MCCreepUpdate

Calculates thermal and irradiation creep rates for (U,Pu)C (mixed mono-carbide) fuel.

Description

MCCreepUpdate calculates the creep of MC due to applied stresses. The models employed are the thermal and irradiation creep rate formulations from Preusser (1982): $var element = document.getElementById("moose-equation-a7713319-1f42-4d8c-9544-ecef1bf719d2");katex.render(" \\begin{aligned} & \\dot{\\epsilon}_{total} = \\dot{\\epsilon}_{th} + \\dot{\\epsilon}_{irr}, \\\\ & \\dot{\\epsilon}_{th} = 1.49\\times 10^{10} \\sigma^{2.44} \\exp(-63200/T), \\\\ & \\dot{\\epsilon}_{irr} = 3.6\\times 10^{-22} F \\sigma, \\end{aligned}", element, {displayMode:true,throwOnError:false});$ where the total strain rate $var element = document.getElementById("moose-equation-463c1dd8-1b6e-45b5-a58e-d77010f1a8fd");katex.render("\\dot{\\epsilon}_{total}", element, {displayMode:false,throwOnError:false});$ (1/h) is split into the thermal and irradiation contributions, $var element = document.getElementById("moose-equation-dd0f5391-7242-4e29-a69c-fc5497d0aabf");katex.render("\\dot{\\epsilon}_{th}", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-db1e50e1-fffa-4394-8e15-3ddd8cfba709");katex.render("\\dot{\\epsilon}_{irr}", element, {displayMode:false,throwOnError:false});$ , respectively, $var element = document.getElementById("moose-equation-33f8d69a-a9fd-4165-b71d-b99ff211476a");katex.render("T", element, {displayMode:false,throwOnError:false});$ is the temperature (K), $var element = document.getElementById("moose-equation-260b2671-989f-4d7e-95b4-cc8b7ceb5ff2");katex.render("\\sigma", element, {displayMode:false,throwOnError:false});$ is the effective stress (MPa), and $var element = document.getElementById("moose-equation-92279ff8-a6e3-4d52-8439-657236337407");katex.render("F", element, {displayMode:false,throwOnError:false});$ is the fission rate (fissions/cm $var element = document.getElementById("moose-equation-76adab01-b0ac-42c9-8d0a-32461c6a89cb");katex.render("^3", element, {displayMode:false,throwOnError:false});$ /s). The $var element = document.getElementById("moose-equation-af0cfa0d-3381-4167-af4b-831b869d8125");katex.render("\\dot{\\epsilon}_{irr}", element, {displayMode:false,throwOnError:false});$ model roughly agrees with that suggested in Blank (2006), but the $var element = document.getElementById("moose-equation-a6518114-49af-4dca-a8d9-796691653856");katex.render("\\dot{\\epsilon}_{th}", element, {displayMode:false,throwOnError:false});$ model results in creep rates an order of magnitude lower than in Blank (2006). This model will be retained due to its use in previous fuel performance simulations in Preusser (1982). Note that the units will be converted in the code to use the fission rate in fissions/m $var element = document.getElementById("moose-equation-bbd7f2e8-0c5e-45a7-8ade-eea66a9ac199");katex.render("^3", element, {displayMode:false,throwOnError:false});$ /s, the effective stress in Pa, and return the creep rate in 1/s.

Example Input Syntax

note:Need for inelastic strain return mapping stress

MCCreepUpdate must be run in conjunction with the inelastic strain return mapping stress calculator, as shown below.

[Materials<<<{"href": "../../../syntax/Materials/index.html"}>>>]
  [creep]
    type = MCCreepUpdate<<<{"description": "Calculates thermal and irradiation creep rates for (U,Pu)C (mixed mono-carbide) fuel.", "href": "MCCreepUpdate.html"}>>>
    temperature<<<{"description": "The coupled temperature (K)"}>>> = temp
    fission_rate<<<{"description": "Fission rate material property name"}>>> = 1.042e20
  []

  [radial_return_stress]
    type = ComputeMultipleInelasticStress<<<{"description": "Compute state (stress and internal parameters such as plastic strains and internal parameters) using an iterative process.  Combinations of creep models and plastic models may be used.", "href": "../ComputeMultipleInelasticStress.html"}>>>
    inelastic_models<<<{"description": "The material objects to use to calculate stress and inelastic strains. Note: specify creep models first and plasticity models second."}>>> = 'creep'
  []
[]

Input Parameters

fission_rateFission rate material property name
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:Fission rate material property name
temperatureThe coupled temperature (K)
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The coupled temperature (K)

