TangentialMortarLMMechanicalContact

The TangentialMortarLMMechanicalContact class is used to ensure that the Karush-Kuhn-Tucker conditions of Coulomb frictional contact are satisfied:

$var element = document.getElementById("moose-equation-e7b91c85-56cd-441b-9e53-42b77c90c3d4");katex.render("\\begin{aligned} \\phi &= \\mu\\lambda_N - \\lvert \\lambda_T \\rvert \\ge 0\\\\ \\gamma &= \\frac{v_T}{\\lambda_T} \\ge 0\\\\ \\gamma\\phi &= 0 \\end{aligned}", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$

where $var element = document.getElementById("moose-equation-6024908f-eeab-46f3-814e-89c785b53468");katex.render("\\mu", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is the coefficient of friction, $var element = document.getElementById("moose-equation-c21735f7-7a1c-4491-810c-39a9bc87f2af");katex.render("\\lambda_N", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is the Lagrange multiplier variable representing the contact pressure, $var element = document.getElementById("moose-equation-6f717efb-b4da-4db9-857d-800194abe582");katex.render("v_T", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is the slip velocity of the slave face relative to the master face, and $var element = document.getElementById("moose-equation-790a7956-e80e-4996-9bc3-525cc3cf8cef");katex.render("\\lambda_T", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is the Lagrange multiplier variable representing the tangential stress. The above conditions require that either the slave face is sticking to the master face, or the slave face is slipping and the tangential stress is equal in magnitude to the coefficient of friction times the normal contact pressure. Additionally, if the face is slipping, then the force exerted by the slave face is in the same direction as the slip.

The ncp_function_type parameter specifies the type of nonlinear complimentarity problem (NCP) function to use. The options are either min, which is just the min function, or fb which represents the Fischer-Burmeister function. In our experience, the Fischer-Burmeister function achieves better convergence in the non-linear solve. The c parameter is used to balance the size of the slip velocity and the tangential stress. If the stress is of order 1000, and the velocity is of order 1, then c should be set to 1000 in order to bring components of the NCP function onto the same level and achieve optimal convergence in the non-linear solve.

Ensures that the Karush-Kuhn-Tucker conditions of Coulomb frictional contact are satisfied

Input Parameters

contact_pressureThe normal contact pressure; oftentimes this may be a separate lagrange multiplier variable
C++ Type:NonlinearVariableName
Options:
Description:The normal contact pressure; oftentimes this may be a separate lagrange multiplier variable
friction_coefficientThe friction coefficient
C++ Type:double
Options:
Description:The friction coefficient
master_boundaryThe name of the master boundary sideset.
C++ Type:BoundaryName
Options:
Description:The name of the master boundary sideset.
master_subdomainThe name of the master subdomain.
C++ Type:SubdomainName
Options:
Description:The name of the master subdomain.
slave_boundaryThe name of the slave boundary sideset.
C++ Type:BoundaryName
Options:
Description:The name of the slave boundary sideset.
slave_disp_yThe y displacement variable on the slave face
C++ Type:NonlinearVariableName
Options:
Description:The y displacement variable on the slave face
slave_subdomainThe name of the slave subdomain.
C++ Type:SubdomainName
Options:
Description:The name of the slave subdomain.

