ChromiumPlasticityUpdate

Computes the plastic strain as a function of strain rate for pure chromium. Note: This material must be run in conjunction with ComputeMultipleInelasticStress.

Description

ChromiumPlasticityUpdate calculates the plastic strain for chromium cladding materials as a function of temperature. This material must be run in conjunction with ComputeMultipleInelasticStress. The material model inherits from IsotropicPlasticityStressUpdate and sets the yield_stress_function internally based upon temperature. Then irradiation hardening is incorporated as a function of fast neutron fluence that increases the yield stress. The yield stress as a function of temperature is given by Wagih et al. (2018): $var element = document.getElementById("moose-equation-34d18aac-da22-416b-8907-ae6461c21c9b");katex.render(" \\sigma_y = -8.24 \\times 10^{-7} T^3 + 0.0019 T^2 -1.39 T + 513.17", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-3cc4a5f4-3c08-415a-8bd4-7224e5818e5a");katex.render("\\sigma_y", element, {displayMode:false,throwOnError:false});$ is the yield stress (MPa) and $var element = document.getElementById("moose-equation-38ab850d-ba1b-49a3-8b83-5536b3a36ac0");katex.render("T", element, {displayMode:false,throwOnError:false});$ is the temperature (K). Irradiation hardening is then included via: $var element = document.getElementById("moose-equation-20f02223-af02-46f5-9b4b-c4d3af0453ea");katex.render(" \\sigma_{y_{irr}} = \\sigma_y \\left(5.0 \\times 10^{-27} \\phi + 1 \\right)", element, {displayMode:true,throwOnError:false});$

The user may also add an initial_fast_fluence to the value of the fast neutron fluence reported by the fast_neutron_fluence variable.

Example Input Syntax

[Materials<<<{"href": "../../../syntax/Materials/index.html"}>>>]
  [chromium_plasticity]
    type = ChromiumPlasticityUpdate<<<{"description": "Computes the plastic strain as a function of strain rate for pure chromium. Note: This material must be run in conjunction with ComputeMultipleInelasticStress.", "href": "ChromiumPlasticityUpdate.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = '1 2 3 4'
    temperature<<<{"description": "Coupled Temperature"}>>> = temp
    fast_neutron_fluence<<<{"description": "The coupled fast neutron flux variable."}>>> = fast_neutron_fluence
    hardening_constant<<<{"description": "Hardening slope"}>>> = 0.0
  []
[]

ChromiumPlasticityUpdate must be run in conjunction with the inelastic strain return mapping stress calculator as shown below:

[Materials<<<{"href": "../../../syntax/Materials/index.html"}>>>]
  [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"}>>>
    tangent_operator<<<{"description": "Type of tangent operator to return.  'elastic': return the elasticity tensor.  'nonlinear': return the full, general consistent tangent operator."}>>> = elastic
    inelastic_models<<<{"description": "The material objects to use to calculate stress and inelastic strains. Note: specify creep models first and plasticity models second."}>>> = 'chromium_plasticity'
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = '1 2 3 4'
  []
[]

Input 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.
fast_neutron_fluenceThe coupled fast neutron flux variable.
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The coupled fast neutron flux variable.
hardening_constantHardening slope
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Hardening slope
hardening_functionTrue stress as a function of plastic strain
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:True stress as a function of plastic strain
initial_fast_fluence0Initial fast fluence.
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Initial fast fluence.
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
temperatureCoupled Temperature
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Coupled Temperature
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
yield_stress_functionYield stress as a function of temperature
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:Yield stress as a function of temperature

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_plastic_strainName of the material property that stores the effective inelastic strain
Default:effective_plastic_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

yield_stress_scale_factor1Scale factor to be applied to yield stress. Used for calibration and sensitivity studies
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Scale factor to be applied to yield stress. Used for calibration and sensitivity studies

Advanced: Scaling Factors Parameters

Input Files

(test/tests/solid_mechanics/chromium_plasticity/chromium_unirradiated_plasticity.i)
(test/tests/solid_mechanics/chromium_plasticity/chromium_irradiated_plasticity.i)
(examples/accident_tolerant_fuel/uo2_coated_zircaloy/uo2_coated_zircaloy.i)
(test/tests/solid_mechanics/chromium_plasticity/chromium_initial_fluence_plasticity.i)
(test/tests/solid_mechanics/chromium_plasticity/ad_chromium_irradiated_plasticity.i)
(test/tests/solid_mechanics/chromium_plasticity/ad_chromium_initial_fluence_plasticity.i)
(test/tests/solid_mechanics/chromium_plasticity/ad_chromium_unirradiated_plasticity.i)

References

Malik Wagih, Benjamin Spencer, Jason Hales, and Koroush Shirvan. Fuel performance of chromium-coated zirconium alloy and silicon carbide accident tolerant fuel claddings. Annals of Nuclear Energy, 120:304–318, 2018. doi:10.1016/j.anucene.2018.06.001.

@article{WAGIH2018304,
    author = "Wagih, Malik and Spencer, Benjamin and Hales, Jason and Shirvan, Koroush",
    title = "Fuel performance of chromium-coated zirconium alloy and silicon carbide accident tolerant fuel claddings",
    journal = "Annals of Nuclear Energy",
    volume = "120",
    pages = "304-318",
    year = "2018",
    issn = "0306-4549",
    doi = "10.1016/j.anucene.2018.06.001"
}

(test/tests/solid_mechanics/chromium_plasticity/chromium_irradiated_plasticity.i)

# This input file tests the isotropic plasticity model for pure irradiated
# chromium. There are four blocks subjected to different temperatures to
# calculate the temperature dependent yield stress.  These blocks are subjected
# to temperatures 300, 700, 900 and 1100 K, respectively and loaded in tension
# with a maximum displacement of 0.04 m.  The fast neutron fluence on all the
# blocks is 1e25 n/m^2 at t = 1.0 and 1e26 n/m^2 at t = 2.0. At a fluence of
# 1e25 n/m^2 the yield stress is hardened by 5% from the unirradiated case.
# At 1e26 n/m^2 it is hardened by 50%.
#
# The linear strain hardening slope is set to zero such that
# the material behaves elastic-perfectly plastically.
#
# Once yield occurs the stress in the yy direction should equal
# the yield stress due to the elastic-perfectly plastic material
# behavior.
#
#                    Fluence = 1e25 n/m^2             Fluence = 1e26 n/m^2
#
#   Temp (K)       Analytical        BISON          Analytical        BISON
#                 Yield Stress    Yield Stress     Yield Stress    Yield Stress
#                   (MPa)            (MPa)           (MPa)            (MPa)
#   300            257.168          257.168         367.383          367.383
#   700            197.965          197.965         282.807          282.807
#   900            210.498          210.498         300.711          300.711
#   1100           195.747          195.747         279.638          279.638
#
[GlobalParams]
  displacements = 'disp_x disp_y'
  volumetric_locking_correction = true
[]