Required Parameters

absolute_tolerance1e-11Absolute convergence tolerance for Newton iteration
Default:1e-11
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Absolute convergence tolerance for Newton iteration
acceptable_multiplier10Factor applied to relative and absolute tolerance for acceptable convergence if iterations are no longer making progress
Default:10
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Factor applied to relative and absolute tolerance for acceptable convergence if iterations are no longer making progress
adaptive_substeppingFalseUse adaptive substepping, where the number of substeps is successively doubled until the return mapping model successfully converges or the maximum number of substeps is reached.
Default:False
C++ Type:bool
Controllable:No
Description:Use adaptive substepping, where the number of substeps is successively doubled until the return mapping model successfully converges or the maximum number of substeps is reached.
automatic_differentiation_return_mappingFalseWhether to use automatic differentiation to compute the derivative.
Default:False
C++ Type:bool
Controllable:No
Description:Whether to use automatic differentiation to compute the derivative.
base_nameOptional parameter that defines a prefix for all material properties related to this stress update model. This allows for multiple models of the same type to be used without naming conflicts.
C++ Type:std::string
Controllable:No
Description:Optional parameter that defines a prefix for all material properties related to this stress update model. This allows for multiple models of the same type to be used without naming conflicts.
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
boundaryThe list of boundaries (ids or names) from the mesh where this object applies
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:The list of boundaries (ids or names) from the mesh where this object applies
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 computeQpProperties() 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
Controllable:No
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 computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
declare_suffixAn optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:An optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.
execute_onLINEARThe list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
Default:LINEAR
C++ Type:ExecFlagEnum
Options:XFEM_MARK, NONE, INITIAL, LINEAR, NONLINEAR_CONVERGENCE, NONLINEAR, POSTCHECK, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM
Controllable:No
Description:The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
max_inelastic_increment0.0001The maximum inelastic strain increment allowed in a time step
Default:0.0001
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The maximum inelastic strain increment allowed in a time step
maximum_number_substeps25The maximum number of substeps allowed before cutting the time step.
Default:25
C++ Type:unsigned int
Controllable:No
Description:The maximum number of substeps allowed before cutting the time step.
relative_tolerance1e-08Relative convergence tolerance for Newton iteration
Default:1e-08
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Relative convergence tolerance for Newton iteration
use_substep_integration_errorFalseIf true, it establishes a substep size that will yield, at most,the creep numerical integration error given by substep_strain_tolerance.
Default:False
C++ Type:bool
Controllable:No
Description:If true, it establishes a substep size that will yield, at most,the creep numerical integration error given by substep_strain_tolerance.
use_substeppingNONEWhether and how to use substepping
Default:NONE
C++ Type:MooseEnum
Options:NONE, ERROR_BASED, INCREMENT_BASED
Controllable:No
Description:Whether and how to use substepping
value_range_behaviorEXCEPTIONWhat to do if input value is outside the range of applicability.
Default:EXCEPTION
C++ Type:MooseEnum
Options:ERROR, WARN, IGNORE, EXCEPTION
Controllable:No
Description:What to do if input value is outside the range of applicability.

Optional Parameters

apply_strainTrueFlag to apply strain. Used for testing.
Default:True
C++ Type:bool
Controllable:No
Description:Flag to apply strain. Used for testing.
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.
effective_inelastic_strain_nameeffective_creep_strainName of the material property that stores the effective inelastic strain
Default:effective_creep_strain
C++ Type:std::string
Controllable:No
Description:Name of the material property that stores the effective inelastic strain
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
substep_strain_tolerance0.1Maximum ratio of the initial elastic strain increment at start of the return mapping solve to the maximum inelastic strain allowable in a single substep. Reduce this value to increase the number of substeps
Default:0.1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Maximum ratio of the initial elastic strain increment at start of the return mapping solve to the maximum inelastic strain allowable in a single substep. Reduce this value to increase the number of substeps
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

internal_solve_full_iteration_historyFalseSet true to output full internal Newton iteration history at times determined by `internal_solve_output_on`. If false, only a summary is output.
Default:False
C++ Type:bool
Controllable:No
Description:Set true to output full internal Newton iteration history at times determined by `internal_solve_output_on`. If false, only a summary is output.
internal_solve_output_onon_errorWhen to output internal Newton solve information
Default:on_error
C++ Type:MooseEnum
Options:never, on_error, always
Controllable:No
Description:When to output internal Newton solve information

Debug Parameters

output_propertiesList of material properties, from this material, to output (outputs must also be defined to an output type)
C++ Type:std::vector<std::string>
Controllable:No
Description:List of material properties, from this material, to output (outputs must also be defined to an output type)
outputsnone Vector of output names where you would like to restrict the output of variables(s) associated with this object
Default:none
C++ Type:std::vector<OutputName>
Controllable:No
Description:Vector of output names where you would like to restrict the output of variables(s) associated with this object

Outputs Parameters

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
Unit:(no unit assumed)
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.
use_interpolated_stateFalseFor the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.
Default:False
C++ Type:bool
Controllable:No
Description:For the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.

