AD Compute Multiple Porous Inelastic Stress

Compute state (stress and internal parameters such as plastic strains and internal parameters) using an iterative process. A porosity material property is defined and is calculated from the trace of inelastic strain increment.

Description

ADComputeMultiplePorousInelasticStress computes the stress and a decomposition of the strain into elastic and inelastic components for a series of different inelastic material models (e.g. creep and plasticity) which inherit from ADStressUpdateBase. The tangent operator and relevant Jacobian information is computed using automatic differentiation techniques. ADComputeMultiplePorousInelasticStress operates almost exactly the same as ADComputeMultipleInelasticStress but adds a porosity material property. After a inelastic strain $var element = document.getElementById("moose-equation-151640d7-041e-46bf-9f74-a8c075efb358");katex.render("\\epsilon_{in}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is calculated, the porosity, $var element = document.getElementById("moose-equation-8d787347-f4a4-4943-b072-71f522dafd43");katex.render("f", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is updated by, $var element = document.getElementById("moose-equation-61d946d2-87e7-4b45-9956-d822c251de8e");katex.render(" \\dot{f} = [1.0 - f] * \\dot{\\epsilon}_{in}.\\text{tr}()", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ The porosity can then in turn be used by viscoplasticity methods or other porosity dependent materials

Refer to ADComputeMultipleInelasticStress for the remainder of the details of how ADComputeMultiplePorousInelasticStress computes stress.

Example Input Files

ADComputeMultiplePorousInelasticStress can take individual or combinations of different inelastic material models that inherit from ADStressUpdateBase.

[Materials]
  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 1e10
    poissons_ratio = 0.3
  [../]
  [./stress]
    type = ADComputeMultiplePorousInelasticStress
    inelastic_models = 'one two'
    initial_porosity = 0.1
    outputs = all
  [../]

  [./one]
    type = ADViscoplasticityStressUpdate
    coefficient = 'coef_3'
    power = 3
    base_name = 'lps_1'
    outputs = all
    relative_tolerance = 1e-11
  [../]
  [./two]
    type = ADViscoplasticityStressUpdate
    coefficient = 1e-10
    power = 1
    base_name = 'lps_3'
    outputs = all
    relative_tolerance = 1e-11
  [../]
  [./coef]
    type = ParsedMaterial
    f_name = coef_3
    # Example of creep power law
    function = '0.5e-18 * exp(-4e4 / 1.987 / 1200)'
  [../]
[]

/opt/civet/build_0/moose/modules/tensor_mechanics/test/tests/ad_viscoplasticity_stress_update/lps_dual.i

# This test provides an example of combining two LPS viscoplasticity models with different stress
# exponents.

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 1
  ny = 1
  xmax = 0.002
  ymax = 0.002
[]

[Modules/TensorMechanics/Master/All]
  strain = FINITE
  add_variables = true
  generate_output = 'strain_xx strain_yy strain_xy hydrostatic_stress vonmises_stress'
  use_automatic_differentiation = true
[]

[Functions]
  [./pull]
    type = PiecewiseLinear
    x = '0 0.1'
    y = '0 1e-5'
  [../]
  [./tot_effective_viscoplasticity]
    type = ParsedFunction
    vals = 'lps_1_eff_creep_strain lps_3_eff_creep_strain'
    vars = 'lps_1_eff_creep_strain lps_3_eff_creep_strain'
    value = 'lps_1_eff_creep_strain+lps_3_eff_creep_strain'
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 1e10
    poissons_ratio = 0.3
  [../]
  [./stress]
    type = ADComputeMultiplePorousInelasticStress
    inelastic_models = 'one two'
    initial_porosity = 0.1
    outputs = all
  [../]

  [./one]
    type = ADViscoplasticityStressUpdate
    coefficient = 'coef_3'
    power = 3
    base_name = 'lps_1'
    outputs = all
    relative_tolerance = 1e-11
  [../]
  [./two]
    type = ADViscoplasticityStressUpdate
    coefficient = 1e-10
    power = 1
    base_name = 'lps_3'
    outputs = all
    relative_tolerance = 1e-11
  [../]
  [./coef]
    type = ParsedMaterial
    f_name = coef_3
    # Example of creep power law
    function = '0.5e-18 * exp(-4e4 / 1.987 / 1200)'
  [../]
[]

