[AuxVariables]
  [temperature]
    initial_condition = 400
  []
  [voltage]
    initial_condition = 210
  []
[]

[AuxKernels]
  [temperature]
    type = FunctionAux
    function = '25* x + 40 * y + 400'
    variable = temperature
  []
  [voltage]
    type = FunctionAux
    function = '10 * x + 4 * y + 210'
    variable = voltage
  []
[]

[BCs]
  [left_x]
    type = DirichletBC
    variable = disp_x
    boundary = left
    value = 0
  []
  [left_y]
    type = DirichletBC
    variable = disp_y
    boundary = pin
    value = 0
  []

  inactive = 'right_dirichlet'
  [right_neumann]
    type = FunctionNeumannBC
    variable = disp_x
    function = t/10
    boundary = right
  []
  [right_dirichlet]
    type = FunctionDirichletBC
    variable = disp_x
    function = t/10
    boundary = right
  []
[]

[UserObjects]
  [uel]
    type = AbaqusUserElement
    variables = 'disp_x disp_y'
    plugin = ../../../examples/uel_tri_states_tests/uel
    use_displaced_mesh = false
    num_state_vars = 8
    constant_properties = '100 0.3' # E nu
    external_fields = 'temperature voltage'
    extra_vector_tags = 'kernel_residual'
  []
[]

[Problem]
  kernel_coverage_check = false
  extra_tag_vectors = 'kernel_residual'
[]

[AuxVariables]
  [res_x]
  []
  [res_y]
  []
[]

[AuxKernels]
  [res_x]
    type = TagVectorAux
    variable = res_x
    v = disp_x
    vector_tag = kernel_residual
  []
  [res_y]
    type = TagVectorAux
    variable = res_y
    v = disp_y
    vector_tag = kernel_residual
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  dt = 1
  num_steps = 15
[]

[Postprocessors]
  [delta_l]
    type = SideAverageValue
    variable = disp_x
    boundary = right
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [V]
    type = ElementIntegralMaterialProperty
    mat_prop = 1
    use_displaced_mesh = true
    execute_on = 'INITIAL TIMESTEP_END'
  []
[]

[Outputs]
  exodus = true
  csv = true
[]

(modules/navier_stokes/test/tests/finite_element/ins/coupled-force/gravity-through-coupled-force.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 1.0
    ymin = 0
    ymax = 1.0
    nx = 16
    ny = 16
  []
  [./corner_node]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node'
    nodes = '0'
    input = gen
  [../]
[]

[Variables]
  [./velocity]
    family = LAGRANGE_VEC
  [../]
  [./p]
  [../]
  [u]
    family = LAGRANGE_VEC
  []
[]

[AuxVariables]
  [gravity]
    family = LAGRANGE_VEC
  []
[]

[ICs]
  [velocity]
    type = VectorConstantIC
    x_value = 1e-15
    y_value = 1e-15
    variable = velocity
  []
  [gravity]
    type = VectorConstantIC
    x_value = '0'
    y_value = '-9.81'
    variable = gravity
  []
[]

[Kernels]
  inactive = 'momentum_coupled_forces_two_vars momentum_coupled_forces_two_funcs'

  [./mass]
    type = INSADMass
    variable = p
  [../]
  [./mass_pspg]
    type = INSADMassPSPG
    variable = p
  [../]

  [./momentum_convection]
    type = INSADMomentumAdvection
    variable = velocity
  [../]

  [./momentum_viscous]
    type = INSADMomentumViscous
    variable = velocity
  [../]

  [./momentum_pressure]
    type = INSADMomentumPressure
    variable = velocity
    pressure = p
    integrate_p_by_parts = true
  [../]

  [momentum_coupled_forces_var_and_func]
    type = INSADMomentumCoupledForce
    variable = velocity
    coupled_vector_var = u
    vector_function = 'vector_gravity_func'
  []

  [momentum_coupled_forces_two_vars]
    type = INSADMomentumCoupledForce
    variable = velocity
    coupled_vector_var = 'u gravity'
  []

  [momentum_coupled_forces_two_funcs]
    type = INSADMomentumCoupledForce
    variable = velocity
    vector_function = 'vector_func vector_gravity_func'
  []

  [./momentum_supg]
    type = INSADMomentumSUPG
    variable = velocity
    velocity = velocity
  [../]

  [u_diff]
    type = VectorDiffusion
    variable = u
  []
[]

[BCs]
  [./no_slip]
    type = VectorFunctionDirichletBC
    variable = velocity
    boundary = 'bottom right left top'
  [../]

  [./pressure_pin]
    type = DirichletBC
    variable = p
    boundary = 'pinned_node'
    value = 0
  [../]

  [u_left]
    type = VectorFunctionDirichletBC
    variable = u
    boundary = 'left'
    function_x = 1
    function_y = 1
  []

  [u_right]
    type = VectorFunctionDirichletBC
    variable = u
    boundary = 'right'
    function_x = -1
    function_y = -1
  []
[]

[Materials]
  [./const]
    type = ADGenericConstantMaterial
    prop_names = 'rho mu'
    prop_values = '1  1'
  [../]
  [ins_mat]
    type = INSADTauMaterial
    velocity = velocity
    pressure = p
  []
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -sub_pc_factor_levels -ksp_gmres_restart'
  petsc_options_value = 'asm      6                     200'
  line_search = 'none'
  nl_rel_tol = 1e-12
  nl_max_its = 6
[]

[Outputs]
  [out]
    type = Exodus
    hide = 'gravity'
  []
[]

[Functions]
  [vector_func]
    type = ParsedVectorFunction
    expression_x = '-2*x + 1'
    expression_y = '-2*x + 1'
  []
  [vector_gravity_func]
    type = ParsedVectorFunction
    expression_x = '0'
    expression_y = '-9.81'
  []
[]

(modules/xfem/test/tests/bimaterials/glued_bimaterials_2d.i)

# This test is for two layer materials with different youngs modulus
# The global stress is determined by switching the stress based on level set values
# The material interface is marked by a level set function
# The two layer materials are glued together

[GlobalParams]
  order = FIRST
  family = LAGRANGE
  displacements = 'disp_x disp_y'
[]

[XFEM]
  qrule = volfrac
  output_cut_plane = true
[]

[UserObjects]
  [./level_set_cut_uo]
    type = LevelSetCutUserObject
    level_set_var = ls
  [../]
[]

[Mesh]
  displacements = 'disp_x disp_y'
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 5
    ny = 5
    xmin = 0.0
    xmax = 5.
    ymin = 0.0
    ymax = 5.
    elem_type = QUAD4
  []
  [./left_bottom]
    type = ExtraNodesetGenerator
    new_boundary = 'left_bottom'
    coord = '0.0 0.0'
    input = gen
  [../]
  [./left_top]
    type = ExtraNodesetGenerator
    new_boundary = 'left_top'
    coord = '0.0 5.'
    input = left_bottom
  [../]
[]

[AuxVariables]
  [./ls]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxKernels]
  [./ls_function]
    type = FunctionAux
    variable = ls
    function = ls_func
  [../]
[]

[Variables]
  [./disp_x]
  [../]
  [./disp_y]
  [../]
[]

[Functions]
  [./ls_func]
    type = ParsedFunction
    expression = 'y-2.5'
  [../]
[]

[AuxVariables]
  [./stress_xx]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./stress_yy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./stress_xy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./a_strain_xx]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./a_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./a_strain_xy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./b_strain_xx]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./b_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./b_strain_xy]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[Kernels]
  [./TensorMechanics]
  [../]
[]

[AuxKernels]
  [./stress_xx]
    type = RankTwoAux
    rank_two_tensor = stress
    index_i = 0
    index_j = 0
    variable = stress_xx
  [../]
  [./stress_yy]
    type = RankTwoAux
    rank_two_tensor = stress
    index_i = 1
    index_j = 1
    variable = stress_yy
  [../]
  [./stress_xy]
    type = RankTwoAux
    rank_two_tensor = stress
    index_i = 0
    index_j = 1
    variable = stress_xy
  [../]
  [./a_strain_xx]
    type = RankTwoAux
    rank_two_tensor = A_total_strain
    index_i = 0
    index_j = 0
    variable = a_strain_xx
  [../]
  [./a_strain_yy]
    type = RankTwoAux
    rank_two_tensor = A_total_strain
    index_i = 1
    index_j = 1
    variable = a_strain_yy
  [../]
  [./a_strain_xy]
    type = RankTwoAux
    rank_two_tensor = A_total_strain
    index_i = 0
    index_j = 1
    variable = a_strain_xy
  [../]
  [./b_strain_xx]
    type = RankTwoAux
    rank_two_tensor = B_total_strain
    index_i = 0
    index_j = 0
    variable = b_strain_xx
  [../]
  [./b_strain_yy]
    type = RankTwoAux
    rank_two_tensor = B_total_strain
    index_i = 1
    index_j = 1
    variable = b_strain_yy
  [../]
  [./b_strain_xy]
    type = RankTwoAux
    rank_two_tensor = B_total_strain
    index_i = 0
    index_j = 1
    variable = b_strain_xy
  [../]
[]

[Constraints]
  [./dispx_constraint]
    type = XFEMSingleVariableConstraint
    use_displaced_mesh = false
    variable = disp_x
    alpha = 1e8
    geometric_cut_userobject = 'level_set_cut_uo'
  [../]
  [./dispy_constraint]
    type = XFEMSingleVariableConstraint
    use_displaced_mesh = false
    variable = disp_y
    alpha = 1e8
    geometric_cut_userobject = 'level_set_cut_uo'
  [../]
[]

[BCs]
  [./bottomx]
    type = DirichletBC
    boundary = bottom
    variable = disp_x
    value = 0.0
  [../]
  [./bottomy]
    type = DirichletBC
    boundary = bottom
    variable = disp_y
    value = 0.0
  [../]
  [./topx]
    type = FunctionDirichletBC
    boundary = top
    variable = disp_x
    function = 0.03*t
  [../]
  [./topy]
    type = FunctionDirichletBC
    boundary = top
    variable = disp_y
    function = '0.03*t'
  [../]
[]

[Materials]
  [./elasticity_tensor_A]
    type = ComputeIsotropicElasticityTensor
    base_name = A
    youngs_modulus = 1e9
    poissons_ratio = 0.3
  [../]
  [./strain_A]
    type = ComputeSmallStrain
    base_name = A
  [../]
  [./stress_A]
    type = ComputeLinearElasticStress
    base_name = A
  [../]
  [./elasticity_tensor_B]
    type = ComputeIsotropicElasticityTensor
    base_name = B
    youngs_modulus = 1e5
    poissons_ratio = 0.3
  [../]
  [./strain_B]
    type = ComputeSmallStrain
    base_name = B
  [../]
  [./stress_B]
    type = ComputeLinearElasticStress
    base_name = B
  [../]
  [./combined_stress]
    type = LevelSetBiMaterialRankTwo
    levelset_positive_base = 'A'
    levelset_negative_base = 'B'
    level_set_var = ls
    prop_name = stress
  [../]
  [./combined_dstressdstrain]
    type = LevelSetBiMaterialRankFour
    levelset_positive_base = 'A'
    levelset_negative_base = 'B'
    level_set_var = ls
    prop_name = Jacobian_mult
  [../]
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'
  petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
  petsc_options_value = '201                hypre    boomeramg      8'

  line_search = 'bt'

# controls for linear iterations
  l_max_its = 20
  l_tol = 1e-3

# controls for nonlinear iterations
  nl_max_its = 15
  nl_rel_tol = 1e-14
  nl_abs_tol = 1e-7

# time control
  start_time = 0.0
  dt = 0.1
  num_steps = 2

  max_xfem_update = 1
[]

[Outputs]
  exodus = true
  execute_on = timestep_end
  [./console]
    type = Console
    output_linear = true
  [../]
[]

(modules/solid_mechanics/test/tests/global_strain/global_strain_pressure_3D.i)

[Mesh]
  [generated_mesh]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 2
    ny = 2
    nz = 2
    xmin = -0.5
    xmax = 0.5
    ymin = -0.5
    ymax = 0.5
    zmin = -0.5
    zmax = 0.5
  []
  [cnode]
    type = ExtraNodesetGenerator
    coord = '0.0 0.0 0.0'
    new_boundary = 100
    input = generated_mesh
  []
[]

[Variables]
  [./u_x]
  [../]
  [./u_y]
  [../]
  [./u_z]
  [../]
  [./global_strain]
    order = SIXTH
    family = SCALAR
  [../]
[]

[AuxVariables]
  [./disp_x]
  [../]
  [./disp_y]
  [../]
  [./disp_z]
  [../]
  [./s00]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./s11]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./e00]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./e11]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[AuxKernels]
  [./disp_x]
    type = GlobalDisplacementAux
    variable = disp_x
    scalar_global_strain = global_strain
    global_strain_uo = global_strain_uo
    component = 0
  [../]
  [./disp_y]
    type = GlobalDisplacementAux
    variable = disp_y
    scalar_global_strain = global_strain
    global_strain_uo = global_strain_uo
    component = 1
  [../]
  [./disp_z]
    type = GlobalDisplacementAux
    variable = disp_z
    scalar_global_strain = global_strain
    global_strain_uo = global_strain_uo
    component = 2
  [../]
  [./s00]
    type = RankTwoAux
    variable = s00
    rank_two_tensor = stress
    index_i = 0
    index_j = 0
  [../]
  [./s11]
    type = RankTwoAux
    variable = s11
    rank_two_tensor = stress
    index_i = 1
    index_j = 1
  [../]
  [./e00]
    type = RankTwoAux
    variable = e00
    rank_two_tensor = total_strain
    index_i = 0
    index_j = 0
  [../]
  [./e11]
    type = RankTwoAux
    variable = e11
    rank_two_tensor = total_strain
    index_i = 1
    index_j = 1
  [../]
[]

[GlobalParams]
  displacements = 'u_x u_y u_z'
  block = 0
[]

[Kernels]
  [SolidMechanics]
  [../]
[]

[ScalarKernels]
  [./global_strain]
    type = GlobalStrain
    variable = global_strain
    global_strain_uo = global_strain_uo
  [../]
[]

[BCs]
  [./Periodic]
    [./all]
      auto_direction = 'x z'
      variable = ' u_x u_y u_z'
    [../]
  [../]

  # fix center point location
  [./centerfix_x]
    type = DirichletBC
    boundary = 100
    variable = u_x
    value = 0
  [../]
  [./fix_y]
    type = DirichletBC
    boundary = 100
    variable = u_y
    value = 0
  [../]
  [./centerfix_z]
    type = DirichletBC
    boundary = 100
    variable = u_z
    value = 0
  [../]
  [./Pressure]
    [./top]
      boundary = top
      function = 0.3
    [../]
    [./bottom]
      boundary = bottom
      function = 0.3
    [../]
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeElasticityTensor
    block = 0
    C_ijkl = '7 0.33'
    fill_method = symmetric_isotropic_E_nu
  [../]
  [./strain]
    type = ComputeSmallStrain
    global_strain = global_strain
  [../]
  [./global_strain]
    type = ComputeGlobalStrain
    scalar_global_strain = global_strain
    global_strain_uo = global_strain_uo
  [../]
  [./stress]
    type = ComputeLinearElasticStress
  [../]
[]

[UserObjects]
  [./global_strain_uo]
    type = GlobalStrainUserObject
    execute_on = 'Initial Linear Nonlinear'
  [../]
[]

[Preconditioning]
  [./SMP]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = Transient
  scheme = bdf2
  solve_type = 'PJFNK'

  line_search = basic

  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_ksp_type -sub_pc_type -pc_asm_overlap'
  petsc_options_value = 'asm         31   preonly   lu      1'

  l_max_its = 30
  nl_max_its = 12

  l_tol = 1.0e-4

  nl_rel_tol = 1.0e-6
  nl_abs_tol = 1.0e-10

  start_time = 0.0
  num_steps = 2
[]

[Outputs]
  exodus = true
[]

(modules/navier_stokes/test/tests/finite_element/ins/lid_driven/ad_lid_driven_stabilized.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 1.0
    ymin = 0
    ymax = 1.0
    nx = 64
    ny = 64
  []
  [./corner_node]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node'
    nodes = '0'
    input = gen
  [../]
[]

[AuxVariables]
  [vel_x]
  []
  [vel_y]
  []
[]

[AuxKernels]
  [vel_x]
    type = VectorVariableComponentAux
    variable = vel_x
    vector_variable = velocity
    component = 'x'
  []
  [vel_y]
    type = VectorVariableComponentAux
    variable = vel_y
    vector_variable = velocity
    component = 'y'
  []
[]

[Variables]
  [./velocity]
    family = LAGRANGE_VEC
  [../]
  [./p]
  [../]
[]

[ICs]
  [velocity]
    type = VectorConstantIC
    x_value = 0
    y_value = 0
    variable = velocity
  []
[]

[Kernels]
  [./mass]
    type = INSADMass
    variable = p
  [../]
  [./mass_pspg]
    type = INSADMassPSPG
    variable = p
  [../]

  [./momentum_convection]
    type = INSADMomentumAdvection
    variable = velocity
  [../]

  [./momentum_viscous]
    type = INSADMomentumViscous
    variable = velocity
  [../]

  [./momentum_pressure]
    type = INSADMomentumPressure
    variable = velocity
    pressure = p
    integrate_p_by_parts = true
  [../]

  [./momentum_supg]
    type = INSADMomentumSUPG
    variable = velocity
    velocity = velocity
  [../]
[]

[BCs]
  [./no_slip]
    type = VectorFunctionDirichletBC
    variable = velocity
    boundary = 'bottom right left'
  [../]

  [./lid]
    type = VectorFunctionDirichletBC
    variable = velocity
    boundary = 'top'
    function_x = 'lid_function'
  [../]

  [./pressure_pin]
    type = DirichletBC
    variable = p
    boundary = 'pinned_node'
    value = 0
  [../]
[]

[Materials]
  [./const]
    type = ADGenericConstantMaterial
    prop_names = 'rho mu'
    prop_values = '1  1'
  [../]
  [ins_mat]
    type = INSADTauMaterial
    velocity = velocity
    pressure = p
    alpha = .1
  []
[]

[Functions]
  [./lid_function]
    # We pick a function that is exactly represented in the velocity
    # space so that the Dirichlet conditions are the same regardless
    # of the mesh spacing.
    type = ParsedFunction
    expression = '4*x*(1-x)'
  [../]
[]

[Preconditioning]
  [./SMP]
    type = SMP
    full = true
    solve_type = 'NEWTON'
  [../]
[]

[Executioner]
  type = Steady
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  line_search = 'none'
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-13
  nl_max_its = 6
  l_tol = 1e-6
  l_max_its = 500
[]

[Outputs]
  exodus = true
  file_base = lid_driven_stabilized_out
[]

[Postprocessors]
  [lin]
    type = NumLinearIterations
  []
  [nl]
    type = NumNonlinearIterations
  []
  [lin_tot]
    type = CumulativeValuePostprocessor
    postprocessor = 'lin'
  []
  [nl_tot]
    type = CumulativeValuePostprocessor
    postprocessor = 'nl'
  []
[]

(modules/navier_stokes/test/tests/finite_element/ins/lid_driven/mixed-transient-steady/mixed.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 1.0
    ymin = 0
    ymax = 1.0
    nx = 16
    ny = 16
  []
  [./corner_node]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node'
    nodes = '0'
    input = gen
  [../]
[]

[Variables]
  [./velocity]
    family = LAGRANGE_VEC
  [../]
  [./p]
  [../]
  [temperature]
    [InitialCondition]
      type = ConstantIC
      value = 1.0
    []
  []
[]

[ICs]
  [velocity]
    type = VectorConstantIC
    x_value = 1e-15
    y_value = 1e-15
    variable = velocity
  []
[]

[Kernels]
  [./mass]
    type = INSADMass
    variable = p
  [../]
  [./mass_pspg]
    type = INSADMassPSPG
    variable = p
  [../]

  [./momentum_time]
    type = INSADMomentumTimeDerivative
    variable = velocity
  [../]

  [./momentum_convection]
    type = INSADMomentumAdvection
    variable = velocity
  [../]

  [./momentum_viscous]
    type = INSADMomentumViscous
    variable = velocity
  [../]

  [./momentum_pressure]
    type = INSADMomentumPressure
    variable = velocity
    pressure = p
    integrate_p_by_parts = true
  [../]

  [./momentum_supg]
    type = INSADMomentumSUPG
    variable = velocity
    velocity = velocity
  [../]

 [./temperature_advection]
   type = INSADEnergyAdvection
   variable = temperature
 [../]

 [./temperature_conduction]
   type = ADHeatConduction
   variable = temperature
   thermal_conductivity = 'k'
 [../]

  [temperature_supg]
    type = INSADEnergySUPG
    variable = temperature
    velocity = velocity
  []
[]

[BCs]
  [./no_slip]
    type = VectorFunctionDirichletBC
    variable = velocity
    boundary = 'bottom right left'
  [../]

  [./lid]
    type = VectorFunctionDirichletBC
    variable = velocity
    boundary = 'top'
    function_x = 'lid_function'
  [../]

  [./pressure_pin]
    type = DirichletBC
    variable = p
    boundary = 'pinned_node'
    value = 0
  [../]

  [./temperature_hot]
    type = DirichletBC
    variable = temperature
    boundary = 'bottom'
    value = 1
  [../]

  [./temperature_cold]
    type = DirichletBC
    variable = temperature
    boundary = 'top'
    value = 0
  [../]
[]

[Materials]
  [./const]
    type = ADGenericConstantMaterial
    prop_names = 'rho mu cp k'
    prop_values = '1  1  1  .01'
  [../]
  [ins_mat]
    type = INSADStabilized3Eqn
    velocity = velocity
    pressure = p
    temperature = temperature
  []
[]

[Functions]
  [./lid_function]
    # We pick a function that is exactly represented in the velocity
    # space so that the Dirichlet conditions are the same regardless
    # of the mesh spacing.
    type = ParsedFunction
    expression = '4*x*(1-x)'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'NEWTON'
  # Run for 100+ timesteps to reach steady state.
  num_steps = 5
  dt = .5
  dtmin = .5
  petsc_options_iname = '-pc_type -sub_pc_factor_levels -ksp_gmres_restart'
  petsc_options_value = 'asm      6                     200'
  line_search = 'none'
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-12
  nl_max_its = 6
[]

[Outputs]
  exodus = true
[]

(modules/solid_mechanics/test/tests/cohesive_zone_model/bilinear_mixed_scale_strength.i)

[Mesh]
  [msh]
    type = GeneratedMeshGenerator
    dim = 2
    xmax = 1
    ymax = 2
    nx = 5
    ny = 10
  []
  [block1]
    type = SubdomainBoundingBoxGenerator
    input = 'msh'
    bottom_left = '0 0 0'
    top_right = '1 1 0'
    block_id = 1
    block_name = 'block1'
  []
  [block2]
    type = SubdomainBoundingBoxGenerator
    input = 'block1'
    bottom_left = '0 1 0'
    top_right = '1 2 0'
    block_id = 2
    block_name = 'block2'
  []
  [split]
    type = BreakMeshByBlockGenerator
    input = block2
  []
  [top_node]
    type = ExtraNodesetGenerator
    coord = '0 2 0'
    input = split
    new_boundary = top_node
  []
  [bottom_node]
    type = ExtraNodesetGenerator
    coord = '0 0 0'
    input = top_node
    new_boundary = bottom_node
  []
[]

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Physics]
  [SolidMechanics]
    [QuasiStatic]
      generate_output = 'stress_yy'
      [all]
        strain = FINITE
        add_variables = true
        use_automatic_differentiation = true
        decomposition_method = TaylorExpansion
      []
    []
  []
[]

[BCs]
  [fix_x]
    type = DirichletBC
    preset = true
    value = 0.0
    boundary = bottom_node
    variable = disp_x
  []

  [fix_top]
    type = DirichletBC
    preset = true
    boundary = top
    variable = disp_x
    value = 0
  []

  [top]
    type = FunctionDirichletBC
    boundary = top
    variable = disp_y
    function = 'if(t<=0.3,t,if(t<=0.6,0.3-(t-0.3),0.6-t))'
    preset = true
  []

  [bottom]
    type = DirichletBC
    boundary = bottom
    variable = disp_y
    value = 0
    preset = true
  []
[]

[AuxVariables]
  [mode_mixity_ratio]
    order = CONSTANT
    family = MONOMIAL
  []
  [damage]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [mode_mixity_ratio]
    type = MaterialRealAux
    variable = mode_mixity_ratio
    property = mode_mixity_ratio
    execute_on = timestep_end
    boundary = interface
  []
  [damage]
    type = MaterialRealAux
    variable = damage
    property = damage
    execute_on = timestep_end
    boundary = interface
  []
[]

[Physics/SolidMechanics/CohesiveZone]
  [czm_ik]
    boundary = 'interface'
  []
[]