Required Parameters

c1Parameter for balancing the size of the velocity and the pressures
Default:1
C++ Type:double
Options:
Description:Parameter for balancing the size of the velocity and the pressures
compute_lm_residualsTrueWhether to compute Lagrange Multiplier residuals
Default:True
C++ Type:bool
Options:
Description:Whether to compute Lagrange Multiplier residuals
compute_primal_residualsFalseWhether to compute residuals for the primal variable.
Default:False
C++ Type:bool
Options:
Description:Whether to compute residuals for the primal variable.
execute_onLINEARThe list of flag(s) indicating when this object should be executed, the available options include NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, FINAL, CUSTOM.
Default:LINEAR
C++ Type:ExecFlagEnum
Options:NONE INITIAL LINEAR NONLINEAR TIMESTEP_END TIMESTEP_BEGIN FINAL CUSTOM
Description:The list of flag(s) indicating when this object should be executed, the available options include NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, FINAL, CUSTOM.
master_disp_yThe y displacement variable on the master face
C++ Type:NonlinearVariableName
Options:
Description:The y displacement variable on the master face
master_variablePrimal variable on master surface. If this parameter is not provided then the master variable will be initialized to the slave variable
C++ Type:VariableName
Options:
Description:Primal variable on master surface. If this parameter is not provided then the master variable will be initialized to the slave variable
ncp_function_typefbThe type of the nonlinear complimentarity function; options are min or fb where fb stands for Fischer-Burmeister
Default:fb
C++ Type:MooseEnum
Options:min fb
Description:The type of the nonlinear complimentarity function; options are min or fb where fb stands for Fischer-Burmeister
periodicFalseWhether this constraint is going to be used to enforce a periodic condition. This has the effect of changing the normals vector for projection from outward to inward facing
Default:False
C++ Type:bool
Options:
Description:Whether this constraint is going to be used to enforce a periodic condition. This has the effect of changing the normals vector for projection from outward to inward facing
slave_variablePrimal variable on slave surface.
C++ Type:VariableName
Options:
Description:Primal variable on slave surface.
variableThe name of the lagrange multiplier variable that this constraint is applied to. This parameter may not be supplied in the case of using penalty methods for example
C++ Type:NonlinearVariableName
Options:
Description:The name of the lagrange multiplier variable that this constraint is applied to. This parameter may not be supplied in the case of using penalty methods for example

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector
Options:
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Options:
Description:Set the enabled status of the MooseObject.
use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:False
C++ Type:bool
Options:
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

Advanced Parameters

extra_matrix_tagsThe extra tags for the matrices this Kernel should fill
C++ Type:std::vector
Options:
Description:The extra tags for the matrices this Kernel should fill
extra_vector_tagsThe extra tags for the vectors this Kernel should fill
C++ Type:std::vector
Options:
Description:The extra tags for the vectors this Kernel should fill
matrix_tagssystemThe tag for the matrices this Kernel should fill
Default:system
C++ Type:MultiMooseEnum
Options:nontime system
Description:The tag for the matrices this Kernel should fill
vector_tagsnontimeThe tag for the vectors this Kernel should fill
Default:nontime
C++ Type:MultiMooseEnum
Options:nontime time
Description:The tag for the vectors this Kernel should fill

Tagging Parameters

Input Files

modules/contact/test/tests/bouncing-block-contact/grid-sequencing/grid-sequencing.i
modules/contact/test/tests/bouncing-block-contact/frictional-mortar-fb-lm-mortar-disp.i
modules/combined/test/tests/sliding_block/in_and_out/constraint/frictional_lm.i
modules/contact/test/tests/bouncing-block-contact/frictional-nodal-min-normal-lm-mortar-fb-tangential-lm-mortar-disp.i
modules/contact/test/tests/bouncing-block-contact/frictional-mortar-min-lm-mortar-disp.i

modules/contact/test/tests/bouncing-block-contact/grid-sequencing/grid-sequencing.i

starting_point = 2e-1

# We offset slightly so we avoid the case where the bottom of the slave block and the top of the
# master block are perfectly vertically aligned which can cause the backtracking line search some
# issues for a coarsest mesh (basic line search handles that fine)
offset = 1e-2

[GlobalParams]
  displacements = 'disp_x disp_y'
  diffusivity = 1e0
[]

[Mesh]
  file = level0.e
[]

[Variables]
  [./disp_x]
    block = '1 2'
  [../]
  [./disp_y]
    block = '1 2'
  [../]
  [./normal_lm]
    block = 3
  [../]
  [./tangential_lm]
    block = 3
    family = MONOMIAL
    order = CONSTANT
  [../]
[]

[ICs]
  [./disp_y]
    block = 2
    variable = disp_y
    value = ${fparse starting_point + offset}
    type = ConstantIC
  [../]
[]

[Kernels]
  [./disp_x]
    type = MatDiffusion
    variable = disp_x
  [../]
  [./disp_y]
    type = MatDiffusion
    variable = disp_y
  [../]
[]


