GeneralizedPlaneStrainAction

Set up the GeneralizedPlaneStrain environment

Description

This action simplifies the input syntax for creating a generalized plane strain model. It creates the objects associated with the scalar out-of-plane strain variable and the out-of-plane equilibrium equation. A detailed description of the formulation is available on the generalized plane strain page.

warning:For 2D and 1D Simulations

GeneralizedPlaneStrainAction supports 1D axisymmetric or 2D generalized plane strain cases. For 1D axisymmetric and 2D Cartesian cases in the x-y plane, the number of displacement variables must be one or two, respectively.

For 2D generalized plane strain cases in the x-z or y-z planes, the number of displacement variables must be three.

Constructed Objects

Without automatic differentiation, the action creates the UserObject, ScalarKernel, and off-diagonal Kernel objects listed below.

Table 1: Non-AD objects created by GeneralizedPlaneStrainAction

Object	Purpose
Generalized Plane Strain Off Diagonal	Couples the in-plane displacement variables and the scalar out-of-plane strain variable in the off-diagonal Jacobian.
Generalized Plane Strain Scalar Kernel	Assembles the scalar out-of-plane equilibrium residual.
Generalized Plane Strain User Object	Computes the residual and diagonal Jacobian data used by the scalar kernel.

With "use_automatic_differentiation", the action creates exactly one ADGeneralizedPlaneStrain object. The non-AD UserObject, ScalarKernel, and off-diagonal Kernel objects are not created because ADKernelScalarBase assembles the scalar residual and its couplings through automatic differentiation. When "use_displaced_mesh" is true, the AD kernel uses displaced-mesh quadrature weights for that scalar assembly.

Table 2: AD objects created by GeneralizedPlaneStrainAction

Object	Purpose
ADGeneralizedPlaneStrain	Assembles the scalar out-of-plane equilibrium residual and AD couplings.

The action also creates the scalar out-of-plane strain variable named by "scalar_out_of_plane_strain" when it is missing. The automatically created scalar variable is a FIRST order nonlinear scalar variable in the nonlinear system that contains the in-plane displacement variables. If the named scalar variable already exists in that system, the action reuses it. A field variable or a scalar variable in a different nonlinear system with the same name is rejected.

Out-of-Plane Pressure

The residual assembled for the scalar out-of-plane strain is $var element = document.getElementById("moose-equation-2527719c-a386-4b1b-82f8-91f575aca190");katex.render(" R_s = \\int_A \\left( \\sigma_{oo} + p_o \\right) dA = 0,", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ where $var element = document.getElementById("moose-equation-ed37fc94-e8fb-4de1-a62c-8575b7a6810c");katex.render("p_o", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the out-of-plane pressure. Positive pressure is applied toward the body. In Cartesian coordinates, the out-of-plane x, y, and z directions use $var element = document.getElementById("moose-equation-92924146-ee4a-411e-ab12-6c05190a194d");katex.render("\\sigma_{xx}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , $var element = document.getElementById("moose-equation-e2ba020f-a4f7-4516-95c7-e74aa5775dfc");katex.render("\\sigma_{yy}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , and $var element = document.getElementById("moose-equation-0435a2a3-8abf-4796-bdc0-ec40fa140848");katex.render("\\sigma_{zz}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , respectively. In RZ axisymmetry, the out-of-plane direction is the axial y direction and the residual uses axisymmetric coordinate weighting.

The pressure may be supplied with "out_of_plane_pressure_function", with "out_of_plane_pressure_material", or with both; the two contributions are summed and scaled by "pressure_factor". With automatic differentiation, the pressure material is read as a regular Real material property, so it does not add derivatives to the scalar equation.

Example Input Syntax

Subblocks

The subblocks of the GeneralizedPlaneStrain action trigger object construction. If a generalized plane strain model is applied to the whole simulation domain, use a single subblock.

[./GeneralizedPlaneStrain]
  [./gps]
    use_displaced_mesh = true
    displacements = 'disp_x disp_y'
    scalar_out_of_plane_strain = scalar_strain_zz
    out_of_plane_pressure_function = traction_function
    pressure_factor = 1e5
  [../]
[../]

If different mesh subdomains use different generalized plane strain models, use multiple subblocks with subdomain restrictions.

