Nodal Rank Two AuxKernel

Description

AuxKernel NodalRankTwoPD is used to output the components of strain and stress tensors and their equivalent scalar quantities for bond-based and ordinary state-based models. And this is only applies to elastic materials. For correspondence models, the UserObjects NodalRankTwoComponentPD and NodalRankTwoScalarPD should be used.

This is a stand-alone calculation based on the concept of deformation gradient in correspondence model for postprocessing. Given the deformation gradient at each material point, other rank two tensors (strain, stress) can be calculated using the relationships from continuum mechanics theory.

For stress calculation, material constants, i.e., Young's modulus and Poisson's ratio, are required as input parameters.

Input Parameters

displacementsNonlinear variable names for the displacements
C++ Type:std::vector
Options:
Description:Nonlinear variable names for the displacements
output_typeType of output: component or scalar
C++ Type:std::string
Options:
Description:Type of output: component or scalar
rank_two_tensorParameter to set which rank two tensor: total_strain, mechanical_strain or stress
C++ Type:std::string
Options:
Description:Parameter to set which rank two tensor: total_strain, mechanical_strain or stress
variableThe name of the variable that this object applies to
C++ Type:AuxVariableName
Options:
Description:The name of the variable that this object applies to

Required Parameters

blockThe list of block ids (SubdomainID) that this object will be applied
C++ Type:std::vector
Options:
Description:The list of block ids (SubdomainID) that this object will be applied
boundaryThe list of boundary IDs from the mesh where this boundary condition applies
C++ Type:std::vector
Options:
Description:The list of boundary IDs from the mesh where this boundary condition applies
execute_onLINEAR TIMESTEP_ENDThe 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, PRE_DISPLACE.
Default:LINEAR TIMESTEP_END
C++ Type:ExecFlagEnum
Options:NONE INITIAL LINEAR NONLINEAR TIMESTEP_END TIMESTEP_BEGIN FINAL CUSTOM PRE_DISPLACE
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, PRE_DISPLACE.
index_i0The index i of ij for the tensor to output (0, 1, 2)
Default:0
C++ Type:unsigned int
Options:
Description:The index i of ij for the tensor to output (0, 1, 2)
index_j0The index j of ij for the tensor to output (0, 1, 2)
Default:0
C++ Type:unsigned int
Options:
Description:The index j of ij for the tensor to output (0, 1, 2)
plane_stressFalsePlane stress problem or not
Default:False
C++ Type:bool
Options:
Description:Plane stress problem or not
point10 0 0Start point for axis used to calculate some direction dependent material tensor scalar quantities
Default:0 0 0
C++ Type:libMesh::Point
Options:
Description:Start point for axis used to calculate some direction dependent material tensor scalar quantities
point21 0 0End point for axis used to calculate some direction dependent material tensor scalar quantities
Default:1 0 0
C++ Type:libMesh::Point
Options:
Description:End point for axis used to calculate some direction dependent material tensor scalar quantities
poissons_ratio0Material constant: Poisson's ratio
Default:0
C++ Type:double
Options:
Description:Material constant: Poisson's ratio
scalar_out_of_plane_strainScalar variable for strain in the out-of-plane direction
C++ Type:std::vector
Options:
Description:Scalar variable for strain in the out-of-plane direction
scalar_typeType of scalar output
C++ Type:MooseEnum
Options:VonMisesStress EffectiveStrain Hydrostatic L2norm MaxPrincipal MidPrincipal MinPrincipal VolumetricStrain FirstInvariant SecondInvariant ThirdInvariant AxialStress HoopStress RadialStress TriaxialityStress Direction MaxShear StressIntensity
Description:Type of scalar output
stress_free_temperature0Stress free temperature
Default:0
C++ Type:double
Options:
Description:Stress free temperature
temperatureNonlinear variable name for the temperature
C++ Type:std::vector
Options:
Description:Nonlinear variable name for the temperature
thermal_expansion_coeff0Value of material thermal expansion coefficient
Default:0
C++ Type:double
Options:
Description:Value of material thermal expansion coefficient
youngs_modulus0Material constant: Young's modulus
Default:0
C++ Type:double
Options:
Description:Material constant: Young's modulus

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.
seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Options:
Description:The seed for the master random number generator
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