[Constraints]
  [normal_lm]
    type = NormalNodalLMMechanicalContact
    slave = 10
    master = 20
    variable = normal_lm
    master_variable = disp_x
    disp_y = disp_y
    ncp_function_type = min
  [../]
  [normal_x]
    type = NormalMortarMechanicalContact
    master_boundary = 20
    slave_boundary = 10
    master_subdomain = 4
    slave_subdomain = 3
    variable = normal_lm
    slave_variable = disp_x
    component = x
    use_displaced_mesh = true
    compute_lm_residuals = false
  []
  [normal_y]
    type = NormalMortarMechanicalContact
    master_boundary = 20
    slave_boundary = 10
    master_subdomain = 4
    slave_subdomain = 3
    variable = normal_lm
    slave_variable = disp_y
    component = y
    use_displaced_mesh = true
    compute_lm_residuals = false
  []
  [tangential_lm]
    type = TangentialMortarLMMechanicalContact
    master_boundary = 20
    slave_boundary = 10
    master_subdomain = 4
    slave_subdomain = 3
    variable = tangential_lm
    slave_variable = disp_x
    slave_disp_y = disp_y
    use_displaced_mesh = true
    compute_primal_residuals = false
    contact_pressure = normal_lm
    friction_coefficient = .1
    ncp_function_type = fb
  []
  [tangential_x]
    type = TangentialMortarMechanicalContact
    master_boundary = 20
    slave_boundary = 10
    master_subdomain = 4
    slave_subdomain = 3
    variable = tangential_lm
    slave_variable = disp_x
    component = x
    use_displaced_mesh = true
    compute_lm_residuals = false
  []
  [tangential_y]
    type = TangentialMortarMechanicalContact
    master_boundary = 20
    slave_boundary = 10
    master_subdomain = 4
    slave_subdomain = 3
    variable = tangential_lm
    slave_variable = disp_y
    component = y
    use_displaced_mesh = true
    compute_lm_residuals = false
  []
[]

[BCs]
  [./botx]
    type = DirichletBC
    variable = disp_x
    boundary = 40
    value = 0.0
  [../]
  [./boty]
    type = DirichletBC
    variable = disp_y
    boundary = 40
    value = 0.0
  [../]
  [./topy]
    type = FunctionDirichletBC
    variable = disp_y
    boundary = 30
    function = '${starting_point} * cos(2 * pi / 40 * t) + ${offset}'
  [../]
  [./leftx]
    type = FunctionDirichletBC
    variable = disp_x
    boundary = 50
    function = '1e-2 * t'
  [../]
[]

[Executioner]
  type = Transient
  end_time = 200
  num_steps = 3
  dt = 5
  dtmin = .1
  solve_type = 'PJFNK'
  petsc_options = '-snes_converged_reason -ksp_converged_reason -snes_linesearch_monitor'
  petsc_options_iname = '-pc_type -pc_factor_shift_type -pc_factor_shift_amount -mat_mffd_err'
  petsc_options_value = 'lu       NONZERO               1e-15                   1e-5'
  l_max_its = 30
  nl_max_its = 20
  line_search = 'none'
  nl_abs_tol = 1e-10
  num_grids = 5
[]

[Debug]
  show_var_residual_norms = true
[]

[Outputs]
  [exo]
    type = Exodus
    sync_times = '15'
    sync_only = true
  []
[]

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

[Postprocessors]
  [./num_nl]
    type = NumNonlinearIterations
  [../]
  [./cumulative]
    type = CumulativeValuePostprocessor
    postprocessor = num_nl
  [../]
  [contact]
    type = ContactDOFSetSize
    variable = normal_lm
    subdomain = '3'
    execute_on = 'nonlinear timestep_end'
  []
[]

modules/contact/test/tests/bouncing-block-contact/frictional-mortar-fb-lm-mortar-disp.i

starting_point = 2e-1

# We offset slightly so we avoid the case where the bottom of the slave block and the top of the
# master block are perfectly vertically aligned which can cause the backtracking line search some
# issues for a coarse mesh (basic line search handles that fine)
offset = 1e-2

[GlobalParams]
  displacements = 'disp_x disp_y'
  diffusivity = 1e0
  scaling = 1e0
[]

[Mesh]
  file = long-bottom-block-1elem-blocks.e
[]