[./GeneralizedPlaneStrain]
  [./gps1]
    use_displaced_mesh = true
    displacements = 'disp_x disp_y'
    scalar_out_of_plane_strain = scalar_strain_zz1
    block = '1'
  [../]
  [./gps2]
    use_displaced_mesh = true
    displacements = 'disp_x disp_y'
    scalar_out_of_plane_strain = scalar_strain_zz2
    block = '2'
  [../]
[../]

An example of using generalized plane strain through the Solid Mechanics QuasiStatic physics block with an "out_of_plane_direction" different from the default $var element = document.getElementById("moose-equation-1ccee81c-b8d1-4893-91f5-acf6857faa3f");katex.render("z", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ direction is given by:

[./generalized_plane_strain]
  block = 1
  strain = SMALL
  scalar_out_of_plane_strain = scalar_strain_yy
  out_of_plane_direction = y
  planar_formulation = GENERALIZED_PLANE_STRAIN
  eigenstrain_names = 'eigenstrain'
  generate_output = 'stress_xx stress_xz stress_yy stress_zz strain_xx strain_xz strain_yy strain_zz'
[../]

Parameters supplied at the [Physics/SolidMechanics/GeneralizedPlaneStrain] level act as defaults for the QuasiStatic Physics subblocks.

The following input shows a standalone [Physics/SolidMechanics/GeneralizedPlaneStrain] action block. The action creates the missing scalar out-of-plane strain variable for a model that uses AD.

[Physics<<<{"href": "../../syntax/Physics/index.html"}>>>]
  [SolidMechanics<<<{"href": "../../syntax/Physics/SolidMechanics/index.html"}>>>]
    [GeneralizedPlaneStrain<<<{"href": "../../syntax/Physics/SolidMechanics/GeneralizedPlaneStrain/index.html"}>>>]
      [gps]
        use_automatic_differentiation<<<{"description": "Use automatic differentiation to assemble the generalized plane strain equation and its coupling terms"}>>> = true
        use_displaced_mesh<<<{"description": "Whether to use displaced mesh"}>>> = true
        displacements<<<{"description": "The displacement variables"}>>> = 'disp_x disp_y'
        scalar_out_of_plane_strain<<<{"description": "Scalar variable for the out-of-plane strain (in y direction for 1D Axisymmetric or in z direction for 2D Cartesian problems)"}>>> = scalar_strain_zz
        out_of_plane_pressure_function<<<{"description": "Function used to prescribe pressure (applied toward the body) in the out-of-plane direction (y for 1D Axisymmetric or z for 2D Cartesian problems)"}>>> = traction_function
        pressure_factor<<<{"description": "Scale factor applied to prescribed out-of-plane pressure (both material and function)"}>>> = 1e5
      []
    []
  []
[]

Generalized Plane Strain and Reference Residual

Generalized plane strain problems may use ReferenceResidualProblem. In this case, a reference scalar variable is needed to correspond with the scalar strain variable.

[Problem<<<{"href": "../../syntax/Problem/index.html"}>>>]
  type = ReferenceResidualProblem
  extra_tag_vectors = 'ref'
  reference_vector = 'ref'
[]

The reference scalar variable is set using the AuxScalarKernel Generalized Plane Strain Reference Residual using the Generalized Plane Strain UserObject.

[AuxScalarKernels<<<{"href": "../../syntax/AuxScalarKernels/index.html"}>>>]
  [./gps_ref_res]
    type = GeneralizedPlaneStrainReferenceResidual<<<{"description": "Generalized Plane Strain Reference Residual Scalar Kernel", "href": "../auxkernels/GeneralizedPlaneStrainReferenceResidual.html"}>>>
    variable<<<{"description": "The name of the variable that this kernel operates on"}>>> = saved_zz
    generalized_plane_strain<<<{"description": "The name of the GeneralizedPlaneStrainUserObject"}>>> = gps_GeneralizedPlaneStrainUserObject
  [../]
[]

Input Parameters

displacementsThe displacement variables
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The displacement variables
scalar_out_of_plane_strainScalar variable for the out-of-plane strain (in y direction for 1D Axisymmetric or in z direction for 2D Cartesian problems)
C++ Type:VariableName
Unit:(no unit assumed)
Controllable:No
Description:Scalar variable for the out-of-plane strain (in y direction for 1D Axisymmetric or in z direction for 2D Cartesian problems)