[Mesh]
  coord_type = RZ
  [mesh]
    type = FileMeshGenerator
    file = 'vertical_squares.e'
  []
[]

[Variables]
  [disp_x]
    order = FIRST
    family = LAGRANGE
  []

  [disp_y]
    order = FIRST
    family = LAGRANGE
  []
  [temp]
    order = FIRST
    family = LAGRANGE
  []
[]

[AuxVariables]
  [fast_neutron_fluence]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Physics]
  [SolidMechanics]
    [QuasiStatic]
      [all]
        strain = FINITE
        generate_output = 'stress_yy strain_yy plastic_strain_xx plastic_strain_yy plastic_strain_zz'
      []
    []
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = temp
  []
[]

[AuxKernels]
  [fast_neutron_fluence]
    type = FunctionAux
    function = fast_neutron_fluence
    variable = fast_neutron_fluence
  []
[]

[Functions]
  [top_pull]
    type = ParsedFunction
    expression = t*(0.02)
  []
  [fast_neutron_fluence]
    type = PiecewiseLinear
    x = '0 1 2'
    y = '0 1.0e25 1.0e26'
  []
[]

[BCs]
  [square1]
    type = DirichletBC
    variable = temp
    boundary = '1 2 3 4'
    value = 300
  []

  [square2]
    type = DirichletBC
    variable = temp
    boundary = '5 6 7 8'
    value = 700
  []

  [square3]
    type = DirichletBC
    variable = temp
    boundary = '9 10 11 12'
    value = 900
  []

  [square4]
    type = DirichletBC
    variable = temp
    boundary = '13 14 15 16'
    value = 1100
  []

  [top_pull]
    type = FunctionDirichletBC
    boundary = '1 5 9 13'
    variable = disp_y
    function = top_pull
  []

  [y_bot]
    type = DirichletBC
    boundary = '3 7 11 15'
    variable = disp_y
    value = 0.0
  []
  [x_bot]
    type = DirichletBC
    boundary = ' 2 6 10 14'
    variable = disp_x
    value = 0.0
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = '1 2 3 4'
    youngs_modulus = 1e10
    poissons_ratio = 0.3
  []
  [stress]
    type = ComputeMultipleInelasticStress
    tangent_operator = elastic
    inelastic_models = 'chromium_plasticity'
    block = '1 2 3 4'
  []
  [chromium_plasticity]
    type = ChromiumPlasticityUpdate
    block = '1 2 3 4'
    temperature = temp
    fast_neutron_fluence = fast_neutron_fluence
    hardening_constant = 0.0
  []
  [heat_conduction]
    type = HeatConductionMaterial
    block = '1 2 3 4'
    thermal_conductivity = 1
    specific_heat = 1
  []
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
  petsc_options_value = '201                hypre    boomeramg      4'

  line_search = 'none'

  l_max_its = 100
  nl_max_its = 100
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-10
  l_tol = 1e-10

  start_time = 0.0
  end_time = 2.0
  dt = 0.1
[]

[Outputs]
  exodus = true
[]

(test/tests/solid_mechanics/chromium_plasticity/chromium_irradiated_plasticity.i)

# This input file tests the isotropic plasticity model for pure irradiated
# chromium. There are four blocks subjected to different temperatures to
# calculate the temperature dependent yield stress.  These blocks are subjected
# to temperatures 300, 700, 900 and 1100 K, respectively and loaded in tension
# with a maximum displacement of 0.04 m.  The fast neutron fluence on all the
# blocks is 1e25 n/m^2 at t = 1.0 and 1e26 n/m^2 at t = 2.0. At a fluence of
# 1e25 n/m^2 the yield stress is hardened by 5% from the unirradiated case.
# At 1e26 n/m^2 it is hardened by 50%.
#
# The linear strain hardening slope is set to zero such that
# the material behaves elastic-perfectly plastically.
#
# Once yield occurs the stress in the yy direction should equal
# the yield stress due to the elastic-perfectly plastic material
# behavior.
#
#                    Fluence = 1e25 n/m^2             Fluence = 1e26 n/m^2
#
#   Temp (K)       Analytical        BISON          Analytical        BISON
#                 Yield Stress    Yield Stress     Yield Stress    Yield Stress
#                   (MPa)            (MPa)           (MPa)            (MPa)
#   300            257.168          257.168         367.383          367.383
#   700            197.965          197.965         282.807          282.807
#   900            210.498          210.498         300.711          300.711
#   1100           195.747          195.747         279.638          279.638
#
[GlobalParams]
  displacements = 'disp_x disp_y'
  volumetric_locking_correction = true
[]

[Mesh]
  coord_type = RZ
  [mesh]
    type = FileMeshGenerator
    file = 'vertical_squares.e'
  []
[]

[Variables]
  [disp_x]
    order = FIRST
    family = LAGRANGE
  []

  [disp_y]
    order = FIRST
    family = LAGRANGE
  []
  [temp]
    order = FIRST
    family = LAGRANGE
  []
[]

[AuxVariables]
  [fast_neutron_fluence]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Physics]
  [SolidMechanics]
    [QuasiStatic]
      [all]
        strain = FINITE
        generate_output = 'stress_yy strain_yy plastic_strain_xx plastic_strain_yy plastic_strain_zz'
      []
    []
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = temp
  []
[]

[AuxKernels]
  [fast_neutron_fluence]
    type = FunctionAux
    function = fast_neutron_fluence
    variable = fast_neutron_fluence
  []
[]

[Functions]
  [top_pull]
    type = ParsedFunction
    expression = t*(0.02)
  []
  [fast_neutron_fluence]
    type = PiecewiseLinear
    x = '0 1 2'
    y = '0 1.0e25 1.0e26'
  []
[]

[BCs]
  [square1]
    type = DirichletBC
    variable = temp
    boundary = '1 2 3 4'
    value = 300
  []

  [square2]
    type = DirichletBC
    variable = temp
    boundary = '5 6 7 8'
    value = 700
  []

  [square3]
    type = DirichletBC
    variable = temp
    boundary = '9 10 11 12'
    value = 900
  []

  [square4]
    type = DirichletBC
    variable = temp
    boundary = '13 14 15 16'
    value = 1100
  []

  [top_pull]
    type = FunctionDirichletBC
    boundary = '1 5 9 13'
    variable = disp_y
    function = top_pull
  []