[BCs]
  [./no_disp_x]
    type = ADDirichletBC
    variable = disp_x
    boundary = left
    value = 0.0
  [../]
  [./no_disp_y]
    type = ADDirichletBC
    variable = disp_y
    boundary = bottom
    value = 0.0
  [../]
  [./pull_disp_y]
    type = ADFunctionDirichletBC
    variable = disp_y
    boundary = top
    function = pull
  [../]
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  dt = 0.01
  end_time = 0.12
[]

[Postprocessors]
  [./disp_x]
    type = SideAverageValue
    variable = disp_x
    boundary = right
  [../]
  [./disp_y]
    type = SideAverageValue
    variable = disp_y
    boundary = top
  [../]
  [./avg_hydro]
    type = ElementAverageValue
    variable = hydrostatic_stress
  [../]
  [./avg_vonmises]
    type = ElementAverageValue
    variable = vonmises_stress
  [../]
  [./dt]
    type = TimestepSize
  [../]
  [./num_lin]
    type = NumLinearIterations
    outputs = console
  [../]
  [./num_nonlin]
    type = NumNonlinearIterations
    outputs = console
  [../]
  [./lps_1_eff_creep_strain]
    type = ElementAverageValue
    variable = lps_1_effective_viscoplasticity
  [../]
  [./lps_3_eff_creep_strain]
    type = ElementAverageValue
    variable = lps_3_effective_viscoplasticity
  [../]
  [./lps_1_gauge_stress]
    type = ElementAverageValue
    variable = lps_1_gauge_stress
  [../]
  [./lps_3_gauge_stress]
    type = ElementAverageValue
    variable = lps_3_gauge_stress
  [../]
  [./eff_creep_strain_tot]
    type = FunctionValuePostprocessor
    function = tot_effective_viscoplasticity
  [../]
  [./porosity]
    type = ElementAverageValue
    variable = porosity
  [../]
[]

[Outputs]
  csv = true
[]

Input Parameters

inelastic_modelsThe material objects to use to calculate stress and inelastic strains. Note: specify creep models first and plasticity models second.
C++ Type:std::vector
Options:
Description:The material objects to use to calculate stress and inelastic strains. Note: specify creep models first and plasticity models second.
initial_porosityInitial porosity
C++ Type:double
Options:
Description:Initial porosity

Required Parameters

absolute_tolerance1e-05Absolute convergence tolerance for the stress update iterations over the stress change after all update materials are called
Default:1e-05
C++ Type:double
Options:
Description:Absolute convergence tolerance for the stress update iterations over the stress change after all update materials are called
base_nameOptional parameter that allows the user to define multiple mechanics material systems on the same block, i.e. for multiple phases
C++ Type:std::string
Options:
Description:Optional parameter that allows the user to define multiple mechanics material systems on the same block, i.e. for multiple phases
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
combined_inelastic_strain_weightsThe combined_inelastic_strain Material Property is a weighted sum of the model inelastic strains. This parameter is a vector of weights, of the same length as inelastic_models. Default = '1 1 ... 1'. This parameter is set to 1 if the number of models = 1
C++ Type:std::vector
Options:
Description:The combined_inelastic_strain Material Property is a weighted sum of the model inelastic strains. This parameter is a vector of weights, of the same length as inelastic_models. Default = '1 1 ... 1'. This parameter is set to 1 if the number of models = 1
computeTrueWhen false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
Default:True
C++ Type:bool
Options:
Description:When false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
constant_onNONEWhen ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeSubdomainProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
Default:NONE
C++ Type:MooseEnum
Options:NONE ELEMENT SUBDOMAIN
Description:When ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeSubdomainProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
cycle_modelsFalseAt time step N use only inelastic model N % num_models.
Default:False
C++ Type:bool
Options:
Description:At time step N use only inelastic model N % num_models.
extra_stress_namesMaterial property names of rank two tensors to be added to the stress.
C++ Type:std::vector
Options:
Description:Material property names of rank two tensors to be added to the stress.
internal_solve_full_iteration_historyFalseSet to true to output stress update iteration information over the stress change
Default:False
C++ Type:bool
Options:
Description:Set to true to output stress update iteration information over the stress change
max_iterations30Maximum number of the stress update iterations over the stress change after all update materials are called
Default:30
C++ Type:unsigned int
Options:
Description:Maximum number of the stress update iterations over the stress change after all update materials are called
perform_finite_strain_rotationsTrueTensors are correctly rotated in finite-strain simulations. For optimal performance you can set this to 'false' if you are only ever using small strains
Default:True
C++ Type:bool
Options:
Description:Tensors are correctly rotated in finite-strain simulations. For optimal performance you can set this to 'false' if you are only ever using small strains
porosity_nameporosityName of porosity material property
Default:porosity
C++ Type:MaterialPropertyName
Options:
Description:Name of porosity material property
relative_tolerance1e-05Relative convergence tolerance for the stress update iterations over the stress change after all update materials are called
Default:1e-05
C++ Type:double
Options:
Description:Relative convergence tolerance for the stress update iterations over the stress change after all update materials are called