Required Parameters

absolute_value_vector_tagsThe tag names for extra vectors that the absolute value of the residual should be accumulated into
C++ Type:std::vector<TagName>
Controllable:No
Description:The tag names for extra vectors that the absolute value of the residual should be accumulated into
active__all__ If specified only the blocks named will be visited and made active
Default:__all__
C++ Type:std::vector<std::string>
Controllable:No
Description:If specified only the blocks named will be visited and made active
base_nameMaterial property base name
C++ Type:std::string
Controllable:No
Description:Material property base name
blockThe list of ids of the blocks (subdomain) that the GeneralizedPlaneStrain kernels will be applied to
C++ Type:std::vector<SubdomainName>
Controllable:No
Description:The list of ids of the blocks (subdomain) that the GeneralizedPlaneStrain kernels will be applied to
extra_vector_tagsThe tag names for extra vectors that residual data should be saved into
C++ Type:std::vector<TagName>
Controllable:No
Description:The tag names for extra vectors that residual data should be saved into
inactiveIf specified blocks matching these identifiers will be skipped.
C++ Type:std::vector<std::string>
Controllable:No
Description:If specified blocks matching these identifiers will be skipped.
out_of_plane_directionzThe direction of the out-of-plane strain.
Default:z
C++ Type:MooseEnum
Options:x, y, z
Controllable:No
Description:The direction of the out-of-plane strain.
out_of_plane_pressure_functionFunction used to prescribe pressure (applied toward the body) in the out-of-plane direction (y for 1D Axisymmetric or z for 2D Cartesian problems)
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:Function used to prescribe pressure (applied toward the body) in the out-of-plane direction (y for 1D Axisymmetric or z for 2D Cartesian problems)
out_of_plane_pressure_material0Material used to prescribe pressure (applied toward the body) in the out-of-plane direction
Default:0
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:Material used to prescribe pressure (applied toward the body) in the out-of-plane direction
pressure_factorScale factor applied to prescribed out-of-plane pressure (both material and function)
C++ Type:Real
Unit:(no unit assumed)
Controllable:No
Description:Scale factor applied to prescribed out-of-plane pressure (both material and function)
temperatureThe temperature variable
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The temperature variable
use_automatic_differentiationFalseUse automatic differentiation to assemble the generalized plane strain equation and its coupling terms
Default:False
C++ Type:bool
Controllable:No
Description:Use automatic differentiation to assemble the generalized plane strain equation and its coupling terms
use_displaced_meshFalseWhether to use displaced mesh
Default:False
C++ Type:bool
Controllable:No
Description:Whether to use displaced mesh

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.

Advanced Parameters

(modules/solid_mechanics/test/tests/generalized_plane_strain/out_of_plane_pressure.i)

# Tests for application of out-of-plane pressure in generalized plane strain.

[Mesh]
  [./square]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 2
    ny = 2
  [../]
  displacements = 'disp_x disp_y'
[]

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

[AuxVariables]
  [./saved_x]
    order = FIRST
    family = LAGRANGE
  [../]
  [./saved_y]
    order = FIRST
    family = LAGRANGE
  [../]

  [./stress_xx]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./stress_xy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./stress_yy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./stress_zz]
    order = CONSTANT
    family = MONOMIAL
  [../]

  [./strain_xx]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./strain_xy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./strain_yy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./strain_zz]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[Postprocessors]
  [./react_z]
    type = MaterialTensorIntegral
    rank_two_tensor = stress
    index_i = 2
    index_j = 2
  [../]
[]

[Physics]
  [SolidMechanics]
    [./GeneralizedPlaneStrain]
      [./gps]
        use_displaced_mesh = true
        displacements = 'disp_x disp_y'
        scalar_out_of_plane_strain = scalar_strain_zz
        out_of_plane_pressure_function = traction_function
        pressure_factor = 1e5
      [../]
    [../]
  [../]
[]

[Kernels]
  [SolidMechanics]
    use_displaced_mesh = false
    displacements = 'disp_x disp_y'
    save_in = 'saved_x saved_y'
  [../]
[]

[AuxKernels]
  [./stress_xx]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_xx
    index_i = 0
    index_j = 0
  [../]
  [./stress_xy]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_xy
    index_i = 0
    index_j = 1
  [../]
  [./stress_yy]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_yy
    index_i = 1
    index_j = 1
  [../]
  [./stress_zz]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_zz
    index_i = 2
    index_j = 2
  [../]