  [y_bot]
    type = DirichletBC
    boundary = '3 7 11 15'
    variable = disp_y
    value = 0.0
  []
  [x_bot]
    type = DirichletBC
    boundary = ' 2 6 10 14'
    variable = disp_x
    value = 0.0
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = '1 2 3 4'
    youngs_modulus = 1e10
    poissons_ratio = 0.3
  []
  [stress]
    type = ComputeMultipleInelasticStress
    tangent_operator = elastic
    inelastic_models = 'chromium_plasticity'
    block = '1 2 3 4'
  []
  [chromium_plasticity]
    type = ChromiumPlasticityUpdate
    block = '1 2 3 4'
    temperature = temp
    fast_neutron_fluence = fast_neutron_fluence
    hardening_constant = 0.0
  []
  [heat_conduction]
    type = HeatConductionMaterial
    block = '1 2 3 4'
    thermal_conductivity = 1
    specific_heat = 1
  []
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
  petsc_options_value = '201                hypre    boomeramg      4'

  line_search = 'none'

  l_max_its = 100
  nl_max_its = 100
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-10
  l_tol = 1e-10

  start_time = 0.0
  end_time = 2.0
  dt = 0.1
[]

[Outputs]
  exodus = true
[]

(test/tests/solid_mechanics/chromium_plasticity/chromium_unirradiated_plasticity.i)

# This input file tests the isotropic plasticity model for pure unirradiated
# chromium. There are four blocks subjected to different temperatures to
# calculate the temperature dependent yield stress.  These blocks are subjected
# to temperatures 300, 700, 900 and 1100 K, respectively and loaded in tension
# with a maximum displacement of 0.04 m.
#
# The linear strain hardening slope is set to zero such that
# the material behaves elastic-perfectly plastically.
#
# Once yield occurs the stress in the yy direction should equal
# the yield stress due to the elastic-perfectly plastic material
# behavior.
#
#   Temp (K)       Analytical                 BISON
#                 Yield Stress             Yield Stress
#                   (MPa)                     (MPa)
#   300            244.922                  244.922
#   700            188.538                  188.538
#   900            200.474                  200.474
#   1100           186.426                  186.426
#
[GlobalParams]
  displacements = 'disp_x disp_y'
  volumetric_locking_correction = true
[]

[Mesh]
  coord_type = RZ
  [mesh]
    type = FileMeshGenerator
    file = 'vertical_squares.e'
  []
[]

[Variables]
  [disp_x]
    order = FIRST
    family = LAGRANGE
  []

  [disp_y]
    order = FIRST
    family = LAGRANGE
  []
  [temp]
    order = FIRST
    family = LAGRANGE
  []
[]

[Physics]
  [SolidMechanics]
    [QuasiStatic]
      [all]
        strain = FINITE
        generate_output = 'stress_yy strain_yy plastic_strain_xx plastic_strain_yy plastic_strain_zz'
      []
    []
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = temp
  []
[]

[Functions]
  [top_pull]
    type = ParsedFunction
    expression = t*(0.02)
  []
[]

[BCs]
  [square1]
    type = DirichletBC
    variable = temp
    boundary = '1 2 3 4'
    value = 300
  []

  [square2]
    type = DirichletBC
    variable = temp
    boundary = '5 6 7 8'
    value = 700
  []

  [square3]
    type = DirichletBC
    variable = temp
    boundary = '9 10 11 12'
    value = 900
  []

  [square4]
    type = DirichletBC
    variable = temp
    boundary = '13 14 15 16'
    value = 1100
  []

  [top_pull]
    type = FunctionDirichletBC
    boundary = '1 5 9 13'
    variable = disp_y
    function = top_pull
  []

  [y_bot]
    type = DirichletBC
    boundary = '3 7 11 15'
    variable = disp_y
    value = 0.0
  []
  [x_bot]
    type = DirichletBC
    boundary = ' 2 6 10 14'
    variable = disp_x
    value = 0.0
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = '1 2 3 4'
    youngs_modulus = 1e10
    poissons_ratio = 0.3
  []
  [stress]
    type = ComputeMultipleInelasticStress
    tangent_operator = elastic
    inelastic_models = 'chromium_plasticity'
    block = '1 2 3 4'
  []
  [chromium_plasticity]
    type = ChromiumPlasticityUpdate
    block = '1 2 3 4'
    temperature = temp
    hardening_constant = 0.0
  []
  [heat_conduction]
    type = HeatConductionMaterial
    block = '1 2 3 4'
    thermal_conductivity = 1
    specific_heat = 1
  []
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
  petsc_options_value = '201                hypre    boomeramg      4'

  line_search = 'none'

  l_max_its = 100
  nl_max_its = 100
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-10
  l_tol = 1e-10

  start_time = 0.0
  end_time = 2.0
  dt = 0.1
[]

[Outputs]
  exodus = true
[]

(test/tests/solid_mechanics/chromium_plasticity/chromium_irradiated_plasticity.i)

# This input file tests the isotropic plasticity model for pure irradiated
# chromium. There are four blocks subjected to different temperatures to
# calculate the temperature dependent yield stress.  These blocks are subjected
# to temperatures 300, 700, 900 and 1100 K, respectively and loaded in tension
# with a maximum displacement of 0.04 m.  The fast neutron fluence on all the
# blocks is 1e25 n/m^2 at t = 1.0 and 1e26 n/m^2 at t = 2.0. At a fluence of
# 1e25 n/m^2 the yield stress is hardened by 5% from the unirradiated case.
# At 1e26 n/m^2 it is hardened by 50%.
#
# The linear strain hardening slope is set to zero such that
# the material behaves elastic-perfectly plastically.
#
# Once yield occurs the stress in the yy direction should equal
# the yield stress due to the elastic-perfectly plastic material
# behavior.
#
#                    Fluence = 1e25 n/m^2             Fluence = 1e26 n/m^2
#
#   Temp (K)       Analytical        BISON          Analytical        BISON
#                 Yield Stress    Yield Stress     Yield Stress    Yield Stress
#                   (MPa)            (MPa)           (MPa)            (MPa)
#   300            257.168          257.168         367.383          367.383
#   700            197.965          197.965         282.807          282.807
#   900            210.498          210.498         300.711          300.711
#   1100           195.747          195.747         279.638          279.638
#
[GlobalParams]
  displacements = 'disp_x disp_y'
  volumetric_locking_correction = true
[]

[Mesh]
  coord_type = RZ
  [mesh]
    type = FileMeshGenerator
    file = 'vertical_squares.e'
  []
[]

[Variables]
  [disp_x]
    order = FIRST
    family = LAGRANGE
  []

  [disp_y]
    order = FIRST
    family = LAGRANGE
  []
  [temp]
    order = FIRST
    family = LAGRANGE
  []
[]

[AuxVariables]
  [fast_neutron_fluence]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Physics]
  [SolidMechanics]
    [QuasiStatic]
      [all]
        strain = FINITE
        generate_output = 'stress_yy strain_yy plastic_strain_xx plastic_strain_yy plastic_strain_zz'
      []
    []
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = temp
  []
[]

[AuxKernels]
  [fast_neutron_fluence]
    type = FunctionAux
    function = fast_neutron_fluence
    variable = fast_neutron_fluence
  []
[]

[Functions]
  [top_pull]
    type = ParsedFunction
    expression = t*(0.02)
  []
  [fast_neutron_fluence]
    type = PiecewiseLinear
    x = '0 1 2'
    y = '0 1.0e25 1.0e26'
  []
[]