[Variables]
  [./disp_x]
    block = '1 2'
    # order = SECOND
  [../]
  [./disp_y]
    block = '1 2'
    # order = SECOND
  [../]
  [./normal_lm]
    block = 3
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./tangential_lm]
    block = 3
    family = MONOMIAL
    order = CONSTANT
  [../]
[]

[ICs]
  [./disp_y]
    block = 2
    variable = disp_y
    value = ${fparse starting_point + offset}
    type = ConstantIC
  [../]
[]

[Kernels]
  [./disp_x]
    type = MatDiffusion
    variable = disp_x
  [../]
  [./disp_y]
    type = MatDiffusion
    variable = disp_y
  [../]
[]


[Constraints]
  [normal_lm]
    type = NormalMortarLMMechanicalContact
    master_boundary = 20
    slave_boundary = 10
    master_subdomain = 4
    slave_subdomain = 3
    variable = normal_lm
    slave_variable = disp_x
    slave_disp_y = disp_y
    use_displaced_mesh = true
    compute_primal_residuals = false
    ncp_function_type = fb
  []
  [normal_x]
    type = NormalMortarMechanicalContact
    master_boundary = 20
    slave_boundary = 10
    master_subdomain = 4
    slave_subdomain = 3
    variable = normal_lm
    slave_variable = disp_x
    component = x
    use_displaced_mesh = true
    compute_lm_residuals = false
  []
  [normal_y]
    type = NormalMortarMechanicalContact
    master_boundary = 20
    slave_boundary = 10
    master_subdomain = 4
    slave_subdomain = 3
    variable = normal_lm
    slave_variable = disp_y
    component = y
    use_displaced_mesh = true
    compute_lm_residuals = false
  []
  [tangential_lm]
    type = TangentialMortarLMMechanicalContact
    master_boundary = 20
    slave_boundary = 10
    master_subdomain = 4
    slave_subdomain = 3
    variable = tangential_lm
    slave_variable = disp_x
    slave_disp_y = disp_y
    use_displaced_mesh = true
    compute_primal_residuals = false
    contact_pressure = normal_lm
    friction_coefficient = .1
    ncp_function_type = fb
  []
  [tangential_x]
    type = TangentialMortarMechanicalContact
    master_boundary = 20
    slave_boundary = 10
    master_subdomain = 4
    slave_subdomain = 3
    variable = tangential_lm
    slave_variable = disp_x
    component = x
    use_displaced_mesh = true
    compute_lm_residuals = false
  []
  [tangential_y]
    type = TangentialMortarMechanicalContact
    master_boundary = 20
    slave_boundary = 10
    master_subdomain = 4
    slave_subdomain = 3
    variable = tangential_lm
    slave_variable = disp_y
    component = y
    use_displaced_mesh = true
    compute_lm_residuals = false
  []
[]

[BCs]
  [./botx]
    type = DirichletBC
    variable = disp_x
    boundary = 40
    value = 0.0
  [../]
  [./boty]
    type = DirichletBC
    variable = disp_y
    boundary = 40
    value = 0.0
  [../]
  [./topy]
    type = FunctionDirichletBC
    variable = disp_y
    boundary = 30
    function = '${starting_point} * cos(2 * pi / 40 * t) + ${offset}'
  [../]
  [./leftx]
    type = FunctionDirichletBC
    variable = disp_x
    boundary = 50
    function = '1e-2 * t'
  [../]
[]

[Executioner]
  type = Transient
  end_time = 200
  dt = 5
  dtmin = .1
  solve_type = 'PJFNK'
  petsc_options = '-snes_converged_reason -ksp_converged_reason -pc_svd_monitor -snes_linesearch_monitor -snes_ksp_ew'
  petsc_options_iname = '-pc_type -pc_factor_shift_type -pc_factor_shift_amount -mat_mffd_err'
  petsc_options_value = 'lu       NONZERO               1e-15                   1e-5'
  l_max_its = 30
  nl_max_its = 20
  line_search = 'none'

  # [./Predictor]
  #   type = SimplePredictor
  #   scale = 1.0
  # [../]
[]

[Debug]
  show_var_residual_norms = true
[]

[Outputs]
  exodus = true
  # checkpoint = true
  # [./dofmap]
  #   type = DOFMap
  #   execute_on = 'initial'
  # [../]
[]