[Materials]
  [stress]
    type = ADComputeFiniteStrainElasticStress
  []
  [elasticity_tensor]
    type = ADComputeElasticityTensor
    fill_method = symmetric9
    C_ijkl = '1.684e5 0.176e5 0.176e5 1.684e5 0.176e5 1.684e5 0.754e5 0.754e5 0.754e5'
  []
  [normal_strength]
    type = GenericFunctionMaterial
    prop_names = 'N'
    prop_values = 'if(x<0.5,1,100)*1e4'
  []
  [czm]
    type = BiLinearMixedModeTraction
    boundary = 'interface'
    penalty_stiffness = 1e6
    GI_c = 1e3
    GII_c = 1e2
    normal_strength = N
    shear_strength = 1e3
    displacements = 'disp_x disp_y'
    eta = 2.2
    viscosity = 1e-3
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient

  solve_type = 'NEWTON'
  line_search = none

  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'

  automatic_scaling = true

  l_max_its = 2
  l_tol = 1e-14
  nl_max_its = 30
  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-10
  start_time = 0.0
  dt = 0.01
  end_time = 0.05
  dtmin = 0.01
[]

[Outputs]
  exodus = true
[]

(modules/combined/examples/optimization/thermomechanical/thermomechanical_main.i)

vol_frac = 0.4

power = 2.0

E0 = 1.0e-6
E1 = 1.0

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  [MeshGenerator]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 40
    ny = 40
    xmin = 0
    xmax = 40
    ymin = 0
    ymax = 40
  []
  [node]
    type = ExtraNodesetGenerator
    input = MeshGenerator
    new_boundary = hold
    nodes = 0
  []
  [push_left]
    type = ExtraNodesetGenerator
    input = node
    new_boundary = push_left
    coord = '16 0 0'
  []
  [push_center]
    type = ExtraNodesetGenerator
    input = push_left
    new_boundary = push_center
    coord = '24 0 0'
  []
  [extra]
    type = SideSetsFromBoundingBoxGenerator
    input = push_center
    bottom_left = '-0.01 17.999  0'
    top_right = '5 22.001  0'
    boundary_new = n1
    included_boundaries = left
  []
  [dirichlet_bc]
    type = SideSetsFromNodeSetsGenerator
    input = extra
  []
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
[]

[AuxVariables]
  [mat_den]
    family = MONOMIAL
    order = FIRST
    initial_condition = 0.02
  []
  [sensitivity_one]
    family = MONOMIAL
    order = FIRST
    initial_condition = -1.0
  []
  [sensitivity_two]
    family = MONOMIAL
    order = FIRST
    initial_condition = -1.0
  []
  [total_sensitivity]
    family = MONOMIAL
    order = FIRST
    initial_condition = -1.0
  []
[]

[AuxKernels]
  [total_sensitivity]
    type = ParsedAux
    variable = total_sensitivity
    expression = '(1-1.0e-7)*sensitivity_one + 1.0e-7*sensitivity_two'
    coupled_variables = 'sensitivity_one sensitivity_two'
    execute_on = 'LINEAR TIMESTEP_END'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = SMALL
    add_variables = true
    incremental = false
  []
[]

[BCs]
  [no_y]
    type = DirichletBC
    variable = disp_y
    boundary = hold
    value = 0.0
  []
  [no_x_symm]
    type = DirichletBC
    variable = disp_x
    boundary = right
    value = 0.0
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeVariableIsotropicElasticityTensor
    youngs_modulus = E_phys
    poissons_ratio = poissons_ratio
    args = 'mat_den'
  []
  [E_phys]
    type = DerivativeParsedMaterial
    # Emin + (density^penal) * (E0 - Emin)
    expression = '${E1} + (mat_den ^ ${power}) * (${E1}-${E0})'
    coupled_variables = 'mat_den'
    property_name = E_phys
  []
  [poissons_ratio]
    type = GenericConstantMaterial
    prop_names = poissons_ratio
    prop_values = 0.3
  []
  [stress]
    type = ComputeLinearElasticStress
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[UserObjects]
  # We do filtering in the subapps
  [update]
    type = DensityUpdate
    density_sensitivity = total_sensitivity
    design_density = mat_den
    volume_fraction = ${vol_frac}
    execute_on = MULTIAPP_FIXED_POINT_BEGIN
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'
  nl_abs_tol = 1e-8
  dt = 1.0
  num_steps = 2
[]

[Outputs]
  [out]
    type = CSV
    execute_on = 'TIMESTEP_END'
  []
  print_linear_residuals = false
  exodus = true
[]

[Postprocessors]
  [mesh_volume]
    type = VolumePostprocessor
    execute_on = 'initial timestep_end'
  []
  [total_vol]
    type = ElementIntegralVariablePostprocessor
    variable = mat_den
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [vol_frac]
    type = ParsedPostprocessor
    expression = 'total_vol / mesh_volume'
    pp_names = 'total_vol mesh_volume'
  []
  [sensitivity]
    type = ElementIntegralVariablePostprocessor
    variable = total_sensitivity
  []
[]

[MultiApps]
  [sub_app_one]
    type = TransientMultiApp
    input_files = structural_sub.i
  []
  [sub_app_two]
    type = TransientMultiApp
    input_files = thermal_sub.i
  []
[]

[Transfers]
  # First SUB-APP: STRUCTURAL
  # To subapp densities
  [subapp_one_density]
    type = MultiAppCopyTransfer
    to_multi_app = sub_app_one
    source_variable = mat_den # Here
    variable = mat_den
  []
  # From subapp sensitivity
  [subapp_one_sensitivity]
    type = MultiAppCopyTransfer
    from_multi_app = sub_app_one
    source_variable = Dc # sensitivity_var
    variable = sensitivity_one # Here
  []
  # Second SUB-APP: HEAT CONDUCTIVITY
  # To subapp densities
  [subapp_two_density]
    type = MultiAppCopyTransfer
    to_multi_app = sub_app_two
    source_variable = mat_den # Here
    variable = mat_den
  []
  # From subapp sensitivity
  [subapp_two_sensitivity]
    type = MultiAppCopyTransfer
    from_multi_app = sub_app_two
    source_variable = Tc # sensitivity_var
    variable = sensitivity_two # Here
  []
[]

(modules/solid_mechanics/test/tests/CylindricalRankTwoAux/test.i)

[Mesh]
  [file_mesh]
    type = FileMeshGenerator
    file = circle.e
  []
  [cnode]
    type = ExtraNodesetGenerator
    coord = '1000.0 0.0'
    new_boundary = 10
    input = file_mesh
  []
[]

[Variables]
  [./disp_x]
  [../]
  [./disp_y]
  [../]
[]

[AuxVariables]
  [./T]
  [../]
  [./stress_rr]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./stress_tt]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[ICs]
  [./T_IC]
    type = FunctionIC
    variable = T
    function = '1000-0.7*sqrt(x^2+y^2)'
  [../]
[]

[Kernels]
  [SolidMechanics]
    displacements = 'disp_x disp_y'
  [../]
[]

[AuxKernels]
  [./stress_rr]
    type = CylindricalRankTwoAux
    variable = stress_rr
    rank_two_tensor = stress
    index_j = 0
    index_i = 0
    center_point = '0 0 0'
  [../]
  [./stress_tt]
    type = CylindricalRankTwoAux
    variable = stress_tt
    rank_two_tensor = stress
    index_j = 1
    index_i = 1
    center_point = '0 0 0'
  [../]
[]

[BCs]
  [./outer_x]
    type = DirichletBC
    variable = disp_x
    boundary = 2
    value = 0
  [../]
  [./outer_y]
    type = DirichletBC
    variable = disp_y
    boundary = '2 10'
    value = 0
  [../]
[]

[Materials]
  [./iso_C]
    type = ComputeElasticityTensor
    fill_method = symmetric_isotropic
    C_ijkl = '2.15e5 0.74e5'
    block = 1
  [../]
  [./strain]
    type = ComputeSmallStrain
    displacements = 'disp_x disp_y'
    block = 1
    eigenstrain_names = eigenstrain
  [../]
  [./stress]
    type = ComputeLinearElasticStress
    block = 1
  [../]
  [./thermal_strain]
    type= ComputeThermalExpansionEigenstrain
    thermal_expansion_coeff = 1e-6
    temperature = T
    stress_free_temperature = 273
    block = 1
    eigenstrain_name = eigenstrain
  [../]
[]

[Executioner]
  type = Steady
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type -ksp_gmres_restart'
  petsc_options_value = 'hypre boomeramg 101'
  l_max_its = 30
  nl_max_its = 10
  nl_abs_tol = 1e-9
  nl_rel_tol = 1e-14
  l_tol = 1e-4
[]

[Outputs]
  exodus = true
  perf_graph = true
[]

(modules/combined/examples/optimization/2d_mbb_pde.i)

vol_frac = 0.5
E0 = 1
Emin = 1e-8
power = 2
[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  [MeshGenerator]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 150
    ny = 50
    xmin = 0
    xmax = 30
    ymin = 0
    ymax = 10
  []
  [node]
    type = ExtraNodesetGenerator
    input = MeshGenerator
    new_boundary = hold_y
    nodes = 0
  []
  [push]
    type = ExtraNodesetGenerator
    input = node
    new_boundary = push
    coord = '30 10 0'
  []

[]

[Variables]
  [Dc]
    initial_condition = -1.0
  []
[]

[AuxVariables]
  [Emin]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = ${Emin}
  []
  [power]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = ${power}
  []
  [E0]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = ${E0}
  []
  [sensitivity]
    family = MONOMIAL
    order = FIRST
    initial_condition = -1.0
    [AuxKernel]
      type = MaterialRealAux
      variable = sensitivity
      property = sensitivity
      execute_on = LINEAR
    []
  []
  [mat_den]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = ${vol_frac}
  []
  [Dc_elem]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = -1.0
    [AuxKernel]
      type = SelfAux
      variable = Dc_elem
      v = Dc
      execute_on = 'TIMESTEP_END'
    []
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = SMALL
    add_variables = true
    incremental = false
  []
[]
[Kernels]
  [diffusion]
    type = FunctionDiffusion
    variable = Dc
    function = 0.15 # radius coeff
  []
  [potential]
    type = Reaction
    variable = Dc
  []
  [source]
    type = CoupledForce
    variable = Dc
    v = sensitivity
  []
[]
[BCs]
  [no_x]
    type = DirichletBC
    variable = disp_y
    boundary = hold_y
    value = 0.0
  []
  [no_y]
    type = DirichletBC
    variable = disp_x
    boundary = right
    value = 0.0
  []
  [boundary_penalty]
    type = ADRobinBC
    variable = Dc
    boundary = 'left top'
    coefficient = 10
  []
  [boundary_penalty_right]
    type = ADRobinBC
    variable = Dc
    boundary = 'right'
    coefficient = 10
  []
[]
[NodalKernels]
  [push]
    type = NodalGravity
    variable = disp_y
    boundary = push
    gravity_value = -1
    mass = 1
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeVariableIsotropicElasticityTensor
    youngs_modulus = E_phys
    poissons_ratio = poissons_ratio
    args = 'Emin mat_den power E0'
  []
  [E_phys]
    type = DerivativeParsedMaterial
    # Emin + (density^penal) * (E0 - Emin)
    expression = '${Emin} + (mat_den ^ ${power}) * (${E0}-${Emin})'
    coupled_variables = 'mat_den'
    property_name = E_phys
  []
  [poissons_ratio]
    type = GenericConstantMaterial
    prop_names = poissons_ratio
    prop_values = 0.3
  []
  [stress]
    type = ComputeLinearElasticStress
  []
  [dc]
    type = ComplianceSensitivity
    design_density = mat_den
    youngs_modulus = E_phys
    incremental = false
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]
[UserObjects]
  [update]
    type = DensityUpdate
    density_sensitivity = Dc_elem
    design_density = mat_den
    volume_fraction = ${vol_frac}
    execute_on = TIMESTEP_BEGIN
    force_postaux = true
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'
  line_search = none
  nl_abs_tol = 1e-4
  l_max_its = 200
  start_time = 0.0
  dt = 1.0
  num_steps = 70
[]

[Outputs]
  [out]
    type = Exodus
    execute_on = 'INITIAL TIMESTEP_END'
  []
  print_linear_residuals = false
[]

[Postprocessors]
  [total_vol]
    type = ElementIntegralVariablePostprocessor
    variable = mat_den
    execute_on = 'INITIAL TIMESTEP_END'
  []
[]

[Controls]
  [first_period]
    type = TimePeriod
    start_time = 0.0
    end_time = 10
    enable_objects = 'BCs::boundary_penalty_right'
    execute_on = 'initial timestep_begin'
  []
[]

(modules/navier_stokes/test/tests/auxkernels/peclet-number-functor-aux/fe-thermal.i)

rho = 1
mu = 1
k = 1
cp = 1

[GlobalParams]
  gravity = '0 0 0'
  pspg = true
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 10
  []
  [corner_node]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node'
    nodes = '0'
    input = gen
  []
[]

[AuxVariables]
  [Pe]
    family = MONOMIAL
    order = FIRST
  []
[]

[AuxKernels]
  [Pe]
    type = PecletNumberFunctorAux
    variable = Pe
    speed = speed
    thermal_diffusivity = 'thermal_diffusivity'
  []
[]

[Variables]
  [vel_x][]
  [vel_y][]
  [p][]
  [T][]
[]

[Kernels]
  # mass
  [mass]
    type = INSMass
    variable = p
    u = vel_x
    v = vel_y
    pressure = p
  []
  # x-momentum, space
  [x_momentum_space]
    type = INSMomentumLaplaceForm
    variable = vel_x
    u = vel_x
    v = vel_y
    pressure = p
    component = 0
  []
  # y-momentum, space
  [y_momentum_space]
    type = INSMomentumLaplaceForm
    variable = vel_y
    u = vel_x
    v = vel_y
    pressure = p
    component = 1
  []
  [temperature_space]
    type = INSTemperature
    variable = T
    u = vel_x
    v = vel_y
  []
[]

[BCs]
  [x_no_slip]
    type = DirichletBC
    variable = vel_x
    boundary = 'bottom right left'
    value = 0.0
  []
  [lid]
    type = FunctionDirichletBC
    variable = vel_x
    boundary = 'top'
    function = 'lid_function'
  []
  [y_no_slip]
    type = DirichletBC
    variable = vel_y
    boundary = 'bottom right top left'
    value = 0.0
  []
  [pressure_pin]
    type = DirichletBC
    variable = p
    boundary = 'pinned_node'
    value = 0
  []
  [T_hot]
    type = DirichletBC
    variable = T
    boundary = 'bottom'
    value = 1
  []
  [T_cold]
    type = DirichletBC
    variable = T
    boundary = 'top'
    value = 0
  []
[]

[Materials]
  [const]
    type = GenericConstantMaterial
    block = 0
    prop_names = 'rho mu k cp'
    prop_values = '${rho} ${mu} ${k} ${cp}'
  []
  [speed]
    type = ADVectorMagnitudeFunctorMaterial
    x_functor = vel_x
    y_functor = vel_y
    vector_magnitude_name = speed
  []
  [thermal_diffusivity]
    type = ThermalDiffusivityFunctorMaterial
    k = ${k}
    rho = ${rho}
    cp = ${cp}
  []
[]

[Functions]
  [lid_function]
    # We pick a function that is exactly represented in the velocity
    # space so that the Dirichlet conditions are the same regardless
    # of the mesh spacing.
    type = ParsedFunction
    expression = '4*x*(1-x)'
  []
[]

[Preconditioning]
  [SMP]
    type = SMP
    full = true
    solve_type = 'NEWTON'
  []
[]

[Executioner]
  type = Steady
  petsc_options_iname = '-pc_type -pc_asm_overlap -sub_pc_type'
  petsc_options_value = 'asm      2               lu'
  line_search = 'none'
  nl_rel_tol = 1e-12
[]

[Outputs]
  exodus = true
[]

(modules/combined/examples/optimization/multi-load/square_main.i)

# This example is intended to reproduce a 2D example with opposing horizontal
# loads (see [1]). This test has an undefined solution if reguar SIMP is applied.
# Using multi-loads SIMP, on the other hand, generates a structure that optimizes
# the response to both loads individually,
# [1]. Lat. Am. j. solids struct. 12 (5), May 2015
# Topological derivative-based topology optimization of structures subject to multiple load-cases

vol_frac = 0.5

power = 1.0
E0 = 1.0
Emin = 1.0e-6

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  [Bottom]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 100
    ny = 100
    xmin = 0
    xmax = 150
    ymin = 0
    ymax = 150
  []
  [left_load]
    type = ExtraNodesetGenerator
    input = Bottom
    new_boundary = left_load
    coord = '0 150 0'
  []
  [right_load]
    type = ExtraNodesetGenerator
    input = left_load
    new_boundary = right_load
    coord = '150 150 0'
  []
  [left_support]
    type = ExtraNodesetGenerator
    input = right_load
    new_boundary = left_support
    coord = '0 0 0'
  []
  [right_support]
    type = ExtraNodesetGenerator
    input = left_support
    new_boundary = right_support
    coord = '150 0 0'
  []
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
[]

[AuxVariables]
  [mat_den]
    family = MONOMIAL
    order = CONSTANT
  []
  [sensitivity_one]
    family = MONOMIAL
    order = SECOND
    initial_condition = -1.0
  []
  [sensitivity_two]
    family = MONOMIAL
    order = SECOND
    initial_condition = -1.0
  []
  [total_sensitivity]
    family = MONOMIAL
    order = SECOND
    initial_condition = -1.0
  []
[]

[ICs]
  [mat_den]
    type = RandomIC
    seed = 7
    variable = mat_den
    max = '${fparse vol_frac+0.35}'
    min = '${fparse vol_frac-0.35}'
  []
[]

[AuxKernels]
  [total_sensitivity]
    type = ParsedAux
    variable = total_sensitivity
    expression = '0.5*sensitivity_one + 0.5*sensitivity_two'
    coupled_variables = 'sensitivity_one sensitivity_two'
    execute_on = 'LINEAR TIMESTEP_END'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = SMALL
    add_variables = true
    incremental = false
  []
[]

[BCs]
  [no_y]
    type = DirichletBC
    variable = disp_y
    boundary = left_support
    value = 0.0
  []
  [no_x]
    type = DirichletBC
    variable = disp_x
    boundary = left_support
    value = 0.0
  []
  [no_y_right]
    type = DirichletBC
    variable = disp_y
    boundary = right_support
    value = 0.0
  []
  [no_x_right]
    type = DirichletBC
    variable = disp_x
    boundary = right_support
    value = 0.0
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeVariableIsotropicElasticityTensor
    youngs_modulus = E_phys
    poissons_ratio = poissons_ratio
    args = 'mat_den'
  []
  [E_phys]
    type = DerivativeParsedMaterial
    # Emin + (density^penal) * (E0 - Emin)
    expression = '${Emin} + (mat_den ^ ${power}) * (${E0}-${Emin})'
    coupled_variables = 'mat_den'
    property_name = E_phys
  []
  [poissons_ratio]
    type = GenericConstantMaterial
    prop_names = poissons_ratio
    prop_values = 0.3
  []
  [stress]
    type = ComputeLinearElasticStress
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[UserObjects]
  [update]
    type = DensityUpdate
    density_sensitivity = total_sensitivity
    design_density = mat_den
    volume_fraction = ${vol_frac}
    execute_on = MULTIAPP_FIXED_POINT_BEGIN
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'
  nl_abs_tol = 1e-10
  dt = 1.0
  num_steps = 10
[]

[Outputs]
  exodus = true
  [out]
    type = CSV
    execute_on = 'TIMESTEP_END'
  []
  print_linear_residuals = false
[]

[Postprocessors]
  [mesh_volume]
    type = VolumePostprocessor
    execute_on = 'initial timestep_end'
  []
  [total_vol]
    type = ElementIntegralVariablePostprocessor
    variable = mat_den
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [vol_frac]
    type = ParsedPostprocessor
    expression = 'total_vol / mesh_volume'
    pp_names = 'total_vol mesh_volume'
  []
  [sensitivity]
    type = ElementIntegralVariablePostprocessor
    variable = total_sensitivity
  []
[]

[MultiApps]
  [sub_app_one]
    type = TransientMultiApp
    input_files = square_subapp_one.i
  []
  [sub_app_two]
    type = TransientMultiApp
    input_files = square_subapp_two.i
  []
[]

[Transfers]
  # First SUB-APP
  # To subapp densities
  [subapp_one_density]
    type = MultiAppCopyTransfer
    to_multi_app = sub_app_one
    source_variable = mat_den # Here
    variable = mat_den
  []
  # From subapp sensitivity
  [subapp_one_sensitivity]
    type = MultiAppCopyTransfer
    from_multi_app = sub_app_one
    source_variable = Dc # sensitivity_var
    variable = sensitivity_one # Here
  []
  # Second SUB-APP
  # To subapp densities
  [subapp_two_density]
    type = MultiAppCopyTransfer
    to_multi_app = sub_app_two
    source_variable = mat_den # Here
    variable = mat_den
  []
  # From subapp sensitivity
  [subapp_two_sensitivity]
    type = MultiAppCopyTransfer
    from_multi_app = sub_app_two
    source_variable = Dc # sensitivity_var
    variable = sensitivity_two # Here
  []
[]

(modules/combined/test/tests/optimization/optimization_density_update/top_opt_3d_pde_filter.i)

vol_frac = 0.4
E0 = 1e5
Emin = 1e-4
power = 2
[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
[]

[Mesh]
  [MeshGenerator]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 24
    ny = 12
    nz = 12
    xmin = 0
    xmax = 20
    ymin = 0
    ymax = 10
    zmin = 0
    zmax = 10
  []
  [middle_bottom_left_edge]
    type = ExtraNodesetGenerator
    input = MeshGenerator
    new_boundary = pull
    coord = '0 0 5'
  []
[]

[Variables]
  [Dc]
    initial_condition = -1.0
  []
[]

[AuxVariables]
  [sensitivity]
    family = MONOMIAL
    order = FIRST
    initial_condition = -1.0
    [AuxKernel]
      type = MaterialRealAux
      variable = sensitivity
      property = sensitivity
      execute_on = LINEAR
    []
  []

  [compliance]
    family = MONOMIAL
    order = CONSTANT
  []

  [mat_den]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = ${vol_frac}
  []
  [Dc_elem]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = -1.0
    [AuxKernel]
      type = SelfAux
      variable = Dc_elem
      v = Dc
      execute_on = 'TIMESTEP_END'
    []
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = SMALL
    add_variables = true
    incremental = false
  []
[]

[Kernels]
  [diffusion]
    type = FunctionDiffusion
    variable = Dc
    function = 0.05
  []
  [potential]
    type = Reaction
    variable = Dc
  []
  [source]
    type = CoupledForce
    variable = Dc
    v = sensitivity
  []
[]

[BCs]
  [no_x]
    type = DirichletBC
    variable = disp_x
    boundary = right
    value = 0.0
  []
  [no_y]
    type = DirichletBC
    variable = disp_y
    boundary = right
    value = 0.0
  []
  [no_z]
    type = DirichletBC
    variable = disp_z
    boundary = right
    value = 0.0
  []
  [boundary_penalty]
    type = ADRobinBC
    variable = Dc
    boundary = 'left top front back'
    coefficient = 10
  []
[]
[NodalKernels]
  [pull]
    type = NodalGravity
    variable = disp_y
    boundary = pull
    gravity_value = -1
    mass = 1
  []
[]
[Materials]
  [elasticity_tensor]
    type = ComputeVariableIsotropicElasticityTensor
    youngs_modulus = E_phys
    poissons_ratio = poissons_ratio
    args = 'mat_den'
  []
  [E_phys]
    type = DerivativeParsedMaterial
    # Emin + (density^penal) * (E0 - Emin)
    expression = '${Emin} + (mat_den ^ ${power}) * (${E0}-${Emin})'
    coupled_variables = 'mat_den'
    property_name = E_phys
  []
  [poissons_ratio]
    type = GenericConstantMaterial
    prop_names = poissons_ratio
    prop_values = 0.3
  []
  [stress]
    type = ComputeLinearElasticStress
  []
  [dc]
    type = ComplianceSensitivity
    design_density = mat_den
    youngs_modulus = E_phys
    incremental = false
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[UserObjects]
  [update]
    type = DensityUpdate
    density_sensitivity = Dc_elem
    design_density = mat_den
    volume_fraction = ${vol_frac}
    execute_on = TIMESTEP_BEGIN
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type '
  petsc_options_value = 'lu'
  nl_abs_tol = 1e-10
  line_search = none
  dt = 1.0
  num_steps = 10
[]

[Outputs]
  [out]
    type = Exodus
    time_step_interval = 10
  []
[]

(modules/navier_stokes/test/tests/finite_element/ins/energy_source/steady-var.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 1.0
    ymin = 0
    ymax = 1.0
    nx = 16
    ny = 16
  []
  [./corner_node]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node'
    nodes = '0'
    input = gen
  [../]
[]

[AuxVariables]
  [u]
    initial_condition = 1
  []
[]

[Variables]
  [./velocity]
    family = LAGRANGE_VEC
  [../]
  [./p]
  [../]
  [temperature][]
[]

[ICs]
  [velocity]
    type = VectorConstantIC
    x_value = 1e-15
    y_value = 1e-15
    variable = velocity
  []
[]

[Kernels]
  [./mass]
    type = INSADMass
    variable = p
  [../]
  [./mass_pspg]
    type = INSADMassPSPG
    variable = p
  [../]

  [./momentum_convection]
    type = INSADMomentumAdvection
    variable = velocity
  [../]

  [./momentum_viscous]
    type = INSADMomentumViscous
    variable = velocity
  [../]

  [./momentum_pressure]
    type = INSADMomentumPressure
    variable = velocity
    pressure = p
    integrate_p_by_parts = true
  [../]