[BCs]
  [square1]
    type = DirichletBC
    variable = temp
    boundary = '1 2 3 4'
    value = 300
  []

  [square2]
    type = DirichletBC
    variable = temp
    boundary = '5 6 7 8'
    value = 700
  []

  [square3]
    type = DirichletBC
    variable = temp
    boundary = '9 10 11 12'
    value = 900
  []

  [square4]
    type = DirichletBC
    variable = temp
    boundary = '13 14 15 16'
    value = 1100
  []

  [top_pull]
    type = FunctionDirichletBC
    boundary = '1 5 9 13'
    variable = disp_y
    function = top_pull
  []

  [y_bot]
    type = DirichletBC
    boundary = '3 7 11 15'
    variable = disp_y
    value = 0.0
  []
  [x_bot]
    type = DirichletBC
    boundary = ' 2 6 10 14'
    variable = disp_x
    value = 0.0
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = '1 2 3 4'
    youngs_modulus = 1e10
    poissons_ratio = 0.3
  []
  [stress]
    type = ComputeMultipleInelasticStress
    tangent_operator = elastic
    inelastic_models = 'chromium_plasticity'
    block = '1 2 3 4'
  []
  [chromium_plasticity]
    type = ChromiumPlasticityUpdate
    block = '1 2 3 4'
    temperature = temp
    fast_neutron_fluence = fast_neutron_fluence
    hardening_constant = 0.0
  []
  [heat_conduction]
    type = HeatConductionMaterial
    block = '1 2 3 4'
    thermal_conductivity = 1
    specific_heat = 1
  []
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
  petsc_options_value = '201                hypre    boomeramg      4'

  line_search = 'none'

  l_max_its = 100
  nl_max_its = 100
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-10
  l_tol = 1e-10

  start_time = 0.0
  end_time = 2.0
  dt = 0.1
[]

[Outputs]
  exodus = true
[]

(examples/accident_tolerant_fuel/uo2_coated_zircaloy/uo2_coated_zircaloy.i)


initial_fuel_density = 10431.0

[GlobalParams]
  # Set initial fuel density, other global parameters
  density = ${initial_fuel_density}
  order = SECOND
  family = LAGRANGE
  energy_per_fission = 3.2e-11 # J/fission
  displacements = 'disp_x disp_y'
[]

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

[Mesh]
  coord_type = RZ
  [smeared_pellet_mesh]
    type = FuelPinMeshGenerator
    clad_top_gap_height = 0.026
    pellet_height = 0.1186
    pellet_quantity = 1
    clad_bot_gap_height = 0
    pellet_outer_radius = 4.1e-3
    clad_gap_width = 80e-6
    clad_thickness = 0.57e-3
    coating_thickness = 40e-6
    clad_mesh_density = customize
    pellet_mesh_density = customize
    nx_c = 3
    ny_c = 40
    nx_p = 11
    ny_p = 40
    nx_coating = 2
    elem_type = QUAD8
  []
  patch_update_strategy = auto
  partitioner = centroid
  centroid_partitioner_direction = y
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [temperature]
    initial_condition = 293.0
  []
[]

[UserObjects]
  [pin_geometry]
    type = FuelPinGeometry
    clad_inner_wall = 5
    clad_outer_wall = 2
    clad_top = 3
    clad_bottom = 1
    pellet_exteriors = 8
  []
[]

[AuxVariables]
  [fast_neutron_flux]
    block = clad
  []
  [fast_neutron_fluence]
    block = clad
  []
  [grain_radius]
    block = pellet
    initial_condition = 10e-6
  []
  [gap_cond]
    order = CONSTANT
    family = MONOMIAL
  []
  [coolant_htc]
    order = CONSTANT
    family = MONOMIAL
  []
  [oxide_thickness]
    order = CONSTANT
    family = MONOMIAL
  []
  [total_hoop_strain]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_hoop]
    order = CONSTANT
    family = MONOMIAL
  []
  [hoop_stress]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [power_history]
    type = PiecewiseLinear
    x = '0 1e4 1e8'
    y = '0 2.5e4 2.5e4'
    scale_factor = 1
  []

  [axial_peaking_factors]
    type = ParsedFunction
    expression = 1
  []

  [pressure_ramp]
    type = PiecewiseLinear
    x = '-200 0 1e8'
    y = '6.537e-3 1 1'
    scale_factor = 15.5e6
  []

  [mass_flux_func]
    type = PiecewiseLinear
    x = '-200 0  1e8'
    y = '3800. 3800. 3800.'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [pellets]
    block = pellet
    strain = FINITE
    eigenstrain_names = 'fuel_relocation_strain fuel_thermal_strain fuel_volumetric_strain'
    generate_output = 'vonmises_stress stress_xx stress_yy stress_zz'
    extra_vector_tags = 'ref'
  []
  [clad]
    block = clad
    strain = FINITE
    eigenstrain_names = 'clad_thermal_eigenstrain clad_irradiation_strain'
    generate_output = 'vonmises_stress stress_xx stress_yy stress_zz'
    extra_vector_tags = 'ref'
  []
  [coating]
    block = coating
    strain = FINITE
    eigenstrain_names = 'coating_thermal_eigenstrain'
    generate_output = 'vonmises_stress stress_xx stress_yy stress_zz'
    extra_vector_tags = 'ref'
  []
[]

[Kernels]
  [gravity]
    type = Gravity
    variable = disp_y
    value = -9.81
    extra_vector_tags = 'ref'
  []

  [heat]
    type = HeatConduction
    variable = temperature
    extra_vector_tags = 'ref'
  []

  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temperature
    extra_vector_tags = 'ref'
  []

  [heat_source]
    type = NeutronHeatSource
    variable = temperature
    block = pellet
    burnup_function = burnup
    extra_vector_tags = 'ref'
  []
[]

[Burnup]
  [burnup]
    block = pellet
    rod_ave_lin_pow = power_history
    axial_power_profile = axial_peaking_factors
    num_radial = 81
    num_axial = 11
    fuel_pin_geometry = pin_geometry
    fuel_volume_ratio = 1.0
    RPF = RPF
  []
[]