Material Property Retrieval Parameters

Input Files

(test/tests/solid_mechanics/mc_creep/ad.i)
(test/tests/solid_mechanics/mc_creep/exact.i)
(test/tests/solid_mechanics/mc_creep/ad_cycle.i)
(test/tests/solid_mechanics/mc_creep/nonad.i)
(assessment/carbide/EBRII/WSA32/analysis/base.i)

References

Hubert Blank. Nonoxide Ceramic Nuclear Fuels, chapter, pages. John Wiley & Sons, Ltd, 2006. URL: https://onlinelibrary.wiley.com/doi/abs/10.1002/9783527603978.mst0108, doi:10.1002/9783527603978.mst0108.

@inbook{blank:2006,
    author = "Blank, Hubert",
    publisher = "John Wiley \\& Sons, Ltd",
    isbn = "9783527603978",
    title = "Nonoxide Ceramic Nuclear Fuels",
    booktitle = "Materials Science and Technology",
    chapter = "",
    pages = "",
    doi = "10.1002/9783527603978.mst0108",
    url = "https://onlinelibrary.wiley.com/doi/abs/10.1002/9783527603978.mst0108",
    year = "2006"
}

Timm Preusser. Modeling of carbide fuel rods. Nuclear Technology, 57(3):343–371, 1982. URL: https://doi.org/10.13182/NT82-A26303, arXiv:https://doi.org/10.13182/NT82-A26303, doi:10.13182/NT82-A26303.

@article{preusser:1982,
    author = "Preusser, Timm",
    title = "Modeling of Carbide Fuel Rods",
    journal = "Nuclear Technology",
    volume = "57",
    number = "3",
    pages = "343-371",
    year = "1982",
    publisher = "Taylor \& Francis",
    doi = "10.13182/NT82-A26303",
    URL = "https://doi.org/10.13182/NT82-A26303",
    eprint = "https://doi.org/10.13182/NT82-A26303"
}

(test/tests/solid_mechanics/mc_creep/nonad.i)

# Tests the MCCreepUpdate models with other non-AD thermo-mechanical models

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  coord_type = RZ
  [mesh]
    type = ExamplePatchMeshGenerator
    dim = 2
  []
[]

[Variables]
  [temp]
    initial_condition = 900
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [pellets]
    add_variables = true
    strain = FINITE
    incremental = true
    generate_output = 'stress_yy strain_xx strain_yy'
  []
[]

[Kernels]
  [heat_ie]
    type = TimeDerivative
    variable = temp
  []
[]

[BCs]
  [Pressure]
    [u_top_pull]
      boundary = top
      factor = -2e7
    []
  []
  [u_bottom_fix]
    type = DirichletBC
    variable = disp_y
    boundary = bottom
    value = 0.0
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 7.5e10
    poissons_ratio = 0.3
  []
  [creep]
    type = MCCreepUpdate
    temperature = temp
    fission_rate = 1.042e20
  []
  [radial_return_stress]
    type = ComputeMultipleInelasticStress
    inelastic_models = 'creep'
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'

  num_steps = 10
  dt = 10000
[]

[Postprocessors]
   [average_stress_yy]
     type = ElementAverageValue
     variable = stress_yy
   []
   [average_strain_xx]
     type = ElementAverageValue
     variable = strain_xx
   []
   [average_strain_yy]
     type = ElementAverageValue
     variable = strain_yy
   []
   [disp_x]
     type = NodalVariableValue
     nodeid = 7
     variable = disp_x
  []
  [disp_y]
     type = NodalVariableValue
     nodeid = 7
     variable = disp_y
  []
[]

[Outputs]
  exodus = true
[]

(test/tests/solid_mechanics/mc_creep/ad.i)

# Tests the ADMCCreepUpdate models with other AD thermo-mechanical models

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  coord_type = RZ
  [mesh]
    type = ExamplePatchMeshGenerator
    dim = 2
  []
[]

[Variables]
  [temp]
    initial_condition = 900
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [pellets]
    add_variables = true
    strain = FINITE
    incremental = true
    generate_output = 'stress_yy strain_xx strain_yy'
    use_automatic_differentiation = true
  []
[]

[Kernels]
  [heat_ie]
    type = ADTimeDerivative
    variable = temp
  []
[]

[BCs]
  [Pressure]
    [u_top_pull]
      boundary = top
      factor = -2e7
      use_automatic_differentiation = true
    []
  []
  [u_bottom_fix]
    type = ADDirichletBC
    variable = disp_y
    boundary = bottom
    value = 0.0
  []
[]