  [./momentum_supg]
    type = INSADMomentumSUPG
    variable = velocity
    velocity = velocity
  [../]

 [./temperature_advection]
   type = INSADEnergyAdvection
   variable = temperature
 [../]

  [./temperature_conduction]
    type = ADHeatConduction
    variable = temperature
    thermal_conductivity = 'k'
  [../]

  [temperature_source]
    type = INSADEnergySource
    variable = temperature
    source_variable = u
  []

  [temperature_supg]
    type = INSADEnergySUPG
    variable = temperature
    velocity = velocity
  []
[]

[BCs]
  [./no_slip]
    type = VectorFunctionDirichletBC
    variable = velocity
    boundary = 'bottom right left'
  [../]

  [./lid]
    type = VectorFunctionDirichletBC
    variable = velocity
    boundary = 'top'
    function_x = 'lid_function'
  [../]

  [./pressure_pin]
    type = DirichletBC
    variable = p
    boundary = 'pinned_node'
    value = 0
  [../]

  [./temperature_hot]
    type = DirichletBC
    variable = temperature
    boundary = 'bottom'
    value = 1
  [../]

  [./temperature_cold]
    type = DirichletBC
    variable = temperature
    boundary = 'top'
    value = 0
  [../]
[]

[Materials]
  [./const]
    type = ADGenericConstantMaterial
    prop_names = 'rho mu cp k'
    prop_values = '1  1  1  .01'
  [../]
  [ins_mat]
    type = INSADStabilized3Eqn
    velocity = velocity
    pressure = p
    temperature = temperature
  []
[]

[Functions]
  [./lid_function]
    # We pick a function that is exactly represented in the velocity
    # space so that the Dirichlet conditions are the same regardless
    # of the mesh spacing.
    type = ParsedFunction
    expression = '4*x*(1-x)'
  [../]
[]

[Executioner]
  type = Steady
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -sub_pc_factor_levels -ksp_gmres_restart'
  petsc_options_value = 'asm      6                     200'
  line_search = 'none'
  nl_rel_tol = 1e-12
  nl_max_its = 6
[]

[Outputs]
  [out]
    type = Exodus
    hide = 'u'
  []
[]

(modules/navier_stokes/test/tests/finite_element/ins/jeffery_hamel/wedge_dirichlet.i)

# This input file tests whether we can converge to the semi-analytical
# solution for flow in a 2D wedge.
[GlobalParams]
  gravity = '0 0 0'

  # Params used by the WedgeFunction for computing the exact solution.
  # The value of K is only required for comparing the pressure to the
  # exact solution, and is computed by the associated jeffery_hamel.py
  # script.
  alpha_degrees = 15
  Re = 30
  K = -9.78221333616
  f = f_theta
[]

[Mesh]
  [file]
    type = FileMeshGenerator
    # file = wedge_4x6.e
    file = wedge_8x12.e
    # file = wedge_16x24.e
    # file = wedge_32x48.e
    # file = wedge_64x96.e
  []
  [./corner_node]
    # Pin is on the centerline of the channel on the left-hand side of
    # the domain at r=1.  If you change the domain, you will need to
    # update this pin location for the pressure exact solution to
    # work.
    type = ExtraNodesetGenerator
    new_boundary = pinned_node
    coord = '1 0'
    input = file
  [../]
[]


[Variables]
  [./vel_x]
    order = SECOND
    family = LAGRANGE
  [../]
  [./vel_y]
    order = SECOND
    family = LAGRANGE
  [../]
  [./p]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./mass]
    type = INSMass
    variable = p
    u = vel_x
    v = vel_y
    pressure = p
  [../]
  [./x_momentum_time]
    type = INSMomentumTimeDerivative
    variable = vel_x
  [../]
  [./x_momentum_space]
    type = INSMomentumLaplaceForm
    variable = vel_x
    u = vel_x
    v = vel_y
    pressure = p
    component = 0
  [../]
  [./y_momentum_time]
    type = INSMomentumTimeDerivative
    variable = vel_y
  [../]
  [./y_momentum_space]
    type = INSMomentumLaplaceForm
    variable = vel_y
    u = vel_x
    v = vel_y
    pressure = p
    component = 1
  [../]
[]

[BCs]
  [./vel_x_no_slip]
    type = DirichletBC
    variable = vel_x
    boundary = 'top_wall bottom_wall'
    value = 0.0
  [../]
  [./vel_y_no_slip]
    type = DirichletBC
    variable = vel_y
    boundary = 'top_wall bottom_wall'
    value = 0.0
  [../]
  [./vel_x_inlet]
    type = FunctionDirichletBC
    variable = vel_x
    boundary = 'inlet outlet'
    function = 'vel_x_exact'
  [../]
  [./vel_y_inlet]
    type = FunctionDirichletBC
    variable = vel_y
    boundary = 'inlet outlet'
    function = 'vel_y_exact'
  [../]
  [./pressure_pin]
    type = DirichletBC
    variable = p
    boundary = 'pinned_node'
    value = 0
  [../]
[]

[Materials]
  [./const]
    type = GenericConstantMaterial
    block = 1
    prop_names = 'rho mu'
    prop_values = '1  1'
  [../]
[]

[Preconditioning]
  [./SMP_PJFNK]
    type = SMP
    full = true
    solve_type = NEWTON
  [../]
[]

[Executioner]
  type = Transient
  dt = 1.e-2
  dtmin = 1.e-2
  num_steps = 5
  petsc_options_iname = '-ksp_gmres_restart -pc_type -sub_pc_type -sub_pc_factor_levels'
  petsc_options_value = '300                bjacobi  ilu          4'
  line_search = none
  nl_rel_tol = 1e-13
  nl_abs_tol = 1e-11
  nl_max_its = 10
  l_tol = 1e-6
  l_max_its = 300
[]

[Outputs]
  exodus = true
[]

[Functions]
  [./f_theta]
    # Non-dimensional solution values f(eta), 0 <= eta <= 1 for
    # alpha=15 deg, Re=30.  Note: this introduces an input file
    # ordering dependency: this Function must appear *before* the two
    # functions below which use it since apparently proper dependency
    # resolution is not done in this scenario.
    type = PiecewiseLinear
    data_file = 'f.csv'
    format = 'columns'
  [../]
  [./vel_x_exact]
    type = WedgeFunction
    var_num = 0
    mu = 1
    rho = 1
  [../]
  [./vel_y_exact]
    type = WedgeFunction
    var_num = 1
    mu = 1
    rho = 1
  [../]
  [./p_exact]
    type = WedgeFunction
    var_num = 2
    mu = 1
    rho = 1
  [../]
[]

[Postprocessors]
  [./vel_x_L2_error]
    type = ElementL2Error
    variable = vel_x
    function = vel_x_exact
    execute_on = 'initial timestep_end'
  [../]
  [./vel_y_L2_error]
    type = ElementL2Error
    variable = vel_y
    function = vel_y_exact
    execute_on = 'initial timestep_end'
  [../]
  [./p_L2_error]
    type = ElementL2Error
    variable = p
    function = p_exact
    execute_on = 'initial timestep_end'
  [../]
[]

(modules/combined/examples/optimization/thermomechanical/thermal_sub.i)

vol_frac = 0.4

power = 2.0

E0 = 1.0e-6
E1 = 1.0

rho0 = 0.0
rho1 = 1.0

C0 = 1.0e-6
C1 = 1.0

TC0 = 1.0e-16
TC1 = 1.0

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  [MeshGenerator]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 40
    ny = 40
    xmin = 0
    xmax = 40
    ymin = 0
    ymax = 40
  []
  [node]
    type = ExtraNodesetGenerator
    input = MeshGenerator
    new_boundary = hold
    nodes = 0
  []
  [push_left]
    type = ExtraNodesetGenerator
    input = node
    new_boundary = push_left
    coord = '16 0 0'
  []
  [push_center]
    type = ExtraNodesetGenerator
    input = push_left
    new_boundary = push_center
    coord = '24 0 0'
  []
  [extra]
    type = SideSetsFromBoundingBoxGenerator
    input = push_center
    bottom_left = '-0.01 17.999  0'
    top_right = '5 22.001  0'
    boundary_new = n1
    included_boundaries = left
  []
  [dirichlet_bc]
    type = SideSetsFromNodeSetsGenerator
    input = extra
  []
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [temp]
    initial_condition = 100.0
  []
[]

[AuxVariables]
  [Dc]
    family = MONOMIAL
    order = FIRST
    initial_condition = -1.0
  []
  [Cc]
    family = MONOMIAL
    order = FIRST
    initial_condition = -1.0
  []
  [Tc]
    family = MONOMIAL
    order = FIRST
    initial_condition = -1.0
  []
  [Cost]
    family = MONOMIAL
    order = FIRST
    initial_condition = -1.0
  []
  [mat_den]
    family = MONOMIAL
    order = FIRST
    initial_condition = ${vol_frac}
  []
[]

[AuxKernels]
  [Cost]
    type = MaterialRealAux
    variable = Cost
    property = Cost_mat
  []
[]

[Kernels]
  [heat_conduction]
    type = HeatConduction
    variable = temp
    diffusion_coefficient = thermal_cond
  []
  [heat_source]
    type = HeatSource
    value = 1e-2 # W/m^3
    variable = temp
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = SMALL
    add_variables = true
    incremental = false
  []
[]

[BCs]
  [no_y]
    type = DirichletBC
    variable = disp_y
    boundary = hold
    value = 0.0
  []
  [no_x_symm]
    type = DirichletBC
    variable = disp_x
    boundary = right
    value = 0.0
  []
  [left_n1]
    type = DirichletBC
    variable = temp
    boundary = n1
    value = 0.0
  []
  [top]
    type = NeumannBC
    variable = temp
    boundary = top
    value = 0
  []
  [bottom]
    type = NeumannBC
    variable = temp
    boundary = bottom
    value = 0
  []
  [right]
    type = NeumannBC
    variable = temp
    boundary = right
    value = 0
  []
  [left]
    type = NeumannBC
    variable = temp
    boundary = left
    value = 0
  []
[]

[NodalKernels]
  [push_left]
    type = NodalGravity
    variable = disp_y
    boundary = push_left
    gravity_value = 0.0 # -1e-8
    mass = 1
  []
  [push_center]
    type = NodalGravity
    variable = disp_y
    boundary = push_center
    gravity_value = 0.0 # -1e-8
    mass = 1
  []
[]

[Materials]
  [thermal_cond]
    type = DerivativeParsedMaterial
    # ordered multimaterial simp
    expression = "A1:=(${TC0}-${TC1})/(${rho0}^${power}-${rho1}^${power}); "
                 "B1:=${TC0}-A1*${rho0}^${power}; TC1:=A1*mat_den^${power}+B1; TC1"
    coupled_variables = 'mat_den'
    property_name = thermal_cond
    outputs = 'exodus'
  []
  [thermal_compliance]
    type = ThermalCompliance
    temperature = temp
    thermal_conductivity = thermal_cond
    outputs = 'exodus'
  []
  [elasticity_tensor]
    type = ComputeVariableIsotropicElasticityTensor
    youngs_modulus = E_phys
    poissons_ratio = poissons_ratio
    args = 'mat_den'
  []
  [E_phys]
    type = DerivativeParsedMaterial
    # ordered multimaterial simp
    expression = "A1:=(${E0}-${E1})/(${rho0}^${power}-${rho1}^${power}); "
                 "B1:=${E0}-A1*${rho0}^${power}; E1:=A1*mat_den^${power}+B1; E1"
    coupled_variables = 'mat_den'
    property_name = E_phys
  []
  [Cost_mat]
    type = DerivativeParsedMaterial
    # ordered multimaterial simp
    expression = "A1:=(${C0}-${C1})/(${rho0}^(1/${power})-${rho1}^(1/${power})); "
                 "B1:=${C0}-A1*${rho0}^(1/${power}); C1:=A1*mat_den^(1/${power})+B1; C1"
    coupled_variables = 'mat_den'
    property_name = Cost_mat
  []
  [CostDensity]
    type = ParsedMaterial
    property_name = CostDensity
    coupled_variables = 'mat_den Cost'
    expression = 'mat_den*Cost'
  []
  [poissons_ratio]
    type = GenericConstantMaterial
    prop_names = poissons_ratio
    prop_values = 0.3
  []
  [stress]
    type = ComputeLinearElasticStress
  []
  [dc]
    type = ComplianceSensitivity
    design_density = mat_den
    youngs_modulus = E_phys
  []
  [cc]
    type = CostSensitivity
    design_density = mat_den
    cost = Cost_mat
    outputs = 'exodus'
  []
  [tc]
    type = ThermalSensitivity
    design_density = mat_den
    thermal_conductivity = thermal_cond
    temperature = temp
    outputs = 'exodus'
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[UserObjects]
  [rad_avg]
    type = RadialAverage
    radius = 0.1
    weights = linear
    prop_name = sensitivity
    execute_on = TIMESTEP_END
    force_preaux = true
  []
  [rad_avg_cost]
    type = RadialAverage
    radius = 0.1
    weights = linear
    prop_name = cost_sensitivity
    execute_on = TIMESTEP_END
    force_preaux = true
  []
  [rad_avg_thermal]
    type = RadialAverage
    radius = 0.1
    weights = linear
    prop_name = thermal_sensitivity
    execute_on = TIMESTEP_END
    force_preaux = true
  []
  # Provides Dc
  [calc_sense]
    type = SensitivityFilter
    density_sensitivity = Dc
    design_density = mat_den
    filter_UO = rad_avg
    execute_on = TIMESTEP_END
    force_postaux = true
  []
  # Provides Cc
  [calc_sense_cost]
    type = SensitivityFilter
    density_sensitivity = Cc
    design_density = mat_den
    filter_UO = rad_avg_cost
    execute_on = TIMESTEP_END
    force_postaux = true
  []
  # Provides Tc
  [calc_sense_thermal]
    type = SensitivityFilter
    density_sensitivity = Tc
    design_density = mat_den
    filter_UO = rad_avg_thermal
    execute_on = TIMESTEP_END
    force_postaux = true
  []
[]

[Executioner]
  type = Transient
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'
  nl_abs_tol = 1e-12
  dt = 1.0
  num_steps = 500
[]

[Outputs]
  exodus = true
  [out]
    type = CSV
    execute_on = 'TIMESTEP_END'
  []
  print_linear_residuals = false
[]

[Postprocessors]
  [right_flux]
    type = SideDiffusiveFluxAverage
    variable = temp
    boundary = right
    diffusivity = 10
  []
  [mesh_volume]
    type = VolumePostprocessor
    execute_on = 'initial timestep_end'
  []
  [total_vol]
    type = ElementIntegralVariablePostprocessor
    variable = mat_den
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [vol_frac]
    type = ParsedPostprocessor
    expression = 'total_vol / mesh_volume'
    pp_names = 'total_vol mesh_volume'
  []
  [sensitivity]
    type = ElementIntegralMaterialProperty
    mat_prop = sensitivity
  []
  [cost_sensitivity]
    type = ElementIntegralMaterialProperty
    mat_prop = cost_sensitivity
  []
  [cost]
    type = ElementIntegralMaterialProperty
    mat_prop = CostDensity
  []
  [cost_frac]
    type = ParsedPostprocessor
    expression = 'cost / mesh_volume'
    pp_names = 'cost mesh_volume'
  []
  [objective]
    type = ElementIntegralMaterialProperty
    mat_prop = strain_energy_density
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [objective_thermal]
    type = ElementIntegralMaterialProperty
    mat_prop = thermal_compliance
    execute_on = 'INITIAL TIMESTEP_END'
  []
[]

(modules/combined/tutorials/introduction/thermal_mechanical_contact/thermomech_cont_step02.i)

#
# Three shell thermo mechanical contact
# https://mooseframework.inl.gov/modules/combined/tutorials/introduction/step02.html
#

[GlobalParams]
  displacements = 'disp_x disp_y'
  block = '0 1 2'
[]

[Mesh]
  # inner cylinder
  [inner]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 40
    xmax = 1
    ymin = -1.75
    ymax = 1.75
    boundary_name_prefix = inner
  []

  # middle shell with subdomain ID 1
  [middle_elements]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 40
    xmin = 1.1
    xmax = 2.1
    ymin = -2.5
    ymax = 2.5
    boundary_name_prefix = middle
    boundary_id_offset = 4
  []
  [middle]
    type = SubdomainIDGenerator
    input = middle_elements
    subdomain_id = 1
  []

  # outer shell with subdomain ID 2
  [outer_elements]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 48
    xmin = 2.2
    xmax = 3.2
    ymin = -3
    ymax = 3
    boundary_name_prefix = outer
    boundary_id_offset = 8
  []
  [outer]
    type = SubdomainIDGenerator
    input = outer_elements
    subdomain_id = 2
  []

  [collect_meshes]
    type = MeshCollectionGenerator
    inputs = 'inner middle outer'
  []

  # add set of 3 nodes to remove rigid body modes for y-translation in each block
  [pin]
    type = ExtraNodesetGenerator
    input = collect_meshes
    new_boundary = pin
    coord = '0 0 0; 1.6 0 0; 2.7 0 0'
  []

  patch_update_strategy = iteration

  # switch to an axisymmetric coordinate system
  coord_type = RZ
[]

[Variables]
  # temperature field variable (first order Lagrange by default)
  [T]
  []
  # temperature lagrange multipliers
  [Tlm1]
    block = 'inner_gap_secondary_subdomain'
  []
  [Tlm2]
    block = 'outer_gap_secondary_subdomain'
  []
[]

[Kernels]
  [heat_conduction]
    type = HeatConduction
    variable = T
  []
  [dTdt]
    type = HeatConductionTimeDerivative
    variable = T
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    add_variables = true
    strain = FINITE
    eigenstrain_names = thermal
    generate_output = 'vonmises_stress stress_xx strain_xx stress_yy strain_yy'
    volumetric_locking_correction = true
    temperature = T
  []
[]

[Contact]
  [inner_gap]
    primary = middle_left
    secondary = inner_right
    model = frictionless
    formulation = mortar
    c_normal = 1e+0
  []
  [outer_gap]
    primary = outer_left
    secondary = middle_right
    model = frictionless
    formulation = mortar
    c_normal = 1e+0
  []
[]

[Constraints]
  # thermal contact constraint
  [Tlm1]
    type = GapConductanceConstraint
    variable = Tlm1
    secondary_variable = T
    use_displaced_mesh = true
    k = 1e-1
    primary_boundary = middle_left
    primary_subdomain = inner_gap_secondary_subdomain
    secondary_boundary = inner_right
    secondary_subdomain = inner_gap_primary_subdomain
  []
  [Tlm2]
    type = GapConductanceConstraint
    variable = Tlm2
    secondary_variable = T
    use_displaced_mesh = true
    k = 1e-1
    primary_boundary = outer_left
    primary_subdomain = outer_gap_secondary_subdomain
    secondary_boundary = middle_right
    secondary_subdomain = outer_gap_primary_subdomain
  []
[]

[BCs]
  [center_axis_fix]
    type = DirichletBC
    variable = disp_x
    boundary = 'inner_left'
    value = 0
  []
  [y_translation_fix]
    type = DirichletBC
    variable = disp_y
    boundary = 'pin'
    value = 0
  []
  [heat_center]
    type = FunctionDirichletBC
    variable = T
    boundary = 'inner_left'
    function = t*40
  []
  [cool_right]
    type = DirichletBC
    variable = T
    boundary = 'outer_right'
    value = 0
  []
[]

[Materials]
  [eigen_strain_inner]
    type = ComputeThermalExpansionEigenstrain
    eigenstrain_name = thermal
    temperature = T
    thermal_expansion_coeff = 1e-3
    stress_free_temperature = 0
    block = 0
  []
  [eigen_strain_middle]
    type = ComputeThermalExpansionEigenstrain
    eigenstrain_name = thermal
    temperature = T
    thermal_expansion_coeff = 2e-4
    stress_free_temperature = 0
    block = 1
  []
  [eigen_strain_outer]
    type = ComputeThermalExpansionEigenstrain
    eigenstrain_name = thermal
    temperature = T
    thermal_expansion_coeff = 1e-5
    stress_free_temperature = 0
    block = 2
  []

  [elasticity]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 1
    poissons_ratio = 0.3
  []
  [stress]
    type = ComputeFiniteStrainElasticStress
  []

  # thermal properties
  [thermal_conductivity_0]
    type = HeatConductionMaterial
    thermal_conductivity = 50
    specific_heat = 1
    block = 0
  []
  [thermal_conductivity_1]
    type = HeatConductionMaterial
    thermal_conductivity = 5
    specific_heat = 1
    block = 1
  []
  [thermal_conductivity_2]
    type = HeatConductionMaterial
    thermal_conductivity = 1
    specific_heat = 1
    block = 2
  []
  [density]
    type = Density
    density = 1
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

# [Debug]
#   show_var_residual_norms = true
# []

[Executioner]
  type = Transient
  solve_type = PJFNK
  line_search = none
  petsc_options_iname = '-pc_type -pc_factor_shift_type'
  petsc_options_value = 'lu       nonzero              '
  snesmf_reuse_base = false
  end_time = 7
  dt = 0.05

  nl_rel_tol = 1e-08
  nl_abs_tol = 1e-50

  [Predictor]
    type = SimplePredictor
    scale = 0.5
  []
[]

[Outputs]
  exodus = true
  print_linear_residuals = false
  perf_graph = true
[]

(modules/solid_mechanics/test/tests/uel/small_test_umat_states_fields_gradient.i)

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 20
    ny = 10
    xmax = 10
    ymax = 3
    elem_type = TRI3
  []
  [pin]
    type = ExtraNodesetGenerator
    nodes = 106
    new_boundary = pin
    input = gen
  []
  displacements = 'disp_x disp_y'
[]

[AuxVariables]
  [temperature]
    initial_condition = 400
  []
  [voltage]
    initial_condition = 210
  []
[]

[AuxKernels]
  [temperature]
    type = FunctionAux
    function = '25* x + 40 * y + 400'
    variable = temperature
  []
  [voltage]
    type = FunctionAux
    function = '10 * x + 4 * y + 210'
    variable = voltage
  []
[]

[BCs]
  [left_x]
    type = DirichletBC
    variable = disp_x
    boundary = left
    value = 0
  []
  [left_y]
    type = DirichletBC
    variable = disp_y
    boundary = pin
    value = 0
  []

  inactive = 'right_dirichlet'
  [right_neumann]
    type = FunctionNeumannBC
    variable = disp_x
    function = t/10
    boundary = right
  []
  [right_dirichlet]
    type = FunctionDirichletBC
    variable = disp_x
    function = t/10
    boundary = right
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    add_variables = true
    strain = SMALL
    incremental = true
    extra_vector_tags = 'kernel_residual'
  []
[]

[Materials]
  [umat]
    type = AbaqusUMATStress
    constant_properties = '100 0.3'
    plugin = '../../plugins/small_elastic_tri_states'
    num_state_vars = 2
    use_one_based_indexing = true
    temperature = 'temperature'
    external_fields = 'voltage'
  []
[]

[Problem]
  kernel_coverage_check = false
  extra_tag_vectors = 'kernel_residual'
[]

[AuxVariables]
  [res_x]
  []
  [res_y]
  []
[]

[AuxKernels]
  [res_x]
    type = TagVectorAux
    variable = res_x
    v = disp_x
    vector_tag = kernel_residual
  []
  [res_y]
    type = TagVectorAux
    variable = res_y
    v = disp_y
    vector_tag = kernel_residual
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  dt = 1
  num_steps = 15
  [Quadrature]
   type = GAUSS
   order = CONSTANT
  []
[]

[Postprocessors]
  [delta_l]
    type = SideAverageValue
    variable = disp_x
    boundary = right
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [V]
    type = ElementIntegralMaterialProperty
    mat_prop = 1
    use_displaced_mesh = true
    execute_on = 'INITIAL TIMESTEP_END'
  []
[]

[Outputs]
  exodus = true
  csv = true
[]

(modules/solid_mechanics/test/tests/uel/tensile_uel_umat_moose_temperature.i)

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
[]

[Mesh]
  [mesh]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 1
    ny = 1
    nz = 1
    elem_type = HEX8
  []
  [extra_nodeset]
    type = ExtraNodesetGenerator
    input = mesh
    new_boundary = 'master'
    coord = '1.0 1.0 1.0'
  []
[]

[AuxVariables]
  [temperature]
    initial_condition = 500
  []
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [disp_z]
  []
[]

[Functions]
  [function_pull]
    type = PiecewiseLinear
    x = '0 100'
    y = '0 0.1'
  []
[]

[Constraints]
  [one]
    type = LinearNodalConstraint
    variable = disp_x
    primary = '6'
    secondary_node_ids = '1 2 5'
    penalty = 1.0e8
    formulation = kinematic
    weights = '1'
  []
  [two]
    type = LinearNodalConstraint
    variable = disp_z
    primary = '6'
    secondary_node_ids = '4 5 7'
    penalty = 1.0e8
    formulation = kinematic
    weights = '1'
  []
[]

[BCs]
  [symmy]
    type = DirichletBC
    variable = disp_y
    boundary = bottom
    value = 0
  []
  [symmx]
    type = DirichletBC
    variable = disp_x
    boundary = left
    value = 0
  []
  [symmz]
    type = DirichletBC
    variable = disp_z
    boundary = back
    value = 0
  []
  # What's done below is to capture the weird constraints
  [axial_load]
    type = FunctionDirichletBC
    variable = disp_y
    boundary = 'top'
    function = function_pull
  []
[]