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

[Postprocessors]
  [./num_nl]
    type = NumNonlinearIterations
  [../]
  [./cumulative]
    type = CumulativeValuePostprocessor
    postprocessor = num_nl
  [../]
  [contact]
    type = ContactDOFSetSize
    variable = normal_lm
    subdomain = '3'
    execute_on = 'nonlinear timestep_end'
  []
[]

modules/combined/test/tests/sliding_block/in_and_out/constraint/frictional_lm.i

[Mesh]
  patch_size = 80
  [file]
    type = FileMeshGenerator
    file = sliding_elastic_blocks_2d.e
  []
  [slave]
    input = file
    type = LowerDBlockFromSidesetGenerator
    sidesets = '3'
    new_block_id = '30'
  []
  [master]
    input = slave
    type = LowerDBlockFromSidesetGenerator
    sidesets = '2'
    new_block_id = '20'
  []
[]

[GlobalParams]
  volumetric_locking_correction = false
  displacements = 'disp_x disp_y'
[]

[Variables]
  [normal_lm]
    block = '30'
  []
  [tangential_lm]
    block = '30'
    family = MONOMIAL
    order = CONSTANT
  []
[]

[BCs]
  [./left_x]
    type = DirichletBC
    variable = disp_x
    boundary = 1
    value = 0.0
  [../]
  [./left_y]
    type = DirichletBC
    variable = disp_y
    boundary = 1
    value = 0.0
  [../]
  [./right_x]
    type = FunctionDirichletBC
    variable = disp_x
    boundary = 4
    function = horizontal_movement
  [../]
  [./right_y]
    type = FunctionDirichletBC
    variable = disp_y
    boundary = 4
    function = vertical_movement
  [../]
[]

[Modules/TensorMechanics/Master]
  [./all]
    add_variables = true
    strain = FINITE
    block = '1 2'
  [../]
[]

[Materials]
  [./tensor]
    type = ComputeIsotropicElasticityTensor
    block = '1 2'
    youngs_modulus = 1e6
    poissons_ratio = 0.3
  [../]
  [./stress]
    type = ComputeFiniteStrainElasticStress
    block = '1 2'
  [../]
[]

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

[Executioner]
  type = Transient
  solve_type = 'PJFNK'
  petsc_options = '-snes_converged_reason -ksp_converged_reason -snes_ksp_ew'
  petsc_options_iname = '-pc_type -mat_mffd_err -pc_factor_shift_type -pc_factor_shift_amount'
  petsc_options_value = 'lu       1e-5          NONZERO               1e-15'
  end_time = 15
  dt = 0.1
  dtmin = 0.01
  l_max_its = 30
  nl_max_its = 20
  line_search = 'none'
  timestep_tolerance = 1e-6

  [./Predictor]
    type = SimplePredictor
    scale = 1.0
  [../]
[]

[Debug]
  show_var_residual_norms = true
[]

[Outputs]
  sync_times = '1 2 3 4 5 6 7 8 9 10 11 12 13 14 15'
  [out]
    type = Exodus
    sync_only = true
  []
  [dof]
    execute_on = 'initial'
    type = DOFMap
  []
  [csv]
    type = CSV
    execute_on = 'nonlinear timestep_end'
  []
[]

[Functions]
  [./vertical_movement]
    type = ParsedFunction
    value = -t
  [../]
  [./horizontal_movement]
    type = ParsedFunction
    value = -0.04*sin(4*t)+0.02
  [../]
[]