  [./strain_xx]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = strain_xx
    index_i = 0
    index_j = 0
  [../]
  [./strain_xy]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = strain_xy
    index_i = 0
    index_j = 1
  [../]
  [./strain_yy]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = strain_yy
    index_i = 1
    index_j = 1
  [../]
  [./strain_zz]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = strain_zz
    index_i = 2
    index_j = 2
  [../]
[]

[Functions]
  [./traction_function]
    type = PiecewiseLinear
    x = '0  2'
    y = '0  1'
  [../]
[]

[BCs]
  [./leftx]
    type = DirichletBC
    boundary = 3
    variable = disp_x
    value = 0.0
  [../]
  [./bottomy]
    type = DirichletBC
    boundary = 0
    variable = disp_y
    value = 0.0
  [../]
[]

[Materials]
  [./elastic_tensor]
    type = ComputeIsotropicElasticityTensor
    poissons_ratio = 0.3
    youngs_modulus = 1e6
  [../]
  [./strain]
    type = ComputePlaneSmallStrain
    displacements = 'disp_x disp_y'
    scalar_out_of_plane_strain = scalar_strain_zz
  [../]
  [./stress]
    type = ComputeLinearElasticStress
  [../]
  # This material is not used for anything in the base verison of this test,
  # but is used in a variant of the test with cli_args
  [./traction_material]
    type = GenericFunctionMaterial
    prop_names = traction_material
    prop_values = traction_function
  [../]
[]

[Executioner]
  type = Transient

  solve_type = PJFNK
  line_search = none

# controls for linear iterations
  l_max_its = 100
  l_tol = 1e-4

# controls for nonlinear iterations
  nl_max_its = 15
  nl_rel_tol = 1e-14
  nl_abs_tol = 1e-11

# time control
  start_time = 0.0
  dt = 1.0
  dtmin = 1.0
  end_time = 2.0
  num_steps = 5000
[]

[Outputs]
  exodus = true
[]

(modules/solid_mechanics/test/tests/generalized_plane_strain/generalized_plane_strain_squares.i)

[Mesh]
  file = 2squares.e
  displacements = 'disp_x disp_y'
[]

[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
  [../]
  [./saved_x]
    order = FIRST
    family = LAGRANGE
  [../]
  [./saved_y]
    order = FIRST
    family = LAGRANGE
  [../]

  [./stress_xx]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./stress_xy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./stress_yy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./stress_zz]
    order = CONSTANT
    family = MONOMIAL
  [../]

  [./strain_xx]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./strain_xy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./strain_yy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./aux_strain_zz]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[Postprocessors]
  [./react_z1]
    type = MaterialTensorIntegral
    rank_two_tensor = stress
    index_i = 2
    index_j = 2
    block = 1
  [../]
  [./react_z2]
    type = MaterialTensorIntegral
    rank_two_tensor = stress
    index_i = 2
    index_j = 2
    block = 2
  [../]
[]

[Physics]
  [SolidMechanics]
    [./GeneralizedPlaneStrain]
      [./gps1]
        use_displaced_mesh = true
        displacements = 'disp_x disp_y'
        scalar_out_of_plane_strain = scalar_strain_zz1
        block = '1'
      [../]
      [./gps2]
        use_displaced_mesh = true
        displacements = 'disp_x disp_y'
        scalar_out_of_plane_strain = scalar_strain_zz2
        block = '2'
      [../]
    [../]
  [../]
[]

[Kernels]
  [SolidMechanics]
    use_displaced_mesh = false
    displacements = 'disp_x disp_y'
    temperature = temp
    save_in = 'saved_x saved_y'
    block = '1 2'
  [../]
[]

[AuxKernels]
  [./tempfuncaux]
    type = FunctionAux
    variable = temp
    function = tempfunc
    use_displaced_mesh = false
  [../]
  [./stress_xx]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_xx
    index_i = 0
    index_j = 0
  [../]
  [./stress_xy]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_xy
    index_i = 0
    index_j = 1
  [../]
  [./stress_yy]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_yy
    index_i = 1
    index_j = 1
  [../]
  [./stress_zz]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_zz
    index_i = 2
    index_j = 2
  [../]