Input Files

modules/peridynamics/test/tests/jacobian_check/generalized_planestrain_thermomechanics_OSPD.i
modules/peridynamics/test/tests/generalized_plane_strain/generalized_plane_strain_OSPD.i
modules/peridynamics/test/tests/jacobian_check/generalized_planestrain_OSPD.i
modules/peridynamics/test/tests/auxkernels/planestrain_thermomechanics_ranktwotensor_OSPD.i
modules/peridynamics/test/tests/generalized_plane_strain/planestrain_prescribed_OSPD.i
modules/peridynamics/test/tests/generalized_plane_strain/generalized_plane_strain_squares_OSPD.i
modules/peridynamics/test/tests/generalized_plane_strain/out_of_plane_pressure_OSPD.i

modules/peridynamics/test/tests/jacobian_check/generalized_planestrain_thermomechanics_OSPD.i


# NOTE: this jacobian test for the coupled thermomechanical model must use displaced mesh, otherwise the difference for the first step is huge

[GlobalParams]
  displacements = 'disp_x disp_y'
  temperature = temp
  scalar_out_of_plane_strain = scalar_strain_zz
  full_jacobian = true
[]

[Mesh]
  type = PeridynamicsMesh
  horizon_number = 3

  [./gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 4
    ny = 4
  [../]
  [./gpd]
    type = MeshGeneratorPD
    input = gmg
    retain_fe_mesh = false
  [../]
[]

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

  [./temp]
    initial_condition = 0.5
  [../]

  [./scalar_strain_zz]
    order = FIRST
    family = SCALAR
  [../]
[]

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

[Modules/Peridynamics/Mechanics]
  [./Master]
    [./all]
      formulation = ORDINARY_STATE
    [../]
  [../]
  [./GeneralizedPlaneStrain]
    [./all]
      formulation = ORDINARY_STATE
      out_of_plane_stress_variable = stress_zz
    [../]
  [../]
[]

[Kernels]
  [./heat]
    type = HeatConductionBPD
    variable = temp
  [../]
[]

[AuxKernels]
  [./stress_zz]
    type = NodalRankTwoPD
    variable = stress_zz

    poissons_ratio = 0.3
    youngs_modulus = 1e6
    thermal_expansion_coeff = 0.02
    stress_free_temperature = 0.5

    rank_two_tensor = stress
    output_type = component
    index_i = 2
    index_j = 2
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    poissons_ratio = 0.3
    youngs_modulus = 1e6
  [../]

  [./force_density]
    type = ComputeSmallStrainConstantHorizonMaterialOSPD
    thermal_expansion_coeff = 0.02
    stress_free_temperature = 0.5
  [../]
  [./thermal_mat]
    type = ThermalConstantHorizonMaterialBPD
    thermal_conductivity = 1.0
  [../]
[]

[Preconditioning]
  [./SMP]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -snes_type'
    petsc_options_value = 'bcgs bjacobi test'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  end_time = 1
  dt = 1
  num_steps = 1
[]

modules/peridynamics/test/tests/generalized_plane_strain/generalized_plane_strain_OSPD.i

[GlobalParams]
  displacements = 'disp_x disp_y'
  scalar_out_of_plane_strain = scalar_strain_zz
[]

[Mesh]
  type = PeridynamicsMesh
  horizon_number = 3

  [./gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 4
    ny = 4
  [../]
  [./gpd]
    type = MeshGeneratorPD
    input = gmg
    retain_fe_mesh = false
  [../]
[]

[Variables]
  [./disp_x]
  [../]
  [./disp_y]
  [../]
  [./scalar_strain_zz]
    order = FIRST
    family = SCALAR
  [../]
[]

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

  [./stress_zz]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Modules/Peridynamics/Mechanics]
  [./Master]
    [./all]
      formulation = ORDINARY_STATE
    [../]
  [../]
  [./GeneralizedPlaneStrain]
    [./all]
      formulation = ORDINARY_STATE
      out_of_plane_stress_variable = stress_zz
    [../]
  [../]
[]

[AuxKernels]
  [./tempfuncaux]
    type = FunctionAux
    variable = temp
    function = tempfunc
    use_displaced_mesh = false
  [../]

  [./stress_zz]
    type = NodalRankTwoPD
    variable = stress_zz

    poissons_ratio = 0.3
    youngs_modulus = 1e6
    temperature = temp
    thermal_expansion_coeff = 0.02
    stress_free_temperature = 0.5

    rank_two_tensor = stress
    output_type = component
    index_i = 2
    index_j = 2
  [../]
[]