[UserObjects]
  [uel]
    type = AbaqusUserElement
    variables = 'disp_x disp_y'
    plugin = '../../../../solid_mechanics/examples/uel_build/uel'
    use_displaced_mesh = false

    aux_variables = temperature # TODO
    #use_one_based_indexing = true # TODO

    jtype = 17
    num_state_vars = 177
    constant_properties = '190 28.0 3.0 1.0 6.0 0.0 0.0 23.0 25.0 26.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 '
                          '0.0 0.0 0.0 0.0 0.0 31700000.0 0.32 6.67e-06 1e-08 5000.0 4.0' # 28 properties
    extra_vector_tags = 'kernel_residual'
  []
[]

[Problem]
  kernel_coverage_check = false
  extra_tag_vectors = 'kernel_residual'
[]

[AuxVariables]
  [res_x]
  []
  [res_y]
  []
[]

[AuxKernels]
  [res_x]
    type = TagVectorAux
    variable = res_x
    v = disp_x
    vector_tag = kernel_residual
  []
  [res_y]
    type = TagVectorAux
    variable = res_y
    v = disp_y
    vector_tag = kernel_residual
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient

  l_max_its = 100
  l_tol = 1e-8
  nl_max_its = 50
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-8

  dtmin = 1
  dt = 5
  end_time = 100
[]

[Outputs]
  exodus = true
[]

(modules/navier_stokes/test/tests/finite_element/ins/boussinesq/boussinesq_square.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmax = .05
    ymax = .05
    nx = 20
    ny = 20
    elem_type = QUAD9
  []
  [./bottom_left]
    type = ExtraNodesetGenerator
    new_boundary = corner
    coord = '0 0'
    input = gen
  [../]
[]


[Preconditioning]
  [./Newton_SMP]
    type = SMP
    full = true
    solve_type = 'NEWTON'
  [../]
[]

[Executioner]
  type = Steady

  nl_rel_tol = 1e-12
  petsc_options_iname = '-pc_type -sub_pc_type -sub_pc_factor_shift_type -ksp_gmres_restart'
  petsc_options_value = 'bjacobi  lu           NONZERO                   200'
[]

[Debug]
  show_var_residual_norms = true
[]

[Outputs]
  [out]
    type = Exodus
    execute_on = 'final'
  []
[]

[Variables]
  [velocity]
    family = LAGRANGE_VEC
    order = SECOND
  []
  [p][]
  [./temp]
    order = SECOND
    initial_condition = 340
    scaling = 1e-4
  [../]
[]


[BCs]
  [./velocity_dirichlet]
    type = VectorDirichletBC
    boundary = 'left right bottom top'
    variable = velocity
    # The third entry is to satisfy RealVectorValue
    values = '0 0 0'
  [../]
  # Even though we are integrating by parts, because there are no integrated
  # boundary conditions on the velocity p doesn't appear in the system of
  # equations. Thus we must pin the pressure somewhere in order to ensure a
  # unique solution
  [./p_zero]
    type = DirichletBC
    boundary = corner
    variable = p
    value = 0
  [../]
  [./cold]
    type = DirichletBC
    variable = temp
    boundary = left
    value = 300
  [../]
  [./hot]
    type = DirichletBC
    variable = temp
    boundary = right
    value = 400
  [../]
[]


[Kernels]
  [./mass]
    type = INSADMass
    variable = p
  [../]
  [./momentum_viscous]
    type = INSADMomentumViscous
    variable = velocity
  [../]
  [momentum_advection]
    type = INSADMomentumAdvection
    variable = velocity
  []
  [momentum_pressure]
    type = INSADMomentumPressure
    variable = velocity
    pressure = p
    integrate_p_by_parts = true
  []
  [temp_advection]
    type = INSADEnergyAdvection
    variable = temp
  []
  [temp_conduction]
    type = ADHeatConduction
    variable = temp
    thermal_conductivity = 'k'
  [../]
  [./buoyancy]
    type = INSADBoussinesqBodyForce
    variable = velocity
    temperature = temp
    gravity = '0 -9.81 0'
  [../]
  [./gravity]
    type = INSADGravityForce
    variable = velocity
    gravity = '0 -9.81 0'
  [../]
[]

[Materials]
  [./ad_const]
    type = ADGenericConstantMaterial
    # alpha = coefficient of thermal expansion where rho  = rho0 -alpha * rho0 * delta T
    prop_names =  'mu        rho   alpha   k        cp'
    prop_values = '30.74e-6  .5757 2.9e-3  46.38e-3 1054'
  [../]
  [./const]
    type = GenericConstantMaterial
    prop_names =  'temp_ref'
    prop_values = '900'
  [../]
  [ins_mat]
    type = INSAD3Eqn
    velocity = velocity
    pressure = p
    temperature = temp
  []
[]

(modules/solid_mechanics/test/tests/global_strain/global_strain_shear.i)

[Mesh]
  [generated_mesh]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 1
    ny = 1
    nz = 1
  []
  [cnode]
    type = ExtraNodesetGenerator
    coord = '0.0 0.0 0.0'
    new_boundary = 100
    input = generated_mesh
  []
[]

[Variables]
  [./u_x]
  [../]
  [./u_y]
  [../]
  [./u_z]
  [../]
  [./global_strain]
    order = SIXTH
    family = SCALAR
  [../]
[]

[AuxVariables]
  [./disp_x]
  [../]
  [./disp_y]
  [../]
  [./disp_z]
  [../]
  [./s01]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./e01]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[AuxKernels]
  [./disp_x]
    type = GlobalDisplacementAux
    variable = disp_x
    scalar_global_strain = global_strain
    global_strain_uo = global_strain_uo
    component = 1
  [../]
  [./disp_y]
    type = GlobalDisplacementAux
    variable = disp_y
    scalar_global_strain = global_strain
    global_strain_uo = global_strain_uo
    component = 1
  [../]
  [./disp_z]
    type = GlobalDisplacementAux
    variable = disp_z
    scalar_global_strain = global_strain
    global_strain_uo = global_strain_uo
    component = 2
  [../]
  [./s01]
    type = RankTwoAux
    variable = s01
    rank_two_tensor = stress
    index_i = 0
    index_j = 1
  [../]
  [./e01]
    type = RankTwoAux
    variable = e01
    rank_two_tensor = total_strain
    index_i = 0
    index_j = 1
  [../]
[]

[GlobalParams]
  displacements = 'u_x u_y u_z'
  block = 0
[]

[Kernels]
  [SolidMechanics]
  [../]
[]

[ScalarKernels]
  [./global_strain]
    type = GlobalStrain
    variable = global_strain
    global_strain_uo = global_strain_uo
  [../]
[]

[BCs]
  [./Periodic]
    [./all]
      auto_direction = 'x y z'
      variable = ' u_x u_y u_z'
    [../]
  [../]

  # fix center point location
  [./centerfix_x]
    type = DirichletBC
    boundary = 100
    variable = u_x
    value = 0
  [../]
  [./centerfix_y]
    type = DirichletBC
    boundary = 100
    variable = u_y
    value = 0
  [../]
  [./centerfix_z]
    type = DirichletBC
    boundary = 100
    variable = u_z
    value = 0
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeElasticityTensor
    block = 0
    C_ijkl = '70e9 0.33'
    fill_method = symmetric_isotropic_E_nu
  [../]
  [./strain]
    type = ComputeSmallStrain
    global_strain = global_strain
  [../]
  [./global_strain]
    type = ComputeGlobalStrain
    scalar_global_strain = global_strain
    global_strain_uo = global_strain_uo
  [../]
  [./stress]
    type = ComputeLinearElasticStress
  [../]
[]

[UserObjects]
  [./global_strain_uo]
    type = GlobalStrainUserObject
    applied_stress_tensor = '0 0 0 5e9 5e9 5e9'
    execute_on = 'Initial Linear Nonlinear'
  [../]
[]

[Postprocessors]
  [./l2err_e01]
    type = ElementL2Error
    variable = e01
    function = 0.095 #Shear strain check
  [../]
[]

[Preconditioning]
  [./SMP]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = Transient
  scheme = bdf2
  solve_type = 'PJFNK'

  line_search = basic

  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_ksp_type -sub_pc_type -pc_asm_overlap'
  petsc_options_value = 'asm         31   preonly   lu      1'

  l_max_its = 30
  nl_max_its = 12

  l_tol = 1.0e-4

  nl_rel_tol = 1.0e-8
  nl_abs_tol = 1.0e-10

  start_time = 0.0
  num_steps = 2
[]

[Outputs]
  exodus = true
[]

(modules/navier_stokes/test/tests/finite_element/ins/mms/supg/supg_pspg_adv_dominated_mms.i)

mu=1.5e-4
rho=2.5

[GlobalParams]
  gravity = '0 0 0'
  supg = true
  pspg = true
  convective_term = true
  integrate_p_by_parts = false
  transient_term = true
  laplace = true
  u = vel_x
  v = vel_y
  pressure = p
  alpha = 1e0
  order = FIRST
  family = LAGRANGE
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 1.0
    ymin = 0
    ymax = 1.0
    elem_type = QUAD9
    nx = 4
    ny = 4
  []
  [./corner_node]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node'
    nodes = '0'
    input = gen
  [../]
[]

[Variables]
  [./vel_x]
  [../]

  [./vel_y]
  [../]

  [./p]
    order = FIRST
  [../]
[]

[Kernels]
  # mass
  [./mass]
    type = INSMass
    variable = p
    x_vel_forcing_func = vel_x_source_func
    y_vel_forcing_func = vel_y_source_func
  [../]

  [./x_time]
    type = INSMomentumTimeDerivative
    variable = vel_x
  [../]
  [./y_time]
    type = INSMomentumTimeDerivative
    variable = vel_y
  [../]

  # x-momentum, space
  [./x_momentum_space]
    type = INSMomentumLaplaceForm
    variable = vel_x
    component = 0
    forcing_func = vel_x_source_func
  [../]

  # y-momentum, space
  [./y_momentum_space]
    type = INSMomentumLaplaceForm
    variable = vel_y
    component = 1
    forcing_func = vel_y_source_func
  [../]

  [./p_source]
    type = BodyForce
    function = p_source_func
    variable = p
  [../]
[]

[BCs]
  [./vel_x]
    type = FunctionDirichletBC
    boundary = 'left right top bottom'
    function = vel_x_func
    variable = vel_x
  [../]
  [./vel_y]
    type = FunctionDirichletBC
    boundary = 'left right top bottom'
    function = vel_y_func
    variable = vel_y
  [../]
  [./p]
    type = FunctionDirichletBC
    boundary = 'left right top bottom'
    function = p_func
    variable = p
  [../]
[]

[Functions]
  [./vel_x_source_func]
    type = ParsedFunction
    expression = '-${mu}*(-0.028*pi^2*x^2*sin(0.2*pi*x*y) - 0.028*pi^2*y^2*sin(0.2*pi*x*y) - 0.1*pi^2*sin(0.5*pi*x) - 0.4*pi^2*sin(pi*y)) + ${rho}*(0.14*pi*x*cos(0.2*pi*x*y) + 0.4*pi*cos(pi*y))*(0.6*sin(0.8*pi*x) + 0.3*sin(0.3*pi*y) + 0.2*sin(0.3*pi*x*y) + 0.3) + ${rho}*(0.14*pi*y*cos(0.2*pi*x*y) + 0.2*pi*cos(0.5*pi*x))*(0.4*sin(0.5*pi*x) + 0.4*sin(pi*y) + 0.7*sin(0.2*pi*x*y) + 0.5) + 0.1*pi*y*cos(0.2*pi*x*y) + 0.25*pi*cos(0.5*pi*x)'
  [../]
  [./vel_y_source_func]
    type = ParsedFunction
    expression = '-${mu}*(-0.018*pi^2*x^2*sin(0.3*pi*x*y) - 0.018*pi^2*y^2*sin(0.3*pi*x*y) - 0.384*pi^2*sin(0.8*pi*x) - 0.027*pi^2*sin(0.3*pi*y)) + ${rho}*(0.06*pi*x*cos(0.3*pi*x*y) + 0.09*pi*cos(0.3*pi*y))*(0.6*sin(0.8*pi*x) + 0.3*sin(0.3*pi*y) + 0.2*sin(0.3*pi*x*y) + 0.3) + ${rho}*(0.06*pi*y*cos(0.3*pi*x*y) + 0.48*pi*cos(0.8*pi*x))*(0.4*sin(0.5*pi*x) + 0.4*sin(pi*y) + 0.7*sin(0.2*pi*x*y) + 0.5) + 0.1*pi*x*cos(0.2*pi*x*y) + 0.3*pi*cos(0.3*pi*y)'
  [../]
  [./p_source_func]
    type = ParsedFunction
    expression = '-0.06*pi*x*cos(0.3*pi*x*y) - 0.14*pi*y*cos(0.2*pi*x*y) - 0.2*pi*cos(0.5*pi*x) - 0.09*pi*cos(0.3*pi*y)'
  [../]
  [./vel_x_func]
    type = ParsedFunction
    expression = '0.4*sin(0.5*pi*x) + 0.4*sin(pi*y) + 0.7*sin(0.2*pi*x*y) + 0.5'
  [../]
  [./vel_y_func]
    type = ParsedFunction
    expression = '0.6*sin(0.8*pi*x) + 0.3*sin(0.3*pi*y) + 0.2*sin(0.3*pi*x*y) + 0.3'
  [../]
  [./p_func]
    type = ParsedFunction
    expression = '0.5*sin(0.5*pi*x) + 1.0*sin(0.3*pi*y) + 0.5*sin(0.2*pi*x*y) + 0.5'
  [../]
  [./vxx_func]
    type = ParsedFunction
    expression = '0.14*pi*y*cos(0.2*pi*x*y) + 0.2*pi*cos(0.5*pi*x)'
  [../]
[]

[Materials]
  [./const]
    type = GenericConstantMaterial
    block = 0
    prop_names = 'rho mu'
    prop_values = '${rho}  ${mu}'
  [../]
[]

[Preconditioning]
  [./SMP]
    type = SMP
    full = true
    solve_type = 'NEWTON'
  [../]
[]

[Executioner]
  petsc_options = '-snes_converged_reason -ksp_converged_reason -snes_view'
  petsc_options_iname = '-pc_type -pc_factor_shift_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu NONZERO superlu_dist'
  line_search = 'none'
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-12
  nl_max_its = 10
  l_tol = 1e-6
  l_max_its = 10
  # To run to steady-state, set num-steps to some large number (1000000 for example)
  type = Transient
  num_steps = 10
  steady_state_detection = true
  steady_state_tolerance = 1e-10
  [./TimeStepper]
    dt = .1
    type = IterationAdaptiveDT
    cutback_factor = 0.4
    growth_factor = 1.2
    optimal_iterations = 20
  [../]
[]

[Outputs]
  execute_on = 'final'
  [./exodus]
    type = Exodus
  [../]
  [./csv]
    type = CSV
  [../]
[]

[Postprocessors]
  [./L2vel_x]
    type = ElementL2Error
    variable = vel_x
    function = vel_x_func
    outputs = 'console'    execute_on = 'timestep_end'
  [../]
  [./L2vel_y]
    variable = vel_y
    function = vel_y_func
    type = ElementL2Error
    outputs = 'console'    execute_on = 'timestep_end'
  [../]
  [./L2p]
    variable = p
    function = p_func
    type = ElementL2Error
    outputs = 'console'    execute_on = 'timestep_end'
  [../]
  [./L2vxx]
    variable = vxx
    function = vxx_func
    type = ElementL2Error
    outputs = 'console'    execute_on = 'timestep_end'
  [../]
[]

[AuxVariables]
  [./vxx]
    family = MONOMIAL
    order = FIRST
  [../]
[]

[AuxKernels]
  [./vxx]
    type = VariableGradientComponent
    component = x
    variable = vxx
    gradient_variable = vel_x
  [../]
[]

(modules/solid_mechanics/test/tests/global_strain/global_strain_direction.i)

[Mesh]
  [generated_mesh]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 2
    ny = 2
    xmin = -0.5
    xmax = 0.5
    ymin = -0.5
    ymax = 0.5
  []
  [cnode]
    type = ExtraNodesetGenerator
    coord = '0 0'
    new_boundary = 100
    input = generated_mesh
  []
[]

[Variables]
  [./u_x]
  [../]
  [./u_y]
  [../]
  [./global_strain]
    order = THIRD
    family = SCALAR
  [../]
[]

[AuxVariables]
  [./disp_x]
  [../]
  [./disp_y]
  [../]
[]

[AuxKernels]
  [./disp_x]
    type = GlobalDisplacementAux
    variable = disp_x
    scalar_global_strain = global_strain
    global_strain_uo = global_strain_uo
    component = 0
  [../]
  [./disp_y]
    type = GlobalDisplacementAux
    variable = disp_y
    scalar_global_strain = global_strain
    global_strain_uo = global_strain_uo
    component = 1
  [../]
[]

[GlobalParams]
  displacements = 'u_x u_y'
  block = 0
[]

[Kernels]
  [SolidMechanics]
  [../]
[]

[ScalarKernels]
  [./global_strain]
    type = GlobalStrain
    variable = global_strain
    global_strain_uo = global_strain_uo
  [../]
[]

[BCs]
  [./Periodic]
    [./left-right]
      auto_direction = 'x'
      variable = 'u_x u_y'
    [../]
  [../]

  # fix center point location
  [./centerfix_x]
    type = DirichletBC
    boundary = 100
    variable = u_x
    value = 0
  [../]
  [./fix_y]
    type = DirichletBC
    boundary = bottom
    variable = u_y
    value = 0
  [../]
  [./appl_y]
    type = DirichletBC
    boundary = top
    variable = u_y
    value = -0.1
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeElasticityTensor
    block = 0
    C_ijkl = '1 1'
    fill_method = symmetric_isotropic
  [../]
  [./strain]
    type = ComputeSmallStrain
    global_strain = global_strain
  [../]
  [./global_strain]
    type = ComputeGlobalStrain
    scalar_global_strain = global_strain
    global_strain_uo = global_strain_uo
  [../]
  [./stress]
    type = ComputeLinearElasticStress
  [../]
[]

[UserObjects]
  [./global_strain_uo]
    type = GlobalStrainUserObject
    execute_on = 'Initial Linear Nonlinear'
  [../]
[]

[Preconditioning]
  [./SMP]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = Transient
  scheme = bdf2
  solve_type = 'PJFNK'
  line_search = basic
  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_ksp_type -sub_pc_type -pc_asm_overlap'
  petsc_options_value = 'asm         31   preonly   lu      1'

  l_max_its = 30
  nl_max_its = 12

  l_tol = 1.0e-4

  nl_rel_tol = 1.0e-8
  nl_abs_tol = 1.0e-10

  start_time = 0.0
  num_steps = 2
[]

[Outputs]
exodus = true
[]

(modules/xfem/test/tests/crack_tip_enrichment/edge_crack_2d.i)

[XFEM]
  qrule = volfrac
  output_cut_plane = true
  use_crack_tip_enrichment = true
  crack_front_definition = crack_tip
  enrichment_displacements = 'enrich1_x enrich2_x enrich3_x enrich4_x enrich1_y enrich2_y enrich3_y enrich4_y'
  displacements = 'disp_x disp_y'
  cut_off_boundary = all
  cut_off_radius = 0.2
[]

[UserObjects]
  [./line_seg_cut_uo]
    type = LineSegmentCutUserObject
    cut_data = '0.0 1.0 0.5 1.0'
    time_start_cut = 0.0
    time_end_cut = 0.0
  [../]
  [./crack_tip]
    type = CrackFrontDefinition
    crack_direction_method = CrackDirectionVector
    crack_front_points = '0.5 1.0 0'
    crack_direction_vector = '1 0 0'
    2d = true
    axis_2d = 2
  [../]
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 5
    ny = 9
    xmin = 0.0
    xmax = 1.0
    ymin = 0.0
    ymax = 2.0
    elem_type = QUAD4
  []
  [./all_node]
    type = BoundingBoxNodeSetGenerator
    new_boundary = 'all'
    top_right = '1 2 0'
    bottom_left = '0 0 0'
    input = gen
  [../]
  [./right_bottom_node]
    type = ExtraNodesetGenerator
    new_boundary = 'right_bottom_node'
    coord = '1.0 0.0'
    input = all_node
  [../]
  [./right_top_node]
    type = ExtraNodesetGenerator
    new_boundary = 'right_top_node'
    coord = '1.0 2.0'
    input = right_bottom_node
  [../]
[]

[Variables]
  [./disp_x]
    order = FIRST
    family = LAGRANGE
  [../]
  [./disp_y]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
 [./saved_x]
  [../]
  [./saved_y]
  [../]
  [./stress_xx]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./stress_yy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./stress_xy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./vonmises]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[Kernels]
  [./TensorMechanics]
    displacements = 'disp_x disp_y'
  [../]
[]

[AuxKernels]
  [./stress_xx]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_xx
    index_i = 0
    index_j = 0
    execute_on = timestep_end
  [../]
  [./stress_yy]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_yy
    index_i = 1
    index_j = 1
    execute_on = timestep_end
  [../]
  [./stress_xy]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_xy
    index_i = 0
    index_j = 1
    execute_on = timestep_end
  [../]
  [./vonmises]
    type = RankTwoScalarAux
    rank_two_tensor = stress
    variable = vonmises
    scalar_type = vonmisesStress
    execute_on = timestep_end
  [../]
[]

[BCs]
  [./top_y]
    type = Pressure
    variable = disp_y
    boundary = top
    factor = -1
    displacements = 'disp_x disp_y'
  [../]
  [./bottom_y]
    type = Pressure
    variable = disp_y
    boundary = bottom
    factor = -1
    displacements = 'disp_x disp_y'
  [../]
  [./fix_y]
    type = DirichletBC
    boundary = right_bottom_node
    variable = disp_y
    value = 0.0
  [../]
  [./fix_x]
    type = DirichletBC
    boundary = right_bottom_node
    variable = disp_x
    value =  0.0
  [../]
  [./fix_x2]
    type = DirichletBC
    boundary = right_top_node
    variable = disp_x
    value =  0.0
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 1e6
    poissons_ratio = 0.3
  [../]
  [./strain]
    type = ComputeCrackTipEnrichmentSmallStrain
    displacements = 'disp_x disp_y'
    crack_front_definition = crack_tip
    enrichment_displacements = 'enrich1_x enrich2_x enrich3_x enrich4_x enrich1_y enrich2_y enrich3_y enrich4_y'
  [../]
  [./stress]
    type = ComputeLinearElasticStress
  [../]
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu     superlu_dist'

  line_search = 'none'

  # Since we do not sub-triangularize the tip element,
  # we need to use higher order quadrature rule to improve
  # integration accuracy.
  # Here second = SECOND is for regression test only.
  # However, order = SIXTH is recommended.
  [./Quadrature]
    type = GAUSS
    order = SECOND
  [../]

  [./Predictor]
    type = SimplePredictor
    scale = 1.0
  [../]

  # controls for linear iterations
  l_max_its = 10
  l_tol = 1e-4

  # controls for nonlinear iterations
  nl_max_its = 100
  nl_rel_tol = 1e-12 #11
  nl_abs_tol = 1e-12 #12

  # time control
  start_time = 0.0
  dt = 1.0
  end_time = 1.0
  dtmin = 1.0
[]

[Preconditioning]
  [./smp]
    type = SMP
    full = true
  [../]
[]


[Outputs]
  file_base = edge_crack_2d_out
  exodus = true
  [./console]
    type = Console
    output_linear = true
  [../]
[]

(modules/contact/test/tests/cohesive_zone_model/bilinear_mixed.i)

[Mesh]
  [msh]
    type = GeneratedMeshGenerator
    dim = 2
    xmax = 1
    ymax = 2
    nx = 1
    ny = 2
  []
  [block1]
    type = SubdomainBoundingBoxGenerator
    input = 'msh'
    bottom_left = '0 0 0'
    top_right = '1 1 0'
    block_id = 1
    block_name = 'block1'
  []
  [block2]
    type = SubdomainBoundingBoxGenerator
    input = 'block1'
    bottom_left = '0 1 0'
    top_right = '1 2 0'
    block_id = 2
    block_name = 'block2'
  []
  [split]
    type = BreakMeshByBlockGenerator
    input = block2
  []
  [top_node]
    type = ExtraNodesetGenerator
    coord = '0 2 0'
    input = split
    new_boundary = top_node
  []
  [bottom_node]
    type = ExtraNodesetGenerator
    coord = '0 0 0'
    input = top_node
    new_boundary = bottom_node
  []
[]

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Physics]
  [SolidMechanics]
    [QuasiStatic]
      generate_output = 'stress_yy stress_xy strain_xy'
      [all]
        strain = FINITE
        add_variables = true
        use_automatic_differentiation = true
        decomposition_method = TaylorExpansion
      []
    []
  []
[]

[BCs]
  [fix_x]
    type = DirichletBC
    preset = true
    value = 0.0
    boundary = bottom_node
    variable = disp_x
  []
  [fix_top]
    type = DirichletBC
    preset = true
    boundary = top
    variable = disp_x
    value = 0
  []
  [top]
    type = FunctionDirichletBC
    boundary = top
    variable = disp_y
    function = 'if(t<=0.3,t,if(t<=0.6,0.3-(t-0.3),0.6-t))'
    preset = true
  []
  [bottom]
    type = DirichletBC
    boundary = bottom
    variable = disp_y
    value = 0
    preset = true
  []
[]

[Modules/TensorMechanics/CohesiveZoneMaster]
  [czm_ik]
    boundary = 'interface'
  []
[]

[Materials]
  [stress]
    type = ADComputeFiniteStrainElasticStress
  []
  [elasticity_tensor]
    type = ADComputeElasticityTensor
    fill_method = symmetric9
    C_ijkl = '1.684e5 0.176e5 0.176e5 1.684e5 0.176e5 1.684e5 0.754e5 0.754e5 0.754e5'
  []
  [czm]
    type = BiLinearMixedModeTraction
    boundary = 'interface'
    penalty_stiffness = 1e6
    GI_c = 1e3
    GII_c = 1e2
    normal_strength = 1e4
    shear_strength = 1e3
    displacements = 'disp_x disp_y'
    eta = 2.2
    viscosity = 1e-3
  []
[]

[Postprocessors]
  [stress_yy]
    type = ElementExtremeValue
    variable = stress_yy
    value_type = max
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient

  solve_type = 'NEWTON'
  line_search = none

  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'

  automatic_scaling = true

  l_max_its = 2
  l_tol = 1e-14
  nl_max_its = 30
  nl_rel_tol = 1e-50
  nl_abs_tol = 1e-15
  start_time = 0.0
  dt = 0.01
  end_time = 0.85
  dtmin = 0.01
[]

[Outputs]
  exodus = true
  csv = true
[]

(modules/solid_mechanics/test/tests/shell/static/plate_bending2.i)

# Shell element verification test from Abaqus verification manual 1.3.13

# A 40 m x 20 m x 1 m plate that has E = 1000 Pa and Poisson's ratio = 0.3
# is subjected to the following boundary/loading conditions. A single shell
# element is used to model the plate.