  [./strain_xx]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = strain_xx
    index_i = 0
    index_j = 0
  [../]
  [./strain_xy]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = strain_xy
    index_i = 0
    index_j = 1
  [../]
  [./strain_yy]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = strain_yy
    index_i = 1
    index_j = 1
  [../]
  [./aux_strain_zz]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = aux_strain_zz
    index_i = 2
    index_j = 2
  [../]
[]

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

[BCs]
  [./bottom1x]
    type = DirichletBC
    boundary = 1
    variable = disp_x
    value = 0.0
  [../]
  [./bottom1y]
    type = DirichletBC
    boundary = 1
    variable = disp_y
    value = 0.0
  [../]
  [./bottom2x]
    type = DirichletBC
    boundary = 2
    variable = disp_x
    value = 0.0
  [../]
  [./bottom2y]
    type = DirichletBC
    boundary = 2
    variable = disp_y
    value = 0.0
  [../]
[]

[Materials]
  [./elastic_tensor]
    type = ComputeIsotropicElasticityTensor
    poissons_ratio = 0.3
    youngs_modulus = 1e6
    block = '1 2'
  [../]
  [./strain1]
    type = ComputePlaneSmallStrain
    displacements = 'disp_x disp_y'
    scalar_out_of_plane_strain = scalar_strain_zz1
    block = 1
    eigenstrain_names = eigenstrain
  [../]
  [./strain2]
    type = ComputePlaneSmallStrain
    displacements = 'disp_x disp_y'
    scalar_out_of_plane_strain = scalar_strain_zz2
    block = 2
    eigenstrain_names = eigenstrain
  [../]
  [./thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    temperature = temp
    thermal_expansion_coeff = 0.02
    stress_free_temperature = 0.5
    block = '1 2'
    eigenstrain_name = eigenstrain
  [../]
  [./stress]
    type = ComputeLinearElasticStress
    block = '1 2'
  [../]
[]

[Executioner]
  type = Transient

  solve_type = PJFNK
  line_search = none

# controls for linear iterations
  l_max_its = 100
  l_tol = 1e-10

# controls for nonlinear iterations
  nl_max_its = 15
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-10

# time control
  start_time = 0.0
  dt = 1.0
  dtmin = 1.0
  end_time = 2.0
  num_steps = 5000
[]

[Outputs]
  exodus = true
[]

(modules/solid_mechanics/test/tests/2D_different_planes/gps_xz.i)

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

[Mesh]
  file = square_xz_plane.e
[]

[Variables]
  [./disp_x]
  [../]
  [./disp_z]
  [../]
  [./scalar_strain_yy]
    order = FIRST
    family = SCALAR
  [../]
[]

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

[Physics/SolidMechanics/QuasiStatic]
  [./generalized_plane_strain]
    block = 1
    strain = SMALL
    scalar_out_of_plane_strain = scalar_strain_yy
    out_of_plane_direction = y
    planar_formulation = GENERALIZED_PLANE_STRAIN
    eigenstrain_names = 'eigenstrain'
    generate_output = 'stress_xx stress_xz stress_yy stress_zz strain_xx strain_xz strain_yy strain_zz'
  [../]
[]

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

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

[BCs]
  [./bottomx]
    type = DirichletBC
    boundary = 3
    variable = disp_x
    value = 0.0
  [../]
  [./bottomy]
    type = DirichletBC
    boundary = 3
    variable = disp_z
    value = 0.0
  [../]
[]

[Materials]
  [./elastic_stress]
    type = ComputeLinearElasticStress
    block = 1
  [../]
  [./thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    temperature = temp
    thermal_expansion_coeff = 0.02
    stress_free_temperature = 0.5
    eigenstrain_name = eigenstrain
  [../]
  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = 1
    poissons_ratio = 0.3
    youngs_modulus = 1e6
  [../]
[]

[Postprocessors]
  [./react_y]
    type = MaterialTensorIntegral
    use_displaced_mesh = false
    rank_two_tensor = stress
    index_i = 1
    index_j = 1
  [../]
[]

[Executioner]
  type = Transient

  solve_type = PJFNK
  line_search = none

# controls for linear iterations
  l_max_its = 100
  l_tol = 1e-10

# controls for nonlinear iterations
  nl_max_its = 10
  nl_rel_tol = 1e-12

# time control
  start_time = 0.0
  dt = 1.0
  dtmin = 1.0
  end_time = 2.0
[]

[Outputs]
  file_base = gps_xz_small_out
  exodus = true
[]