[AuxKernels]
  [fast_neutron_flux]
    type = FastNeutronFluxAux
    variable = fast_neutron_flux
    block = clad
    rod_ave_lin_pow = power_history
    axial_power_profile = axial_peaking_factors
    factor = 3e13
    execute_on = timestep_begin
  []
  [fast_neutron_fluence]
    type = FastNeutronFluenceAux
    variable = fast_neutron_fluence
    block = clad
    fast_neutron_flux = fast_neutron_flux
    execute_on = timestep_begin
  []
  [grain_radius]
    type = GrainRadiusAux
    block = pellet
    variable = grain_radius
    temperature = temperature
    execute_on = linear
  []
  [hoop_stress]
    type = RankTwoScalarAux
    rank_two_tensor = stress
    variable = hoop_stress
    scalar_type = HoopStress
    execute_on = timestep_end
  []
  [total_hoop_strain]
    type = RankTwoScalarAux
    rank_two_tensor = total_strain
    variable = total_hoop_strain
    scalar_type = HoopStress
    execute_on = timestep_end
  []
  [creep_strain_hoop]
    type = RankTwoScalarAux
    rank_two_tensor = creep_strain
    variable = creep_strain_hoop
    scalar_type = HoopStress
    block = clad
    execute_on = timestep_end
  []
  [conductance]
    type = MaterialRealAux
    property = gap_conductance
    variable = gap_cond
    boundary = 10
  []
  [coolant_htc]
    type = MaterialRealAux
    property = coolant_channel_htc
    variable = coolant_htc
    boundary = 2
  []
[]

[Contact]
  [pellet_clad_mechanical]
    primary = 5
    secondary = 10
    normal_smoothing_distance = 0.1
    penalty = 1e7
  []
[]

[ThermalContact]
  [thermal_contact]
    type = GasGapHeatTransfer
    variable = temperature
    primary = 5
    secondary = 10
    initial_moles = initial_moles
    gas_released = fis_gas_released
    contact_pressure = contact_pressure
    quadrature = true
  []
[]

[BCs]
  [no_x_all]
    type = DirichletBC
    variable = disp_x
    boundary = 12
    value = 0.0
  []

  [no_y_clad_bottom]
    type = DirichletBC
    variable = disp_y
    boundary = 1
    value = 0.0
  []

  [no_y_fuel_bottom]
    type = DirichletBC
    variable = disp_y
    boundary = 1020
    value = 0.0
  []

  [Pressure]
    [coolantPressure]
      boundary = '1 2 3'
      function = pressure_ramp
    []
  []

  [PlenumPressure]
    [plenumPressure]
      boundary = 9
      initial_pressure = 2.0e6
      startup_time = 0
      R = 8.3143
      output_initial_moles = initial_moles
      temperature = ave_temp_interior
      volume = gas_volume
      material_input = fis_gas_released
      output = plenum_pressure
    []
  []

[]

[CoolantChannel]
  [convective_clad_surface]
    boundary = '1 2 3'
    variable = temperature
    inlet_temperature = 580
    inlet_pressure = pressure_ramp
    inlet_massflux = mass_flux_func
    rod_diameter = 9.54e-3
    rod_pitch = 1.26e-2
    linear_heat_rate = power_history
    axial_power_profile = axial_peaking_factors
    oxide_thickness = oxide_thickness
  []
[]

[Materials]
  # Fuel
  [fuel_thermal]
    type = UO2Thermal
    block = pellet
    thermal_conductivity_model = NFIR
    temperature = temperature
    burnup_function = burnup
  []
  [fuel_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = pellet
    youngs_modulus = 2.0e11
    poissons_ratio = 0.345
  []
  [elastic_stress]
    type = ComputeSmearedCrackingStress
    block = pellet
    cracking_stress = 1.68e8
    inelastic_models = 'fuel_creep'
    softening_models = exponential_softening
    shear_retention_factor = 0.1
    max_stress_correction = 0
    cracked_elasticity_type = DIAGONAL
    output_properties = crack_damage
    outputs = exodus
  []
  [exponential_softening]
    type = ExponentialSoftening
  []
  [fuel_creep]
    type = UO2CreepUpdate
    block = pellet
    burnup_function = burnup
    temperature = temperature
  []
  [fuel_relocation]
    type = UO2RelocationEigenstrain
    block = pellet
    burnup_function = burnup
    rod_ave_lin_pow = power_history
    axial_power_profile = axial_peaking_factors
    fuel_pin_geometry = 'pin_geometry'
    relocation_activation1 = 5000
    relocation_model = ESCORE_modified
    eigenstrain_name = fuel_relocation_strain
  []
  [fuel_thermal_expansion]
    type = UO2ThermalExpansionMATPROEigenstrain
    block = pellet
    temperature = temperature
    stress_free_temperature = 295.0
    eigenstrain_name = fuel_thermal_strain
  []
  [fuel_volumetric_swelling]
    type = UO2VolumetricSwellingEigenstrain
    gas_swelling_model_type = SIFGRS
    block = pellet
    temperature = temperature
    burnup_function = burnup
    initial_fuel_density = 10431.0
    eigenstrain_name = fuel_volumetric_strain
  []
  [fission_gas_release]
    type = UO2Sifgrs
    block = pellet
    temperature = temperature
    burnup_function = burnup
    grain_radius = grain_radius
    gbs_model = true
  []
  [fuel_density]
    type = StrainAdjustedDensity
    block = pellet
    strain_free_density = ${initial_fuel_density}
  []

  # Clad
  [clad_thermal]
    type = ZryThermal
    temperature = temperature
    block = clad
  []
  [clad_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 7.5e10
    poissons_ratio = 0.3
    block = clad
  []
  [clad_stress]
    type = ComputeMultipleInelasticStress
    tangent_operator = elastic
    inelastic_models = 'clad_zrycreep clad_plasticity'
    block = clad
  []
  [clad_zrycreep]
    type = ZryCreepLimbackHoppeUpdate
    block = clad
    temperature = temperature
    fast_neutron_flux = fast_neutron_flux
    fast_neutron_fluence = fast_neutron_fluence
    model_irradiation_creep = true
    model_primary_creep = true
    model_thermal_creep = true
    max_inelastic_increment = 1e-4
    zircaloy_material_type = stress_relief_annealed
  []
  [thermal_expansion]
    type = ZryThermalExpansionMATPROEigenstrain
    block = clad
    temperature = temperature
    stress_free_temperature = 295.0
    eigenstrain_name = clad_thermal_eigenstrain
  []
  [irradiation_swelling]
    type = ZryIrradiationGrowthEigenstrain
    block = clad
    fast_neutron_fluence = fast_neutron_fluence
    zircaloy_material_type = stress_relief_annealed
    eigenstrain_name = clad_irradiation_strain
  []
  [clad_plasticity]
    type = ZryPlasticityUpdate
    block = clad
    temperature = temperature
    fast_neutron_flux = fast_neutron_flux
    fast_neutron_fluence = fast_neutron_fluence
    cold_work_factor = 0.5
    plasticity_model_type = MATPRO
    zircaloy_alloy_type = 4
  []
  [clad_density]
    type = StrainAdjustedDensity
    block = clad
    strain_free_density = 6511.0
  []