[Postprocessors]
  [./react_z]
    type = NodalVariableIntegralPD
    variable = stress_zz
  [../]
[]

[Functions]
  [./tempfunc]
    type = ParsedFunction
    value = '(1-x)*t'
  [../]
[]

[BCs]
  [./bottom_x]
    type = DirichletBC
    boundary = 1000
    variable = disp_x
    value = 0.0
  [../]
  [./bottom_y]
    type = DirichletBC
    boundary = 1000
    variable = disp_y
    value = 0.0
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    poissons_ratio = 0.3
    youngs_modulus = 1e6
  [../]

  [./force_density]
    type = ComputeSmallStrainVariableHorizonMaterialOSPD
    temperature = temp
    thermal_expansion_coeff = 0.02
    stress_free_temperature = 0.5
  [../]
[]

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

[Executioner]
  type = Transient

  solve_type = PJFNK
  line_search = none

  nl_rel_tol = 1e-12

  start_time = 0.0
  end_time = 1.0
[]

[Outputs]
  exodus = true
  file_base = generalized_plane_strain_OSPD
[]

modules/peridynamics/test/tests/jacobian_check/generalized_planestrain_OSPD.i

[GlobalParams]
  displacements = 'disp_x disp_y'
  scalar_out_of_plane_strain = scalar_strain_zz
  full_jacobian = true
[]

[Mesh]
  type = PeridynamicsMesh
  horizon_number = 3

  [./gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 4
    ny = 4
  [../]
  [./gpd]
    type = MeshGeneratorPD
    input = gmg
    retain_fe_mesh = false
  [../]
[]

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

  [./scalar_strain_zz]
    order = FIRST
    family = SCALAR
  [../]
[]

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

[Modules/Peridynamics/Mechanics]
  [./Master]
    [./all]
      formulation = ORDINARY_STATE
    [../]
  [../]
  [./GeneralizedPlaneStrain]
    [./all]
      formulation = ORDINARY_STATE
      out_of_plane_stress_variable = stress_zz
    [../]
  [../]
[]

[AuxKernels]
  [./stress_zz]
    type = NodalRankTwoPD
    variable = stress_zz

    poissons_ratio = 0.3
    youngs_modulus = 1e6

    rank_two_tensor = stress
    output_type = component
    index_i = 2
    index_j = 2
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    poissons_ratio = 0.3
    youngs_modulus = 1e6
  [../]

  [./force_density]
    type = ComputeSmallStrainConstantHorizonMaterialOSPD
  [../]
[]

[Preconditioning]
  [./SMP]
    type = SMP
    full = true
    petsc_options_iname = '-ksp_type -pc_type -snes_type'
    petsc_options_value = 'bcgs bjacobi test'
  [../]
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  end_time = 1
  dt = 1
  num_steps = 1
[]

modules/peridynamics/test/tests/auxkernels/planestrain_thermomechanics_ranktwotensor_OSPD.i

[GlobalParams]
  displacements = 'disp_x disp_y'
  temperature = temp

  poissons_ratio = 0.3
  youngs_modulus = 1e6
  thermal_expansion_coeff = 0.0002
  stress_free_temperature = 0.0
[]

[Mesh]
  type = PeridynamicsMesh
  horizon_number = 3

  [./gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 8
    ny = 8
  [../]
  [./gpd]
    type = MeshGeneratorPD
    input = gmg
    retain_fe_mesh = false
  [../]
[]

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

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

  [./tstrain_xx]
    order = FIRST
    family = LAGRANGE
  [../]
  [./tstrain_yy]
    order = FIRST
    family = LAGRANGE
  [../]
  [./tstrain_zz]
    order = FIRST
    family = LAGRANGE
  [../]
  [./tstrain_xy]
    order = FIRST
    family = LAGRANGE
  [../]

  [./mstrain_xx]
    order = FIRST
    family = LAGRANGE
  [../]
  [./mstrain_yy]
    order = FIRST
    family = LAGRANGE
  [../]
  [./mstrain_zz]
    order = FIRST
    family = LAGRANGE
  [../]
  [./mstrain_xy]
    order = FIRST
    family = LAGRANGE
  [../]