(modules/solid_mechanics/test/tests/generalized_plane_strain/generalized_plane_strain_auto_scalar.i)

[Mesh]
  [square]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 2
    ny = 2
  []
  displacements = 'disp_x disp_y'
[]

[Problem]
  nl_sys_names = 'unused mechanics'
[]

[Variables]
  [unused]
    solver_sys = unused
    outputs = none
  []
  [disp_x]
    solver_sys = mechanics
  []
  [disp_y]
    solver_sys = mechanics
  []
[]

[AuxVariables]
  [saved_x]
    order = FIRST
    family = LAGRANGE
  []
  [saved_y]
    order = FIRST
    family = LAGRANGE
  []

  [stress_xx]
    order = CONSTANT
    family = MONOMIAL
  []
  [stress_xy]
    order = CONSTANT
    family = MONOMIAL
  []
  [stress_yy]
    order = CONSTANT
    family = MONOMIAL
  []
  [stress_zz]
    order = CONSTANT
    family = MONOMIAL
  []

  [strain_xx]
    order = CONSTANT
    family = MONOMIAL
  []
  [strain_xy]
    order = CONSTANT
    family = MONOMIAL
  []
  [strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []
  [strain_zz]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Postprocessors]
  [react_z]
    type = ADMaterialTensorIntegral
    rank_two_tensor = stress
    index_i = 2
    index_j = 2
  []
[]

[Physics]
  [SolidMechanics]
    [GeneralizedPlaneStrain]
      [gps]
        use_automatic_differentiation = true
        use_displaced_mesh = true
        displacements = 'disp_x disp_y'
        scalar_out_of_plane_strain = scalar_strain_zz
        out_of_plane_pressure_function = traction_function
        pressure_factor = 1e5
      []
    []
  []
[]

[Kernels]
  [unused]
    type = ADReaction
    variable = unused
  []
  [SolidMechanics]
    use_automatic_differentiation = true
    use_displaced_mesh = false
    displacements = 'disp_x disp_y'
    save_in = 'saved_x saved_y'
  []
[]

[AuxKernels]
  [stress_xx]
    type = ADRankTwoAux
    rank_two_tensor = stress
    variable = stress_xx
    index_i = 0
    index_j = 0
  []
  [stress_xy]
    type = ADRankTwoAux
    rank_two_tensor = stress
    variable = stress_xy
    index_i = 0
    index_j = 1
  []
  [stress_yy]
    type = ADRankTwoAux
    rank_two_tensor = stress
    variable = stress_yy
    index_i = 1
    index_j = 1
  []
  [stress_zz]
    type = ADRankTwoAux
    rank_two_tensor = stress
    variable = stress_zz
    index_i = 2
    index_j = 2
  []

  [strain_xx]
    type = ADRankTwoAux
    rank_two_tensor = total_strain
    variable = strain_xx
    index_i = 0
    index_j = 0
  []
  [strain_xy]
    type = ADRankTwoAux
    rank_two_tensor = total_strain
    variable = strain_xy
    index_i = 0
    index_j = 1
  []
  [strain_yy]
    type = ADRankTwoAux
    rank_two_tensor = total_strain
    variable = strain_yy
    index_i = 1
    index_j = 1
  []
  [strain_zz]
    type = ADRankTwoAux
    rank_two_tensor = total_strain
    variable = strain_zz
    index_i = 2
    index_j = 2
  []
[]

[Functions]
  [traction_function]
    type = PiecewiseLinear
    x = '0  2'
    y = '0  1'
  []
[]

[BCs]
  [leftx]
    type = DirichletBC
    boundary = 3
    variable = disp_x
    value = 0.0
  []
  [bottomy]
    type = DirichletBC
    boundary = 0
    variable = disp_y
    value = 0.0
  []
[]

[Materials]
  [elastic_tensor]
    type = ADComputeIsotropicElasticityTensor
    poissons_ratio = 0.3
    youngs_modulus = 1e6
  []
  [strain]
    type = ADComputePlaneSmallStrain
    displacements = 'disp_x disp_y'
    scalar_out_of_plane_strain = scalar_strain_zz
  []
  [stress]
    type = ADComputeLinearElasticStress
  []
  [traction_material]
    type = ADGenericFunctionMaterial
    prop_names = traction_material
    prop_values = traction_function
  []
[]