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.
implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Options:
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
Options:
Description:The seed for the master random number generator

Advanced Parameters

output_propertiesList of material properties, from this material, to output (outputs must also be defined to an output type)
C++ Type:std::vector
Options:
Description:List of material properties, from this material, to output (outputs must also be defined to an output type)
outputsnone Vector of output names were you would like to restrict the output of variables(s) associated with this object
Default:none
C++ Type:std::vector
Options:
Description:Vector of output names were you would like to restrict the output of variables(s) associated with this object

Outputs Parameters

Input Files

modules/tensor_mechanics/test/tests/ad_viscoplasticity_stress_update/creep.i
modules/tensor_mechanics/test/tests/ad_viscoplasticity_stress_update/lps_single_split.i
modules/tensor_mechanics/test/tests/ad_viscoplasticity_stress_update/lps_dual.i
modules/tensor_mechanics/test/tests/ad_viscoplasticity_stress_update/lps_single.i
modules/tensor_mechanics/test/tests/ad_viscoplasticity_stress_update/gtn_single.i
modules/tensor_mechanics/test/tests/ad_viscoplasticity_stress_update/exact.i

modules/tensor_mechanics/test/tests/ad_viscoplasticity_stress_update/creep.i

# This test is provided as a check to ensure ADComputeMultiplePorousInelasticStress

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 2
  ny = 2
  xmax = 0.002
  ymax = 0.002
[]

[Modules/TensorMechanics/Master/All]
  strain = FINITE
  add_variables = true
  base_name = 'total'
  generate_output = 'strain_xx strain_yy strain_xy hydrostatic_stress vonmises_stress'
  use_automatic_differentiation = true
[]

[Functions]
  [./pull]
    type = PiecewiseLinear
    x = '0 0.1'
    y = '0 1e-5'
  [../]
[]

[Materials]
  active='elasticity_tensor porous_stress creep'
  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 1e10
    poissons_ratio = 0.3
    base_name = 'total'
  [../]
  [./porous_stress]
    type = ADComputeMultiplePorousInelasticStress
    inelastic_models = creep
    initial_porosity = 0.1
    outputs = all
    base_name = 'total'
  [../]
  [./regular_stress]
    type = ADComputeMultipleInelasticStress
    inelastic_models = creep
    outputs = all
    base_name = 'total'
  [../]
  [./porosity]
    type = GenericConstantMaterial
    prop_names = porosity
    prop_values = 0.1
    outputs = all
  [../]
  [./creep]
    type = ADPowerLawCreepStressUpdate
    activation_energy = 4e4
    temperature = 1200
    coefficient = 1e-18
    gas_constant = 1.987
    n_exponent = 3
    base_name = 'creep'
    outputs = all
  [../]
[]

[BCs]
  [./no_disp_x]
    type = ADDirichletBC
    variable = disp_x
    boundary = left
    value = 0.0
  [../]
  [./no_disp_y]
    type = ADDirichletBC
    variable = disp_y
    boundary = bottom
    value = 0.0
  [../]
  [./pull_disp_y]
    type = ADFunctionDirichletBC
    variable = disp_y
    boundary = top
    function = pull
  [../]
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  dt = 0.01
  end_time = 0.12
[]

[Postprocessors]
  [./disp_x]
    type = SideAverageValue
    variable = disp_x
    boundary = right
  [../]
  [./disp_y]
    type = SideAverageValue
    variable = disp_y
    boundary = top
  [../]
  [./avg_hydro]
    type = ElementAverageValue
    variable = total_hydrostatic_stress
  [../]
  [./avg_vonmises]
    type = ElementAverageValue
    variable = total_vonmises_stress
  [../]
  [./dt]
    type = TimestepSize
  [../]
  [./num_lin]
    type = NumLinearIterations
    outputs = console
  [../]
  [./num_nonlin]
    type = NumNonlinearIterations
    outputs = console
  [../]
  [./eff_creep_strain]
    type = ElementAverageValue
    variable = creep_effective_creep_strain
  [../]
  [./porosity]
    type = ElementAverageValue
    variable = porosity
  [../]
[]