  # Coating
  [coat_thermal]
    type = ChromiumThermal
    block = coating
    temperature = temperature
  []
  [coating_elasticity_tensor]
    type = ChromiumElasticityTensor
    temperature = temperature
    block = coating
  []
  [coat_stress]
    type = ComputeMultipleInelasticStress
    tangent_operator = elastic
    inelastic_models = 'coat_creep coat_plasticity'
    block = coating
  []
  [coat_creep]
    type = ChromiumCreepUpdate
    temperature = temperature
    block = coating
  []
  [coat_plasticity]
    type = ChromiumPlasticityUpdate
    temperature = temperature
    block = coating
    fast_neutron_fluence = 0.0
    hardening_constant = 2e9
  []
  [coat_thermal_expansion]
    type = ChromiumThermalExpansionEigenstrain
    block = coating
    temperature = temperature
    stress_free_temperature = 293.0
    eigenstrain_name = coating_thermal_eigenstrain
  []
  [density_coat]
    type = StrainAdjustedDensity
    block = coating
    strain_free_density = 7190.0
  []
[]

[Dampers]
  [limitT]
    type = BoundingValueNodalDamper
    max_value = 3200.0
    min_value = 293.0
    variable = temperature
  []
  [limitX]
    type = MaxIncrement
    max_increment = 1e-5
    variable = disp_x
  []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  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 = 100
  l_tol = 8e-3

  nl_max_its = 25
  nl_rel_tol = 1e-5
  nl_abs_tol = 1e-10

  start_time = -200
  n_startup_steps = 1
  end_time = 5e7

  dtmax = 1e6
  dtmin = 1

  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 2.0e2
    force_step_every_function_point = true
    timestep_limiting_function = power_history
    max_function_change = 5e5
    optimal_iterations = 10
    iteration_window = 2
    linear_iteration_ratio = 100
    growth_factor = 2.0
    timestep_limiting_postprocessor = material_timestep
  []

  [Quadrature]
    order = FIFTH
    side_order = SEVENTH
  []
[]

[Postprocessors]
  [ave_temp_interior]
    type = SideAverageValue
    boundary = 9
    variable = temperature
    execute_on = 'initial linear'
  []

  [avg_clad_temp]
    type = SideAverageValue
    boundary = 7
    variable = temperature
  []

  [fis_gas_produced]
    type = ElementIntegralFisGasGeneratedSifgrs
    block = pellet
  []

  [fis_gas_released]
    type = ElementIntegralFisGasReleasedSifgrs
    block = pellet
  []
  [fis_gas_grain]
    type = ElementIntegralFisGasGrainSifgrs
    block = pellet
  []
  [fis_gas_boundary]
    type = ElementIntegralFisGasBoundarySifgrs
    block = pellet
  []

  [gas_volume]
    type = InternalVolume
    boundary = 9
    execute_on = 'initial linear'
  []

  [_dt]
    type = TimestepSize
  []

  [num_lin_it]
    type = NumLinearIterations
  []
  [num_nonlin_it]
    type = NumNonlinearIterations
  []
  [tot_lin_it]
    type = CumulativeValuePostprocessor
    postprocessor = num_lin_it
  []
  [tot_nonlin_it]
    type = CumulativeValuePostprocessor
    postprocessor = num_nonlin_it
  []
  [alive_time]
    type = PerfGraphData
    section_name = Root
    data_type = TOTAL
  []

  [rod_total_power]
    type = ElementIntegralPower
    variable = temperature
    burnup_function = burnup
    block = pellet
  []

  [alhr_input]
    type = FunctionValuePostprocessor
    function = power_history
  []
  [average_burnup]
    type = ElementAverageValue
    block = pellet
    variable = burnup
  []
  [oxide_thickness]
    type = ElementExtremeValue
    block = clad
    variable = oxide_thickness
  []
  [fis_gas_percent]
    type = FGRPercent
    fission_gas_released = fis_gas_released
    fission_gas_generated = fis_gas_produced
  []
  [material_timestep]
    type = MaterialTimeStepPostprocessor
    block = clad
  []
[]

[Outputs]
  perf_graph = true
  time_step_interval =  1
  exodus = true
  csv = true
  print_linear_residuals = true
  color = false

  [console]
    type = Console
    max_rows = 25
  []
[]

(test/tests/solid_mechanics/chromium_plasticity/chromium_initial_fluence_plasticity.i)

# This input file tests the isotropic plasticity model for pure irradiated
# chromium. There are four blocks subjected to different temperatures to
# calculate the temperature dependent yield stress.  These blocks are subjected
# to temperatures 300, 700, 900 and 1100 K, respectively and loaded in tension
# with a maximum displacement of 0.04 m.  The fast neutron fluence on all the
# blocks is specified through an initial fast fluence of 1e25 n/m^2. At a fluence of
# 1e25 n/m^2 the yield stress is hardened by 5% from the unirradiated case.
#
# The linear strain hardening slope is set to zero such that
# the material behaves elastic-perfectly plastically.
#
# Once yield occurs the stress in the yy direction should equal
# the yield stress due to the elastic-perfectly plastic material
# behavior.
#
#                    Fluence = 1e25 n/m^2
#
#   Temp (K)       Analytical        BISON
#                 Yield Stress    Yield Stress
#                   (MPa)            (MPa)
#   300            257.168          257.168
#   700            197.965          197.965
#   900            210.498          210.498
#   1100           195.747          195.747
#
[GlobalParams]
  displacements = 'disp_x disp_y'
  volumetric_locking_correction = true
[]

[Mesh]
  coord_type = RZ
  [mesh]
    type = FileMeshGenerator
    file = 'vertical_squares.e'
  []
[]

[Variables]
  [disp_x]
    order = FIRST
    family = LAGRANGE
  []

  [disp_y]
    order = FIRST
    family = LAGRANGE
  []
  [temp]
    order = FIRST
    family = LAGRANGE
  []
[]

[AuxVariables]
  [fast_neutron_fluence]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Physics]
  [SolidMechanics]
    [QuasiStatic]
      [all]
        strain = FINITE
        generate_output = 'stress_yy strain_yy plastic_strain_xx plastic_strain_yy plastic_strain_zz'
      []
    []
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = temp
  []
[]

[Functions]
  [top_pull]
    type = ParsedFunction
    expression = t*(0.02)
  []
[]

[BCs]
  [square1]
    type = DirichletBC
    variable = temp
    boundary = '1 2 3 4'
    value = 300
  []

  [square2]
    type = DirichletBC
    variable = temp
    boundary = '5 6 7 8'
    value = 700
  []

  [square3]
    type = DirichletBC
    variable = temp
    boundary = '9 10 11 12'
    value = 900
  []

  [square4]
    type = DirichletBC
    variable = temp
    boundary = '13 14 15 16'
    value = 1100
  []

  [top_pull]
    type = FunctionDirichletBC
    boundary = '1 5 9 13'
    variable = disp_y
    function = top_pull
  []

  [y_bot]
    type = DirichletBC
    boundary = '3 7 11 15'
    variable = disp_y
    value = 0.0
  []
  [x_bot]
    type = DirichletBC
    boundary = ' 2 6 10 14'
    variable = disp_x
    value = 0.0
  []
[]