[Constraints]
  [./lm]
    type = NormalNodalLMMechanicalContact
    slave = 3
    master = 2
    variable = normal_lm
    master_variable = disp_x
    disp_y = disp_y
    ncp_function_type = min
    use_displaced_mesh = true
    c = 1e6 # relative scale difference between pressure and gap
  [../]
  [normal_x]
    type = NormalMortarMechanicalContact
    master_boundary = '2'
    slave_boundary = '3'
    master_subdomain = '20'
    slave_subdomain = '30'
    variable = normal_lm
    slave_variable = disp_x
    component = x
    use_displaced_mesh = true
    compute_lm_residuals = false
  []
  [normal_y]
    type = NormalMortarMechanicalContact
    master_boundary = '2'
    slave_boundary = '3'
    master_subdomain = '20'
    slave_subdomain = '30'
    variable = normal_lm
    slave_variable = disp_y
    component = y
    use_displaced_mesh = true
    compute_lm_residuals = false
  []
  [tangential_lm]
    type = TangentialMortarLMMechanicalContact
    master_boundary = '2'
    slave_boundary = '3'
    master_subdomain = '20'
    slave_subdomain = '30'
    variable = tangential_lm
    slave_variable = disp_x
    slave_disp_y = disp_y
    use_displaced_mesh = true
    compute_primal_residuals = false
    contact_pressure = normal_lm
    friction_coefficient = .4
    ncp_function_type = fb
    c = 1000 # relative scale difference between pressure and velocity
  []
  [tangential_x]
    type = TangentialMortarMechanicalContact
    master_boundary = '2'
    slave_boundary = '3'
    master_subdomain = '20'
    slave_subdomain = '30'
    variable = tangential_lm
    slave_variable = disp_x
    component = x
    use_displaced_mesh = true
    compute_lm_residuals = false
  []
  [tangential_y]
    type = TangentialMortarMechanicalContact
    master_boundary = '2'
    slave_boundary = '3'
    master_subdomain = '20'
    slave_subdomain = '30'
    variable = tangential_lm
    slave_variable = disp_y
    component = y
    use_displaced_mesh = true
    compute_lm_residuals = false
  []
[]

[Postprocessors]
  [./num_nl]
    type = NumNonlinearIterations
  [../]
  [./cumulative]
    type = CumulativeValuePostprocessor
    postprocessor = num_nl
  [../]
  [lin]
    type = NumLinearIterations
  []
  [cum_lin]
    type = CumulativeValuePostprocessor
    postprocessor = lin
  []
  [contact]
    type = ContactDOFSetSize
    variable = normal_lm
    subdomain = '30'
    execute_on = 'nonlinear timestep_end'
  []
[]

modules/contact/test/tests/bouncing-block-contact/frictional-nodal-min-normal-lm-mortar-fb-tangential-lm-mortar-disp.i

starting_point = 2e-1

# We offset slightly so we avoid the case where the bottom of the slave block and the top of the
# master block are perfectly vertically aligned which can cause the backtracking line search some
# issues for a coarse mesh (basic line search handles that fine)
offset = 1e-2

[GlobalParams]
  displacements = 'disp_x disp_y'
  diffusivity = 1e0
  scaling = 1e0
[]

[Mesh]
  [./file_mesh]
    type = FileMeshGenerator
    file = long-bottom-block-1elem-blocks-coarse.e
  [../]
[]

[Variables]
  [./disp_x]
    block = '1 2'
    # order = SECOND
  [../]
  [./disp_y]
    block = '1 2'
    # order = SECOND
  [../]
  [./frictional_normal_lm]
    block = 3
    # family = MONOMIAL
    # order = CONSTANT
  [../]
  [./frictional_tangential_lm]
    block = 3
    family = MONOMIAL
    order = CONSTANT
  [../]
[]

[ICs]
  [./disp_y]
    block = 2
    variable = disp_y
    value = ${fparse starting_point + offset}
    type = ConstantIC
  [../]
[]

[Kernels]
  [./disp_x]
    type = MatDiffusion
    variable = disp_x
  [../]
  [./disp_y]
    type = MatDiffusion
    variable = disp_y
  [../]
[]