[Materials]
  [elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    youngs_modulus = 7.5e10
    poissons_ratio = 0.3
  []
  [creep]
    type = ADMCCreepUpdate
    temperature = temp
    fission_rate = 1.042e20
  []
  [radial_return_stress]
    type = ADComputeMultipleInelasticStress
    inelastic_models = 'creep'
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'

  num_steps = 10
  dt = 10000
[]

[Postprocessors]
   [average_stress_yy]
     type = ElementAverageValue
     variable = stress_yy
   []
   [average_strain_xx]
     type = ElementAverageValue
     variable = strain_xx
   []
   [average_strain_yy]
     type = ElementAverageValue
     variable = strain_yy
   []
   [disp_x]
     type = NodalVariableValue
     nodeid = 7
     variable = disp_x
  []
  [disp_y]
     type = NodalVariableValue
     nodeid = 7
     variable = disp_y
  []
[]

[Outputs]
  exodus = true
[]

(test/tests/solid_mechanics/mc_creep/exact.i)

# Tests the MCCreepUpdate models against hand calculations

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  use_displaced_mesh = false
  coord_type = RZ
  [gen]
    type = ExamplePatchMeshGenerator
    dim = 2
  []
[]

[AuxVariables]
  [temp]
    initial_condition = 600
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [pellets]
    add_variables = true
    strain = SMALL
    incremental = true
    generate_output = 'stress_yy strain_xx strain_yy vonmises_stress'
  []
[]

[AuxKernels]
  [temp_aux]
    type = FunctionAux
    variable = temp
    function = '1000 + .25 * t'
  []
[]

[BCs]
  [Pressure]
    [u_top_pull]
      boundary = top
      factor = -2e9
      function = 't / 1e4'
    []
  []
  [u_bottom_fix]
    type = DirichletBC
    variable = disp_y
    boundary = bottom
    value = 0.0
  []
[]

[Functions]
  [fission_rate_ramp]
    type = PiecewiseLinear
    x = '0    900'
    y = '1e23 0.1'
  []
[]

[Materials]
  [fission_rate]
    type = GenericFunctionMaterial
    prop_names = 'fission_rate'
    prop_values = 'fission_rate_ramp'
    outputs = all
  []
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 7.5e10
    poissons_ratio = 0.3
  []
  [creep]
    type = MCCreepUpdate
    temperature = temp
    fission_rate = fission_rate
    outputs = all
  []
  [radial_return_stress]
    type = ComputeMultipleInelasticStress
    inelastic_models = 'creep'
  []
[]

[Executioner]
  type = Transient
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'

  num_steps = 10
  dt = 100
  dtmin = 100
[]

[Postprocessors]
  [vonmises_avg]
    type = ElementAverageValue
    variable = vonmises_stress
  []
  [strain_xx_avg]
    type = ElementAverageValue
    variable = strain_xx
  []
  [strain_yy_avg]
    type = ElementAverageValue
    variable = strain_yy
  []
  [fission_rate_avg]
    type = ElementAverageValue
    variable = fission_rate
  []
  [creep_rate_avg]
    type = ElementAverageValue
    variable = creep_rate
  []
  [temp_avg]
    type = ElementAverageValue
    variable = temp
  []
  [dt]
    type = TimestepSize
    outputs = none
  []

  [thermal_strain_avg_old]
    type = ElementAverageValue
    variable = thermal_creep_strain
    execute_on = TIMESTEP_BEGIN
    outputs = none
  []
  [thermal_strain_avg]
    type = ElementAverageValue
    variable = thermal_creep_strain
  []
  [thermal_strain_inc]
    type = ParsedPostprocessor
    pp_names = 'temp_avg vonmises_avg dt'
    expression = '(1.49e10 / 3600.0) * (vonmises_avg / 1.0e6)^2.44 * exp(-63200 / temp_avg) * dt'
    outputs = none
  []
  [thermal_strain_exact]
    type = ParsedPostprocessor
    pp_names = 'thermal_strain_inc thermal_strain_avg_old'
    expression = 'thermal_strain_inc + thermal_strain_avg_old'
    outputs = none
  []
  [thermal_strain_diff]
    type = ParsedPostprocessor
    pp_names = 'thermal_strain_exact thermal_strain_avg'
    expression = '(thermal_strain_exact - thermal_strain_avg) / thermal_strain_exact'
    outputs = none
  []
  [thermal_strain_diff_max]
    type = TimeExtremeValue
    postprocessor = 'thermal_strain_diff'
    value_type = 'abs_max'
  []