# disp_z = 0 at vertices A (0, 0), B (40, 0) and D (20, 0).
# disp_x and disp_y are zero at all four vertices.

# F_z = -2.0 N at vertex C (40, 20).
# M_x = 20.0 Nm at vertices A and B (bottom boundary)
# M_x = -20.0 Nm at vertices C and D (top boundary)
# M_y = 10.0 Nm at vertices B and C (right boundary)
# M_y = -10.0 Nm at vertices A and D (left boundary)

# The disp_z at vertex C is -12.54 m using S4 elements in Abaqus.
# The solution obtained using Moose is -12.519 m with a relative error
# of 0.16%.

[Mesh]
  [./gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 1
    ny = 1
    xmin = 0.0
    xmax = 40.0
    ymin = 0.0
    ymax = 20.0
  [../]

  [./c_node]
    type = ExtraNodesetGenerator
    input = gmg
    new_boundary = 100
    coord = '40.0 20.0'
  [../]
[]

[Variables]
  [./disp_x]
    order = FIRST
    family = LAGRANGE
  [../]
  [./disp_y]
    order = FIRST
    family = LAGRANGE
  [../]
  [./disp_z]
    order = FIRST
    family = LAGRANGE
  [../]
  [./rot_x]
    order = FIRST
    family = LAGRANGE
  [../]
  [./rot_y]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[BCs]
  [./simply_support_x]
    type = DirichletBC
    variable = disp_x
    boundary = 'right top bottom left'
    value = 0.0
  [../]
  [./simply_support_y]
    type = DirichletBC
    variable = disp_y
    boundary = 'right top bottom left'
    value = 0.0
  [../]
  [./simply_support_z]
    type = DirichletBC
    variable = disp_z
    boundary = 'bottom left'
    value = 0.0
  [../]
[]

[NodalKernels]
  [./force_C]
    type = ConstantRate
    variable = disp_z
    boundary = 100
    rate = -2.0
  [../]
  [./Mx_AB]
    type = ConstantRate
    variable = rot_x
    boundary = bottom
    rate = 20.0
  [../]
  [./Mx_CD]
    type = ConstantRate
    variable = rot_x
    boundary = top
    rate = -20.0
  [../]
  [./My_BC]
    type = ConstantRate
    variable = rot_y
    boundary = right
    rate = 10.0
  [../]
  [./My_AD]
    type = ConstantRate
    variable = rot_y
    boundary = left
    rate = -10.0
  [../]
[]

[Preconditioning]
  [./smp]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  line_search = 'none'
  #nl_max_its = 2
  nl_rel_tol = 1e-10
  nl_abs_tol = 6e-6

  dt = 1.0
  dtmin = 1.0
  end_time = 3
[]

[Kernels]
  [./solid_disp_x]
    type = ADStressDivergenceShell
    block = '0'
    component = 0
    variable = disp_x
    through_thickness_order = SECOND
  [../]
  [./solid_disp_y]
    type = ADStressDivergenceShell
    block = '0'
    component = 1
    variable = disp_y
    through_thickness_order = SECOND
  [../]
  [./solid_disp_z]
    type = ADStressDivergenceShell
    block = '0'
    component = 2
    variable = disp_z
    through_thickness_order = SECOND
  [../]
  [./solid_rot_x]
    type = ADStressDivergenceShell
    block = '0'
    component = 3
    variable = rot_x
    through_thickness_order = SECOND
  [../]
  [./solid_rot_y]
    type = ADStressDivergenceShell
    block = '0'
    component = 4
    variable = rot_y
    through_thickness_order = SECOND
  [../]
[]

[Materials]
  [./elasticity]
    type = ADComputeIsotropicElasticityTensorShell
    youngs_modulus = 1e3
    poissons_ratio = 0.3
    block = 0
    through_thickness_order = SECOND
  [../]
  [./strain]
    type = ADComputeIncrementalShellStrain
    block = '0'
    displacements = 'disp_x disp_y disp_z'
    rotations = 'rot_x rot_y'
    thickness = 1.0
    through_thickness_order = SECOND
  [../]
  [./stress]
    type = ADComputeShellStress
    block = 0
    through_thickness_order = SECOND
  [../]
[]

[Postprocessors]
  [./disp_z2]
    type = PointValue
    point = '40.0 20.0 0.0'
    variable = disp_z
  [../]
[]

[Outputs]
  exodus = true
[]

(modules/xfem/test/tests/mesh_cut_2D_fracture/inclined_center_crack.i)

# Center inclined crack. To run convergence study, run angles for theta=0-90 and refinement mesh_h=201,401,801
#
# @article{moes1999finite,
#   title={A finite element method for crack growth without remeshing},
#   author={Mo{\"e}s, Nicolas and Dolbow, John and Belytschko, Ted},
#   journal={International journal for numerical methods in engineering},
#   volume={46},
#   number={1},
#   pages={131--150},
#   year={1999},
#   publisher={Wiley Online Library}
# }
# @article{richardson2011xfem,
#   title={An XFEM method for modeling geometrically elaborate crack propagation in brittle materials},
#   author={Richardson, Casey L and Hegemann, Jan and Sifakis, Eftychios and Hellrung, Jeffrey and Teran, Joseph M},
#   journal={International Journal for Numerical Methods in Engineering},
#   volume={88},
#   number={10},
#   pages={1042--1065},
#   year={2011},
#   publisher={Wiley Online Library}
# }
H = 40
W = 40
a = 1
theta = 20  #measured from x-axis
poissons = 0.3
youngs = 30e6
stress_load = 10000
mesh_h=201

[GlobalParams]
  displacements = 'disp_x disp_y'
  volumetric_locking_correction = true
[]


[Mesh]
  [cutter_mesh]
    type = PolyLineMeshGenerator
    points = '-${fparse a*cos(theta*pi/180)} -${fparse a*sin(theta*pi/180)} 0
              ${fparse a*cos(theta*pi/180)} ${fparse a*sin(theta*pi/180)} 0'
    loop = false
    num_edges_between_points = 2
    save_with_name = cut_mesh
  []
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = ${mesh_h}
    ny = ${mesh_h}
    xmin = -${fparse W/2}
    xmax = ${fparse W/2}
    ymin = -${fparse H/2}
    ymax = ${fparse H/2}
    elem_type = QUAD4
  []
  [center_block]
    type = SubdomainBoundingBoxGenerator
    input = gen
    block_id = 10
    bottom_left = '-${fparse 1.5*a} -${fparse 1.5*a} 0'
    top_right = '${fparse 1.5*a} ${fparse 1.5*a} 0'
  []
  [center_left_node]
    type = ExtraNodesetGenerator
    coord = '-${fparse W/2} 0 0'
    input = gen
    new_boundary = 'center_left_node'
    use_closest_node = true
  []
  [center_right_node]
    type = ExtraNodesetGenerator
    coord = '${fparse W/2} 0 0'
    input = center_left_node
    new_boundary = 'center_right_node'
    use_closest_node = true
  []
  final_generator = 'center_right_node'
[]

#### - adaptivity causes segfault, see #31714
# [AuxVariables]
#   [constant_refine]
#     initial_condition = 2
#     order = CONSTANT
#     family = MONOMIAL
#     block = 10
#   []
# []
# [Adaptivity]
#   initial_marker = constant_refine
#   max_h_level = 2
#   initial_steps = 2
# []

[XFEM]
  geometric_cut_userobjects = 'cut_mesh'
  qrule = volfrac
  output_cut_plane = true
[]

[UserObjects]
  [cut_mesh]
    type = MeshCut2DFractureUserObject
    mesh_generator_name = 'cut_mesh'
    growth_increment = 0.05
    ki_vectorpostprocessor = "II_KI_1"
    kii_vectorpostprocessor = "II_KII_1"
    k_critical = 1000 # big, don't want to grow
  []
[]

[DomainIntegral]
  integrals = 'Jintegral InteractionIntegralKI InteractionIntegralKII'
  displacements = 'disp_x disp_y'
  crack_front_points_provider = cut_mesh
  2d = true
  number_points_from_provider = 2
  crack_direction_method = CurvedCrackFront
  radius_inner = '0.2'
  radius_outer = '0.8'
  poissons_ratio = ${poissons}
  youngs_modulus = ${youngs}
  block = 0
  incremental = false
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = SMALL
    incremental = false
    planar_formulation = plane_strain
    generate_output = 'stress_xx stress_yy stress_zz vonmises_stress max_principal_stress'
    add_variables = true
  []
[]

[Postprocessors]
  [theta]
    type = ConstantPostprocessor
    value = ${theta}
  []
  [stress_load]
    type = ConstantPostprocessor
    value = ${stress_load}
  []
  [ki_analytic]
    type = ParsedPostprocessor
    expression = '(${fparse stress_load*sqrt(pi*a)*cos(theta*pi/180)*cos(theta*pi/180)})'
  []
  [kii_analytic]
    type = ParsedPostprocessor
    expression = '(${fparse stress_load*sqrt(pi*a)*cos(theta*pi/180)*sin(theta*pi/180)})'
  []
[]

[BCs]
  [left_x]
    type = DirichletBC
    boundary = 'center_left_node'
    variable = disp_x
    value = 0
  []
  [left_y]
    type = DirichletBC
    boundary = 'center_left_node'
    variable = disp_y
    value = 0
  []
  [right_y]
    type = DirichletBC
    boundary = 'center_right_node'
    variable = disp_y
    value = 0
  []
  [bottom_load]
    type = NeumannBC
    boundary = 'bottom'
    variable = disp_y
    value = -${stress_load}
  []
  [top_load]
    type = NeumannBC
    boundary = 'top'
    variable = disp_y
    value = ${stress_load}
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = ${youngs}
    poissons_ratio = ${poissons}
  []
  [stress]
    type = ComputeLinearElasticStress
  []
[]

[Executioner]
  type = Transient
  solve_type = 'NEWTON'
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -pc_factor_shift_type -pc_factor_shift_amount'
  petsc_options_value = ' lu       superlu_dist                 NONZERO               1e-20'
  line_search = 'none'
  nl_abs_tol = 1e-7
  start_time = 0.0
  dt = 1.0
  end_time = 1
  max_xfem_update = 0
[]

[Outputs]
  csv = true
  # uncomment for convergence study
  # file_base = inclined_crack/results_theta_${theta}_h_${mesh_h}
[]

(modules/navier_stokes/test/tests/finite_element/ins/block-restriction/one-mat-two-eqn-sets.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 2
    ymin = 0
    ymax = 1
    nx = 16
    ny = 8
    elem_type = QUAD9
  []
  [./corner_node_0]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node_0'
    coord = '0 0 0'
    input = gen
  [../]
  [./corner_node_1]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node_1'
    coord = '1 0 0'
    input = corner_node_0
  [../]
  [./subdomain1]
    input = corner_node_1
    type = SubdomainBoundingBoxGenerator
    bottom_left = '1 0 0'
    top_right = '2 1 0'
    block_id = 1
  [../]
  [./break_boundary]
    input = subdomain1
    type = BreakBoundaryOnSubdomainGenerator
  [../]
  [./interface0]
    type = SideSetsBetweenSubdomainsGenerator
    input = break_boundary
    primary_block = '0'
    paired_block = '1'
    new_boundary = 'interface0'
  [../]
  [./interface1]
    type = SideSetsBetweenSubdomainsGenerator
    input = interface0
    primary_block = '1'
    paired_block = '0'
    new_boundary = 'interface1'
  [../]
[]

[Variables]
  [velocity0]
    order = SECOND
    family = LAGRANGE_VEC
  []
  [T0]
    order = SECOND
    [InitialCondition]
      type = ConstantIC
      value = 1.0
    []
  []
  [p0]
  []
[]

[Kernels]
  [./mass0]
    type = INSADMass
    variable = p0
    block = 0
  [../]
  [./momentum_time0]
    type = INSADMomentumTimeDerivative
    variable = velocity0
    block = 0
  [../]
  [./momentum_convection0]
    type = INSADMomentumAdvection
    variable = velocity0
    block = 0
  [../]
  [./momentum_viscous0]
    type = INSADMomentumViscous
    variable = velocity0
    block = 0
  [../]
  [./momentum_pressure0]
    type = INSADMomentumPressure
    variable = velocity0
    pressure = p0
    integrate_p_by_parts = true
    block = 0
  [../]
  [./temperature_time0]
    type = INSADHeatConductionTimeDerivative
    variable = T0
    block = 0
  [../]
  [./temperature_advection0]
    type = INSADEnergyAdvection
    variable = T0
    block = 0
  [../]
  [./temperature_conduction0]
    type = ADHeatConduction
    variable = T0
    thermal_conductivity = 'k'
    block = 0
  [../]

  [./mass1]
    type = INSADMass
    variable = p0
    block = 1
  [../]
  [./momentum_time1]
    type = INSADMomentumTimeDerivative
    variable = velocity0
    block = 1
  [../]
  [./momentum_convection1]
    type = INSADMomentumAdvection
    variable = velocity0
    block = 1
  [../]
  [./momentum_viscous1]
    type = INSADMomentumViscous
    variable = velocity0
    block = 1
  [../]
  [./momentum_pressure1]
    type = INSADMomentumPressure
    variable = velocity0
    pressure = p0
    integrate_p_by_parts = true
    block = 1
  [../]
  [./temperature_time1]
    type = INSADHeatConductionTimeDerivative
    variable = T0
    block = 1
  [../]
  [./temperature_advection1]
    type = INSADEnergyAdvection
    variable = T0
    block = 1
  [../]
  [./temperature_conduction1]
    type = ADHeatConduction
    variable = T0
    thermal_conductivity = 'k'
    block = 1
  [../]
[]

[BCs]
  [./no_slip0]
    type = VectorFunctionDirichletBC
    variable = velocity0
    boundary = 'bottom_to_0 interface0 left'
  [../]
  [./lid0]
    type = VectorFunctionDirichletBC
    variable = velocity0
    boundary = 'top_to_0'
    function_x = 'lid_function0'
  [../]
  [./T_hot0]
    type = DirichletBC
    variable = T0
    boundary = 'bottom_to_0'
    value = 1
  [../]
  [./T_cold0]
    type = DirichletBC
    variable = T0
    boundary = 'top_to_0'
    value = 0
  [../]
  [./pressure_pin0]
    type = DirichletBC
    variable = p0
    boundary = 'pinned_node_0'
    value = 0
  [../]

  [./no_slip1]
    type = VectorFunctionDirichletBC
    variable = velocity0
    boundary = 'bottom_to_1 interface1 right'
  [../]
  [./lid1]
    type = VectorFunctionDirichletBC
    variable = velocity0
    boundary = 'top_to_1'
    function_x = 'lid_function1'
  [../]
  [./T_hot1]
    type = DirichletBC
    variable = T0
    boundary = 'bottom_to_1'
    value = 1
  [../]
  [./T_cold1]
    type = DirichletBC
    variable = T0
    boundary = 'top_to_1'
    value = 0
  [../]
[]

[Materials]
  [./const]
    type = ADGenericConstantMaterial
    prop_names = 'rho mu cp k'
    prop_values = '1  1  1  .01'
  [../]
  [ins_mat0]
    type = INSAD3Eqn
    velocity = velocity0
    pressure = p0
    temperature = T0
    block = '0 1'
  []
[]

[Functions]
    # We pick a function that is exactly represented in the velocity
    # space so that the Dirichlet conditions are the same regardless
    # of the mesh spacing.
  [./lid_function0]
    type = ParsedFunction
    expression = '4*x*(1-x)'
  [../]
  [./lid_function1]
    type = ParsedFunction
    expression = '4*(x-1)*(2-x)'
  [../]
[]

[Preconditioning]
  [./SMP]
    type = SMP
    full = true
    solve_type = 'NEWTON'
  [../]
[]

[Executioner]
  type = Transient
  # Run for 100+ timesteps to reach steady state.
  num_steps = 5
  dt = .5
  dtmin = .5
  petsc_options_iname = '-pc_type -pc_asm_overlap -sub_pc_type -sub_pc_factor_levels -sub_pc_factor_shift_type'
  petsc_options_value = 'asm      2               ilu          4                     NONZERO'
  line_search = 'none'
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-13
  nl_max_its = 6
  l_tol = 1e-6
  l_max_its = 500
[]

[Outputs]
  exodus = true
[]

(modules/solid_mechanics/test/tests/global_strain/global_strain_disp.i)

[Mesh]
  [generated_mesh]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 2
    ny = 2
    nz = 2
    xmin = -0.5
    xmax = 0.5
    ymin = -0.5
    ymax = 0.5
    zmin = -0.5
    zmax = 0.5
  []
  [cnode]
    type = ExtraNodesetGenerator
    coord = '0 -0.5 0'
    new_boundary = 100
    input = generated_mesh
  []
[]

[Variables]
  [./u_x]
  [../]
  [./u_y]
  [../]
  [./u_z]
  [../]
  [./global_strain]
    order = SIXTH
    family = SCALAR
  [../]
[]

[AuxVariables]
  [./disp_x]
  [../]
  [./disp_y]
  [../]
  [./disp_z]
  [../]
  [./s00]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./s11]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./e00]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./e11]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[AuxKernels]
  [./disp_x]
    type = GlobalDisplacementAux
    variable = disp_x
    scalar_global_strain = global_strain
    global_strain_uo = global_strain_uo
    component = 0
  [../]
  [./disp_y]
    type = GlobalDisplacementAux
    variable = disp_y
    scalar_global_strain = global_strain
    global_strain_uo = global_strain_uo
    component = 1
  [../]
  [./disp_z]
    type = GlobalDisplacementAux
    variable = disp_z
    scalar_global_strain = global_strain
    global_strain_uo = global_strain_uo
    component = 2
  [../]
  [./s00]
    type = RankTwoAux
    variable = s00
    rank_two_tensor = stress
    index_i = 0
    index_j = 0
  [../]
  [./s11]
    type = RankTwoAux
    variable = s11
    rank_two_tensor = stress
    index_i = 1
    index_j = 1
  [../]
  [./e00]
    type = RankTwoAux
    variable = e00
    rank_two_tensor = total_strain
    index_i = 0
    index_j = 0
  [../]
  [./e11]
    type = RankTwoAux
    variable = e11
    rank_two_tensor = total_strain
    index_i = 1
    index_j = 1
  [../]
[]

[GlobalParams]
  displacements = 'u_x u_y u_z'
  block = 0
[]

[Kernels]
  [SolidMechanics]
  [../]
[]

[ScalarKernels]
  [./global_strain]
    type = GlobalStrain
    variable = global_strain
    global_strain_uo = global_strain_uo
  [../]
[]

[BCs]
  [./Periodic]
    [./all]
      auto_direction = 'z'
      variable = 'u_x u_y u_z'
    [../]
  [../]

  # fix center point location
  [./centerfix_x]
    type = DirichletBC
    boundary = 100
    variable = u_x
    value = 0
  [../]
  [./fix_y]
    type = DirichletBC
    boundary = bottom
    variable = u_y
    value = 0
  [../]
  [./centerfix_z]
    type = DirichletBC
    boundary = 100
    variable = u_z
    value = 0
  [../]
  [./appl_y]
    type = DirichletBC
    boundary = top
    variable = u_y
    value = 0.033
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeElasticityTensor
    block = 0
    C_ijkl = '7 0.33'
    fill_method = symmetric_isotropic_E_nu
  [../]
  [./strain]
    type = ComputeSmallStrain
    global_strain = global_strain
  [../]
  [./global_strain]
    type = ComputeGlobalStrain
    scalar_global_strain = global_strain
    global_strain_uo = global_strain_uo
  [../]
  [./stress]
    type = ComputeLinearElasticStress
  [../]
[]

[UserObjects]
  [./global_strain_uo]
    type = GlobalStrainUserObject
    execute_on = 'Initial Linear Nonlinear'
  [../]
[]

[Preconditioning]
  [./SMP]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = Transient
  scheme = bdf2
  solve_type = 'PJFNK'

  line_search = basic

  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_ksp_type -sub_pc_type -pc_asm_overlap'
  petsc_options_value = 'asm         31   preonly   lu      1'

  l_max_its = 30
  nl_max_its = 12

  l_tol = 1.0e-4

  nl_rel_tol = 1.0e-6
  nl_abs_tol = 1.0e-10

  start_time = 0.0
  num_steps = 2
[]

[Outputs]
  exodus = true
[]

(modules/porous_flow/examples/tidal/atm_tides_open_hole.i)

# A 100m x 10m "slab" of height 100m is subjected to cyclic pressure at its top
# Assumptions:
# the boundaries are impermeable, except the top boundary
# only vertical displacement is allowed
# the atmospheric pressure sets the total stress at the top of the model
# at the slab left-hand side there is a borehole that taps into the base of the slab.
[Mesh]
  [the_mesh]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 10
    ny = 1
    nz = 10
    xmin = 0
    xmax = 100
    ymin = -5
    ymax = 5
    zmin = -100
    zmax = 0
  []
  [bh_back]
    type = ExtraNodesetGenerator
    coord = '0 -5 -100'
    input = the_mesh
    new_boundary = 11
  []
[]

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  PorousFlowDictator = dictator
  block = 0
  biot_coefficient = 0.6
  multiply_by_density = false
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [disp_z]
  []
  [porepressure]
    scaling = 1E11
  []
[]

[ICs]
  [porepressure]
    type = FunctionIC
    variable = porepressure
    function = '-10000*z'  # this is only approximately correct
  []
[]

[Functions]
  [ini_stress_zz]
    type = ParsedFunction
    expression = '(25000 - 0.6*10000)*z' # remember this is effective stress
  []
  [cyclic_porepressure]
    type = ParsedFunction
    expression = 'if(t>0,5000 * sin(2 * pi * t / 3600.0 / 24.0),0)'
  []
  [cyclic_porepressure_at_depth]
    type = ParsedFunction
    expression = '-10000*z + if(t>0,5000 * sin(2 * pi * t / 3600.0 / 24.0),0)'
  []
  [neg_cyclic_porepressure]
    type = ParsedFunction
    expression = '-if(t>0,5000 * sin(2 * pi * t / 3600.0 / 24.0),0)'
  []
[]

[BCs]
  # zmin is called 'back'
  # zmax is called 'front'
  # ymin is called 'bottom'
  # ymax is called 'top'
  # xmin is called 'left'
  # xmax is called 'right'
  [no_x_disp]
    type = DirichletBC
    variable = disp_x
    value = 0
    boundary = 'bottom top' # because of 1-element meshing, this fixes u_x=0 everywhere
  []
  [no_y_disp]
    type = DirichletBC
    variable = disp_y
    value = 0
    boundary = 'bottom top' # because of 1-element meshing, this fixes u_y=0 everywhere
  []
  [no_z_disp_at_bottom]
    type = DirichletBC
    variable = disp_z
    value = 0
    boundary = back
  []
  [pp]
    type = FunctionDirichletBC
    variable = porepressure
    function = cyclic_porepressure
    boundary = front
  []
  [pp_downhole]
    type = FunctionDirichletBC
    variable = porepressure
    function = cyclic_porepressure_at_depth
    boundary = 11
  []
  [total_stress_at_top]
    type = FunctionNeumannBC
    variable = disp_z
    function = neg_cyclic_porepressure
    boundary = front
  []
[]

[FluidProperties]
  [the_simple_fluid]
    type = SimpleFluidProperties
    thermal_expansion = 0.0
    bulk_modulus = 2E9
    viscosity = 1E-3
    density0 = 1000.0
  []
[]