[Executioner]
  type = Transient

  solve_type = PJFNK
  line_search = none

  l_max_its = 100
  l_tol = 1e-4

  nl_max_its = 15
  nl_rel_tol = 1e-14
  nl_abs_tol = 1e-11

  start_time = 0.0
  dt = 1.0
  dtmin = 1.0
  end_time = 2.0
  num_steps = 2
[]

[Outputs]
  exodus = true
[]

(modules/combined/test/tests/generalized_plane_strain_tm_contact/out_of_plane_pressure.i)

# Tests for application of out-of-plane pressure in generalized plane strain.

[Mesh]
  type = GeneratedMesh
  nx = 2
  ny = 2
  dim = 2
  xmin = 0.0
  xmax = 1.0
  ymin = 0.0
  ymax = 1.0
  displacements = 'disp_x disp_y'
[]

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

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

[AuxVariables]
  [./saved_x]
    order = FIRST
    family = LAGRANGE
  [../]
  [./saved_y]
    order = FIRST
    family = LAGRANGE
  [../]
  [./saved_zz]
    order = FIRST
    family = SCALAR
  [../]

  [./stress_xx]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./stress_xy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./stress_yy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./stress_zz]
    order = CONSTANT
    family = MONOMIAL
  [../]

  [./strain_xx]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./strain_xy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./strain_yy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./strain_zz]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[Postprocessors]
  [./react_z]
    type = MaterialTensorIntegral
    rank_two_tensor = stress
    index_i = 2
    index_j = 2
  [../]
[]

[Physics]
  [./SolidMechanics]
    [./GeneralizedPlaneStrain]
      [./gps]
        displacements = 'disp_x disp_y'
        scalar_out_of_plane_strain = scalar_strain_zz
        out_of_plane_pressure = traction_function
        factor = 1e5
      [../]
    [../]
  [../]
[]

[Kernels]
  [./TensorMechanics]
    use_displaced_mesh = true
    displacements = 'disp_x disp_y'
    save_in = 'saved_x saved_y'
    extra_vector_tags = 'ref'
  [../]
[]

[AuxScalarKernels]
  [./gps_ref_res]
    type = GeneralizedPlaneStrainReferenceResidual
    variable = saved_zz
    generalized_plane_strain = gps_GeneralizedPlaneStrainUserObject
  [../]
[]

[AuxKernels]
  [./stress_xx]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_xx
    index_i = 0
    index_j = 0
  [../]
  [./stress_xy]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_xy
    index_i = 0
    index_j = 1
  [../]
  [./stress_yy]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_yy
    index_i = 1
    index_j = 1
  [../]
  [./stress_zz]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_zz
    index_i = 2
    index_j = 2
  [../]

  [./strain_xx]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = strain_xx
    index_i = 0
    index_j = 0
  [../]
  [./strain_xy]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = strain_xy
    index_i = 0
    index_j = 1
  [../]
  [./strain_yy]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = strain_yy
    index_i = 1
    index_j = 1
  [../]
  [./strain_zz]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = strain_zz
    index_i = 2
    index_j = 2
  [../]
[]

[Functions]
  [./traction_function]
    type = PiecewiseLinear
    x = '0  2'
    y = '0  1'
  [../]
[]

[BCs]
  [./leftx]
    type = DirichletBC
    boundary = left
    variable = disp_x
    value = 0.0
  [../]
  [./bottomy]
    type = DirichletBC
    boundary = bottom
    variable = disp_y
    value = 0.0
  [../]
[]

[Materials]
  [./elastic_tensor]
    type = ComputeIsotropicElasticityTensor
    poissons_ratio = 0.3
    youngs_modulus = 1e6
  [../]
  [./strain]
    type = ComputePlaneSmallStrain
    displacements = 'disp_x disp_y'
    scalar_out_of_plane_strain = scalar_strain_zz
  [../]
  [./stress]
    type = ComputeLinearElasticStress
  [../]
[]

[Executioner]
  type = Transient

  solve_type = PJFNK
  line_search = none

# controls for linear iterations
  l_max_its = 100
  l_tol = 1e-4

# controls for nonlinear iterations
  nl_max_its = 15
  nl_rel_tol = 1e-14
  nl_abs_tol = 1e-11

# time control
  start_time = 0.0
  dt = 1.0
  dtmin = 1.0
  end_time = 2.0
  num_steps = 5000
[]

[Outputs]
  exodus = true
[]