  [irradiation_strain_avg_old]
    type = ElementAverageValue
    variable = irradiation_creep_strain
    execute_on = TIMESTEP_BEGIN
    outputs = none
  []
  [irradiation_strain_avg]
    type = ElementAverageValue
    variable = irradiation_creep_strain
  []
  [irradiation_strain_inc]
    type = ParsedPostprocessor
    pp_names = 'vonmises_avg fission_rate_avg dt'
    expression = '(3.6e-22 / 3600.0 ) * (fission_rate_avg / 1.0e6) * (vonmises_avg / 1.0e6) * dt'
    outputs = none
  []
  [irradiation_strain_exact]
    type = ParsedPostprocessor
    pp_names = 'irradiation_strain_inc irradiation_strain_avg_old'
    expression = 'irradiation_strain_inc + irradiation_strain_avg_old'
    outputs = none
  []
  [irradiation_strain_diff]
    type = ParsedPostprocessor
    pp_names = 'irradiation_strain_exact irradiation_strain_avg'
    expression = '(irradiation_strain_exact - irradiation_strain_avg) / irradiation_strain_exact'
    outputs = none
  []
  [irradiation_strain_diff_max]
    type = TimeExtremeValue
    postprocessor = 'irradiation_strain_diff'
    value_type = 'abs_max'
  []

  [creep_rate_exact]
    type = ParsedPostprocessor
    pp_names = 'thermal_strain_inc irradiation_strain_inc dt'
    expression = '(thermal_strain_inc + irradiation_strain_inc) / dt'
    outputs = none
  []
  [creep_rate_diff]
    type = ParsedPostprocessor
    pp_names = 'creep_rate_exact creep_rate_avg'
    expression = '(creep_rate_exact - creep_rate_avg) / creep_rate_exact'
    outputs = none
  []
  [creep_rate_max_diff]
    type = TimeExtremeValue
    postprocessor = 'creep_rate_diff'
    value_type = 'abs_max'
  []
[]

[Outputs]
  csv = true
[]

(test/tests/solid_mechanics/mc_creep/ad_cycle.i)

# Tests the ADMCCreepUpdate models with other AD thermo-mechanical models for a variety of conditions for mixed mono-carbide fuel that can be cycled through ADComputeMultipleInelasticStress.

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  coord_type = RZ
  [mesh]
    type = ExamplePatchMeshGenerator
    dim = 2
  []
[]

[Variables]
  [temp]
    initial_condition = 900
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [pellets]
    add_variables = true
    strain = FINITE
    incremental = true
    generate_output = 'stress_yy strain_xx strain_yy'
    use_automatic_differentiation = true
  []
[]

[Kernels]
  [heat_ie]
    type = ADTimeDerivative
    variable = temp
  []
[]

[BCs]
  [Pressure]
    [u_top_pull]
      boundary = top
      factor = -2e7
      use_automatic_differentiation = true
    []
  []
  [u_bottom_fix]
    type = ADDirichletBC
    variable = disp_y
    boundary = bottom
    value = 0.0
  []
[]

[Materials]
  [elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    youngs_modulus = 7.5e10
    poissons_ratio = 0.3
  []
  [creep_1]
    type = ADMCCreepUpdate
    base_name = 1
    temperature = temp
    fission_rate = 1.042e20
  []
  [creep_2]
    type = ADMCCreepUpdate
    base_name = 2
    temperature = temp
    fission_rate = 1.042e20
  []
  [radial_return_stress]
    type = ADComputeMultipleInelasticStress
    inelastic_models = 'creep_1 creep_2'
    cycle_models = true
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'

  num_steps = 10
  dt = 10000
[]

[Postprocessors]
   [average_stress_yy]
     type = ElementAverageValue
     variable = stress_yy
   []
   [average_strain_xx]
     type = ElementAverageValue
     variable = strain_xx
   []
   [average_strain_yy]
     type = ElementAverageValue
     variable = strain_yy
   []
   [disp_x]
     type = NodalVariableValue
     nodeid = 7
     variable = disp_x
  []
  [disp_y]
     type = NodalVariableValue
     nodeid = 7
     variable = disp_y
  []
[]

[Outputs]
  exodus = true
[]

(test/tests/solid_mechanics/mc_creep/nonad.i)

# Tests the MCCreepUpdate models with other non-AD thermo-mechanical models

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  coord_type = RZ
  [mesh]
    type = ExamplePatchMeshGenerator
    dim = 2
  []
[]

[Variables]
  [temp]
    initial_condition = 900
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [pellets]
    add_variables = true
    strain = FINITE
    incremental = true
    generate_output = 'stress_yy strain_xx strain_yy'
  []
[]

[Kernels]
  [heat_ie]
    type = TimeDerivative
    variable = temp
  []
[]

[BCs]
  [Pressure]
    [u_top_pull]
      boundary = top
      factor = -2e7
    []
  []
  [u_bottom_fix]
    type = DirichletBC
    variable = disp_y
    boundary = bottom
    value = 0.0
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 7.5e10
    poissons_ratio = 0.3
  []
  [creep]
    type = MCCreepUpdate
    temperature = temp
    fission_rate = 1.042e20
  []
  [radial_return_stress]
    type = ComputeMultipleInelasticStress
    inelastic_models = 'creep'
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'

  num_steps = 10
  dt = 10000
[]

