UPuZrPlasticityUpdateTable

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

Description

UPuZrPlasticityUpdateTable calculates the plastic strain for UPuZr fuel as a function of temperature and zirconium content. This material which must be run in conjunction with ComputeMultipleInelasticStress. The material model inherits from IsotropicPlasticityStressUpdate and sets the yield_stress_function internally based upon temperature and zirconium content. The yield stress as a function of temperature and zirconium content is a piecewise bilinear function based upon the experimental data of Janney and Adkins (2018).

Data from Janney and Adkins (2018)` only covers temperatures ranging from 290 to $var element = document.getElementById("moose-equation-35ce0db3-9e77-4dea-b2db-96a2e37b950d");katex.render("\\sim", element, {displayMode:false,throwOnError:false});$ 948 K and Zr content ranging from 6.3 to 12.2 wt.%. Based on research by Janney and Adkins (2018), the yield strength (YS) and ultimate tensile strength (UTS) are temperature dependent, along with being dependent on the Zr and Pu content within the fuel mixture regions. However, Pu content dependency is not implemented into the code due to the lack of Pu dependent data available. Due to limited amount of temperature dependent data available compared to measurements available at room temperature, applicability of the data is cautioned to the user. In the low temperature region, the UTS drops relatively slowly, and linearly, with increasing temperatures up to 948 K. For temperatures above 948 K, it is assumed that the YS is linearly interpolated to 0 at a temperature of 1523 K, which is the approximate melting temperature of U-10Zr. This temperature value was added to smoothly transition to melting if phase-change were to be implemented.

The minimum or maximum yield stress is used if the temperature is outside the temperature bounds presented here. For example, if the temperature is 280 K and Zr content is 0%, the yield stress is taken as 670.171 MPa.

Table 1: Value of the UPuZr Yield Stress as a Function of Temperature

Temperature (K)	Yield Stress (MPa)	Pu Content (wt%)	Zr Content (wt%)
290.735	670.171	11.1	6.30
623.000	349.835	11.0	6.30
723.000	253.639	11.0	6.30
798.000	181.492	11.0	6.30
898.000	85.2943	11.1	6.30
948.000	10.7843	11.1	6.30
1523.00	0.0	11.1	6.30
290.735	670.171	16.6	6.30
623.000	325.135	16.0	6.30
723.000	221.521	16.0	6.30
798.000	143.811	16.0	6.30
898.000	40.1962	16.6	6.30
948.000	10.7843	16.6	6.30
1523.00	0.0	16.6	6.30
290.735	762.560	15.0	10.0
623.000	302.941	15.0	10.0
723.000	216.363	15.0	10.0
798.000	153.636	15.0	10.0
898.000	70.5884	15.0	10.0
948.000	16.6667	15.0	10.0
1523.00	0.0	15.0	10.0
290.735	999.740	15.0	12.2
623.000	379.412	15.0	12.2
723.000	47.0589	15.0	12.2
798.000	28.3144	15.0	12.2
898.000	24.5099	15.0	12.2
948.000	22.5491	15.0	12.2
1523.00	0.0	15.0	12.2

Example Input Syntax

[Materials<<<{"href": "../../../syntax/Materials/index.html"}>>>]
  [upuzr_plasticity_1]
    type = UPuZrPlasticityUpdateTable<<<{"description": "Computes the plastic strain as a function of strain rate for UPuZr fuel. Note: This material must be run in conjunction with ComputeMultipleInelasticStress.", "href": "UPuZrPlasticityUpdateTable.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = '1'
    temperature<<<{"description": "Coupled Temperature"}>>> = temp
    yield_stress<<<{"description": "The point at which plastic strain begins accumulating"}>>> = 1e-6 #should be ignored
    hardening_constant<<<{"description": "Hardening slope"}>>> = 0.0
    X_Zr<<<{"description": "Coupled zirconium atom fraction"}>>> = 0.15
  []
[]

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

[Materials<<<{"href": "../../../syntax/Materials/index.html"}>>>]
  [stress1]
    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."}>>> = 'upuzr_plasticity_1'
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = '1'
  []
[]

Input Parameters

X_ZrCoupled zirconium atom fraction
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Coupled zirconium atom fraction
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.
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
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_stressThe point at which plastic strain begins accumulating
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The point at which plastic strain begins accumulating
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/upuzr_plasticity/linear_strain_hardening/upuzr_plasticity_rz.i)

References

D. E. Janney and C. A. Adkins. Metallic Fuels Handbook, Part 1: Alloys Based on U-Zr, Pu-Zr, U-P, or U-Pu-Zr, Including Those with Minor Actinides (Np, Am, Cm), Rare-earth Elements (La, Ce, Pr, Nd, Gd), and Y. Technical Report NTRD-FUEL-2018-000085; INL/EXT-15-36520, Idaho National Laboratory, 2018.