[Constraints]
  [frictional_normal_lm]
    type = NormalNodalLMMechanicalContact
    slave = 10
    master = 20
    variable = frictional_normal_lm
    master_variable = disp_x
    disp_y = disp_y
    ncp_function_type = min
  [../]
  [normal_x]
    type = NormalMortarMechanicalContact
    master_boundary = 20
    slave_boundary = 10
    master_subdomain = 4
    slave_subdomain = 3
    variable = frictional_normal_lm
    slave_variable = disp_x
    component = x
    use_displaced_mesh = true
    compute_lm_residuals = false
  []
  [normal_y]
    type = NormalMortarMechanicalContact
    master_boundary = 20
    slave_boundary = 10
    master_subdomain = 4
    slave_subdomain = 3
    variable = frictional_normal_lm
    slave_variable = disp_y
    component = y
    use_displaced_mesh = true
    compute_lm_residuals = false
  []
  [frictional_tangential_lm]
    type = TangentialMortarLMMechanicalContact
    master_boundary = 20
    slave_boundary = 10
    master_subdomain = 4
    slave_subdomain = 3
    variable = frictional_tangential_lm
    slave_variable = disp_x
    slave_disp_y = disp_y
    use_displaced_mesh = true
    compute_primal_residuals = false
    contact_pressure = frictional_normal_lm
    friction_coefficient = .1
    ncp_function_type = fb
  []
  [tangential_x]
    type = TangentialMortarMechanicalContact
    master_boundary = 20
    slave_boundary = 10
    master_subdomain = 4
    slave_subdomain = 3
    variable = frictional_tangential_lm
    slave_variable = disp_x
    component = x
    use_displaced_mesh = true
    compute_lm_residuals = false
  []
  [tangential_y]
    type = TangentialMortarMechanicalContact
    master_boundary = 20
    slave_boundary = 10
    master_subdomain = 4
    slave_subdomain = 3
    variable = frictional_tangential_lm
    slave_variable = disp_y
    component = y
    use_displaced_mesh = true
    compute_lm_residuals = false
  []
[]

[BCs]
  [./botx]
    type = DirichletBC
    variable = disp_x
    boundary = 40
    value = 0.0
  [../]
  [./boty]
    type = DirichletBC
    variable = disp_y
    boundary = 40
    value = 0.0
  [../]
  [./topy]
    type = FunctionDirichletBC
    variable = disp_y
    boundary = 30
    function = '${starting_point} * cos(2 * pi / 40 * t) + ${offset}'
  [../]
  [./leftx]
    type = FunctionDirichletBC
    variable = disp_x
    boundary = 50
    function = '1e-2 * t'
  [../]
[]

[Executioner]
  type = Transient
  end_time = 200
  dt = 5
  dtmin = .1
  solve_type = 'PJFNK'
  petsc_options = '-snes_converged_reason -ksp_converged_reason -pc_svd_monitor -snes_linesearch_monitor -snes_ksp_ew'
  petsc_options_iname = '-pc_type -pc_factor_shift_type -pc_factor_shift_amount -mat_mffd_err'
  petsc_options_value = 'lu       NONZERO               1e-15                   1e-5'
  l_max_its = 30
  nl_max_its = 20
  line_search = 'none'

  # [./Predictor]
  #   type = SimplePredictor
  #   scale = 1.0
  # [../]
[]

[Debug]
  show_var_residual_norms = true
[]

[Outputs]
  exodus = true
  # checkpoint = true
  # [./dofmap]
  #   type = DOFMap
  #   execute_on = 'initial'
  # [../]
[]

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

[Postprocessors]
  [./num_nl]
    type = NumNonlinearIterations
  [../]
  [./cumulative]
    type = CumulativeValuePostprocessor
    postprocessor = num_nl
  [../]
  [contact]
    type = ContactDOFSetSize
    variable = frictional_normal_lm
    subdomain = '3'
    execute_on = 'nonlinear timestep_end'
  []
[]

modules/contact/test/tests/bouncing-block-contact/frictional-mortar-min-lm-mortar-disp.i

starting_point = 2e-1

# We offset slightly so we avoid the case where the bottom of the slave block and the top of the
# master block are perfectly vertically aligned which can cause the backtracking line search some
# issues for a coarse mesh (basic line search handles that fine)
offset = 1e-2

[GlobalParams]
  displacements = 'disp_x disp_y'
  diffusivity = 1e0
  scaling = 1e0
[]

[Mesh]
  file = long-bottom-block-1elem-blocks.e
[]

[Variables]
  [./disp_x]
    block = '1 2'
    # order = SECOND
  [../]
  [./disp_y]
    block = '1 2'
    # order = SECOND
  [../]
  [./normal_lm]
    block = 3
    family = MONOMIAL
    order = CONSTANT
  [../]
  [./tangential_lm]
    block = 3
    family = MONOMIAL
    order = CONSTANT
  [../]
[]

