HomogenizationConstraintScalarKernel

Overview

This ScalarKernel inputs the residual contributions from the Lagrangian kernel homogenization system. The HomogenizationConstraint UserObject computes the actual values of the residual volume integrals and the HomogenizedTotalLagrangianStressDivergence Kernel handles all the off-diagonal Jacobian terms. This ScalarKernel only supplies the residual and on-diagonal Jacobian.

The TensorMechanics/MasterAction can add this object automatically, which is the recommended way to set up homogenization constraints.

Example Input File Syntax

The following example manually specifies the parameters required to setup the object for a 3D, large deformation homogenization problem. In this case the name of the HomogenizationConstraint is integrator, ndim sets the dimensionality of the problem, and large_kinematics controls if large or small deformation kinematics apply.

[ScalarKernels]
  [enforce]
    type = HomogenizationConstraintScalarKernel
    variable = hvar
  []
[]

Input Parameters

homogenization_constraintThe UserObject defining the homogenization constraint
C++ Type:UserObjectName
Controllable:No
Description:The UserObject defining the homogenization constraint
variableThe name of the variable that this residual object operates on
C++ Type:NonlinearVariableName
Controllable:No
Description:The name of the variable that this residual object operates on

Required Parameters

absolute_value_vector_tagsThe tags for the vectors this residual object should fill with the absolute value of the residual contribution
C++ Type:std::vector<TagName>
Controllable:No
Description:The tags for the vectors this residual object should fill with the absolute value of the residual contribution
extra_matrix_tagsThe extra tags for the matrices this Kernel should fill
C++ Type:std::vector<TagName>
Controllable:No
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<TagName>
Controllable:No
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
Controllable:No
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
Controllable:No
Description:The tag for the vectors this Kernel should fill

Tagging 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.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:Yes
Description:Set the enabled status of the MooseObject.
implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Controllable:No
Description:Determines whether this object is calculated using an implicit or explicit form
seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Controllable:No
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
Controllable:No
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

(../moose/modules/tensor_mechanics/test/tests/lagrangian/cartesian/total/homogenization/large-tests/3d.i)

# 2D test with just strain control

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  large_kinematics = true
  macro_gradient = hvar
  homogenization_constraint = homogenization
[]

[Mesh]
  [base]
    type = FileMeshGenerator
    file = '3d.exo'
  []

  [sidesets]
    type = SideSetsFromNormalsGenerator
    input = base
    normals = '-1 0 0
                1 0 0
                0 -1 0
                0 1 0
            '
              '    0 0 -1
                0 0 1'
    fixed_normal = true
    new_boundary = 'left right bottom top back front'
  []
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [disp_z]
  []
  [hvar]
    family = SCALAR
    order = NINTH
  []
[]

[AuxVariables]
  [s11]
    family = MONOMIAL
    order = CONSTANT
  []
  [s21]
    family = MONOMIAL
    order = CONSTANT
  []
  [s31]
    family = MONOMIAL
    order = CONSTANT
  []
  [s12]
    family = MONOMIAL
    order = CONSTANT
  []
  [s22]
    family = MONOMIAL
    order = CONSTANT
  []
  [s32]
    family = MONOMIAL
    order = CONSTANT
  []
  [s13]
    family = MONOMIAL
    order = CONSTANT
  []
  [s23]
    family = MONOMIAL
    order = CONSTANT
  []
  [s33]
    family = MONOMIAL
    order = CONSTANT
  []

  [F11]
    family = MONOMIAL
    order = CONSTANT
  []
  [F21]
    family = MONOMIAL
    order = CONSTANT
  []
  [F31]
    family = MONOMIAL
    order = CONSTANT
  []
  [F12]
    family = MONOMIAL
    order = CONSTANT
  []
  [F22]
    family = MONOMIAL
    order = CONSTANT
  []
  [F32]
    family = MONOMIAL
    order = CONSTANT
  []
  [F13]
    family = MONOMIAL
    order = CONSTANT
  []
  [F23]
    family = MONOMIAL
    order = CONSTANT
  []
  [F33]
    family = MONOMIAL
    order = CONSTANT
  []
[]