@techreport{janney2018,
    Author = "Janney, D. E. and Adkins, C. A.",
    Institution = "Idaho National Laboratory",
    Number = "NTRD-FUEL-2018-000085; INL/EXT-15-36520",
    Title = "{Metallic Fuels Handbook, Part 1: Alloys Based on U-Zr, Pu-Zr, U-P, or U-Pu-Zr, Including Those with Minor Actinides (Np, Am, Cm), Rare-earth Elements (La, Ce, Pr, Nd, Gd), and Y}",
    Year = "2018"
}

(test/tests/solid_mechanics/upuzr_plasticity/linear_strain_hardening/upuzr_plasticity_rz.i)

# This input file tests the isotropic plasticity of UPuZr
# alloys. There are four blocks at different temperatures to
# calculated the yield stress at the four different
# temperatures 290, 623, 898 and 948 K and loaded in tension
# with a maximum displacement of 0.09 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.
#
[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]

  [stress_yy]
    order = CONSTANT
    family = MONOMIAL
  []

  [total_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []

  [plastic_strain_xx]
    order = CONSTANT
    family = MONOMIAL
  []

  [plastic_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []

  [plastic_strain_zz]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = finite
  []
[]

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

[Functions]
  [top_pull]
    type = ParsedFunction
    expression = t*(0.015)
  []
[]

[AuxKernels]

  [stress_yy]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_yy
    index_i = 1
    index_j = 1
  []

  [total_strain_yy]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = total_strain_yy
    index_i = 1
    index_j = 1
    execute_on = timestep_end
  []

  [plastic_strain_xx]
    type = RankTwoAux
    rank_two_tensor = plastic_strain
    variable = plastic_strain_xx
    index_i = 0
    index_j = 0
  []

  [plastic_strain_yy]
    type = RankTwoAux
    rank_two_tensor = plastic_strain
    variable = plastic_strain_yy
    index_i = 1
    index_j = 1
  []

  [plastic_strain_zz]
    type = RankTwoAux
    rank_two_tensor = plastic_strain
    variable = plastic_strain_zz
    index_i = 2
    index_j = 2
  []

[]

[BCs]
  [square1]
    type = DirichletBC
    variable = temp
    boundary = '1 2 3 4'
    value = 290.73
  []

  [square2]
    type = DirichletBC
    variable = temp
    boundary = '5 6 7 8'
    value = 623
  []

  [square3]
    type = DirichletBC
    variable = temp
    boundary = '9 10 11 12'
    value = 898
  []

  [square4]
    type = DirichletBC
    variable = temp
    boundary = '13 14 15 16'
    value = 948
  []

  [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
  []
  [stress1]
    type = ComputeMultipleInelasticStress
    tangent_operator = elastic
    inelastic_models = 'upuzr_plasticity_1'
    block = '1'
  []
  [stress2]
    type = ComputeMultipleInelasticStress
    tangent_operator = elastic
    inelastic_models = 'upuzr_plasticity_2'
    block = '2'
  []
  [stress3]
    type = ComputeMultipleInelasticStress
    tangent_operator = elastic
    inelastic_models = 'upuzr_plasticity_3'
    block = '3'
  []
  [stress4]
    type = ComputeMultipleInelasticStress
    tangent_operator = elastic
    inelastic_models = 'upuzr_plasticity_4'
    block = '4'
  []
  [upuzr_plasticity_1]
    type = UPuZrPlasticityUpdateTable
    block = '1'
    temperature = temp
    yield_stress = 1e-6 #should be ignored
    hardening_constant = 0.0
    X_Zr = 0.15
  []
  [upuzr_plasticity_2]
    type = UPuZrPlasticityUpdateTable
    block = '2'
    temperature = temp
    yield_stress = 1e-6 #should be ignored
    hardening_constant = 0.0
    X_Zr = 0.226
  []
  [upuzr_plasticity_3]
    type = UPuZrPlasticityUpdateTable
    block = '3'
    temperature = temp
    yield_stress = 1e-6 #should be ignored
    hardening_constant = 0.0
    X_Zr = 0.226
  []
  [upuzr_plasticity_4]
    type = UPuZrPlasticityUpdateTable
    block = '4'
    temperature = temp
    yield_stress = 1e-6 #should be ignored
    hardening_constant = 0.0
    X_Zr = 0.5
  []
  [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 = 6
  dt = 0.1
[]