[ICs]
  [./disp_y]
    block = 2
    variable = disp_y
    value = ${fparse starting_point + offset}
    type = ConstantIC
  [../]
[]

[Kernels]
  [./disp_x]
    type = MatDiffusion
    variable = disp_x
  [../]
  [./disp_y]
    type = MatDiffusion
    variable = disp_y
  [../]
[]


[Constraints]
  [normal_lm]
    type = NormalMortarLMMechanicalContact
    master_boundary = 20
    slave_boundary = 10
    master_subdomain = 4
    slave_subdomain = 3
    variable = normal_lm
    slave_variable = disp_x
    slave_disp_y = disp_y
    use_displaced_mesh = true
    compute_primal_residuals = false
    ncp_function_type = min
  []
  [normal_x]
    type = NormalMortarMechanicalContact
    master_boundary = 20
    slave_boundary = 10
    master_subdomain = 4
    slave_subdomain = 3
    variable = normal_lm
    slave_variable = disp_x
    component = x
    use_displaced_mesh = true
    compute_lm_residuals = false
  []
  [normal_y]
    type = NormalMortarMechanicalContact
    master_boundary = 20
    slave_boundary = 10
    master_subdomain = 4
    slave_subdomain = 3
    variable = normal_lm
    slave_variable = disp_y
    component = y
    use_displaced_mesh = true
    compute_lm_residuals = false
  []
  [tangential_lm]
    type = TangentialMortarLMMechanicalContact
    master_boundary = 20
    slave_boundary = 10
    master_subdomain = 4
    slave_subdomain = 3
    variable = tangential_lm
    slave_variable = disp_x
    slave_disp_y = disp_y
    use_displaced_mesh = true
    compute_primal_residuals = false
    contact_pressure = normal_lm
    friction_coefficient = .1
    ncp_function_type = min
  []
  [tangential_x]
    type = TangentialMortarMechanicalContact
    master_boundary = 20
    slave_boundary = 10
    master_subdomain = 4
    slave_subdomain = 3
    variable = tangential_lm
    slave_variable = disp_x
    component = x
    use_displaced_mesh = true
    compute_lm_residuals = false
  []
  [tangential_y]
    type = TangentialMortarMechanicalContact
    master_boundary = 20
    slave_boundary = 10
    master_subdomain = 4
    slave_subdomain = 3
    variable = tangential_lm
    slave_variable = disp_y
    component = y
    use_displaced_mesh = true
    compute_lm_residuals = false
  []
[]

[BCs]
  [./botx]
    type = DirichletBC
    variable = disp_x
    preset = false
    boundary = 40
    value = 0.0
  [../]
  [./boty]
    type = DirichletBC
    variable = disp_y
    preset = false
    boundary = 40
    value = 0.0
  [../]
  [./topy]
    type = FunctionDirichletBC
    variable = disp_y
    preset = false
    boundary = 30
    function = '${starting_point} * cos(2 * pi / 40 * t) + ${offset}'
  [../]
  [./leftx]
    type = FunctionDirichletBC
    variable = disp_x
    preset = false
    boundary = 50
    function = '1e-2 * t'
  [../]
[]

[Executioner]
  type = Transient
  end_time = 200
  dt = 5
  dtmin = .1
  solve_type = 'PJFNK'
  petsc_options = '-snes_converged_reason -ksp_converged_reason -pc_svd_monitor -snes_linesearch_monitor -snes_ksp_ew'
  petsc_options_iname = '-pc_type -pc_factor_shift_type -pc_factor_shift_amount -mat_mffd_err'
  petsc_options_value = 'lu       NONZERO               1e-15                   1e-5'
  l_max_its = 30
  nl_max_its = 20
  line_search = 'none'
[]

[Debug]
  show_var_residual_norms = true
[]

[Outputs]
  exodus = true
[]

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

[Postprocessors]
  [./num_nl]
    type = NumNonlinearIterations
  [../]
  [./cumulative]
    type = CumulativeValuePostprocessor
    postprocessor = num_nl
  [../]
  [contact]
    type = ContactDOFSetSize
    variable = normal_lm
    subdomain = '3'
    execute_on = 'nonlinear timestep_end'
  []
[]

References

Input Parameters
Input Files
References

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