[Outputs]
  csv = true
[]

modules/tensor_mechanics/test/tests/ad_viscoplasticity_stress_update/lps_single_split.i

# This test provides an example of combining two LPS viscoplasticity model.
# The answer should be close, but not exactly the same, as lps_single.i

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 1
  ny = 1
  xmax = 0.002
  ymax = 0.002
[]

[Modules/TensorMechanics/Master/All]
  strain = FINITE
  add_variables = true
  generate_output = 'strain_xx strain_yy strain_xy hydrostatic_stress vonmises_stress'
  use_automatic_differentiation = true
[]

[Functions]
  [./pull]
    type = PiecewiseLinear
    x = '0 0.1'
    y = '0 1e-5'
  [../]
  [./tot_effective_viscoplasticity]
    type = ParsedFunction
    vals = 'lps_1_eff_creep_strain lps_2_eff_creep_strain'
    vars = 'lps_1_eff_creep_strain lps_2_eff_creep_strain'
    value = 'lps_1_eff_creep_strain+lps_2_eff_creep_strain'
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 1e10
    poissons_ratio = 0.3
  [../]
  [./stress]
    type = ADComputeMultiplePorousInelasticStress
    inelastic_models = 'one two'
    initial_porosity = 0.1
    outputs = all
  [../]

  [./one]
    type = ADViscoplasticityStressUpdate
    coefficient = 'coef'
    power = 3
    base_name = 'lps_first'
    outputs = all
    relative_tolerance = 1e-11
  [../]
  [./two]
    type = ADViscoplasticityStressUpdate
    coefficient = 'coef'
    power = 3
    base_name = 'lps_second'
    outputs = all
    relative_tolerance = 1e-11
  [../]
  [./coef]
    type = ParsedMaterial
    f_name = coef
    # Example of creep power law
    function = '0.5e-18 * exp(-4e4 / 1.987 / 1200)'
  [../]
[]

[BCs]
  [./no_disp_x]
    type = ADDirichletBC
    variable = disp_x
    boundary = left
    value = 0.0
  [../]
  [./no_disp_y]
    type = ADDirichletBC
    variable = disp_y
    boundary = bottom
    value = 0.0
  [../]
  [./pull_disp_y]
    type = ADFunctionDirichletBC
    variable = disp_y
    boundary = top
    function = pull
  [../]
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  dt = 0.01
  end_time = 0.12
[]

[Postprocessors]
  [./disp_x]
    type = SideAverageValue
    variable = disp_x
    boundary = right
  [../]
  [./disp_y]
    type = SideAverageValue
    variable = disp_y
    boundary = top
  [../]
  [./avg_hydro]
    type = ElementAverageValue
    variable = hydrostatic_stress
  [../]
  [./avg_vonmises]
    type = ElementAverageValue
    variable = vonmises_stress
  [../]
  [./dt]
    type = TimestepSize
  [../]
  [./num_lin]
    type = NumLinearIterations
    outputs = console
  [../]
  [./num_nonlin]
    type = NumNonlinearIterations
    outputs = console
  [../]
  [./lps_1_eff_creep_strain]
    type = ElementAverageValue
    variable = lps_first_effective_viscoplasticity
    outputs = none
  [../]
  [./lps_2_eff_creep_strain]
    type = ElementAverageValue
    variable = lps_second_effective_viscoplasticity
    outputs = none
  [../]
  [./eff_creep_strain_tot]
    type = FunctionValuePostprocessor
    function = tot_effective_viscoplasticity
  [../]
  [./porosity]
    type = ElementAverageValue
    variable = porosity
  [../]
[]

[Outputs]
  csv = true
[]

modules/tensor_mechanics/test/tests/ad_viscoplasticity_stress_update/lps_dual.i

# This test provides an example of combining two LPS viscoplasticity models with different stress
# exponents.

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 1
  ny = 1
  xmax = 0.002
  ymax = 0.002
[]

[Modules/TensorMechanics/Master/All]
  strain = FINITE
  add_variables = true
  generate_output = 'strain_xx strain_yy strain_xy hydrostatic_stress vonmises_stress'
  use_automatic_differentiation = true
[]