[Postprocessors]
  [yield_stress_block_1]
    type = ElementExtremeValue
    variable = stress_yy
    block = 1
  []
  [yield_stress_block_2]
    type = ElementExtremeValue
    variable = stress_yy
    block = 2
  []
  [yield_stress_block_3]
    type = ElementExtremeValue
    variable = stress_yy
    block = 3
  []
  [yield_stress_block_4]
    type = ElementExtremeValue
    variable = stress_yy
    block = 4
  []
[]

[Outputs]
  exodus = true
[]

(test/tests/solid_mechanics/upuzr_plasticity/linear_strain_hardening/upuzr_plasticity_rz.i)

# This input file tests the isotropic plasticity of UPuZr
# alloys. There are four blocks at different temperatures to
# calculated the yield stress at the four different
# temperatures 290, 623, 898 and 948 K and loaded in tension
# with a maximum displacement of 0.09 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.
#
[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]

  [stress_yy]
    order = CONSTANT
    family = MONOMIAL
  []

  [total_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []

  [plastic_strain_xx]
    order = CONSTANT
    family = MONOMIAL
  []

  [plastic_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []

  [plastic_strain_zz]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = finite
  []
[]

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

[Functions]
  [top_pull]
    type = ParsedFunction
    expression = t*(0.015)
  []
[]

[AuxKernels]

  [stress_yy]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_yy
    index_i = 1
    index_j = 1
  []

  [total_strain_yy]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = total_strain_yy
    index_i = 1
    index_j = 1
    execute_on = timestep_end
  []

  [plastic_strain_xx]
    type = RankTwoAux
    rank_two_tensor = plastic_strain
    variable = plastic_strain_xx
    index_i = 0
    index_j = 0
  []

  [plastic_strain_yy]
    type = RankTwoAux
    rank_two_tensor = plastic_strain
    variable = plastic_strain_yy
    index_i = 1
    index_j = 1
  []

  [plastic_strain_zz]
    type = RankTwoAux
    rank_two_tensor = plastic_strain
    variable = plastic_strain_zz
    index_i = 2
    index_j = 2
  []

[]

[BCs]
  [square1]
    type = DirichletBC
    variable = temp
    boundary = '1 2 3 4'
    value = 290.73
  []

  [square2]
    type = DirichletBC
    variable = temp
    boundary = '5 6 7 8'
    value = 623
  []

  [square3]
    type = DirichletBC
    variable = temp
    boundary = '9 10 11 12'
    value = 898
  []

  [square4]
    type = DirichletBC
    variable = temp
    boundary = '13 14 15 16'
    value = 948
  []

  [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
  []
  [stress1]
    type = ComputeMultipleInelasticStress
    tangent_operator = elastic
    inelastic_models = 'upuzr_plasticity_1'
    block = '1'
  []
  [stress2]
    type = ComputeMultipleInelasticStress
    tangent_operator = elastic
    inelastic_models = 'upuzr_plasticity_2'
    block = '2'
  []
  [stress3]
    type = ComputeMultipleInelasticStress
    tangent_operator = elastic
    inelastic_models = 'upuzr_plasticity_3'
    block = '3'
  []
  [stress4]
    type = ComputeMultipleInelasticStress
    tangent_operator = elastic
    inelastic_models = 'upuzr_plasticity_4'
    block = '4'
  []
  [upuzr_plasticity_1]
    type = UPuZrPlasticityUpdateTable
    block = '1'
    temperature = temp
    yield_stress = 1e-6 #should be ignored
    hardening_constant = 0.0
    X_Zr = 0.15
  []
  [upuzr_plasticity_2]
    type = UPuZrPlasticityUpdateTable
    block = '2'
    temperature = temp
    yield_stress = 1e-6 #should be ignored
    hardening_constant = 0.0
    X_Zr = 0.226
  []
  [upuzr_plasticity_3]
    type = UPuZrPlasticityUpdateTable
    block = '3'
    temperature = temp
    yield_stress = 1e-6 #should be ignored
    hardening_constant = 0.0
    X_Zr = 0.226
  []
  [upuzr_plasticity_4]
    type = UPuZrPlasticityUpdateTable
    block = '4'
    temperature = temp
    yield_stress = 1e-6 #should be ignored
    hardening_constant = 0.0
    X_Zr = 0.5
  []
  [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 = 6
  dt = 0.1
[]

[Postprocessors]
  [yield_stress_block_1]
    type = ElementExtremeValue
    variable = stress_yy
    block = 1
  []
  [yield_stress_block_2]
    type = ElementExtremeValue
    variable = stress_yy
    block = 2
  []
  [yield_stress_block_3]
    type = ElementExtremeValue
    variable = stress_yy
    block = 3
  []
  [yield_stress_block_4]
    type = ElementExtremeValue
    variable = stress_yy
    block = 4
  []
[]