[PorousFlowBasicTHM]
  coupling_type = HydroMechanical
  displacements = 'disp_x disp_y disp_z'
  porepressure = porepressure
  gravity = '0 0 -10'
  fp = the_simple_fluid
[]

[Materials]
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    bulk_modulus = 10.0E9 # drained bulk modulus
    poissons_ratio = 0.25
  []
  [strain]
    type = ComputeSmallStrain
    eigenstrain_names = ini_stress
  []
  [stress]
    type = ComputeLinearElasticStress
  []
  [ini_stress]
    type = ComputeEigenstrainFromInitialStress
    initial_stress = '0 0 0  0 0 0  0 0 ini_stress_zz'
    eigenstrain_name = ini_stress
  []
  [porosity]
    type = PorousFlowPorosityConst # only the initial value of this is ever used
    porosity = 0.1
  []
  [biot_modulus]
    type = PorousFlowConstantBiotModulus
    solid_bulk_compliance = 1E-10
    fluid_bulk_modulus = 2E9
  []
  [permeability]
    type = PorousFlowPermeabilityConst
    permeability = '1E-14 0 0   0 1E-14 0   0 0 1E-14'
  []
  [density]
    type = GenericConstantMaterial
    prop_names = density
    prop_values = 2500.0
  []
[]

[Postprocessors]
  [p0_0]
    type = PointValue
    outputs = csv
    point = '0 0 0'
    variable = porepressure
  []
  [p100_0]
    type = PointValue
    outputs = csv
    point = '100 0 0'
    variable = porepressure
  []
  [p0_100]
    type = PointValue
    outputs = csv
    point = '0 0 -100'
    variable = porepressure
  []
  [p100_100]
    type = PointValue
    outputs = csv
    point = '100 0 -100'
    variable = porepressure
  []
  [uz0]
    type = PointValue
    outputs = csv
    point = '0 0 0'
    variable = disp_z
  []
  [uz100]
    type = PointValue
    outputs = csv
    point = '100 0 0'
    variable = disp_z
  []
[]


[Preconditioning]
  [andy]
    type = SMP
    full = true
  []
[]

[Executioner]
  type = Transient
  solve_type = Newton
  start_time = -3600
  dt = 3600
  end_time = 172800
  nl_rel_tol = 1E-10
  nl_abs_tol = 1E-5
[]

[Outputs]
  print_linear_residuals = false
  csv = true
[]

(modules/navier_stokes/test/tests/finite_element/ins/lid_driven/ad_lid_driven_stabilized_with_temp_transient.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 1.0
    ymin = 0
    ymax = 1.0
    nx = 16
    ny = 16
  []
  [./corner_node]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node'
    nodes = '0'
    input = gen
  [../]
[]

[Variables]
  [./velocity]
    family = LAGRANGE_VEC
  [../]
  [./p]
  [../]
  [temperature]
    [InitialCondition]
      type = ConstantIC
      value = 1.0
    []
  []
[]

[ICs]
  [velocity]
    type = VectorConstantIC
    x_value = 1e-15
    y_value = 1e-15
    variable = velocity
  []
[]

[Kernels]
  [./mass]
    type = INSADMass
    variable = p
  [../]
  [./mass_pspg]
    type = INSADMassPSPG
    variable = p
  [../]

  [./momentum_time]
    type = INSADMomentumTimeDerivative
    variable = velocity
  [../]

  [./momentum_convection]
    type = INSADMomentumAdvection
    variable = velocity
  [../]

  [./momentum_viscous]
    type = INSADMomentumViscous
    variable = velocity
  [../]

  [./momentum_pressure]
    type = INSADMomentumPressure
    variable = velocity
    pressure = p
    integrate_p_by_parts = true
  [../]

  [./momentum_supg]
    type = INSADMomentumSUPG
    variable = velocity
    velocity = velocity
  [../]

 [./temperature_advection]
   type = INSADEnergyAdvection
   variable = temperature
 [../]

 [temperature_time]
   type = INSADHeatConductionTimeDerivative
   variable = temperature
 []

 [./temperature_conduction]
   type = ADHeatConduction
   variable = temperature
   thermal_conductivity = 'k'
 [../]

  [temperature_supg]
    type = INSADEnergySUPG
    variable = temperature
    velocity = velocity
  []
[]

[BCs]
  [./no_slip]
    type = VectorFunctionDirichletBC
    variable = velocity
    boundary = 'bottom right left'
  [../]

  [./lid]
    type = VectorFunctionDirichletBC
    variable = velocity
    boundary = 'top'
    function_x = 'lid_function'
  [../]

  [./pressure_pin]
    type = DirichletBC
    variable = p
    boundary = 'pinned_node'
    value = 0
  [../]

  [./temperature_hot]
    type = DirichletBC
    variable = temperature
    boundary = 'bottom'
    value = 1
  [../]

  [./temperature_cold]
    type = DirichletBC
    variable = temperature
    boundary = 'top'
    value = 0
  [../]
[]

[Materials]
  [./const]
    type = ADGenericConstantMaterial
    prop_names = 'rho mu cp k'
    prop_values = '1  1  1  .01'
  [../]
  [ins_mat]
    type = INSADStabilized3Eqn
    velocity = velocity
    pressure = p
    temperature = temperature
  []
[]

[Functions]
  [./lid_function]
    # We pick a function that is exactly represented in the velocity
    # space so that the Dirichlet conditions are the same regardless
    # of the mesh spacing.
    type = ParsedFunction
    expression = '4*x*(1-x)'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'NEWTON'
  # Run for 100+ timesteps to reach steady state.
  num_steps = 5
  dt = .5
  dtmin = .5
  petsc_options_iname = '-pc_type -sub_pc_factor_levels -ksp_gmres_restart'
  petsc_options_value = 'asm      6                     200'
  line_search = 'none'
  nl_rel_tol = 1e-12
  nl_abs_tol =  1e-12
  nl_max_its = 6
[]

[Outputs]
  exodus = true
[]

(test/tests/mortar/periodic_segmental_constraint/penalty_periodic_simple3d.i)

[Mesh]
  [left_block]
    type = GeneratedMeshGenerator
    dim = 3
    xmin = -3.0
    xmax = 3.0
    ymin = -3.0
    ymax = 3.0
    zmin = -3.0
    zmax = 3.0
    nx = 3
    ny = 3
    nz = 3
    elem_type = HEX8
  []
  [left_block_sidesets]
    type = RenameBoundaryGenerator
    input = left_block
    old_boundary = '0 1 2 3 4 5'
    new_boundary = '10 11 12 13 14 15'
  []
  [left_block_id]
    type = SubdomainIDGenerator
    input = left_block_sidesets
    subdomain_id = 1
  []
  [left]
    type = LowerDBlockFromSidesetGenerator
    input = left_block_id
    sidesets = '14'
    new_block_id = '10004'
    new_block_name = 'secondary_left'
  []
  [right]
    type = LowerDBlockFromSidesetGenerator
    input = left
    sidesets = '12'
    new_block_id = '10002'
    new_block_name = 'primary_right'
  []
  [bottom]
    type = LowerDBlockFromSidesetGenerator
    input = right
    sidesets = '10'
    new_block_id = '10000'
    new_block_name = 'secondary_bottom'
  []
  [top]
    type = LowerDBlockFromSidesetGenerator
    input = bottom
    sidesets = '15'
    new_block_id = '10005'
    new_block_name = 'primary_top'
  []
  [back]
    type = LowerDBlockFromSidesetGenerator
    input = top
    sidesets = '11'
    new_block_id = '10001'
    new_block_name = 'secondary_back'
  []
  [front]
    type = LowerDBlockFromSidesetGenerator
    input = back
    sidesets = '13'
    new_block_id = '10003'
    new_block_name = 'primary_front'
  []

  [corner_node]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node'
    nodes = '0'
    input = front
  []
[]

[Variables]
  [u]
    order = FIRST
    family = LAGRANGE
  []
  [epsilon]
    order = THIRD
    family = SCALAR
  []
[]

[AuxVariables]
  [sigma]
    order = THIRD
    family = SCALAR
  []
[]

[AuxScalarKernels]
  [sigma]
    type = FunctionScalarAux
    variable = sigma
    function = '1 2 3'
    execute_on = initial #timestep_end
  []
[]

[Kernels]
  [diff1]
    type = Diffusion
    variable = u
    block = 1
  []
[]

[Problem]
  kernel_coverage_check = false
  error_on_jacobian_nonzero_reallocation = true
[]

[BCs]
  [fix_right]
    type = DirichletBC
    variable = u
    boundary = pinned_node
    value = 0
  []
[]

[Constraints]
  [mortarlr]
    type = PenaltyEqualValueConstraint
    primary_boundary = '12'
    secondary_boundary = '14'
    primary_subdomain = 'primary_right'
    secondary_subdomain = 'secondary_left'
    secondary_variable = u
    correct_edge_dropping = true
    penalty_value = 1.e2
  []
  [periodiclr]
    type = PenaltyPeriodicSegmentalConstraint
    primary_boundary = '12'
    secondary_boundary = '14'
    primary_subdomain = 'primary_right'
    secondary_subdomain = 'secondary_left'
    secondary_variable = u
    epsilon = epsilon
    sigma = sigma
    correct_edge_dropping = true
    penalty_value = 1.e2
  []
  [mortarbt]
    type = PenaltyEqualValueConstraint
    primary_boundary = '15'
    secondary_boundary = '10'
    primary_subdomain = 'primary_top'
    secondary_subdomain = 'secondary_bottom'
    secondary_variable = u
    correct_edge_dropping = true
    penalty_value = 1.e2
  []
  [periodicbt]
    type = PenaltyPeriodicSegmentalConstraint
    primary_boundary = '15'
    secondary_boundary = '10'
    primary_subdomain = 'primary_top'
    secondary_subdomain = 'secondary_bottom'
    secondary_variable = u
    epsilon = epsilon
    sigma = sigma
    correct_edge_dropping = true
    penalty_value = 1.e2
  []
  [mortarbf]
    type = PenaltyEqualValueConstraint
    primary_boundary = '13'
    secondary_boundary = '11'
    primary_subdomain = 'primary_front'
    secondary_subdomain = 'secondary_back'
    secondary_variable = u
    correct_edge_dropping = true
    penalty_value = 1.e2
  []
  [periodicbf]
    type = PenaltyPeriodicSegmentalConstraint
    primary_boundary = '13'
    secondary_boundary = '11'
    primary_subdomain = 'primary_front'
    secondary_subdomain = 'secondary_back'
    secondary_variable = u
    epsilon = epsilon
    sigma = sigma
    correct_edge_dropping = true
    penalty_value = 1.e2
  []
[]

[Preconditioning]
  [smp]
    full = true
    type = SMP
  []
[]

[Executioner]
  type = Steady
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  solve_type = NEWTON
[]

[Outputs]
  csv = true
[]

(modules/solid_mechanics/test/tests/ad_anisotropic_creep/ad_aniso_iso_creep_x_3d.i)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 10
    ny = 2
    nz = 2
    xmin = 0.0
    ymin = 0.0
    zmin = 0.0

    xmax = 10.0
    ymax = 1.0
    zmax = 1.0
  []
  [corner_node]
    type = ExtraNodesetGenerator
    new_boundary = '100'
    nodes = '3 69'
    input = gen
  []
  [corner_node_2]
    type = ExtraNodesetGenerator
    new_boundary = '101'
    nodes = '4 47'
    input = corner_node
  []
[]

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  volumetric_locking_correction = true
[]

[AuxVariables]
  [hydrostatic_stress]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_xx]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_xy]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_zz]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_xz]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_yz]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [hydrostatic_stress]
    type = ADRankTwoScalarAux
    variable = hydrostatic_stress
    rank_two_tensor = stress
    scalar_type = Hydrostatic
  []
  [creep_strain_xx]
    type = ADRankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_xx
    index_i = 0
    index_j = 0
  []
  [creep_strain_xy]
    type = ADRankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_xy
    index_i = 0
    index_j = 1
  []
  [creep_strain_yy]
    type = ADRankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_yy
    index_i = 1
    index_j = 1
  []
  [creep_strain_zz]
    type = ADRankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_zz
    index_i = 2
    index_j = 2
  []
  [creep_strain_xz]
    type = ADRankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_xz
    index_i = 0
    index_j = 2
  []
  [creep_strain_yz]
    type = ADRankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_yz
    index_i = 1
    index_j = 2
  []
  [sigma_xx]
    type = ADRankTwoAux
    rank_two_tensor = stress
    variable = stress_xx
    index_i = 1
    index_j = 1
  []
[]

[Functions]
  [pull]
    type = PiecewiseLinear
    x = '0 1.0e-9 1.0'
    y = '0 -4e1 -4e1'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = FINITE
    generate_output = 'elastic_strain_xx stress_xx'
    use_automatic_differentiation = true
    add_variables = true
  []
[]

[Materials]
  [elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    youngs_modulus = 700
    poissons_ratio = 0.0
  []

  [elastic_strain]
    type = ADComputeMultipleInelasticStress
    # inelastic_models = 'trial_creep_iso'
    max_iterations = 50
  []

  [hill_tensor]
    type = ADHillConstants
    # F G H L M N
    hill_constants = "0.5 0.5 0.5 1.5 1.5 1.5"
  []

  [trial_creep_aniso_iso]
    type = ADHillCreepStressUpdate
    coefficient = 1e-16
    n_exponent = 9
    m_exponent = 0
    activation_energy = 0
    max_inelastic_increment = 0.00003
    relative_tolerance = 1e-20
    absolute_tolerance = 1e-20
    internal_solve_output_on = never
    # Force it to not use integration error
    max_integration_error = 1.0
  []

  [trial_creep_iso]
    type = ADPowerLawCreepStressUpdate
    coefficient = 1e-16
    n_exponent = 9
    m_exponent = 0
    activation_energy = 0
    # F G H L M N
    max_inelastic_increment = 0.00003
    relative_tolerance = 1e-16
    absolute_tolerance = 1e-16
    internal_solve_output_on = never
  []
[]

[BCs]
  [no_disp_x]
    type = ADDirichletBC
    variable = disp_x
    boundary = left
    value = 0.0
  []

  [no_disp_y]
    type = ADDirichletBC
    variable = disp_y
    boundary = 100
    value = 0.0
  []

  [no_disp_z]
    type = ADDirichletBC
    variable = disp_z
    boundary = 101
    value = 0.0
  []

  [Pressure]
    [Side1]
      boundary = right
      function = pull
    []
  []

[]

[Executioner]
  type = Transient

  solve_type = NEWTON
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu     superlu_dist'

  nl_rel_tol = 1e-13
  nl_abs_tol = 1.0e-14
  l_max_its = 90
  num_steps = 10
  dt = 5.0e-4
  start_time = 0
  automatic_scaling = true
[]

[Postprocessors]
  [matl_ts_min]
    type = MaterialTimeStepPostprocessor
  []
  [max_disp_x]
    type = ElementExtremeValue
    variable = disp_x
  []
  [max_disp_y]
    type = ElementExtremeValue
    variable = disp_y
  []
  [max_hydro]
    type = ElementAverageValue
    variable = hydrostatic_stress
  []
  [dt]
    type = TimestepSize
  []
  [num_lin]
    type = NumLinearIterations
    outputs = console
  []
  [num_nonlin]
    type = NumNonlinearIterations
    outputs = console
  []
  [creep_strain_xx]
    type = ElementalVariableValue
    variable = creep_strain_xx
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [creep_strain_yy]
    type = ElementalVariableValue
    variable = creep_strain_yy
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [creep_strain_zz]
    type = ElementalVariableValue
    variable = creep_strain_zz
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [creep_strain_xy]
    type = ElementalVariableValue
    variable = creep_strain_xy
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [creep_strain_yz]
    type = ElementalVariableValue
    variable = creep_strain_yz
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [creep_strain_xz]
    type = ElementalVariableValue
    variable = creep_strain_xz
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [elastic_strain_xx]
    type = ElementalVariableValue
    variable = elastic_strain_xx
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [sigma_xx]
    type = ElementalVariableValue
    variable = stress_xx
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
[]

[Outputs]
  csv = true
  exodus = true
  perf_graph = true
[]

(modules/combined/examples/optimization/2d_mbb_pde_amr.i)

vol_frac = 0.5
E0 = 1
Emin = 1e-8
power = 2
[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  [MeshGenerator]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 30
    ny = 10
    xmin = 0
    xmax = 30
    ymin = 0
    ymax = 10
  []
  [node]
    type = ExtraNodesetGenerator
    input = MeshGenerator
    new_boundary = pull
    nodes = 0
  []
  [push]
    type = ExtraNodesetGenerator
    input = node
    new_boundary = push
    coord = '30 10 0'
  []

[]

[Variables]
  [Dc]
    initial_condition = -1.0
  []
[]

[AuxVariables]
  [Emin]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = ${Emin}
  []
  [power]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = ${power}
  []
  [E0]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = ${E0}
  []
  [sensitivity]
    family = MONOMIAL
    order = FIRST
    initial_condition = -1.0
    [AuxKernel]
      type = MaterialRealAux
      variable = sensitivity
      property = sensitivity
      execute_on = LINEAR
    []
  []
  [mat_den]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = ${vol_frac}
  []
  [Dc_elem]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = -1.0
    [AuxKernel]
      type = SelfAux
      variable = Dc_elem
      v = Dc
      execute_on = 'TIMESTEP_END'
    []
  []
  [mat_den_nodal]
    family = L2_LAGRANGE
    order = FIRST
    initial_condition = ${vol_frac}
    [AuxKernel]
      type = SelfAux
      execute_on = TIMESTEP_END
      variable = mat_den_nodal
      v = mat_den
    []
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = SMALL
    add_variables = true
    incremental = false
  []
[]
[Kernels]
  [diffusion]
    type = FunctionDiffusion
    variable = Dc
    function = 0.15 # radius coeff
  []
  [potential]
    type = Reaction
    variable = Dc
  []
  [source]
    type = CoupledForce
    variable = Dc
    v = sensitivity
  []
[]
[BCs]
  [no_x]
    type = DirichletBC
    variable = disp_y
    boundary = pull
    value = 0.0
  []
  [no_y]
    type = DirichletBC
    variable = disp_x
    boundary = right
    value = 0.0
  []
  [boundary_penalty]
    type = ADRobinBC
    variable = Dc
    boundary = 'left top'
    coefficient = 10
  []
  [boundary_penalty_right]
    type = ADRobinBC
    variable = Dc
    boundary = 'right'
    coefficient = 10
  []
[]
[NodalKernels]
  [pull]
    type = NodalGravity
    variable = disp_y
    boundary = push
    gravity_value = -1
    mass = 1
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeVariableIsotropicElasticityTensor
    youngs_modulus = E_phys
    poissons_ratio = poissons_ratio
    args = 'Emin mat_den power E0'
  []
  [E_phys]
    type = DerivativeParsedMaterial
    # Emin + (density^penal) * (E0 - Emin)
    expression = '${Emin} + (mat_den ^ ${power}) * (${E0}-${Emin})'
    coupled_variables = 'mat_den'
    property_name = E_phys
  []
  [poissons_ratio]
    type = GenericConstantMaterial
    prop_names = poissons_ratio
    prop_values = 0.3
  []
  [stress]
    type = ComputeLinearElasticStress
  []
  [dc]
    type = ComplianceSensitivity
    design_density = mat_den
    youngs_modulus = E_phys
    incremental = false
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]
[UserObjects]
  [update]
    type = DensityUpdate
    density_sensitivity = Dc_elem
    design_density = mat_den
    volume_fraction = ${vol_frac}
    execute_on = TIMESTEP_BEGIN
    force_postaux = true
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'
  line_search = none
  nl_abs_tol = 1e-4
  l_max_its = 200
  start_time = 0.0
  dt = 1.0
  num_steps = 70
[]

[Outputs]
  [out]
    type = Exodus
    execute_on = 'INITIAL TIMESTEP_END'
  []
  print_linear_residuals = false
[]

[Postprocessors]
  [total_vol]
    type = ElementIntegralVariablePostprocessor
    variable = mat_den
    execute_on = 'INITIAL TIMESTEP_END'
  []
[]

[Controls]
  [first_period]
    type = TimePeriod
    start_time = 0.0
    end_time = 40
    enable_objects = 'BCs::boundary_penalty_right'
    execute_on = 'initial timestep_begin'
  []
[]

[Adaptivity]
  max_h_level = 2
  recompute_markers_during_cycles = true
  interval = 1
  cycles_per_step = 1
  marker = density_marker
  [Indicators]
    [density_jump]
      type = ValueJumpIndicator
      variable = mat_den_nodal
    []
  []
  [Markers]
    [density_marker]
      type = ErrorToleranceMarker
      indicator = density_jump
      coarsen = 0.1
      refine = 0.1
    []
  []
[]

(modules/navier_stokes/test/tests/finite_element/ins/velocity_channel/velocity_inletBC_no_parts.i)

# This input file tests outflow boundary conditions for the incompressible NS equations.

[GlobalParams]
  gravity = '0 0 0'
  integrate_p_by_parts = false
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    xmin = 0
    xmax = 3.0
    ymin = 0
    ymax = 1.0
    nx = 30
    ny = 10
    elem_type = QUAD9
  []
  [./corner_node]
    type = ExtraNodesetGenerator
    new_boundary = top_right
    coord = '3 1'
    input = gen
  [../]
[]


[Variables]
  [./vel_x]
    order = SECOND
    family = LAGRANGE
  [../]
  [./vel_y]
    order = SECOND
    family = LAGRANGE
  [../]
  [./p]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [./mass]
    type = INSMass
    variable = p
    u = vel_x
    v = vel_y
    pressure = p
  [../]
  [./x_momentum_space]
    type = INSMomentumLaplaceForm
    variable = vel_x
    u = vel_x
    v = vel_y
    pressure = p
    component = 0
  [../]
  [./y_momentum_space]
    type = INSMomentumLaplaceForm
    variable = vel_y
    u = vel_x
    v = vel_y
    pressure = p
    component = 1
  [../]
[]

[BCs]
  [./x_no_slip]
    type = DirichletBC
    variable = vel_x
    boundary = 'top bottom'
    value = 0.0
  [../]
  [./y_no_slip]
    type = DirichletBC
    variable = vel_y
    boundary = 'left top bottom'
    value = 0.0
  [../]
  [./x_inlet]
    type = FunctionDirichletBC
    variable = vel_x
    boundary = 'left'
    function = 'inlet_func'
  [../]
  [./p_corner]
    # Since the pressure is not integrated by parts in this example,
    # it is only specified up to a constant by the natural outflow BC.
    # Therefore, we need to pin its value at a single location.
    type = DirichletBC
    boundary = top_right
    value = 0
    variable = p
  [../]
[]

[Materials]
  [./const]
    type = GenericConstantMaterial
    block = 0
    prop_names = 'rho mu'
    prop_values = '1  1'
  [../]
[]

[Preconditioning]
  [./SMP_PJFNK]
    type = SMP
    full = true
    solve_type = NEWTON
  [../]
[]

[Executioner]
  type = Steady
  petsc_options_iname = '-ksp_gmres_restart -pc_type -sub_pc_type -sub_pc_factor_levels'
  petsc_options_value = '300                bjacobi  ilu          4'
  line_search = none
  nl_rel_tol = 1e-12
  nl_max_its = 6
  l_tol = 1e-6
  l_max_its = 300
[]

[Outputs]
  [./out]
    type = Exodus
  [../]
[]

[Functions]
  [./inlet_func]
    type = ParsedFunction
    expression = '-4 * (y - 0.5)^2 + 1'
  [../]
[]

(modules/combined/examples/mortar/eigenstrain.i)

#
# Eigenstrain with Mortar gradient periodicity
#

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 50
    ny = 50
    xmin = -0.5
    xmax = 0.5
    ymin = -0.5
    ymax = 0.5
  []
  [./cnode]
    input = gen
    type = ExtraNodesetGenerator
    coord = '0.0 0.0'
    new_boundary = 100
  [../]
  [./anode]
    input = cnode
    type = ExtraNodesetGenerator
    coord = '0.0 0.5'
    new_boundary = 101
  [../]
  [secondary_x]
    input = anode
    type = LowerDBlockFromSidesetGenerator
    sidesets = '3'
    new_block_id = 10
    new_block_name = "secondary_x"
  []
  [primary_x]
    input = secondary_x
    type = LowerDBlockFromSidesetGenerator
    sidesets = '1'
    new_block_id = 12
    new_block_name = "primary_x"
  []
  [secondary_y]
    input = primary_x
    type = LowerDBlockFromSidesetGenerator
    sidesets = '0'
    new_block_id = 11
    new_block_name = "secondary_y"
  []
  [primary_y]
    input = secondary_y
    type = LowerDBlockFromSidesetGenerator
    sidesets = '2'
    new_block_id = 13
    new_block_name = "primary_y"
  []
[]

[GlobalParams]
  derivative_order = 2
  enable_jit = true
  displacements = 'disp_x disp_y'
[]

# AuxVars to compute the free energy density for outputting
[AuxVariables]
  [./local_energy]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[AuxKernels]
  [./local_free_energy]
    type = TotalFreeEnergy
    block = 0
    execute_on = 'initial LINEAR'
    variable = local_energy
    interfacial_vars = 'c'
    kappa_names = 'kappa_c'
  [../]
[]