[Materials]
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = '1 2 3 4'
    youngs_modulus = 1e10
    poissons_ratio = 0.3
  []
  [stress]
    type = ComputeMultipleInelasticStress
    tangent_operator = elastic
    inelastic_models = 'chromium_plasticity'
    block = '1 2 3 4'
  []
  [chromium_plasticity]
    type = ChromiumPlasticityUpdate
    block = '1 2 3 4'
    temperature = temp
    initial_fast_fluence = 1e25
    hardening_constant = 0.0
  []
  [heat_conduction]
    type = HeatConductionMaterial
    block = '1 2 3 4'
    thermal_conductivity = 1
    specific_heat = 1
  []
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
  petsc_options_value = '201                hypre    boomeramg      4'

  line_search = 'none'

  l_max_its = 100
  nl_max_its = 100
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-10
  l_tol = 1e-10

  start_time = 0.0
  end_time = 2.0
  dt = 0.1
[]

[Outputs]
  exodus = true
[]

(test/tests/solid_mechanics/chromium_plasticity/ad_chromium_irradiated_plasticity.i)

# This input file tests the isotropic plasticity model for pure irradiated
# chromium using automatic differentiation. There are four blocks subjected to different temperatures to
# calculate the temperature dependent yield stress.  These blocks are subjected
# to temperatures 300, 700, 900 and 1100 K, respectively and loaded in tension
# with a maximum displacement of 0.04 m.  The fast neutron fluence on all the
# blocks is 1e25 n/m^2 at t = 1.0 and 1e26 n/m^2 at t = 2.0. At a fluence of
# 1e25 n/m^2 the yield stress is hardened by 5% from the unirradiated case.
# At 1e26 n/m^2 it is hardened by 50%.
#
# The linear strain hardening slope is set to zero such that
# the material behaves elastic-perfectly plastically.
#
# Once yield occurs the stress in the yy direction should equal
# the yield stress due to the elastic-perfectly plastic material
# behavior.
#
#                    Fluence = 1e25 n/m^2             Fluence = 1e26 n/m^2
#
#   Temp (K)       Analytical        BISON          Analytical        BISON
#                 Yield Stress    Yield Stress     Yield Stress    Yield Stress
#                   (MPa)            (MPa)           (MPa)            (MPa)
#   300            257.168          257.168         367.383          367.383
#   700            197.965          197.965         282.807          282.807
#   900            210.498          210.498         300.711          300.711
#   1100           195.747          195.747         279.638          279.638
#
[GlobalParams]
  displacements = 'disp_x disp_y'
  volumetric_locking_correction = true
[]

[Mesh]
  coord_type = RZ
  [mesh]
    type = FileMeshGenerator
    file = 'vertical_squares.e'
  []
[]

[Variables]
  [disp_x]
    order = FIRST
    family = LAGRANGE
  []

  [disp_y]
    order = FIRST
    family = LAGRANGE
  []
  [temp]
    order = FIRST
    family = LAGRANGE
  []
[]

[AuxVariables]
  [fast_neutron_fluence]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Physics]
  [SolidMechanics]
    [QuasiStatic]
      [all]
        strain = FINITE
        generate_output = 'stress_yy strain_yy plastic_strain_xx plastic_strain_yy plastic_strain_zz'
        use_automatic_differentiation = true
      []
    []
  []
[]

[Kernels]
  [heat]
    type = ADHeatConduction
    variable = temp
  []
[]

[AuxKernels]
  [fast_neutron_fluence]
    type = FunctionAux
    function = fast_neutron_fluence
    variable = fast_neutron_fluence
  []
[]

[Functions]
  [top_pull]
    type = ParsedFunction
    expression = t*(0.02)
  []
  [fast_neutron_fluence]
    type = PiecewiseLinear
    x = '0 1 2'
    y = '0 1.0e25 1.0e26'
  []
[]

[BCs]
  [square1]
    type = ADDirichletBC
    variable = temp
    boundary = '1 2 3 4'
    value = 300
  []

  [square2]
    type = ADDirichletBC
    variable = temp
    boundary = '5 6 7 8'
    value = 700
  []

  [square3]
    type = ADDirichletBC
    variable = temp
    boundary = '9 10 11 12'
    value = 900
  []

  [square4]
    type = ADDirichletBC
    variable = temp
    boundary = '13 14 15 16'
    value = 1100
  []

  [top_pull]
    type = ADFunctionDirichletBC
    boundary = '1 5 9 13'
    variable = disp_y
    function = top_pull
  []

  [y_bot]
    type = ADDirichletBC
    boundary = '3 7 11 15'
    variable = disp_y
    value = 0.0
  []
  [x_bot]
    type = ADDirichletBC
    boundary = ' 2 6 10 14'
    variable = disp_x
    value = 0.0
  []
[]

[Materials]
  [elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    block = '1 2 3 4'
    youngs_modulus = 1e10
    poissons_ratio = 0.3
  []
  [stress]
    type = ADComputeMultipleInelasticStress
    inelastic_models = 'chromium_plasticity'
    block = '1 2 3 4'
  []
  [chromium_plasticity]
    type = ADChromiumPlasticityUpdate
    block = '1 2 3 4'
    temperature = temp
    fast_neutron_fluence = fast_neutron_fluence
    hardening_constant = 0.0
  []
  [heat_conduction]
    type = ADHeatConductionMaterial
    block = '1 2 3 4'
    thermal_conductivity = 1
    specific_heat = 1
  []
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
  petsc_options_value = '201                hypre    boomeramg      4'

  line_search = 'none'

  l_max_its = 100
  nl_max_its = 100
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-10
  l_tol = 1e-10

  start_time = 0.0
  end_time = 2.0
  dt = 0.1
[]

[Outputs]
  exodus = true
[]

(test/tests/solid_mechanics/chromium_plasticity/ad_chromium_initial_fluence_plasticity.i)

# This input file tests the isotropic plasticity model for pure irradiated
# chromium using automatic differentation. There are four blocks subjected to different temperatures to
# calculate the temperature dependent yield stress.  These blocks are subjected
# to temperatures 300, 700, 900 and 1100 K, respectively and loaded in tension
# with a maximum displacement of 0.04 m.  The fast neutron fluence on all the
# blocks is specified through an initial fast fluence of 1e25 n/m^2. At a fluence of
# 1e25 n/m^2 the yield stress is hardened by 5% from the unirradiated case.
#
# The linear strain hardening slope is set to zero such that
# the material behaves elastic-perfectly plastically.
#
# Once yield occurs the stress in the yy direction should equal
# the yield stress due to the elastic-perfectly plastic material
# behavior.
#
#                    Fluence = 1e25 n/m^2
#
#   Temp (K)       Analytical        BISON
#                 Yield Stress    Yield Stress
#                   (MPa)            (MPa)
#   300            257.168          257.168
#   700            197.965          197.965
#   900            210.498          210.498
#   1100           195.747          195.747
#
[GlobalParams]
  displacements = 'disp_x disp_y'
  volumetric_locking_correction = true
[]