[Outputs]
  exodus = true
[]

(test/tests/solid_mechanics/upuzr_plasticity/linear_strain_hardening/upuzr_plasticity_rz.i)

# This input file tests the isotropic plasticity of UPuZr
# alloys. There are four blocks at different temperatures to
# calculated the yield stress at the four different
# temperatures 290, 623, 898 and 948 K and loaded in tension
# with a maximum displacement of 0.09 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.
#
[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]

  [stress_yy]
    order = CONSTANT
    family = MONOMIAL
  []

  [total_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []

  [plastic_strain_xx]
    order = CONSTANT
    family = MONOMIAL
  []

  [plastic_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []

  [plastic_strain_zz]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = finite
  []
[]

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

[Functions]
  [top_pull]
    type = ParsedFunction
    expression = t*(0.015)
  []
[]

[AuxKernels]

  [stress_yy]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_yy
    index_i = 1
    index_j = 1
  []

  [total_strain_yy]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = total_strain_yy
    index_i = 1
    index_j = 1
    execute_on = timestep_end
  []

  [plastic_strain_xx]
    type = RankTwoAux
    rank_two_tensor = plastic_strain
    variable = plastic_strain_xx
    index_i = 0
    index_j = 0
  []

  [plastic_strain_yy]
    type = RankTwoAux
    rank_two_tensor = plastic_strain
    variable = plastic_strain_yy
    index_i = 1
    index_j = 1
  []

  [plastic_strain_zz]
    type = RankTwoAux
    rank_two_tensor = plastic_strain
    variable = plastic_strain_zz
    index_i = 2
    index_j = 2
  []

[]

[BCs]
  [square1]
    type = DirichletBC
    variable = temp
    boundary = '1 2 3 4'
    value = 290.73
  []

  [square2]
    type = DirichletBC
    variable = temp
    boundary = '5 6 7 8'
    value = 623
  []

  [square3]
    type = DirichletBC
    variable = temp
    boundary = '9 10 11 12'
    value = 898
  []

  [square4]
    type = DirichletBC
    variable = temp
    boundary = '13 14 15 16'
    value = 948
  []

  [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
  []
  [stress1]
    type = ComputeMultipleInelasticStress
    tangent_operator = elastic
    inelastic_models = 'upuzr_plasticity_1'
    block = '1'
  []
  [stress2]
    type = ComputeMultipleInelasticStress
    tangent_operator = elastic
    inelastic_models = 'upuzr_plasticity_2'
    block = '2'
  []
  [stress3]
    type = ComputeMultipleInelasticStress
    tangent_operator = elastic
    inelastic_models = 'upuzr_plasticity_3'
    block = '3'
  []
  [stress4]
    type = ComputeMultipleInelasticStress
    tangent_operator = elastic
    inelastic_models = 'upuzr_plasticity_4'
    block = '4'
  []
  [upuzr_plasticity_1]
    type = UPuZrPlasticityUpdateTable
    block = '1'
    temperature = temp
    yield_stress = 1e-6 #should be ignored
    hardening_constant = 0.0
    X_Zr = 0.15
  []
  [upuzr_plasticity_2]
    type = UPuZrPlasticityUpdateTable
    block = '2'
    temperature = temp
    yield_stress = 1e-6 #should be ignored
    hardening_constant = 0.0
    X_Zr = 0.226
  []
  [upuzr_plasticity_3]
    type = UPuZrPlasticityUpdateTable
    block = '3'
    temperature = temp
    yield_stress = 1e-6 #should be ignored
    hardening_constant = 0.0
    X_Zr = 0.226
  []
  [upuzr_plasticity_4]
    type = UPuZrPlasticityUpdateTable
    block = '4'
    temperature = temp
    yield_stress = 1e-6 #should be ignored
    hardening_constant = 0.0
    X_Zr = 0.5
  []
  [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 = 6
  dt = 0.1
[]

[Postprocessors]
  [yield_stress_block_1]
    type = ElementExtremeValue
    variable = stress_yy
    block = 1
  []
  [yield_stress_block_2]
    type = ElementExtremeValue
    variable = stress_yy
    block = 2
  []
  [yield_stress_block_3]
    type = ElementExtremeValue
    variable = stress_yy
    block = 3
  []
  [yield_stress_block_4]
    type = ElementExtremeValue
    variable = stress_yy
    block = 4
  []
[]

[Outputs]
  exodus = true
[]

Description
Example Input Syntax
Input Parameters
Input Files
References