[Variables]
  # Solute concentration variable
  [./c]
    [./InitialCondition]
      type = RandomIC
      min = 0.49
      max = 0.51
    [../]
    block = 0
  [../]
  [./w]
    block = 0
  [../]

  # Mesh displacement
  [./disp_x]
    block = 0
  [../]
  [./disp_y]
    block = 0
  [../]

  # Lagrange multipliers for gradient component periodicity
  [./lm_left_right_xx]
    order = FIRST
    family = LAGRANGE
    block = secondary_x
  [../]
  [./lm_left_right_xy]
    order = FIRST
    family = LAGRANGE
    block = secondary_x
  [../]
  [./lm_left_right_yx]
    order = FIRST
    family = LAGRANGE
    block = secondary_x
  [../]
  [./lm_left_right_yy]
    order = FIRST
    family = LAGRANGE
    block = secondary_x
  [../]

  [./lm_up_down_xx]
    order = FIRST
    family = LAGRANGE
    block = secondary_y
  [../]
  [./lm_up_down_xy]
    order = FIRST
    family = LAGRANGE
    block = secondary_y
  [../]
  [./lm_up_down_yx]
    order = FIRST
    family = LAGRANGE
    block = secondary_y
  [../]
  [./lm_up_down_yy]
    order = FIRST
    family = LAGRANGE
    block = secondary_y
  [../]
[]

[Constraints]
  [./ud_disp_x_grad_x]
    type = EqualGradientConstraint
    variable = lm_up_down_xx
    component = 0
    secondary_variable = disp_x
    secondary_boundary = bottom
    primary_boundary = top
    secondary_subdomain = secondary_y
    primary_subdomain = primary_y
    periodic = true
  [../]
  [./ud_disp_x_grad_y]
    type = EqualGradientConstraint
    variable = lm_up_down_xy
    component = 1
    secondary_variable = disp_x
    secondary_boundary = bottom
    primary_boundary = top
    secondary_subdomain = secondary_y
    primary_subdomain = primary_y
    periodic = true
  [../]
  [./ud_disp_y_grad_x]
    type = EqualGradientConstraint
    variable = lm_up_down_yx
    component = 0
    secondary_variable = disp_y
    secondary_boundary = bottom
    primary_boundary = top
    secondary_subdomain = secondary_y
    primary_subdomain = primary_y
    periodic = true
  [../]
  [./ud_disp_y_grad_y]
    type = EqualGradientConstraint
    variable = lm_up_down_yy
    component = 1
    secondary_variable = disp_y
    secondary_boundary = bottom
    primary_boundary = top
    secondary_subdomain = secondary_y
    primary_subdomain = primary_y
    periodic = true
  [../]

  [./lr_disp_x_grad_x]
    type = EqualGradientConstraint
    variable = lm_left_right_xx
    component = 0
    secondary_variable = disp_x
    secondary_boundary = left
    primary_boundary = right
    secondary_subdomain = secondary_x
    primary_subdomain = primary_x
    periodic = true
  [../]
  [./lr_disp_x_grad_y]
    type = EqualGradientConstraint
    variable = lm_left_right_xy
    component = 1
    secondary_variable = disp_x
    secondary_boundary = left
    primary_boundary = right
    secondary_subdomain = secondary_x
    primary_subdomain = primary_x
    periodic = true
  [../]
  [./lr_disp_y_grad_x]
    type = EqualGradientConstraint
    variable = lm_left_right_yx
    component = 0
    secondary_variable = disp_y
    secondary_boundary = left
    primary_boundary = right
    secondary_subdomain = secondary_x
    primary_subdomain = primary_x
    periodic = true
  [../]
  [./lr_disp_y_grad_y]
    type = EqualGradientConstraint
    variable = lm_left_right_yy
    component = 1
    secondary_variable = disp_y
    secondary_boundary = left
    primary_boundary = right
    secondary_subdomain = secondary_x
    primary_subdomain = primary_x
    periodic = true
  [../]
[]

[Kernels]
  # Set up stress divergence kernels
  [./TensorMechanics]
    block = 0
  [../]

  # Cahn-Hilliard kernels
  [./c_dot]
    type = CoupledTimeDerivative
    variable = w
    v = c
    block = 0
  [../]
  [./c_res]
    type = SplitCHParsed
    variable = c
    f_name = F
    kappa_name = kappa_c
    w = w
    block = 0
  [../]
  [./w_res]
    type = SplitCHWRes
    variable = w
    mob_name = M
    block = 0
  [../]
[]

[Materials]
  # declare a few constants, such as mobilities (L,M) and interface gradient prefactors (kappa*)
  [./consts]
    type = GenericConstantMaterial
    block = '0 10 11'
    prop_names  = 'M   kappa_c'
    prop_values = '0.2 0.01   '
  [../]

  [./shear1]
    type = GenericConstantRankTwoTensor
    block = 0
    tensor_values = '0 0 0 0 0 0.5'
    tensor_name = shear1
  [../]
  [./shear2]
    type = GenericConstantRankTwoTensor
    block = 0
    tensor_values = '0 0 0 0 0 -0.5'
    tensor_name = shear2
  [../]
  [./expand3]
    type = GenericConstantRankTwoTensor
    block = 0
    tensor_values = '1 1 0 0 0 0'
    tensor_name = expand3
  [../]

  [./weight1]
    type = DerivativeParsedMaterial
    block = 0
    expression = '0.3*c^2'
    property_name = weight1
    coupled_variables = c
  [../]
  [./weight2]
    type = DerivativeParsedMaterial
    block = 0
    expression = '0.3*(1-c)^2'
    property_name = weight2
    coupled_variables = c
  [../]
  [./weight3]
    type = DerivativeParsedMaterial
    block = 0
    expression = '4*(0.5-c)^2'
    property_name = weight3
    coupled_variables = c
  [../]

  # matrix phase
  [./elasticity_tensor]
    type = ComputeElasticityTensor
    block = 0
    C_ijkl = '1 1'
    fill_method = symmetric_isotropic
  [../]
  [./strain]
    type = ComputeSmallStrain
    block = 0
    displacements = 'disp_x disp_y'
    eigenstrain_names = eigenstrain
  [../]

  [./eigenstrain]
    type = CompositeEigenstrain
    block = 0
    tensors = 'shear1  shear2  expand3'
    weights = 'weight1 weight2 weight3'
    coupled_variables = c
    eigenstrain_name = eigenstrain
  [../]

  [./stress]
    type = ComputeLinearElasticStress
    block = 0
  [../]

  # chemical free energies
  [./chemical_free_energy]
    type = DerivativeParsedMaterial
    block = 0
    property_name = Fc
    expression = '4*c^2*(1-c)^2'
    coupled_variables = 'c'
    outputs = exodus
    output_properties = Fc
  [../]

  # elastic free energies
  [./elastic_free_energy]
    type = ElasticEnergyMaterial
    f_name = Fe
    block = 0
    coupled_variables = 'c'
    outputs = exodus
    output_properties = Fe
  [../]

  # free energy (chemical + elastic)
  [./free_energy]
    type = DerivativeSumMaterial
    block = 0
    property_name = F
    sum_materials = 'Fc Fe'
    coupled_variables = 'c'
  [../]
[]

[BCs]
  [./Periodic]
    [./up_down]
      primary = top
      secondary = bottom
      translation = '0 -1 0'
      variable = 'c w'
    [../]
    [./left_right]
      primary = left
      secondary = right
      translation = '1 0 0'
      variable = 'c w'
    [../]
  [../]

  # fix center point location
  [./centerfix_x]
    type = DirichletBC
    boundary = 100
    variable = disp_x
    value = 0
  [../]
  [./centerfix_y]
    type = DirichletBC
    boundary = 100
    variable = disp_y
    value = 0
  [../]

  # fix side point x coordinate to inhibit rotation
  [./angularfix]
    type = DirichletBC
    boundary = 101
    variable = disp_x
    value = 0
  [../]
[]

[Preconditioning]
  [./SMP]
    type = SMP
    full = true
  [../]
[]

# We monitor the total free energy and the total solute concentration (should be constant)
[Postprocessors]
  [./total_free_energy]
    type = ElementIntegralVariablePostprocessor
    block = 0
    execute_on = 'initial TIMESTEP_END'
    variable = local_energy
  [../]
  [./total_solute]
    type = ElementIntegralVariablePostprocessor
    block = 0
    execute_on = 'initial TIMESTEP_END'
    variable = c
  [../]
  [./min]
    type = ElementExtremeValue
    block = 0
    execute_on = 'initial TIMESTEP_END'
    value_type = min
    variable = c
  [../]
  [./max]
    type = ElementExtremeValue
    block = 0
    execute_on = 'initial TIMESTEP_END'
    value_type = max
    variable = c
  [../]
[]

[Executioner]
  type = Transient
  scheme = bdf2
  solve_type = 'PJFNK'

  line_search = basic

  # mortar currently does not support MPI parallelization
  petsc_options_iname = '-pc_type -pc_factor_shift_type -pc_factor_shift_amount'
  petsc_options_value = ' lu       NONZERO               1e-10'

  l_max_its = 30
  nl_max_its = 12

  l_tol = 1.0e-4

  nl_rel_tol = 1.0e-8
  nl_abs_tol = 1.0e-10

  start_time = 0.0
  num_steps = 200

  [./TimeStepper]
    type = SolutionTimeAdaptiveDT
    dt = 0.01
  [../]
[]

[Outputs]
  execute_on = 'timestep_end'
  print_linear_residuals = false
  exodus = true
  [./table]
    type = CSV
    delimiter = ' '
  [../]
[]

(modules/solid_mechanics/test/tests/ad_anisotropic_creep/3d_bar_orthotropic_90deg_rotation_ad_creep_x.i)

[Mesh]
  [generated_mesh]
    type = GeneratedMeshGenerator
    dim = 3
    xmin = 0
    xmax = 2
    ymin = 0
    ymax = 10
    zmin = 0
    zmax = 2
    nx = 1
    ny = 1
    nz = 1
    elem_type = HEX8
  []
  [corner]
    type = ExtraNodesetGenerator
    new_boundary = 101
    coord = '0 0 0'
    input = generated_mesh
  []
  [side]
    type = ExtraNodesetGenerator
    new_boundary = 102
    coord = '2 0 0'
    input = corner
  []
[]

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = FINITE
    add_variables = true
    volumetric_locking_correction = true
    use_automatic_differentiation = true
    generate_output = 'elastic_strain_xx stress_xx creep_strain_xx creep_strain_yy creep_strain_zz'
  []
[]

[Materials]
  [elastic_strain]
    type = ADComputeMultipleInelasticStress
    inelastic_models = "trial_creep"
    max_iterations = 50
    absolute_tolerance = 1e-18
  []
  [hill_tensor]
    type = ADHillConstants
    # F G H L M N
    hill_constants = "0.25 0.4 0.65 1.5 1.5 1.5"
    use_large_rotation = true
  []
  [trial_creep]
    type = ADHillCreepStressUpdate
    coefficient = 5e-14
    n_exponent = 10
    m_exponent = 0
    activation_energy = 0
    max_inelastic_increment = 0.00003
    absolute_tolerance = 1e-18
    relative_tolerance = 1e-18
    # Force it to not use integration error
    max_integration_error = 100.0
    use_transformation = true
  []
  [elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    youngs_modulus = 500
    poissons_ratio = 0.0
  []
[]

[BCs]
  [fix_x]
    type = ADDirichletBC
    variable = disp_x
    boundary = bottom
    value = 0
  []

  [rot_z]
    type = DisplacementAboutAxis
    boundary = bottom
    function = t
    angle_units = degrees
    axis_origin = '0. 0. 0.'
    axis_direction = '1. 0. 1.0e-13'
    component = 2
    variable = disp_z
  []
  #
  [rot_y]
    type = DisplacementAboutAxis
    boundary = bottom
    function = t
    angle_units = degrees
    axis_origin = '0. 0. 0.'
    axis_direction = '1. 0. 1.0e-13'
    component = 1
    variable = disp_y
  []

  [rot_z90]
    type = DisplacementAboutAxis
    boundary = bottom
    function = 90
    angle_units = degrees
    axis_origin = '0. 0. 0.'
    axis_direction = '1. 0. 1.0e-13'
    component = 2
    variable = disp_z
  []
  #
  [rot_y90]
    type = DisplacementAboutAxis
    boundary = bottom
    function = 90
    angle_units = degrees
    axis_origin = '0. 0. 0.'
    axis_direction = '1. 0. 1.0e-13'
    component = 1
    variable = disp_y
  []

  [press]
    type = Pressure
    boundary = top
    function = '-1.0*(t-90)*0.1'
    use_displaced_mesh = true
    displacements = 'disp_x disp_y disp_z'
    variable = disp_z
  []
[]

[Postprocessors]
  # The strain is along Z axis, naming it creep_strain_yy
  # for better comparison.
  [creep_strain_yy]
    type = ADElementAverageMaterialProperty
    mat_prop = creep_strain_zz
  []
[]

[Controls]
  [c1]
    type = TimePeriod
    enable_objects = 'BCs::rot_z BCs::rot_y'
    disable_objects = 'BCs::rot_z90 BCs::rot_y90 BCs::press'
    start_time = '0'
    end_time = '90'
  []
  [c190plus]
    type = TimePeriod
    enable_objects = 'BCs::rot_z90 BCs::rot_y90 BCs::press'
    disable_objects = 'BCs::rot_z BCs::rot_y '
    start_time = '90'
    end_time = '390'
  []
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-ksp_gmres_restart'
  petsc_options_value = '101'

  line_search = 'none'

  nl_rel_tol = 1e-11
  nl_abs_tol = 1e-11
  nl_max_its = 50

  l_tol = 1e-4
  l_max_its = 50
  start_time = 0.0

  dt = 0.1
  dtmin = 0.1

  num_steps = 1200
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Outputs]
  exodus = false
  csv = true
[]

(modules/solid_mechanics/test/tests/ad_anisotropic_creep/3d_bar_orthotropic_90deg_rotation_ad_creep_z_no_rotation.i)

[Mesh]
  [generated_mesh]
    type = GeneratedMeshGenerator
    dim = 3
    xmin = 0
    xmax = 2
    ymin = 0
    ymax = 10
    zmin = 0
    zmax = 2
    nx = 1
    ny = 1
    nz = 1
    elem_type = HEX8
  []
  [corner]
    type = ExtraNodesetGenerator
    new_boundary = 101
    coord = '0 0 0'
    input = generated_mesh
  []
  [side]
    type = ExtraNodesetGenerator
    new_boundary = 102
    coord = '2 0 0'
    input = corner
  []
[]

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = FINITE
    add_variables = true
    volumetric_locking_correction = true
    use_automatic_differentiation = true
    generate_output = 'elastic_strain_yy stress_yy creep_strain_yy'
  []
[]

[Materials]
  [elastic_strain]
    type = ADComputeMultipleInelasticStress
    inelastic_models = "trial_creep"
    max_iterations = 50
    absolute_tolerance = 1e-18
  []
  [hill_tensor]
    type = ADHillConstants
    # F G H L M N
    hill_constants = "0.5 1.0 0.5 1.5 1.5 1.5"
    use_large_rotation = true
  []
  [trial_creep]
    type = ADHillCreepStressUpdate
    coefficient = 5e-14
    n_exponent = 10
    m_exponent = 0
    activation_energy = 0
    max_inelastic_increment = 0.00003
    absolute_tolerance = 1e-18
    relative_tolerance = 1e-18
    # Force it to not use integration error
    max_integration_error = 100.0
    use_transformation = true
  []
  [elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    youngs_modulus = 500
    poissons_ratio = 0.0
  []
[]

[BCs]
  [fix_z]
    type = ADDirichletBC
    variable = disp_z
    boundary = bottom
    value = 0
  []

  [rot_y]
    type = DisplacementAboutAxis
    boundary = bottom
    function = 0
    angle_units = degrees
    axis_origin = '0. 0. 0.'
    axis_direction = '0. 0. 1.'
    component = 1
    variable = disp_y
  []
  #
  [rot_x]
    type = DisplacementAboutAxis
    boundary = bottom
    function = 0
    angle_units = degrees
    axis_origin = '0. 0. 0.'
    axis_direction = '0. 0. 1.'
    component = 0
    variable = disp_x
  []

  [rot_y90]
    type = DisplacementAboutAxis
    boundary = bottom
    function = 0
    angle_units = degrees
    axis_origin = '0. 0. 0.'
    axis_direction = '0. 0. 1.'
    component = 1
    variable = disp_y
  []
  #
  [rot_x90]
    type = DisplacementAboutAxis
    boundary = bottom
    function = 0
    angle_units = degrees
    axis_origin = '0. 0. 0.'
    axis_direction = '0. 0. 1.'
    component = 0
    variable = disp_x
  []

  [press]
    boundary = top
    function = '-1.0*(t-90)*0.1'
    use_displaced_mesh = true
    displacements = 'disp_x disp_y disp_z'
    type = Pressure
    variable = disp_y
  []

[]

[Controls]
  [c1]
    type = TimePeriod
    enable_objects = 'BCs::rot_x BCs::rot_y'
    disable_objects = 'BCs::rot_x90 BCs::rot_y90 BCs::press'
    start_time = '0'
    end_time = '90'
  []
  [c190plus]
    type = TimePeriod
    enable_objects = 'BCs::rot_x90 BCs::rot_y90 BCs::press'
    disable_objects = 'BCs::rot_x BCs::rot_y '
    start_time = '90'
    end_time = '390'
  []
[]

[Postprocessors]
  [creep_strain_xx]
    type = ADElementAverageMaterialProperty
    mat_prop = creep_strain_yy
  []
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-ksp_gmres_restart'
  petsc_options_value = '101'

  line_search = 'none'

  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-12
  nl_max_its = 50
  automatic_scaling = true
  l_tol = 1e-4
  l_max_its = 50
  start_time = 0.0

  dt = 0.1
  dtmin = 0.1

  num_steps = 1200
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[Outputs]
  exodus = false
  csv = true
[]

(modules/solid_mechanics/test/tests/ad_anisotropic_creep/ad_aniso_creep_x_3d_anisoElasticity.i)

# This test simulates uniaxial tensile test with the material being anisotropic
# in terms of elasticity and creep.
#
# -------------------
# ANALYTICAL SOLUTION
# -------------------
# https://mooseframework.inl.gov/source/materials/HillCreepStressUpdate.html
# q = [F(S22-S33)^2 + G(S33-S11)^2 + H(S11-S22)^2 + 2L(S23)^2 + 2M(S13)^2 + 2N(S12)^2]^0.5
# S11 = 40 Pa; other compoenents of stress are zero since it is a uniaxial test
# F=0.5 G=0.25 H=0.3866 L=1.6413 M=1.6413 N=1.2731 (as used in this test)
# Substituting the values of stress components and F, G, H, L, M and N we obtain
# q = 31.9148868 Pa
#
# Equivalent_creep_strain_rate = A(q)^n (power law creep rate used in this test)
# Substituting A=1e-16 and n=9, and q as calculated above, we obtain
# Equivalent_creep_strain_rate = 3.4351030990356175e-07
#
# The 11 (xx) component of creep_strain_tensor is calculated as below
# creep_strain_tensor_11 = (Equivalent_creep_strain_rate / q) *
#                        (H * (S11 - S22) - G * (S33 - S11)) * time_increment
# Substituting the values and time_increment as 0.001 we obtain the analytical solution.
#
#                               MOOSE               Analytical
#  creep_strain_tensor_11  2.740674587165e-06   2.7407731645305e-06
#
# -----------------------------------------
# PYTHON SCRIPT FOR THE ANALYTICAL SOLUTION
# -----------------------------------------
# import math
# F=0.5; G=0.25; H=0.3866; L=1.6413; M=1.6413; N=1.2731
# S11=40; S22=0; S33=0; S23=0; S13=0; S12=0
# q = math.sqrt(F*(S22-S33)**2 + G*(S33-S11)**2 + H*(S11-S22)**2 + 2*L*(S23)**2 + 2*M*(S13)**2 + 2*N*(S12)**2)
# A=1e-16; n=9; time=0.001
# equivalent_creep_strain_rate = A*(q**n)
# equivalent_creep_strain_rate_11=(equivalent_creep_strain_rate / q) * (H * (S11 - S22) - G * (S33 - S11)) * time
# print(equivalent_creep_strain_rate_11)

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 3
    nx = 10
    ny = 2
    nz = 2
    xmin = 0.0
    ymin = 0.0
    zmin = 0.0

    xmax = 10.0
    ymax = 1.0
    zmax = 1.0
  []
  [corner_node]
    type = ExtraNodesetGenerator
    new_boundary = '100'
    nodes = '3 69'
    input = gen
  []
  [corner_node_2]
    type = ExtraNodesetGenerator
    new_boundary = '101'
    nodes = '4 47'
    input = corner_node
  []
[]

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  volumetric_locking_correction = true
[]

[AuxVariables]
  [hydrostatic_stress]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_xx]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_xy]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [hydrostatic_stress]
    type = ADRankTwoScalarAux
    variable = hydrostatic_stress
    rank_two_tensor = stress
    scalar_type = Hydrostatic
  []
  [creep_strain_xx]
    type = ADRankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_xx
    index_i = 0
    index_j = 0
  []
  [creep_strain_xy]
    type = ADRankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_xy
    index_i = 0
    index_j = 1
  []
  [creep_strain_yy]
    type = ADRankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_strain_yy
    index_i = 1
    index_j = 1
  []
  [sigma_xx]
    type = ADRankTwoAux
    rank_two_tensor = stress
    variable = stress_xx
    index_i = 0
    index_j = 0
  []
[]

[Functions]
  [pull]
    type = PiecewiseLinear
    x = '0 1.0e-9 1.0'
    y = '0 -4e1 -4e1'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = FINITE
    generate_output = 'elastic_strain_xx stress_xx'
    use_automatic_differentiation = true
    add_variables = true
  []
[]

[Materials]
  [elasticity_tensor]
    type = ADComputeElasticityTensor
    C_ijkl = '2925.433 391.979 391.979 2127.590 322.280 2127.590 1805.310 3.96 3.96'
    fill_method = symmetric9
  []

  [elastic_strain]
    type = ADComputeMultipleInelasticStress
    inelastic_models = "trial_creep_two"
    max_iterations = 50
    absolute_tolerance = 1e-16
  []

  [hill_tensor]
    type = ADHillConstants
    # F G H L M N
    hill_constants = "0.5 0.25 0.3866 1.6413 1.6413 1.2731"
  []

  [trial_creep_two]
    type = ADHillCreepStressUpdate
    coefficient = 1e-16
    n_exponent = 9
    m_exponent = 0
    activation_energy = 0
    max_inelastic_increment = 0.00003
    absolute_tolerance = 1e-20
    relative_tolerance = 1e-20
    # Force it to not use integration error
    max_integration_error = 100.0
    anisotropic_elasticity = true
    creep_prefactor = 1.0
  []
[]

[BCs]
  [no_disp_x]
    type = ADDirichletBC
    variable = disp_x
    boundary = left
    value = 0.0
  []

  [no_disp_y]
    type = ADDirichletBC
    variable = disp_y
    boundary = 100
    value = 0.0
  []

  [no_disp_z]
    type = ADDirichletBC
    variable = disp_z
    boundary = 101
    value = 0.0
  []

  [Pressure]
    [Side1]
      boundary = right
      function = pull
    []
  []

[]

[Executioner]
  type = Transient

  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -mat_mffd_err'
  petsc_options_value = 'lu     superlu_dist                    1e-5'

  nl_rel_tol = 1.0e-14
  nl_abs_tol = 1.0e-14
  l_max_its = 10
  num_steps = 5
  dt = 1.0e-4
  start_time = 0
  automatic_scaling = true
[]

[Postprocessors]
  [matl_ts_min]
    type = MaterialTimeStepPostprocessor
  []
  [max_disp_x]
    type = ElementExtremeValue
    variable = disp_x
  []
  [max_disp_y]
    type = ElementExtremeValue
    variable = disp_y
  []
  [max_hydro]
    type = ElementAverageValue
    variable = hydrostatic_stress
  []
  [dt]
    type = TimestepSize
  []
  [num_lin]
    type = NumLinearIterations
    outputs = console
  []
  [num_nonlin]
    type = NumNonlinearIterations
    outputs = console
  []
  [creep_strain_xx]
    type = ElementalVariableValue
    variable = creep_strain_xx
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [elastic_strain_xx]
    type = ElementalVariableValue
    variable = elastic_strain_xx
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
  [sigma_xx]
    type = ElementalVariableValue
    variable = stress_xx
    execute_on = 'TIMESTEP_END'
    elementid = 39
  []
[]

[Outputs]
  csv = true
  exodus = false
  perf_graph = true
  # unnecessary output variables
  hide = 'matl_ts_min max_disp_x max_disp_y max_hydro dt num_lin num_nonlin'
[]

(modules/xfem/test/tests/moving_interface/moving_bimaterial_finite_strain_cut_mesh.i)

# This test is for two layer materials with different youngs modulus with AD
# The global stress is determined by switching the stress based on level set values
# The material interface is marked by a level set function
# The two layer materials are glued together

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[XFEM]
  output_cut_plane = true
[]

[UserObjects]
  [cut]
    type = InterfaceMeshCut2DUserObject
    mesh_file = line.e
    interface_velocity_function = -1
    heal_always = true
  []
[]