[Postprocessors]
   [average_stress_yy]
     type = ElementAverageValue
     variable = stress_yy
   []
   [average_strain_xx]
     type = ElementAverageValue
     variable = strain_xx
   []
   [average_strain_yy]
     type = ElementAverageValue
     variable = strain_yy
   []
   [disp_x]
     type = NodalVariableValue
     nodeid = 7
     variable = disp_x
  []
  [disp_y]
     type = NodalVariableValue
     nodeid = 7
     variable = disp_y
  []
[]

[Outputs]
  exodus = true
[]

(assessment/carbide/EBRII/WSA32/analysis/base.i)

initial_fuel_density = 13630.0

[GlobalParams]
  density = ${initial_fuel_density}
  order = SECOND
  family = LAGRANGE
  energy_per_fission = 3.2e-11 # J/fission
  volumetric_locking_correction = false
  displacements = 'disp_x disp_y'
  value_range_behavior = IGNORE
[]

[Problem]
  type = ReferenceResidualProblem
  reference_vector = 'ref'
  extra_tag_vectors = 'ref'
  group_variables = 'disp_x disp_y'
[]

[Mesh]
  coord_type = RZ
  use_displaced_mesh = false
  [smeared_pellet_mesh]
    type = FuelPinMeshGenerator
    clad_thickness = 0.508e-3
    pellet_outer_radius = 4.301e-3
    pellet_height = 343e-3
    clad_top_gap_height = 43.5e-3
    clad_gap_width = 0.145e-3
    bottom_clad_height = 8e-3
    top_clad_height = 8e-3
    clad_bot_gap_height = 0.2e-3 # unknown
    clad_mesh_density = customize
    pellet_mesh_density = customize
    nx_p = 6
    ny_p = 260
    nx_c = 4
    ny_c = 260
    ny_cu = 3
    ny_cl = 3
    pellet_quantity = 1
    elem_type = QUAD8
  []
  patch_size = 30
  patch_update_strategy = auto
  partitioner = centroid
  centroid_partitioner_direction = y
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [temp]
    initial_condition = 350
  []
[]

[AuxVariables]
  [contact_pressure]
  []
  [layered_side_contact_pressure]
    block = pellet
    order = CONSTANT
    family = MONOMIAL
  []
  [pellet_wall_temp]
    order = CONSTANT
    family = MONOMIAL
  []
  [radial_heat_flux]
    order = CONSTANT
    family = MONOMIAL
  []
  [clad_inner_wall_temp]
    order = CONSTANT
    family = MONOMIAL
  []
  [volumetric_strain]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [power_history]
    type = PiecewiseLinear
    x = '0 1e5   70e6 70100000' # unknown, final burnup was 12.2 %
    y = '0 1     1    0'
  []
  [axial_peaking_factors]
    type = PiecewiseLinear
    axis = y
    x = '0    46e-3 111e-3 200e-3 248e-3 313e-3 352e-3'
    y = '86e3 86e3  97e3   100e3  96e3   87e3   87e3'
  []
  [fission_func]
    type = ParsedFunction
    symbol_names = 'axial_peaking_factors power_history'
    symbol_values = 'axial_peaking_factors power_history'
    expression = 'linear_heating_rate := axial_peaking_factors * power_history;
             pellet_cross_sectional_area := 3.14159 * pow( 4.301e-3, 2 );
             volumetric_power := linear_heating_rate / pellet_cross_sectional_area;
             energy_per_fission := 3.2e-11;
             volumetric_power / energy_per_fission'
  []
  [burnup_func] # Burnup func is needed because BurnupAux doesn't currentl export an ADMaterialProperty.
    type = PiecewiseLinear
    x = '0 1e5   70e6  70100000'
    y = '0 0     0.122 0.122'
  []