[Functions]
  [./pull]
    type = PiecewiseLinear
    x = '0 0.1'
    y = '0 1e-5'
  [../]
  [./tot_effective_viscoplasticity]
    type = ParsedFunction
    vals = 'lps_1_eff_creep_strain lps_3_eff_creep_strain'
    vars = 'lps_1_eff_creep_strain lps_3_eff_creep_strain'
    value = 'lps_1_eff_creep_strain+lps_3_eff_creep_strain'
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 1e10
    poissons_ratio = 0.3
  [../]
  [./stress]
    type = ADComputeMultiplePorousInelasticStress
    inelastic_models = 'one two'
    initial_porosity = 0.1
    outputs = all
  [../]

  [./one]
    type = ADViscoplasticityStressUpdate
    coefficient = 'coef_3'
    power = 3
    base_name = 'lps_1'
    outputs = all
    relative_tolerance = 1e-11
  [../]
  [./two]
    type = ADViscoplasticityStressUpdate
    coefficient = 1e-10
    power = 1
    base_name = 'lps_3'
    outputs = all
    relative_tolerance = 1e-11
  [../]
  [./coef]
    type = ParsedMaterial
    f_name = coef_3
    # Example of creep power law
    function = '0.5e-18 * exp(-4e4 / 1.987 / 1200)'
  [../]
[]

[BCs]
  [./no_disp_x]
    type = ADDirichletBC
    variable = disp_x
    boundary = left
    value = 0.0
  [../]
  [./no_disp_y]
    type = ADDirichletBC
    variable = disp_y
    boundary = bottom
    value = 0.0
  [../]
  [./pull_disp_y]
    type = ADFunctionDirichletBC
    variable = disp_y
    boundary = top
    function = pull
  [../]
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  dt = 0.01
  end_time = 0.12
[]

[Postprocessors]
  [./disp_x]
    type = SideAverageValue
    variable = disp_x
    boundary = right
  [../]
  [./disp_y]
    type = SideAverageValue
    variable = disp_y
    boundary = top
  [../]
  [./avg_hydro]
    type = ElementAverageValue
    variable = hydrostatic_stress
  [../]
  [./avg_vonmises]
    type = ElementAverageValue
    variable = vonmises_stress
  [../]
  [./dt]
    type = TimestepSize
  [../]
  [./num_lin]
    type = NumLinearIterations
    outputs = console
  [../]
  [./num_nonlin]
    type = NumNonlinearIterations
    outputs = console
  [../]
  [./lps_1_eff_creep_strain]
    type = ElementAverageValue
    variable = lps_1_effective_viscoplasticity
  [../]
  [./lps_3_eff_creep_strain]
    type = ElementAverageValue
    variable = lps_3_effective_viscoplasticity
  [../]
  [./lps_1_gauge_stress]
    type = ElementAverageValue
    variable = lps_1_gauge_stress
  [../]
  [./lps_3_gauge_stress]
    type = ElementAverageValue
    variable = lps_3_gauge_stress
  [../]
  [./eff_creep_strain_tot]
    type = FunctionValuePostprocessor
    function = tot_effective_viscoplasticity
  [../]
  [./porosity]
    type = ElementAverageValue
    variable = porosity
  [../]
[]

[Outputs]
  csv = true
[]

modules/tensor_mechanics/test/tests/ad_viscoplasticity_stress_update/lps_single.i

# This test provides an example of an individual LPS viscoplasticity model

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 1
  ny = 1
  xmax = 0.002
  ymax = 0.002
[]

[Modules/TensorMechanics/Master/All]
  strain = FINITE
  add_variables = true
  generate_output = 'strain_xx strain_yy strain_xy hydrostatic_stress vonmises_stress'
  use_automatic_differentiation = true
[]

[Functions]
  [./pull]
    type = PiecewiseLinear
    x = '0 0.1'
    y = '0 1e-5'
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 1e10
    poissons_ratio = 0.3
  [../]
  [./stress]
    type = ADComputeMultiplePorousInelasticStress
    inelastic_models = lps
    initial_porosity = 0.1
    outputs = all
  [../]

  [./lps]
    type = ADViscoplasticityStressUpdate
    coefficient = 'coef'
    power = 3
    outputs = all
    relative_tolerance = 1e-11
  [../]
  [./coef]
    type = ParsedMaterial
    f_name = coef
    # Example of creep power law
    function = '1e-18 * exp(-4e4 / 1.987 / 1200)'
  [../]
[]

[BCs]
  [./no_disp_x]
    type = ADDirichletBC
    variable = disp_x
    boundary = left
    value = 0.0
  [../]
  [./no_disp_y]
    type = ADDirichletBC
    variable = disp_y
    boundary = bottom
    value = 0.0
  [../]
  [./pull_disp_y]
    type = ADFunctionDirichletBC
    variable = disp_y
    boundary = top
    function = pull
  [../]
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  dt = 0.01
  end_time = 0.12
[]