  [./stress_xx]
    order = FIRST
    family = LAGRANGE
  [../]
  [./stress_yy]
    order = FIRST
    family = LAGRANGE
  [../]
  [./stress_zz]
    order = FIRST
    family = LAGRANGE
  [../]
  [./stress_xy]
    order = FIRST
    family = LAGRANGE
  [../]

  [./von_mises]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Modules/Peridynamics/Mechanics/Master]
  [./all]
    formulation = ORDINARY_STATE
  [../]
[]

[AuxKernels]
  [./tempfuncaux]
    type = FunctionAux
    variable = temp
    function = tempfunc
    use_displaced_mesh = false
  [../]

  [./tstrain_xx]
    type = NodalRankTwoPD
    variable = tstrain_xx
    rank_two_tensor = total_strain
    output_type = component
    index_i = 0
    index_j = 0
  [../]
  [./tstrain_yy]
    type = NodalRankTwoPD
    variable = tstrain_yy
    rank_two_tensor = total_strain
    output_type = component
    index_i = 1
    index_j = 1
  [../]
  [./tstrain_zz]
    type = NodalRankTwoPD
    variable = tstrain_zz
    rank_two_tensor = total_strain
    output_type = component
    index_i = 2
    index_j = 2
  [../]
  [./tstrain_xy]
    type = NodalRankTwoPD
    variable = tstrain_xy
    rank_two_tensor = total_strain
    output_type = component
    index_i = 0
    index_j = 1
  [../]

  [./mstrain_xx]
    type = NodalRankTwoPD
    variable = mstrain_xx
    rank_two_tensor = mechanical_strain
    output_type = component
    index_i = 0
    index_j = 0
  [../]
  [./mstrain_yy]
    type = NodalRankTwoPD
    variable = mstrain_yy
    rank_two_tensor = mechanical_strain
    output_type = component
    index_i = 1
    index_j = 1
  [../]
  [./mstrain_zz]
    type = NodalRankTwoPD
    variable = mstrain_zz
    rank_two_tensor = mechanical_strain
    output_type = component
    index_i = 2
    index_j = 2
  [../]
  [./mstrain_xy]
    type = NodalRankTwoPD
    variable = mstrain_xy
    rank_two_tensor = mechanical_strain
    output_type = component
    index_i = 0
    index_j = 1
  [../]

  [./stress_xx]
    type = NodalRankTwoPD
    variable = stress_xx
    rank_two_tensor = stress
    output_type = component
    index_i = 0
    index_j = 0
  [../]
  [./stress_yy]
    type = NodalRankTwoPD
    variable = stress_yy
    rank_two_tensor = stress
    output_type = component
    index_i = 1
    index_j = 1
  [../]
  [./stress_zz]
    type = NodalRankTwoPD
    variable = stress_zz
    rank_two_tensor = stress
    output_type = component
    index_i = 2
    index_j = 2
  [../]
  [./stress_xy]
    type = NodalRankTwoPD
    variable = stress_xy
    rank_two_tensor = stress
    output_type = component
    index_i = 0
    index_j = 1
  [../]

  [./vonmises]
    type = NodalRankTwoPD
    variable = von_mises
    rank_two_tensor = stress
    output_type = scalar
    scalar_type = VonMisesStress
  [../]
[]

[Functions]
  [./tempfunc]
    type = ParsedFunction
    value = 'x*x+y*y'
  [../]
[]

[BCs]
  [./left_x]
    type = DirichletBC
    boundary = 1003
    variable = disp_x
    value = 0.0
  [../]
  [./bottom_y]
    type = DirichletBC
    boundary = 1000
    variable = disp_y
    value = 0.0
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
  [../]

  [./force_density]
    type = ComputeSmallStrainConstantHorizonMaterialOSPD
  [../]
[]

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

[Executioner]
  type = Transient

  solve_type = PJFNK
  line_search = none

  start_time = 0.0
  end_time = 1.0
[]

[Outputs]
  exodus = true
  file_base = planestrain_thermomechanics_ranktwotensor_OSPD
[]

modules/peridynamics/test/tests/generalized_plane_strain/planestrain_prescribed_OSPD.i

[GlobalParams]
  displacements = 'disp_x disp_y'
  scalar_out_of_plane_strain = scalar_strain_zz
[]

[Mesh]
  type = PeridynamicsMesh
  horizon_number = 3

  [./gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 4
    ny = 4
  [../]
  [./gpd]
    type = MeshGeneratorPD
    input = gmg
    retain_fe_mesh = false
  [../]
[]