[Mesh]
  coord_type = RZ
  [mesh]
    type = FileMeshGenerator
    file = 'vertical_squares.e'
  []
[]

[Variables]
  [disp_x]
    order = FIRST
    family = LAGRANGE
  []

  [disp_y]
    order = FIRST
    family = LAGRANGE
  []
  [temp]
    order = FIRST
    family = LAGRANGE
  []
[]

[AuxVariables]
  [fast_neutron_fluence]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Physics]
  [SolidMechanics]
    [QuasiStatic]
      [all]
        strain = FINITE
        generate_output = 'stress_yy strain_yy plastic_strain_xx plastic_strain_yy plastic_strain_zz'
        use_automatic_differentiation = true
      []
    []
  []
[]

[Kernels]
  [heat]
    type = ADHeatConduction
    variable = temp
  []
[]

[Functions]
  [top_pull]
    type = ParsedFunction
    expression = t*(0.02)
  []
[]

[BCs]
  [square1]
    type = ADDirichletBC
    variable = temp
    boundary = '1 2 3 4'
    value = 300
  []

  [square2]
    type = ADDirichletBC
    variable = temp
    boundary = '5 6 7 8'
    value = 700
  []

  [square3]
    type = ADDirichletBC
    variable = temp
    boundary = '9 10 11 12'
    value = 900
  []

  [square4]
    type = ADDirichletBC
    variable = temp
    boundary = '13 14 15 16'
    value = 1100
  []

  [top_pull]
    type = ADFunctionDirichletBC
    boundary = '1 5 9 13'
    variable = disp_y
    function = top_pull
  []

  [y_bot]
    type = ADDirichletBC
    boundary = '3 7 11 15'
    variable = disp_y
    value = 0.0
  []
  [x_bot]
    type = ADDirichletBC
    boundary = ' 2 6 10 14'
    variable = disp_x
    value = 0.0
  []
[]

[Materials]
  [elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    block = '1 2 3 4'
    youngs_modulus = 1e10
    poissons_ratio = 0.3
  []
  [stress]
    type = ADComputeMultipleInelasticStress
    inelastic_models = 'chromium_plasticity'
    block = '1 2 3 4'
  []
  [chromium_plasticity]
    type = ADChromiumPlasticityUpdate
    block = '1 2 3 4'
    temperature = temp
    initial_fast_fluence = 1e25
    hardening_constant = 0.0
  []
  [heat_conduction]
    type = ADHeatConductionMaterial
    block = '1 2 3 4'
    thermal_conductivity = 1
    specific_heat = 1
  []
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
  petsc_options_value = '201                hypre    boomeramg      4'

  line_search = 'none'

  l_max_its = 100
  nl_max_its = 100
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-10
  l_tol = 1e-10

  start_time = 0.0
  end_time = 2.0
  dt = 0.1
[]

[Outputs]
  exodus = true
[]

(test/tests/solid_mechanics/chromium_plasticity/ad_chromium_unirradiated_plasticity.i)

# This input file tests the isotropic plasticity model for pure unirradiated
# chromium using automatic differentiation. There are four blocks subjected to different temperatures to
# calculate the temperature dependent yield stress.  These blocks are subjected
# to temperatures 300, 700, 900 and 1100 K, respectively and loaded in tension
# with a maximum displacement of 0.04 m.
#
# The linear strain hardening slope is set to zero such that
# the material behaves elastic-perfectly plastically.
#
# Once yield occurs the stress in the yy direction should equal
# the yield stress due to the elastic-perfectly plastic material
# behavior.
#
#   Temp (K)       Analytical                 BISON
#                 Yield Stress             Yield Stress
#                   (MPa)                     (MPa)
#   300            244.922                  244.922
#   700            188.538                  188.538
#   900            200.474                  200.474
#   1100           186.426                  186.426
#
[GlobalParams]
  displacements = 'disp_x disp_y'
  volumetric_locking_correction = true
[]

[Mesh]
  coord_type = RZ
  [mesh]
    type = FileMeshGenerator
    file = 'vertical_squares.e'
  []
[]

[Variables]
  [disp_x]
    order = FIRST
    family = LAGRANGE
  []

  [disp_y]
    order = FIRST
    family = LAGRANGE
  []
  [temp]
    order = FIRST
    family = LAGRANGE
  []
[]

[Physics]
  [SolidMechanics]
    [QuasiStatic]
      [all]
        strain = FINITE
        generate_output = 'stress_yy strain_yy plastic_strain_xx plastic_strain_yy plastic_strain_zz'
        use_automatic_differentiation = true
      []
    []
  []
[]

[Kernels]
  [heat]
    type = ADHeatConduction
    variable = temp
  []
[]

[Functions]
  [top_pull]
    type = ParsedFunction
    expression = t*(0.02)
  []
[]

[BCs]
  [square1]
    type = ADDirichletBC
    variable = temp
    boundary = '1 2 3 4'
    value = 300
  []

  [square2]
    type = ADDirichletBC
    variable = temp
    boundary = '5 6 7 8'
    value = 700
  []

  [square3]
    type = ADDirichletBC
    variable = temp
    boundary = '9 10 11 12'
    value = 900
  []

  [square4]
    type = ADDirichletBC
    variable = temp
    boundary = '13 14 15 16'
    value = 1100
  []

  [top_pull]
    type = ADFunctionDirichletBC
    boundary = '1 5 9 13'
    variable = disp_y
    function = top_pull
  []

  [y_bot]
    type = ADDirichletBC
    boundary = '3 7 11 15'
    variable = disp_y
    value = 0.0
  []
  [x_bot]
    type = ADDirichletBC
    boundary = ' 2 6 10 14'
    variable = disp_x
    value = 0.0
  []
[]

[Materials]
  [elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    block = '1 2 3 4'
    youngs_modulus = 1e10
    poissons_ratio = 0.3
  []
  [stress]
    type = ADComputeMultipleInelasticStress
    inelastic_models = 'chromium_plasticity'
    block = '1 2 3 4'
  []
  [chromium_plasticity]
    type = ADChromiumPlasticityUpdate
    block = '1 2 3 4'
    temperature = temp
    hardening_constant = 0.0
  []
  [heat_conduction]
    type = ADHeatConductionMaterial
    block = '1 2 3 4'
    thermal_conductivity = 1
    specific_heat = 1
  []
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
  petsc_options_value = '201                hypre    boomeramg      4'

  line_search = 'none'

  l_max_its = 100
  nl_max_its = 100
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-10
  l_tol = 1e-10

  start_time = 0.0
  end_time = 2.0
  dt = 0.1
[]

[Outputs]
  exodus = true
[]

Description
Example Input Syntax
Input Parameters
Input Files
References