  [coolant_press_ramp]
    type = PiecewiseLinear
    x = '0       70100000'
    y = '0.151e6 0.151e6' # unknown, Na coolant
  []
  [coolant_inlet_temp]
    type = PiecewiseLinear
    x = '0   1e5 70e6 70100000'
    y = '350 644 644  350'
  []
  [coolant_outlet_temp]
    type = PiecewiseLinear
    x = '0   1e5 70e6 70100000'
    y = '350 746 746  350'
  []
  [coolant_wall_temp]
    type = ParsedFunction
    symbol_values = 'coolant_inlet_temp coolant_outlet_temp'
    symbol_names = 'coolant_inlet_temp coolant_outlet_temp'
    expression = 'rod_length := 343e-3 + 43.5e-3 + 2 * 8e-3;
             delta_temp := coolant_outlet_temp - coolant_inlet_temp;
             interpolated_temp := coolant_inlet_temp + y * delta_temp / rod_length;
             max( min( interpolated_temp, coolant_outlet_temp ), coolant_inlet_temp )'
  []
  [radial_heat_flux]
    type = ParsedFunction
    symbol_values = 'coolant_wall_temp power_history axial_peaking_factors'
    symbol_names = 'coolant_wall_temp power_history axial_peaking_factors'
    expression = 'linear_heating_rate := axial_peaking_factors * power_history;
             pellet_radius := 4.301e-3;
             pellet_circumference := 3.14159 * pellet_radius * 2;
             linear_heating_rate / pellet_circumference'
  []
  [clad_inner_wall_temp]
    type = ParsedFunction
    symbol_values = 'radial_heat_flux coolant_wall_temp'
    symbol_names = 'radial_heat_flux coolant_wall_temp'
    expression = 'conductivity_316ss := 22;
             clad_thickness := 0.51e-3;
             coolant_wall_temp + radial_heat_flux / conductivity_316ss * clad_thickness'
  []
  [pellet_wall_temp]
    type = ParsedFunction
    symbol_values = 'radial_heat_flux coolant_wall_temp clad_inner_wall_temp'
    symbol_names = 'radial_heat_flux coolant_wall_temp clad_inner_wall_temp'
    expression = 'conductivity_gap := 1;
             gap_thickness := 0.145e-3;
             clad_inner_wall_temp + radial_heat_flux / conductivity_gap * gap_thickness'
  []

  [contact_pressure_func]
    type = ConstantFunction
    value = 12e6
  []
  [plenum_pressure]
    type = ConstantFunction
    value = 12.4e6 # initial fill
  []

  [porosity_ramp]
    type = PiecewiseLinear
    x = '0    1e5  70e6  70100000'
    y = '0.14 0.14 0.145 0.145' # Pellets start at 88.1% TD, but no data on final porosity.
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [fuel]
    block = pellet
    strain = SMALL
    incremental = true
    extra_vector_tags = 'ref'
    eigenstrain_names = 'fuel_thermal_expansion fuel_swelling'
    use_automatic_differentiation = true
  []
  [clad]
    block = clad
    strain = SMALL
    incremental = true
    extra_vector_tags = 'ref'
    use_automatic_differentiation = true
  []
[]

[Kernels]
  [gravity]
    type = ADGravity
    variable = disp_y
    value = -9.81
    extra_vector_tags = 'ref'
  []
  [heat]
    type = ADHeatConduction
    variable = temp
    extra_vector_tags = 'ref'
  []
  [heat_ie]
    type = ADHeatConductionTimeDerivative
    variable = temp
    extra_vector_tags = 'ref'
  []
  [heat_source]
    type = ADFissionRateHeatSource
    variable = temp
    block = pellet
    fission_rate = fission_rate
    extra_vector_tags = 'ref'
  []
[]

[AuxKernels]
  [contact_pressure_aux]
    type = FunctionAux
    variable = contact_pressure
    function = contact_pressure_func
  []
  [layered_side_contact_pressure]
    type = SpatialUserObjectAux
    variable = layered_side_contact_pressure
    user_object = layered_side_contact_pressure
    block = pellet
  []

  [pellet_wall_temp]
    type = FunctionAux
    variable = pellet_wall_temp
    function = pellet_wall_temp
  []
  [radial_heat_flux]
    type = FunctionAux
    variable = radial_heat_flux
    function = radial_heat_flux
  []
  [clad_inner_wall_temp]
    type = FunctionAux
    variable = clad_inner_wall_temp
    function = clad_inner_wall_temp
  []
  [volumetric_strain]
    type = ADRankTwoScalarAux
    rank_two_tensor = total_strain
    variable = volumetric_strain
    scalar_type = VolumetricStrain
  []
[]

[BCs]
  [no_x_all]
    type = DirichletBC
    variable = disp_x
    boundary = 12
    value = 0.0
  []
  [no_y_fuel]
    type = DirichletBC
    variable = disp_y
    boundary = 20
    value = 0.0
  []
  [no_y_clad]
    type = DirichletBC
    variable = disp_y
    boundary = 1
    value = 0.0
  []
  [Pressure]
    [coolantPressure]
      boundary = '1 2 3'
      function = coolant_press_ramp
    []
    [plenumPressure]
      boundary = 9
      function = plenum_pressure
    []
  []
  [clad_outer_temp]
    type = FunctionDirichletBC
    boundary = '1 2 3'
    function = coolant_wall_temp
    variable = temp
  []
  [pellet_to_clad_cooling]
    type = FunctionDirichletBC
    boundary = 10
    function = pellet_wall_temp
    variable = temp
  []
[]