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

[AuxVariables]
  [./temp]
  [../]
  [./scalar_strain_zz]
    order = FIRST
    family = SCALAR
  [../]

  [./strain_zz]
  [../]
[]

[Modules/Peridynamics/Mechanics/Master]
  [./all]
    formulation = ORDINARY_STATE
  [../]
[]

[AuxKernels]
  [./tempfuncaux]
    type = FunctionAux
    variable = temp
    function = tempfunc
    use_displaced_mesh = false
  [../]

  [./strain_zz]
    type = NodalRankTwoPD
    variable = strain_zz
    rank_two_tensor = total_strain
    output_type = component
    index_i = 2
    index_j = 2
  [../]
[]

[AuxScalarKernels]
  [./scalar_strain_zz]
    type = FunctionScalarAux
    variable = scalar_strain_zz
    function = scalar_strain_zz_func
  [../]
[]

[Functions]
  [./tempfunc]
    type = ParsedFunction
    value = '(1 - x) * t'
  [../]
  [./scalar_strain_zz_func]
    type = PiecewiseLinear
    xy_data = '0 0
               1 7.901e-5
               2 1.103021e-2'
  [../]
[]

[BCs]
  [./bottom_x]
    type = DirichletBC
    boundary = 1000
    variable = disp_x
    value = 0.0
  [../]
  [./bottom_y]
    type = DirichletBC
    boundary = 1000
    variable = disp_y
    value = 0.0
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    poissons_ratio = 0.3
    youngs_modulus = 1e6
  [../]

  [./force_density]
    type = ComputeSmallStrainConstantHorizonMaterialOSPD
    temperature = temp
    thermal_expansion_coeff = 0.02
    stress_free_temperature = 0.5
  [../]
[]

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

[Executioner]
  type = Transient

  solve_type = PJFNK
  line_search = none

  start_time = 0.0
  end_time = 2.0
[]

[Outputs]
  exodus = true
  file_base = planestrain_prescribed_OSPD
[]

modules/peridynamics/test/tests/generalized_plane_strain/generalized_plane_strain_squares_OSPD.i

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  type = PeridynamicsMesh
  horizon_number = 3

  [./fmg]
    type = FileMeshGenerator
    file = squares.e
  [../]
  [./gpd]
    type = MeshGeneratorPD
    input = fmg
    retain_fe_mesh = false
  [../]
[]

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

  [./scalar_strain_zz1]
    order = FIRST
    family = SCALAR
  [../]
  [./scalar_strain_zz2]
    order = FIRST
    family = SCALAR
  [../]
[]

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

  [./stress_zz1]
    order = FIRST
    family = LAGRANGE
  [../]
  [./stress_zz2]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[Modules/Peridynamics/Mechanics]
  [./Master]
    [./block1]
      formulation = ORDINARY_STATE
      block = 1001
    [../]
    [./block2]
      formulation = ORDINARY_STATE
      block = 1002
    [../]
  [../]
  [./GeneralizedPlaneStrain]
    [./block1]
      formulation = ORDINARY_STATE
      scalar_out_of_plane_strain = scalar_strain_zz1
      out_of_plane_stress_variable = stress_zz1
      block = 1001
    [../]
    [./block2]
      formulation = ORDINARY_STATE
      scalar_out_of_plane_strain = scalar_strain_zz2
      out_of_plane_stress_variable = stress_zz2
      block = 1002
    [../]
  [../]
[]

[AuxKernels]
  [./tempfuncaux]
    type = FunctionAux
    variable = temp
    function = tempfunc
    use_displaced_mesh = false
  [../]

  [./stress_zz1]
    type = NodalRankTwoPD
    variable = stress_zz1
    rank_two_tensor = stress
    scalar_out_of_plane_strain = scalar_strain_zz1

    poissons_ratio = 0.3
    youngs_modulus = 1e6
    temperature = temp
    thermal_expansion_coeff = 0.02
    stress_free_temperature = 0.5

    output_type = component
    index_i = 2
    index_j = 2
    block = 1001
  [../]

  [./stress_zz2]
    type = NodalRankTwoPD
    variable = stress_zz2
    scalar_out_of_plane_strain = scalar_strain_zz2

    poissons_ratio = 0.3
    youngs_modulus = 1e6
    temperature = temp
    thermal_expansion_coeff = 0.02
    stress_free_temperature = 0.5

    rank_two_tensor = stress
    output_type = component
    index_i = 2
    index_j = 2
    block = 1002
  [../]
[]