[Mesh]
  use_displaced_mesh = true
  [generated_mesh]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 10
    xmin = 0
    xmax = 5
    ymin = 0
    ymax = 5
    elem_type = QUAD4
  []
  [left_bottom]
    type = ExtraNodesetGenerator
    new_boundary = 'left_bottom'
    coord = '0 0'
    input = generated_mesh
  []
  [left_top]
    type = ExtraNodesetGenerator
    new_boundary = 'left_top'
    coord = '0 5'
    input = left_bottom
  []
[]

# [Functions]
#   [ls_func]
#     type = ParsedFunction
#     expression = 'y-2.73+t'
#   []
# []

[Variables]
  [disp_x]
  []
  [disp_y]
  []
[]

[AuxVariables]
  [ls]
  []
  [a_strain_xx]
    order = CONSTANT
    family = MONOMIAL
  []
  [a_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []
  [a_strain_xy]
    order = CONSTANT
    family = MONOMIAL
  []
  [b_strain_xx]
    order = CONSTANT
    family = MONOMIAL
  []
  [b_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []
  [b_strain_xy]
    order = CONSTANT
    family = MONOMIAL
  []
  [stress_xx]
    order = CONSTANT
    family = MONOMIAL
  []
  [stress_yy]
    order = CONSTANT
    family = MONOMIAL
  []
  [stress_xy]
    order = CONSTANT
    family = MONOMIAL
  []

[]

[AuxKernels]
  # [ls_function]
  #   type = FunctionAux
  #   variable = ls
  #   function = ls_func
  # []
  [a_strain_xx]
    type = RankTwoAux
    variable = a_strain_xx
    rank_two_tensor = A_total_strain
    index_i = 0
    index_j = 0
  []
  [a_strain_yy]
    type = RankTwoAux
    variable = a_strain_yy
    rank_two_tensor = A_total_strain
    index_i = 1
    index_j = 1
  []
  [a_strain_xy]
    type = RankTwoAux
    variable = a_strain_xy
    rank_two_tensor = A_total_strain
    index_i = 0
    index_j = 1
  []
  [b_strain_xx]
    type = RankTwoAux
    variable = b_strain_xx
    rank_two_tensor = B_total_strain
    index_i = 0
    index_j = 0
  []
  [b_strain_yy]
    type = RankTwoAux
    variable = b_strain_yy
    rank_two_tensor = B_total_strain
    index_i = 1
    index_j = 1
  []
  [b_strain_xy]
    type = RankTwoAux
    variable = b_strain_xy
    rank_two_tensor = B_total_strain
    index_i = 0
    index_j = 1
  []
  [stress_xx]
    type = RankTwoAux
    variable = stress_xx
    rank_two_tensor = stress
    index_i = 0
    index_j = 0
  []
  [stress_xy]
    type = RankTwoAux
    variable = stress_xy
    rank_two_tensor = stress
    index_i = 0
    index_j = 1
  []
  [stress_yy]
    type = RankTwoAux
    variable = stress_yy
    rank_two_tensor = stress
    index_i = 1
    index_j = 1
  []
[]

[Kernels]
  [solid_x]
    type = StressDivergenceTensors
    variable = disp_x
    component = 0
    use_displaced_mesh = true
  []
  [solid_y]
    type = StressDivergenceTensors
    variable = disp_y
    component = 1
    use_displaced_mesh = true
  []
[]

[Constraints]
  [dispx_constraint]
    type = XFEMSingleVariableConstraint
    use_displaced_mesh = false
    variable = disp_x
    alpha = 1e8
    geometric_cut_userobject = 'level_set_cut_uo'
  []
  [dispy_constraint]
    type = XFEMSingleVariableConstraint
    use_displaced_mesh = false
    variable = disp_y
    alpha = 1e8
    geometric_cut_userobject = 'level_set_cut_uo'
  []
[]

[BCs]
  [bottomx]
    type = DirichletBC
    boundary = bottom
    variable = disp_x
    value = 0.0
  []
  [bottomy]
    type = DirichletBC
    boundary = bottom
    variable = disp_y
    value = 0.0
  []
  [topx]
    type = FunctionDirichletBC
    boundary = top
    variable = disp_x
    function = 0.03*t
  []
  [topy]
    type = FunctionDirichletBC
    boundary = top
    variable = disp_y
    function = '0.03*t'
  []
[]

[Materials]
  [elasticity_tensor_A]
    type = ComputeIsotropicElasticityTensor
    base_name = A
    youngs_modulus = 1e9
    poissons_ratio = 0.3
  []
  [strain_A]
    type = ComputeFiniteStrain
    base_name = A
  []
  [stress_A]
    type = ComputeFiniteStrainElasticStress
    base_name = A
  []
  [elasticity_tensor_B]
    type = ComputeIsotropicElasticityTensor
    base_name = B
    youngs_modulus = 1e7
    poissons_ratio = 0.3
  []
  [strain_B]
    type = ComputeFiniteStrain
    base_name = B
  []
  [stress_B]
    type = ComputeFiniteStrainElasticStress
    base_name = B
  []
  [combined_stress]
    type = LevelSetBiMaterialRankTwo
    levelset_positive_base = 'A'
    levelset_negative_base = 'B'
    level_set_var = ls
    prop_name = stress
  []
  [combined_jacob_mult]
    type = LevelSetBiMaterialRankFour
    levelset_positive_base = 'A'
    levelset_negative_base = 'B'
    level_set_var = ls
    prop_name = Jacobian_mult
  []
[]

[Postprocessors]
  [disp_x_norm]
    type = ElementL2Norm
    variable = disp_x
  []
  [disp_y_norm]
    type = ElementL2Norm
    variable = disp_y
  []
[]

[Executioner]
  type = Transient

  solve_type = NEWTON
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  automatic_scaling = true

  # controls for nonlinear iterations
  nl_max_its = 15
  nl_rel_tol = 1e-13
  nl_abs_tol = 1e-50

  # time control
  start_time = 0.0
  dt = 0.1
  num_steps = 4

  max_xfem_update = 1
[]

[Outputs]
  print_linear_residuals = false
  exodus = true
[]

(test/tests/mortar/ad_periodic_segmental_constraint/periodic_simple3d.i)

[Mesh]
  [left_block]
    type = GeneratedMeshGenerator
    dim = 3
    xmin = -3.0
    xmax = 3.0
    ymin = -3.0
    ymax = 3.0
    zmin = -3.0
    zmax = 3.0
    nx = 3
    ny = 3
    nz = 3
    elem_type = HEX27
  []
  [left_block_sidesets]
    type = RenameBoundaryGenerator
    input = left_block
    old_boundary = '0 1 2 3 4 5'
    new_boundary = '10 11 12 13 14 15'
  []
  [left_block_id]
    type = SubdomainIDGenerator
    input = left_block_sidesets
    subdomain_id = 1
  []
  [left]
    type = LowerDBlockFromSidesetGenerator
    input = left_block_id
    sidesets = '14'
    new_block_id = '10004'
    new_block_name = 'secondary_left'
  []
  [right]
    type = LowerDBlockFromSidesetGenerator
    input = left
    sidesets = '12'
    new_block_id = '10002'
    new_block_name = 'primary_right'
  []
  [bottom]
    type = LowerDBlockFromSidesetGenerator
    input = right
    sidesets = '10'
    new_block_id = '10000'
    new_block_name = 'secondary_bottom'
  []
  [top]
    type = LowerDBlockFromSidesetGenerator
    input = bottom
    sidesets = '15'
    new_block_id = '10005'
    new_block_name = 'primary_top'
  []
  [back]
    type = LowerDBlockFromSidesetGenerator
    input = top
    sidesets = '11'
    new_block_id = '10001'
    new_block_name = 'secondary_back'
  []
  [front]
    type = LowerDBlockFromSidesetGenerator
    input = back
    sidesets = '13'
    new_block_id = '10003'
    new_block_name = 'primary_front'
  []

  [corner_node]
    type = ExtraNodesetGenerator
    new_boundary = 'pinned_node'
    nodes = '0'
    input = front
  []
[]

[Variables]
  [u]
    order = SECOND
    family = LAGRANGE
  []
  [epsilon]
    order = THIRD
    family = SCALAR
  []
  [./lm1]
    order = FIRST
    family = LAGRANGE
    block = secondary_left
  [../]
  [./lm2]
    order = FIRST
    family = LAGRANGE
    block = secondary_bottom
  [../]
  [./lm3]
    order = FIRST
    family = LAGRANGE
    block = secondary_back
  [../]
[]

[AuxVariables]
  [sigma]
    order = THIRD
    family = SCALAR
  []
[]

[AuxScalarKernels]
  [sigma]
    type = FunctionScalarAux
    variable = sigma
    function = '1 2 3'
    execute_on = initial #timestep_end
  []
[]

[Kernels]
  [diff1]
    type = Diffusion
    variable = u
    block = 1
  []
[]

[Problem]
  kernel_coverage_check = false
  error_on_jacobian_nonzero_reallocation = true
[]

[BCs]
  [fix_right]
    type = DirichletBC
    variable = u
    boundary = pinned_node
    value = 0
  []
[]

[Constraints]
  [mortarlr]
    type = EqualValueConstraint
    primary_boundary = '12'
    secondary_boundary = '14'
    primary_subdomain = 'primary_right'
    secondary_subdomain = 'secondary_left'
    secondary_variable = u
    variable = lm1
    correct_edge_dropping = true
  []
  [periodiclr]
    type = ADPeriodicSegmentalConstraint
    primary_boundary = '12'
    secondary_boundary = '14'
    primary_subdomain = 'primary_right'
    secondary_subdomain = 'secondary_left'
    secondary_variable = u
    epsilon = epsilon
    sigma = sigma
    variable = lm1
    correct_edge_dropping = true
  []
  [mortarbt]
    type = EqualValueConstraint
    primary_boundary = '15'
    secondary_boundary = '10'
    primary_subdomain = 'primary_top'
    secondary_subdomain = 'secondary_bottom'
    secondary_variable = u
    variable = lm2
    correct_edge_dropping = true
  []
  [periodicbt]
    type = ADPeriodicSegmentalConstraint
    primary_boundary = '15'
    secondary_boundary = '10'
    primary_subdomain = 'primary_top'
    secondary_subdomain = 'secondary_bottom'
    secondary_variable = u
    epsilon = epsilon
    sigma = sigma
    variable = lm2
    correct_edge_dropping = true
  []
  [mortarbf]
    type = EqualValueConstraint
    primary_boundary = '13'
    secondary_boundary = '11'
    primary_subdomain = 'primary_front'
    secondary_subdomain = 'secondary_back'
    secondary_variable = u
    variable = lm3
    correct_edge_dropping = true
  []
  [periodicbf]
    type = ADPeriodicSegmentalConstraint
    primary_boundary = '13'
    secondary_boundary = '11'
    primary_subdomain = 'primary_front'
    secondary_subdomain = 'secondary_back'
    secondary_variable = u
    epsilon = epsilon
    sigma = sigma
    variable = lm3
    correct_edge_dropping = true
  []
[]

[Preconditioning]
  [smp]
    full = true
    type = SMP
  []
[]

[Executioner]
  type = Steady
  petsc_options_iname = '-pc_type -pc_factor_shift_type'
  petsc_options_value = 'lu       NONZERO'
  solve_type = NEWTON
[]

[Outputs]
#  exodus = true
  csv = true
[]

(modules/solid_mechanics/test/tests/j2_plasticity/solid_mechanics_j2plasticity.i)

[Mesh]
  displacements = 'x_disp y_disp z_disp'
  [generated_mesh]
    type = GeneratedMeshGenerator
    elem_type = HEX8
    dim = 3
    nx = 1
    ny = 1
    nz = 1
    xmin = 0.0
    xmax = 1.0
    ymin = 0.0
    ymax = 1.0
    zmin = 0.0
    zmax = 1.0
  []
  [cnode]
    type = ExtraNodesetGenerator
    coord = '0.0 0.0 0.0'
    new_boundary = 6
    input = generated_mesh
  []
  [snode]
    type = ExtraNodesetGenerator
    coord = '1.0 0.0 0.0'
    new_boundary = 7
    input = cnode
  []
[]

[Variables]
  [./x_disp]
    order = FIRST
    family = LAGRANGE
  [../]
  [./y_disp]
    order = FIRST
    family = LAGRANGE
  [../]
  [./z_disp]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Kernels]
  [SolidMechanics]
    displacements = 'x_disp y_disp z_disp'
    use_displaced_mesh = true
  [../]
[]

[Materials]
  [./fplastic]
    type = FiniteStrainPlasticMaterial
    block=0
    yield_stress='0. 445. 0.05 610. 0.1 680. 0.38 810. 0.95 920. 2. 950.'
  [../]
  [./elasticity_tensor]
    type = ComputeElasticityTensor
    block = 0
    C_ijkl = '2.827e5 1.21e5 1.21e5 2.827e5 1.21e5 2.827e5 0.808e5 0.808e5 0.808e5'
    fill_method = symmetric9
  [../]
  [./strain]
    type = ComputeFiniteStrain
    block = 0
    displacements = 'x_disp y_disp z_disp'
  [../]
[]

[Functions]
  [./topfunc]
    type = ParsedFunction
    expression = 't'
  [../]
[]

[BCs]
  [./bottom3]
    type = DirichletBC
    variable = z_disp
    boundary = 0
    value = 0.0
  [../]
  [./top]
    type = FunctionDirichletBC
    variable = z_disp
    boundary = 5
    function = topfunc
  [../]
  [./corner1]
    type = DirichletBC
    variable = x_disp
    boundary = 6
    value = 0.0
  [../]
  [./corner2]
    type = DirichletBC
    variable = y_disp
    boundary = 6
    value = 0.0
  [../]
  [./corner3]
    type = DirichletBC
    variable = z_disp
    boundary = 6
    value = 0.0
  [../]
  [./side1]
    type = DirichletBC
    variable = y_disp
    boundary = 7
    value = 0.0
  [../]
  [./side2]
    type = DirichletBC
    variable = z_disp
    boundary = 7
    value = 0.0
  [../]
[]

[AuxVariables]
  [./stress_zz]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./peeq]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./pe11]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./pe22]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./pe33]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[AuxKernels]
  [./stress_zz]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_zz
    index_i = 2
    index_j = 2
  [../]
  [./pe11]
    type = RankTwoAux
    rank_two_tensor = plastic_strain
    variable = pe11
    index_i = 0
    index_j = 0
  [../]
    [./pe22]
    type = RankTwoAux
    rank_two_tensor = plastic_strain
    variable = pe22
    index_i = 1
    index_j = 1
  [../]
  [./pe33]
    type = RankTwoAux
    rank_two_tensor = plastic_strain
    variable = pe33
    index_i = 2
    index_j = 2
  [../]
  [./eqv_plastic_strain]
    type = MaterialRealAux
    property = eqv_plastic_strain
    variable = peeq
  [../]
[]

[Preconditioning]
  [./SMP]
   type = SMP
   full=true
  [../]
[]

[Executioner]
  type = Transient

  dt=0.1
  dtmax=1
  dtmin=0.1
  end_time=1.0

  nl_abs_tol = 1e-10
[]


[Outputs]
  file_base = out
  exodus = true
[]

(modules/solid_mechanics/test/tests/global_strain/global_strain.i)

[Mesh]
  [generated_mesh]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 10
    ny = 10
    xmin = -0.5
    xmax = 0.5
    ymin = -0.5
    ymax = 0.5
  []
  [cnode]
    type = ExtraNodesetGenerator
    coord = '0 0'
    new_boundary = 100
    input = generated_mesh
  []
[]

[Variables]
  [./u_x]
  [../]
  [./u_y]
  [../]
  [./global_strain]
    order = THIRD
    family = SCALAR
  [../]
[]

[AuxVariables]
  [./disp_x]
  [../]
  [./disp_y]
  [../]
[]

[AuxKernels]
  [./disp_x]
    type = GlobalDisplacementAux
    variable = disp_x
    scalar_global_strain = global_strain
    global_strain_uo = global_strain_uo
    component = 0
  [../]
  [./disp_y]
    type = GlobalDisplacementAux
    variable = disp_y
    scalar_global_strain = global_strain
    global_strain_uo = global_strain_uo
    component = 1
  [../]
[]

[GlobalParams]
  displacements = 'u_x u_y'
  block = 0
[]

[Kernels]
  [SolidMechanics]
  [../]
[]

[ScalarKernels]
  [./global_strain]
    type = GlobalStrain
    variable = global_strain
    global_strain_uo = global_strain_uo
  [../]
[]

[BCs]
  [./Periodic]
    [./left-right]
      auto_direction = 'x y'
      variable = 'u_x u_y'
    [../]
  [../]

  # fix center point location
  [./centerfix_x]
    type = DirichletBC
    boundary = 100
    variable = u_x
    value = 0
  [../]
  [./centerfix_y]
    type = DirichletBC
    boundary = 100
    variable = u_y
    value = 0
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeElasticityTensor
    block = 0
    C_ijkl = '1 1'
    fill_method = symmetric_isotropic
  [../]
  [./strain]
    type = ComputeSmallStrain
    global_strain = global_strain
  [../]
  [./global_strain]
    type = ComputeGlobalStrain
    scalar_global_strain = global_strain
    global_strain_uo = global_strain_uo
  [../]
  [./stress]
    type = ComputeLinearElasticStress
  [../]
[]

[UserObjects]
  [./global_strain_uo]
    type = GlobalStrainUserObject
    applied_stress_tensor = '0.1 0.2 0 0 0 -0.2'
    execute_on = 'Initial Linear Nonlinear'
  [../]
[]

[Preconditioning]
  [./SMP]
    type = SMP
    full = true
  [../]
[]

[Executioner]
  type = Transient
  scheme = bdf2
  solve_type = 'PJFNK'

  line_search = basic

  petsc_options_iname = '-pc_type -ksp_gmres_restart -sub_ksp_type -sub_pc_type -pc_asm_overlap'
  petsc_options_value = 'asm         31   preonly   lu      1'

  l_max_its = 30
  nl_max_its = 12

  l_tol = 1.0e-4

  nl_rel_tol = 1.0e-8
  nl_abs_tol = 1.0e-10

  start_time = 0.0
  num_steps = 2
[]

[Outputs]
exodus = true
[]

(modules/combined/examples/optimization/three_materials.i)

vol_frac = 0.4
cost_frac = 0.3

power = 4

E0 = 1.0e-6
E1 = 0.2
E2 = 0.6
E3 = 1.0

rho0 = 1.0e-6
rho1 = 0.4
rho2 = 0.7
rho3 = 1.0

C0 = 1.0e-6
C1 = 0.5
C2 = 0.8
C3 = 1.0

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  [MeshGenerator]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 50
    ny = 50
    xmin = 0
    xmax = 50
    ymin = 0
    ymax = 50
  []
  [node]
    type = ExtraNodesetGenerator
    input = MeshGenerator
    new_boundary = hold
    nodes = 0
  []
  [push_left]
    type = ExtraNodesetGenerator
    input = node
    new_boundary = push_left
    coord = '25 0 0'
  []
  [push_center]
    type = ExtraNodesetGenerator
    input = push_left
    new_boundary = push_center
    coord = '50 0 0'
  []
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
[]

[AuxVariables]
  [Dc]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = -1.0
  []
  [Cc]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = -1.0
  []
  [Cost]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = -1.0
  []
  [mat_den]
    family = MONOMIAL
    order = CONSTANT
    initial_condition = ${vol_frac}
  []
[]

[AuxKernels]
  [Cost]
    type = MaterialRealAux
    variable = Cost
    property = Cost_mat
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = SMALL
    add_variables = true
    incremental = false
  []
[]

[BCs]
  [no_y]
    type = DirichletBC
    variable = disp_y
    boundary = hold
    value = 0.0
  []
  [no_x_symm]
    type = DirichletBC
    variable = disp_x
    boundary = right
    value = 0.0
  []

[]
[NodalKernels]
  [push_left]
    type = NodalGravity
    variable = disp_y
    boundary = push_left
    gravity_value = -1e-3
    mass = 1
  []
  [push_center]
    type = NodalGravity
    variable = disp_y
    boundary = push_center
    gravity_value = -1e-3
    mass = 1
  []
[]
[Materials]
  [elasticity_tensor]
    type = ComputeVariableIsotropicElasticityTensor
    youngs_modulus = E_phys
    poissons_ratio = poissons_ratio
    args = 'mat_den'
  []
  [E_phys]
    type = DerivativeParsedMaterial
    # ordered multimaterial simp
    expression = "A1:=(${E0}-${E1})/(${rho0}^${power}-${rho1}^${power}); "
                 "B1:=${E0}-A1*${rho0}^${power}; E1:=A1*mat_den^${power}+B1; "
                 "A2:=(${E1}-${E2})/(${rho1}^${power}-${rho2}^${power}); "
                 "B2:=${E1}-A2*${rho1}^${power}; E2:=A2*mat_den^${power}+B2; "
                 "A3:=(${E2}-${E3})/(${rho2}^${power}-${rho3}^${power}); "
                 "B3:=${E2}-A3*${rho2}^${power}; E3:=A3*mat_den^${power}+B3; "
                 "if(mat_den<${rho1},E1,if(mat_den<${rho2},E2,E3))"
    coupled_variables = 'mat_den'
    property_name = E_phys
  []

  [Cost_mat]
    type = DerivativeParsedMaterial
    # ordered multimaterial simp
    expression = "A1:=(${C0}-${C1})/(${rho0}^(1/${power})-${rho1}^(1/${power})); "
                 "B1:=${C0}-A1*${rho0}^(1/${power}); C1:=A1*mat_den^(1/${power})+B1; "
                 "A2:=(${C1}-${C2})/(${rho1}^(1/${power})-${rho2}^(1/${power})); "
                 "B2:=${C1}-A2*${rho1}^(1/${power}); C2:=A2*mat_den^(1/${power})+B2; "
                 "A3:=(${C2}-${C3})/(${rho2}^(1/${power})-${rho3}^(1/${power})); "
                 "B3:=${C2}-A3*${rho2}^(1/${power}); C3:=A3*mat_den^(1/${power})+B3; "
                 "if(mat_den<${rho1},C1,if(mat_den<${rho2},C2,C3))"
    coupled_variables = 'mat_den'
    property_name = Cost_mat
  []
  [CostDensity]
    type = ParsedMaterial
    property_name = CostDensity
    coupled_variables = 'mat_den Cost'
    expression = 'mat_den*Cost'
  []
  [poissons_ratio]
    type = GenericConstantMaterial
    prop_names = poissons_ratio
    prop_values = 0.3
  []
  [stress]
    type = ComputeLinearElasticStress
  []
  [dc]
    type = ComplianceSensitivity
    design_density = mat_den
    youngs_modulus = E_phys
  []
  [cc]
    type = CostSensitivity
    design_density = mat_den
    cost = Cost_mat
    outputs = 'exodus'
  []
[]

[Preconditioning]
  [smp]
    type = SMP
    full = true
  []
[]

[UserObjects]
  [rad_avg]
    type = RadialAverage
    radius = 3
    weights = linear
    prop_name = sensitivity
    execute_on = TIMESTEP_END
    force_preaux = true
  []
  [rad_avg_cost]
    type = RadialAverage
    radius = 3
    weights = linear
    prop_name = cost_sensitivity
    execute_on = TIMESTEP_END
    force_preaux = true
  []
  [update]
    type = DensityUpdateTwoConstraints
    # This is
    density_sensitivity = Dc
    cost_density_sensitivity = Cc
    cost = Cost
    cost_fraction = ${cost_frac}
    design_density = mat_den
    volume_fraction = ${vol_frac}
    bisection_lower_bound = 0
    bisection_upper_bound = 1.0e16 # 100
    bisection_move = 0.05
    adaptive_move = true
    relative_tolerance = 1.0e-3
    execute_on = TIMESTEP_BEGIN
  []
  # Provides Dc
  [calc_sense]
    type = SensitivityFilter
    density_sensitivity = Dc
    design_density = mat_den
    filter_UO = rad_avg
    execute_on = TIMESTEP_END
    force_postaux = true
  []
  # Provides Cc
  [calc_sense_cost]
    type = SensitivityFilter
    density_sensitivity = Cc
    design_density = mat_den
    filter_UO = rad_avg_cost
    execute_on = TIMESTEP_END
    force_postaux = true
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'
  nl_abs_tol = 1e-10
  dt = 1.0
  num_steps = 40
[]

[Outputs]
  exodus = true
  [out]
    type = CSV
    execute_on = 'TIMESTEP_END'
  []
  print_linear_residuals = false
[]

[Postprocessors]
  [total_vol]
    type = ElementIntegralVariablePostprocessor
    variable = mat_den
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [mesh_volume]
    type = VolumePostprocessor
    execute_on = 'initial timestep_end'
  []
  [vol_frac]
    type = ParsedPostprocessor
    expression = 'total_vol / mesh_volume'
    pp_names = 'total_vol mesh_volume'
  []
  [sensitivity]
    type = ElementIntegralMaterialProperty
    mat_prop = sensitivity
  []
  [cost_sensitivity]
    type = ElementIntegralMaterialProperty
    mat_prop = cost_sensitivity
  []
  [cost]
    type = ElementIntegralMaterialProperty
    mat_prop = CostDensity
  []
  [cost_frac]
    type = ParsedPostprocessor
    expression = 'cost / mesh_volume'
    pp_names = 'cost mesh_volume'
  []

[]