[Postprocessors]
  [./disp_x]
    type = SideAverageValue
    variable = disp_x
    boundary = right
  [../]
  [./disp_y]
    type = SideAverageValue
    variable = disp_y
    boundary = top
  [../]
  [./avg_hydro]
    type = ElementAverageValue
    variable = hydrostatic_stress
  [../]
  [./avg_vonmises]
    type = ElementAverageValue
    variable = vonmises_stress
  [../]
  [./dt]
    type = TimestepSize
  [../]
  [./num_lin]
    type = NumLinearIterations
    outputs = console
  [../]
  [./num_nonlin]
    type = NumNonlinearIterations
    outputs = console
  [../]
  [./eff_creep_strain]
    type = ElementAverageValue
    variable = effective_viscoplasticity
  [../]
  [./porosity]
    type = ElementAverageValue
    variable = porosity
  [../]
[]

[Outputs]
  csv = true
[]

modules/tensor_mechanics/test/tests/ad_viscoplasticity_stress_update/gtn_single.i

# This test provides an example of an individual GTN viscoplasticity model

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 1
  ny = 1
  xmax = 0.002
  ymax = 0.002
[]

[Modules/TensorMechanics/Master/All]
  strain = FINITE
  add_variables = true
  base_name = 'total'
  generate_output = 'strain_xx strain_yy strain_xy hydrostatic_stress vonmises_stress'
  use_automatic_differentiation = true
[]

[Functions]
  [./pull]
    type = PiecewiseLinear
    x = '0 0.1'
    y = '0 1e-5'
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 1e10
    poissons_ratio = 0.3
    base_name = 'total'
  [../]
  [./stress]
    type = ADComputeMultiplePorousInelasticStress
    inelastic_models = gtn
    initial_porosity = 0.1
    outputs = all
    base_name = 'total'
  [../]

  [./gtn]
    type = ADViscoplasticityStressUpdate
    total_strain_base_name = 'total'
    coefficient = 'coef'
    power = 3
    viscoplasticity_model = GTN
    outputs = all
    relative_tolerance = 1e-11
  [../]
  [./coef]
    type = ParsedMaterial
    f_name = coef
    # Example of creep power law
    function = '1e-18 * exp(-4e4 / 1.987 / 1200)'
  [../]
[]

[BCs]
  [./no_disp_x]
    type = ADDirichletBC
    variable = disp_x
    boundary = left
    value = 0.0
  [../]
  [./no_disp_y]
    type = ADDirichletBC
    variable = disp_y
    boundary = bottom
    value = 0.0
  [../]
  [./pull_disp_y]
    type = ADFunctionDirichletBC
    variable = disp_y
    boundary = top
    function = pull
  [../]
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  dt = 0.01
  end_time = 0.12
[]

[Postprocessors]
  [./disp_x]
    type = SideAverageValue
    variable = disp_x
    boundary = right
  [../]
  [./disp_y]
    type = SideAverageValue
    variable = disp_y
    boundary = top
  [../]
  [./avg_hydro]
    type = ElementAverageValue
    variable = total_hydrostatic_stress
  [../]
  [./avg_vonmises]
    type = ElementAverageValue
    variable = total_vonmises_stress
  [../]
  [./dt]
    type = TimestepSize
  [../]
  [./num_lin]
    type = NumLinearIterations
    outputs = console
  [../]
  [./num_nonlin]
    type = NumNonlinearIterations
    outputs = console
  [../]
  [./eff_creep_strain]
    type = ElementAverageValue
    variable = effective_viscoplasticity
  [../]
  [./porosity]
    type = ElementAverageValue
    variable = porosity
  [../]
[]

[Outputs]
  csv = true
[]

modules/tensor_mechanics/test/tests/ad_viscoplasticity_stress_update/exact.i

# This test provides comparison to calculated values from Leblond:1994kl

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

[Mesh]
  [./msh]
    type = CartesianMeshGenerator
    dim = 3
    dx = 0.01
    dy = 0.01
    dz = 0.01
    iz = 1
    ix = 1
    iy = 1
  [../]
  [./extra_nodeset]
    type = ExtraNodesetGenerator
    input = msh
    new_boundary = 'origin'
    coord = '0 0 0'
  []
[]