[Materials]
  [fission]
    type = ADGenericFunctionMaterial
    prop_names = fission_rate
    prop_values = fission_func
    outputs = all
  []
  [burnup]
    type = ADGenericFunctionMaterial
    block = pellet
    prop_names = burnup
    prop_values = burnup_func
    outputs = all
  []
  [fuel_thermal]
    block = pellet
    type = ADMCThermal
    temperature = temp
    porosity = porosity
    X_Pu = 0.0
    outputs = all
  []
  [fuel_porosity]
    block = pellet
    type = ADGenericFunctionMaterial
    prop_names = porosity
    prop_values = porosity_ramp
    outputs = all
  []
  [fuel_elasticity_tensor]
    block = pellet
    type = ADMCElasticityTensor
    temperature = temp
    porosity = porosity
    output_properties = 'youngs_modulus poissons_ratio'
    outputs = all
  []
  [fuel_thermal_expansion]
    block = pellet
    type = ADMCThermalExpansionEigenstrain
    eigenstrain_name = fuel_thermal_expansion
    stress_free_temperature = 350
    temperature = temp
  []
  [fuel_creep]
    block = pellet
    type = ADMCCreepUpdate
    temperature = temp
    fission_rate = fission_rate
    outputs = all
  []
  [fuel_swelling]
    block = pellet
    type = ADMCVolumetricSwellingEigenstrain
    eigenstrain_name = fuel_swelling
    temperature = temp
    porosity = porosity
    contact_pressure = layered_side_contact_pressure
    burnup = burnup
    outputs = all
  []
  [fuel_radial_return_stress]
    block = pellet
    type = ADComputeMultipleInelasticStress
    inelastic_models = 'fuel_creep'
  []
  [fuel_density]
    block = pellet
    type = ADStrainAdjustedDensity
    strain_free_density = ${initial_fuel_density}
  []

  [clad_elasticity_tensor]
    block = clad
    type = ADComputeIsotropicElasticityTensor
    youngs_modulus = 190e9
    poissons_ratio = 0.265
  []
  [clad_stress]
    block = clad
    type = ADComputeLinearElasticStress
  []
  [clad_thermal]
    block = clad
    type = ADSS316Thermal
    temperature = temp
  []
  [clad_density]
    block = clad
    type = ADStrainAdjustedDensity
    strain_free_density = 8000
  []
[]

[UserObjects]
  [layered_side_contact_pressure]
    # This reads the contact pressure at the pellet OD and propagates it inward so that it can
    # be used in ADMCVolumetricSwellingEigenstrain for inner elements as well.
    type = LayeredSideAverage
    direction = y
    num_layers = 100
    variable = contact_pressure
    execute_on = linear
    boundary = 10
  []
[]

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

[Dampers]
  [limitT]
    type = MaxIncrement
    max_increment = 100.0
    variable = temp
  []
  [limitX]
    type = MaxIncrement
    max_increment = 1e-5
    variable = disp_x
  []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'
  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -ksp_gmres_restart'
  petsc_options_value = 'lu       superlu_dist                  51'
  line_search = 'none'

  l_max_its = 50
  l_tol = 8e-3
  nl_max_its = 15
  nl_rel_tol = 1e-4
  nl_abs_tol = 1e-10

  start_time = -200
  n_startup_steps = 1
  end_time = 70100000
  dtmin = 1
  dtmax = 2e6

  [Quadrature]
    order = fifth
    side_order = seventh
  []

  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 2e2
    time_t = ' 0   1e5 70e6 70100000'
    time_dt = '1e2 1e2 1e2  1e2'
    optimal_iterations = 10
    growth_factor = 2
    cutback_factor = 0.5
    iteration_window = 1
    linear_iteration_ratio = 100
  []
[]

[Postprocessors]
  [_dt]
    type = TimestepSize
  []
  [num_lin_it]
    type = NumLinearIterations
  []
  [num_nonlin_it]
    type = NumNonlinearIterations
  []
  [burnup]
    block = pellet
    type = ADElementAverageMaterialProperty
    mat_prop = burnup
  []
  [FCT]
    type = NodalExtremeValue
    boundary = 12
    variable = temp
    execute_on = 'initial timestep_end'
  []
  [volumetric_strain]
    type = ElementAverageValue
    block = pellet
    variable = volumetric_strain
  []
  [pellet_outer_disp_x]
    type = NodalExtremeValue
    boundary = 10
    variable = disp_x
    execute_on = 'initial timestep_end'
  []
[]

[Outputs]
  color = true
  exodus = true
  perf_graph = true
  csv = true
  [console]
    type = Console
    max_rows = 25
    time_step_interval =  1
    output_linear = true
  []
  [chkfile]
    type = CSV
    hide = 'num_nonlin_it num_lin_it _dt'
  []
[]

Description
Example Input Syntax
Input Parameters
Input Files
References