HomogenizedTotalLagrangianStressDivergence

Total Lagrangian stress equilibrium kernel with homogenization constraint Jacobian terms

Overview

This object provides the total Lagrangian stress equilibrium kernel and corresponding Jacobian for the homogenization system. It is identical to the TotalLagrangianStressDivergence class except it also provides the correct off-diagonal Jacobinan terms for the Lagrangian kernel homogenization system.

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 kernel for a large deformation homogenization problem. The macro_gradient parameter is the name of the ScalarVariable containing the homogenization strain or displacement gradient field. The constraint_types parameters controls the type of constraint (deformation or stress) for each input. The homogenization system documentation lists the order of these inputs for each problem dimension/type.

[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
  []
[]

Input Parameters

componentWhich direction this kernel acts in
C++ Type:unsigned int
Controllable:No
Description:Which direction this kernel acts in
displacementsThe displacement components
C++ Type:std::vector<VariableName>
Controllable:No
Description:The displacement components
homogenization_constraintThe UserObject defining the homogenization constraint
C++ Type:UserObjectName
Controllable:No
Description:The UserObject defining the homogenization constraint
macro_gradientOptional scalar field with the macro gradient
C++ Type:std::vector<VariableName>
Controllable:No
Description:Optional scalar field with the macro gradient
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

base_nameMaterial property base name
C++ Type:std::string
Controllable:No
Description:Material property base name
blockThe list of blocks (ids or names) that this object will be applied
C++ Type:std::vector<SubdomainName>
Controllable:No
Description:The list of blocks (ids or names) that this object will be applied
eigenstrain_namesList of eigenstrains used in the strain calculation. Used for computing their derivatives for off-diagonal Jacobian terms.
C++ Type:std::vector<MaterialPropertyName>
Controllable:No
Description:List of eigenstrains used in the strain calculation. Used for computing their derivatives for off-diagonal Jacobian terms.
large_kinematicsFalseUse large displacement kinematics
Default:False
C++ Type:bool
Controllable:No
Description:Use large displacement kinematics
out_of_plane_strainThe out-of-plane strain variable for weak plane stress formulation.
C++ Type:std::vector<VariableName>
Controllable:No
Description:The out-of-plane strain variable for weak plane stress formulation.
prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Controllable:No
Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
stabilize_strainFalseAverage the volumetric strains
Default:False
C++ Type:bool
Controllable:No
Description:Average the volumetric strains
temperatureThe name of the temperature variable used in the ComputeThermalExpansionEigenstrain. (Not required for simulations without temperature coupling.)
C++ Type:std::vector<VariableName>
Controllable:No
Description:The name of the temperature variable used in the ComputeThermalExpansionEigenstrain. (Not required for simulations without temperature coupling.)

Optional 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.
diag_save_inThe name of auxiliary variables to save this Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector<AuxVariableName>
Controllable:No
Description:The name of auxiliary variables to save this Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
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
save_inThe name of auxiliary variables to save this Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector<AuxVariableName>
Controllable:No
Description:The name of auxiliary variables to save this Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
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

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
[]