[Modules/TensorMechanics/Master/All]
  strain = FINITE
  add_variables = true
  generate_output = 'strain_xx strain_yy strain_xy hydrostatic_stress vonmises_stress'
  use_automatic_differentiation = true
[]

[Functions]
  [./Q_gtn]
    type = ParsedFunction
    vars = 'avg_vonmises gtn_gauge_stress'
    vals = 'avg_vonmises gtn_gauge_stress'
    value = 'avg_vonmises/gtn_gauge_stress'
  [../]
  [./M_gtn]
    type = ParsedFunction
    vars = 'avg_hydro gtn_gauge_stress'
    vals = 'avg_hydro gtn_gauge_stress'
    value = 'abs(avg_hydro) / gtn_gauge_stress'
  [../]
  [./Q_ten]
    type = ParsedFunction
    vars = 'avg_vonmises ten_gauge_stress'
    vals = 'avg_vonmises ten_gauge_stress'
    value = 'avg_vonmises/ten_gauge_stress'
  [../]
  [./M_ten]
    type = ParsedFunction
    vars = 'avg_hydro ten_gauge_stress'
    vals = 'avg_hydro ten_gauge_stress'
    value = 'abs(avg_hydro) / ten_gauge_stress'
  [../]
  [./Q_five]
    type = ParsedFunction
    vars = 'avg_vonmises five_gauge_stress'
    vals = 'avg_vonmises five_gauge_stress'
    value = 'avg_vonmises/five_gauge_stress'
  [../]
  [./M_five]
    type = ParsedFunction
    vars = 'avg_hydro five_gauge_stress'
    vals = 'avg_hydro five_gauge_stress'
    value = 'abs(avg_hydro) / five_gauge_stress'
  [../]
  [./Q_three]
    type = ParsedFunction
    vars = 'avg_vonmises three_gauge_stress'
    vals = 'avg_vonmises three_gauge_stress'
    value = 'avg_vonmises / three_gauge_stress'
  [../]
  [./M_three]
    type = ParsedFunction
    vars = 'avg_hydro three_gauge_stress'
    vals = 'avg_hydro three_gauge_stress'
    value = 'abs(avg_hydro) / three_gauge_stress'
  [../]
  [./Q_two]
    type = ParsedFunction
    vars = 'avg_vonmises two_gauge_stress'
    vals = 'avg_vonmises two_gauge_stress'
    value = 'avg_vonmises/two_gauge_stress'
  [../]
  [./M_two]
    type = ParsedFunction
    vars = 'avg_hydro two_gauge_stress'
    vals = 'avg_hydro two_gauge_stress'
    value = 'abs(avg_hydro) / two_gauge_stress'
  [../]
  [./Q_onepointfive]
    type = ParsedFunction
    vars = 'avg_vonmises onepointfive_gauge_stress'
    vals = 'avg_vonmises onepointfive_gauge_stress'
    value = 'avg_vonmises / onepointfive_gauge_stress'
  [../]
  [./M_onepointfive]
    type = ParsedFunction
    vars = 'avg_hydro onepointfive_gauge_stress'
    vals = 'avg_hydro onepointfive_gauge_stress'
    value = 'abs(avg_hydro) / onepointfive_gauge_stress'
  [../]
  [./Q_one]
    type = ParsedFunction
    vars = 'avg_vonmises one_gauge_stress'
    vals = 'avg_vonmises one_gauge_stress'
    value = 'avg_vonmises / one_gauge_stress'
  [../]
  [./M_one]
    type = ParsedFunction
    vars = 'avg_hydro one_gauge_stress'
    vals = 'avg_hydro one_gauge_stress'
    value = 'abs(avg_hydro) / one_gauge_stress'
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 1e10
    poissons_ratio = 0.3
  [../]
  [./stress]
    type = ADComputeMultiplePorousInelasticStress
    inelastic_models = 'gtn lps_ten lps_five lps_three lps_two lps_onepointfive lps_one'
    initial_porosity = 1e-3
    outputs = all
    extra_stress_names = extra_stress
  [../]