[Postprocessors]
  [./react_z1]
    type = NodalVariableIntegralPD
    variable = stress_zz1
    block = 1001
  [../]
  [./react_z2]
    type = NodalVariableIntegralPD
    variable = stress_zz2
    block = 1002
  [../]
[]

[Functions]
  [./tempfunc]
    type = ParsedFunction
    value = '(1-x)*t'
  [../]
[]

[BCs]
  [./bottom1_x]
    type = DirichletBC
    boundary = 1001
    variable = disp_x
    value = 0.0
  [../]
  [./bottom1_y]
    type = DirichletBC
    boundary = 1001
    variable = disp_y
    value = 0.0
  [../]

  [./bottom2_x]
    type = DirichletBC
    boundary = 1002
    variable = disp_x
    value = 0.0
  [../]
  [./bottom2_y]
    type = DirichletBC
    boundary = 1002
    variable = disp_y
    value = 0.0
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    poissons_ratio = 0.3
    youngs_modulus = 1e6
    block = '1001 1002'
  [../]

  [./force_density1]
    type = ComputeSmallStrainVariableHorizonMaterialOSPD
    temperature = temp
    thermal_expansion_coeff = 0.02
    stress_free_temperature = 0.5
    scalar_out_of_plane_strain = scalar_strain_zz1
    block = 1001
  [../]
  [./force_density2]
    type = ComputeSmallStrainVariableHorizonMaterialOSPD
    temperature = temp
    thermal_expansion_coeff = 0.02
    stress_free_temperature = 0.5
    scalar_out_of_plane_strain = scalar_strain_zz2
    block = 1002
  [../]
[]

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

[Executioner]
  type = Transient

  solve_type = PJFNK
  line_search = none

  l_tol = 1e-8
  nl_rel_tol = 1e-12

  start_time = 0.0
  end_time = 1.0
[]

[Outputs]
  exodus = true
  file_base = generalized_plane_strain_squares_OSPD
[]

modules/peridynamics/test/tests/generalized_plane_strain/out_of_plane_pressure_OSPD.i

[GlobalParams]
  displacements = 'disp_x disp_y'
  scalar_out_of_plane_strain = scalar_strain_zz
[]

[Mesh]
  type = PeridynamicsMesh
  horizon_number = 3

  [./gmg]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 4
    ny = 4
  [../]
  [./gpd]
    type = MeshGeneratorPD
    input = gmg
    retain_fe_mesh = false
  [../]
[]

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

  [./scalar_strain_zz]
    order = FIRST
    family = SCALAR
  [../]
[]

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

[Modules]
  [./Peridynamics/Mechanics]
    [./Master]
      [./all]
        formulation = ORDINARY_STATE
      [../]
    [../]
    [./GeneralizedPlaneStrain]
      [./all]
        formulation = ORDINARY_STATE
        out_of_plane_stress_variable = stress_zz
        out_of_plane_pressure = pressure_function
        factor = 1e5
      [../]
    [../]
  [../]
[]

[AuxKernels]
  [./stress_zz]
    type = NodalRankTwoPD
    variable = stress_zz
    poissons_ratio = 0.3
    youngs_modulus = 1e6
    rank_two_tensor = stress
    output_type = component
    index_i = 2
    index_j = 2
  [../]
[]

[Postprocessors]
  [./react_z]
    type = NodalVariableIntegralPD
    variable = stress_zz
  [../]
[]

[Functions]
  [./pressure_function]
    type = PiecewiseLinear
    x = '0  1'
    y = '0  1'
  [../]
[]

[BCs]
  [./left_x]
    type = DirichletBC
    boundary = 1003
    variable = disp_x
    value = 0.0
  [../]
  [./bottom_y]
    type = DirichletBC
    boundary = 1000
    variable = disp_y
    value = 0.0
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    poissons_ratio = 0.3
    youngs_modulus = 1e6
  [../]

  [./force_density]
    type = ComputeSmallStrainConstantHorizonMaterialOSPD
  [../]
[]

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

[Executioner]
  type = Transient

  solve_type = PJFNK
  line_search = none

  start_time = 0.0
  end_time = 1.0
[]

[Outputs]
  exodus = true
  file_base = out_of_plane_pressure_OSPD
[]

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