[AuxKernels]
  [s11]
    type = RankTwoAux
    variable = s11
    rank_two_tensor = pk1_stress
    index_i = 0
    index_j = 0
  []
  [s21]
    type = RankTwoAux
    variable = s21
    rank_two_tensor = pk1_stress
    index_i = 1
    index_j = 0
  []
  [s31]
    type = RankTwoAux
    variable = s31
    rank_two_tensor = pk1_stress
    index_i = 2
    index_j = 0
  []
  [s12]
    type = RankTwoAux
    variable = s12
    rank_two_tensor = pk1_stress
    index_i = 0
    index_j = 1
  []
  [s22]
    type = RankTwoAux
    variable = s22
    rank_two_tensor = pk1_stress
    index_i = 1
    index_j = 1
  []
  [s32]
    type = RankTwoAux
    variable = s32
    rank_two_tensor = pk1_stress
    index_i = 2
    index_j = 1
  []
  [s13]
    type = RankTwoAux
    variable = s13
    rank_two_tensor = pk1_stress
    index_i = 0
    index_j = 2
  []
  [s23]
    type = RankTwoAux
    variable = s23
    rank_two_tensor = pk1_stress
    index_i = 1
    index_j = 2
  []
  [s33]
    type = RankTwoAux
    variable = s33
    rank_two_tensor = pk1_stress
    index_i = 2
    index_j = 2
  []

  [F11]
    type = RankTwoAux
    variable = F11
    rank_two_tensor = deformation_gradient
    index_i = 0
    index_j = 0
  []
  [F21]
    type = RankTwoAux
    variable = F21
    rank_two_tensor = deformation_gradient
    index_i = 1
    index_j = 0
  []
  [F31]
    type = RankTwoAux
    variable = F31
    rank_two_tensor = deformation_gradient
    index_i = 2
    index_j = 0
  []
  [F12]
    type = RankTwoAux
    variable = F12
    rank_two_tensor = deformation_gradient
    index_i = 0
    index_j = 1
  []
  [F22]
    type = RankTwoAux
    variable = F22
    rank_two_tensor = deformation_gradient
    index_i = 1
    index_j = 1
  []
  [F32]
    type = RankTwoAux
    variable = F32
    rank_two_tensor = deformation_gradient
    index_i = 2
    index_j = 1
  []
  [F13]
    type = RankTwoAux
    variable = F13
    rank_two_tensor = deformation_gradient
    index_i = 0
    index_j = 2
  []
  [F23]
    type = RankTwoAux
    variable = F23
    rank_two_tensor = deformation_gradient
    index_i = 1
    index_j = 2
  []
  [F33]
    type = RankTwoAux
    variable = F33
    rank_two_tensor = deformation_gradient
    index_i = 2
    index_j = 2
  []
[]

[UserObjects]
  [homogenization]
    type = HomogenizationConstraint
    constraint_types = ${constraint_types}
    targets = ${targets}
    execute_on = 'INITIAL LINEAR NONLINEAR'
  []
[]

[Kernels]
  [sdx]
    type = HomogenizedTotalLagrangianStressDivergence
    variable = disp_x
    component = 0
  []
  [sdy]
    type = HomogenizedTotalLagrangianStressDivergence
    variable = disp_y
    component = 1
  []
  [sdz]
    type = HomogenizedTotalLagrangianStressDivergence
    variable = disp_z
    component = 2
  []
[]

[ScalarKernels]
  [enforce]
    type = HomogenizationConstraintScalarKernel
    variable = hvar
  []
[]

[Functions]
  [strain11]
    type = ParsedFunction
    expression = '8.0e-2*t'
  []
  [strain22]
    type = ParsedFunction
    expression = '-4.0e-2*t'
  []
  [strain33]
    type = ParsedFunction
    expression = '8.0e-2*t'
  []
  [strain23]
    type = ParsedFunction
    expression = '2.0e-2*t'
  []
  [strain13]
    type = ParsedFunction
    expression = '-7.0e-2*t'
  []
  [strain12]
    type = ParsedFunction
    expression = '1.0e-2*t'
  []
  [strain32]
    type = ParsedFunction
    expression = '1.0e-2*t'
  []
  [strain31]
    type = ParsedFunction
    expression = '2.0e-2*t'
  []
  [strain21]
    type = ParsedFunction
    expression = '-1.5e-2*t'
  []
  [stress11]
    type = ParsedFunction
    expression = '4.0e2*t'
  []
  [stress22]
    type = ParsedFunction
    expression = '-2.0e2*t'
  []
  [stress33]
    type = ParsedFunction
    expression = '8.0e2*t'
  []
  [stress23]
    type = ParsedFunction
    expression = '2.0e2*t'
  []
  [stress13]
    type = ParsedFunction
    expression = '-7.0e2*t'
  []
  [stress12]
    type = ParsedFunction
    expression = '1.0e2*t'
  []
  [stress32]
    type = ParsedFunction
    expression = '1.0e2*t'
  []
  [stress31]
    type = ParsedFunction
    expression = '2.0e2*t'
  []
  [stress21]
    type = ParsedFunction
    expression = '-1.5e2*t'
  []
[]