  [./gtn]
    type = ADViscoplasticityStressUpdate
    coefficient = 0
    power = 1 # arbitrary
    viscoplasticity_model = GTN
    base_name = gtn
    outputs = all
    relative_tolerance = 1e-30
  [../]
  [./lps_ten]
    type = ADViscoplasticityStressUpdate
    coefficient = 0
    power = 10
    base_name = ten
    outputs = all
    relative_tolerance = 1e-30
  [../]
  [./lps_five]
    type = ADViscoplasticityStressUpdate
    coefficient = 0
    power = 5
    base_name = five
    outputs = all
    relative_tolerance = 1e-30
  [../]
  [./lps_three]
    type = ADViscoplasticityStressUpdate
    coefficient = 0
    power = 3
    base_name = three
    outputs = all
    relative_tolerance = 1e-30
  [../]
  [./lps_two]
    type = ADViscoplasticityStressUpdate
    coefficient = 0
    power = 2
    base_name = two
    outputs = all
    relative_tolerance = 1e-30
  [../]
  [./lps_onepointfive]
    type = ADViscoplasticityStressUpdate
    coefficient = 0
    power = 1.5
    base_name = onepointfive
    outputs = all
    relative_tolerance = 1e-30
  [../]
  [./lps_one]
    type = ADViscoplasticityStressUpdate
    coefficient = 0
    power = 1
    base_name = one
    outputs = all
    relative_tolerance = 1e-30
  [../]

  [./const_stress]
    type = ComputeExtraStressConstant
    extra_stress_tensor = '1 1 1 1 1 1 1 1 1'
    outputs = all
  [../]
[]

[BCs]
  [./no_disp_x]
    type = ADDirichletBC
    variable = disp_x
    boundary = left
    value = 0.0
  [../]
  [./no_disp_y]
    type = ADDirichletBC
    variable = disp_y
    boundary = bottom
    value = 0.0
  [../]
  [./no_disp_z]
    type = ADDirichletBC
    variable = disp_z
    boundary = back
    value = 0.0
  [../]
  [./Pressure]
    [./bcs]
      boundary = 'top right front'
      function = '10^(t/4.5)'
      use_automatic_differentiation = true
    [../]
  [../]
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  num_steps = 10
  nl_abs_tol = 1e-8
[]

[Postprocessors]
  [./avg_hydro]
    type = ElementAverageValue
    variable = hydrostatic_stress
  [../]
  [./avg_vonmises]
    type = ElementAverageValue
    variable = vonmises_stress
  [../]
  [./gtn_gauge_stress]
    type = ElementAverageValue
    variable = gtn_gauge_stress
    outputs = none
  [../]
  [./0Q_gtn]
    type = FunctionValuePostprocessor
    function = Q_gtn
  [../]
  [./0M_gtn]
    type = FunctionValuePostprocessor
    function = M_gtn
  [../]
  [./ten_gauge_stress]
    type = ElementAverageValue
    variable = ten_gauge_stress
    outputs = none
  [../]
  [./1Q_ten]
    type = FunctionValuePostprocessor
    function = Q_ten
  [../]
  [./1M_ten]
    type = FunctionValuePostprocessor
    function = M_ten
  [../]
  [./five_gauge_stress]
    type = ElementAverageValue
    variable = five_gauge_stress
    outputs = none
  [../]
  [./2Q_five]
    type = FunctionValuePostprocessor
    function = Q_five
  [../]
  [./2M_five]
    type = FunctionValuePostprocessor
    function = M_five
  [../]
  [./three_gauge_stress]
    type = ElementAverageValue
    variable = three_gauge_stress
    outputs = none
  [../]
  [./3Q_three]
    type = FunctionValuePostprocessor
    function = Q_three
  [../]
  [./3M_three]
    type = FunctionValuePostprocessor
    function = M_three
  [../]
  [./two_gauge_stress]
    type = ElementAverageValue
    variable = two_gauge_stress
    outputs = none
  [../]
  [./4Q_two]
    type = FunctionValuePostprocessor
    function = Q_two
  [../]
  [./4M_two]
    type = FunctionValuePostprocessor
    function = M_two
  [../]
  [./onepointfive_gauge_stress]
    type = ElementAverageValue
    variable = onepointfive_gauge_stress
    outputs = none
  [../]
  [./5Q_onepointfive]
    type = FunctionValuePostprocessor
    function = Q_onepointfive
  [../]
  [./5M_onepointfive]
    type = FunctionValuePostprocessor
    function = M_onepointfive
  [../]
  [./one_gauge_stress]
    type = ElementAverageValue
    variable = one_gauge_stress
    outputs = none
  [../]
  [./6Q_one]
    type = FunctionValuePostprocessor
    function = Q_one
  [../]
  [./6M_one]
    type = FunctionValuePostprocessor
    function = M_one
  [../]
[]

[Outputs]
  csv = true
  file_base = exact_spherical_out
[]

References

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