(modules/combined/test/tests/generalized_plane_strain_tm_contact/out_of_plane_pressure.i)

# Tests for application of out-of-plane pressure in generalized plane strain.

[Mesh]
  type = GeneratedMesh
  nx = 2
  ny = 2
  dim = 2
  xmin = 0.0
  xmax = 1.0
  ymin = 0.0
  ymax = 1.0
  displacements = 'disp_x disp_y'
[]

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

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

[AuxVariables]
  [./saved_x]
    order = FIRST
    family = LAGRANGE
  [../]
  [./saved_y]
    order = FIRST
    family = LAGRANGE
  [../]
  [./saved_zz]
    order = FIRST
    family = SCALAR
  [../]

  [./stress_xx]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./stress_xy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./stress_yy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./stress_zz]
    order = CONSTANT
    family = MONOMIAL
  [../]

  [./strain_xx]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./strain_xy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./strain_yy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./strain_zz]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[Postprocessors]
  [./react_z]
    type = MaterialTensorIntegral
    rank_two_tensor = stress
    index_i = 2
    index_j = 2
  [../]
[]

[Physics]
  [./SolidMechanics]
    [./GeneralizedPlaneStrain]
      [./gps]
        displacements = 'disp_x disp_y'
        scalar_out_of_plane_strain = scalar_strain_zz
        out_of_plane_pressure = traction_function
        factor = 1e5
      [../]
    [../]
  [../]
[]

[Kernels]
  [./TensorMechanics]
    use_displaced_mesh = true
    displacements = 'disp_x disp_y'
    save_in = 'saved_x saved_y'
    extra_vector_tags = 'ref'
  [../]
[]

[AuxScalarKernels]
  [./gps_ref_res]
    type = GeneralizedPlaneStrainReferenceResidual
    variable = saved_zz
    generalized_plane_strain = gps_GeneralizedPlaneStrainUserObject
  [../]
[]

[AuxKernels]
  [./stress_xx]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_xx
    index_i = 0
    index_j = 0
  [../]
  [./stress_xy]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_xy
    index_i = 0
    index_j = 1
  [../]
  [./stress_yy]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_yy
    index_i = 1
    index_j = 1
  [../]
  [./stress_zz]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_zz
    index_i = 2
    index_j = 2
  [../]

  [./strain_xx]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = strain_xx
    index_i = 0
    index_j = 0
  [../]
  [./strain_xy]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = strain_xy
    index_i = 0
    index_j = 1
  [../]
  [./strain_yy]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = strain_yy
    index_i = 1
    index_j = 1
  [../]
  [./strain_zz]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = strain_zz
    index_i = 2
    index_j = 2
  [../]
[]

[Functions]
  [./traction_function]
    type = PiecewiseLinear
    x = '0  2'
    y = '0  1'
  [../]
[]

[BCs]
  [./leftx]
    type = DirichletBC
    boundary = left
    variable = disp_x
    value = 0.0
  [../]
  [./bottomy]
    type = DirichletBC
    boundary = bottom
    variable = disp_y
    value = 0.0
  [../]
[]

[Materials]
  [./elastic_tensor]
    type = ComputeIsotropicElasticityTensor
    poissons_ratio = 0.3
    youngs_modulus = 1e6
  [../]
  [./strain]
    type = ComputePlaneSmallStrain
    displacements = 'disp_x disp_y'
    scalar_out_of_plane_strain = scalar_strain_zz
  [../]
  [./stress]
    type = ComputeLinearElasticStress
  [../]
[]

[Executioner]
  type = Transient

  solve_type = PJFNK
  line_search = none

# controls for linear iterations
  l_max_its = 100
  l_tol = 1e-4

# controls for nonlinear iterations
  nl_max_its = 15
  nl_rel_tol = 1e-14
  nl_abs_tol = 1e-11

# time control
  start_time = 0.0
  dt = 1.0
  dtmin = 1.0
  end_time = 2.0
  num_steps = 5000
[]

[Outputs]
  exodus = true
[]

Description
Constructed Objects
Out - of - Plane Pressure
Example Input Syntax
Generalized Plane Strain and Reference Residual
Input Parameters