[BCs]
  [Periodic]
    [x]
      variable = disp_x
      auto_direction = 'x y z'
    []
    [y]
      variable = disp_y
      auto_direction = 'x y z'
    []
    [z]
      variable = disp_z
      auto_direction = 'x y z'
    []
  []

  [fix1_x]
    type = DirichletBC
    boundary = "fix_all"
    variable = disp_x
    value = 0
  []
  [fix1_y]
    type = DirichletBC
    boundary = "fix_all"
    variable = disp_y
    value = 0
  []
  [fix1_z]
    type = DirichletBC
    boundary = "fix_all"
    variable = disp_z
    value = 0
  []

  [fix2_x]
    type = DirichletBC
    boundary = "fix_xy"
    variable = disp_x
    value = 0
  []
  [fix2_y]
    type = DirichletBC
    boundary = "fix_xy"
    variable = disp_y
    value = 0
  []

  [fix3_z]
    type = DirichletBC
    boundary = "fix_z"
    variable = disp_z
    value = 0
  []
[]

[Materials]
  [elastic_tensor_1]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 100000.0
    poissons_ratio = 0.3
    block = '1'
  []
  [elastic_tensor_2]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 120000.0
    poissons_ratio = 0.21
    block = '2'
  []
  [elastic_tensor_3]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 80000.0
    poissons_ratio = 0.4
    block = '3'
  []
  [elastic_tensor_4]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 76000.0
    poissons_ratio = 0.11
    block = '4'
  []
  [compute_stress]
    type = ComputeLagrangianLinearElasticStress
  []
  [compute_strain]
    type = ComputeLagrangianStrain
    homogenization_gradient_names = 'homogenization_gradient'
  []
  [compute_homogenization_gradient]
    type = ComputeHomogenizedLagrangianStrain
  []
[]

[Postprocessors]
  [s11]
    type = ElementAverageValue
    variable = s11
    execute_on = 'initial timestep_end'
  []
  [s21]
    type = ElementAverageValue
    variable = s21
    execute_on = 'initial timestep_end'
  []
  [s31]
    type = ElementAverageValue
    variable = s31
    execute_on = 'initial timestep_end'
  []
  [s12]
    type = ElementAverageValue
    variable = s12
    execute_on = 'initial timestep_end'
  []
  [s22]
    type = ElementAverageValue
    variable = s22
    execute_on = 'initial timestep_end'
  []
  [s32]
    type = ElementAverageValue
    variable = s32
    execute_on = 'initial timestep_end'
  []
  [s13]
    type = ElementAverageValue
    variable = s13
    execute_on = 'initial timestep_end'
  []
  [s23]
    type = ElementAverageValue
    variable = s23
    execute_on = 'initial timestep_end'
  []
  [s33]
    type = ElementAverageValue
    variable = s33
    execute_on = 'initial timestep_end'
  []

  [F11]
    type = ElementAverageValue
    variable = F11
    execute_on = 'initial timestep_end'
  []
  [F21]
    type = ElementAverageValue
    variable = F21
    execute_on = 'initial timestep_end'
  []
  [F31]
    type = ElementAverageValue
    variable = F31
    execute_on = 'initial timestep_end'
  []
  [F12]
    type = ElementAverageValue
    variable = F12
    execute_on = 'initial timestep_end'
  []
  [F22]
    type = ElementAverageValue
    variable = F22
    execute_on = 'initial timestep_end'
  []
  [F32]
    type = ElementAverageValue
    variable = F32
    execute_on = 'initial timestep_end'
  []
  [F13]
    type = ElementAverageValue
    variable = F13
    execute_on = 'initial timestep_end'
  []
  [F23]
    type = ElementAverageValue
    variable = F23
    execute_on = 'initial timestep_end'
  []
  [F33]
    type = ElementAverageValue
    variable = F33
    execute_on = 'initial timestep_end'
  []
[]

[Executioner]
  type = Transient

  solve_type = 'newton'
  line_search = none

  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'

  l_max_its = 2
  l_tol = 1e-14
  nl_max_its = 10
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-10

  start_time = 0.0
  dt = 0.2
  dtmin = 0.2
  end_time = 1.0
[]

[Outputs]
  csv = true
[]