UO2HotPressingPlasticityUpdate

Calculates the effective inelastic strain increment required to return the isotropic stress state to a J2 yield surface. This class is intended to be a parent class for classes with specific constitutive models.

note:Activation Possible through Another Model

The functionality in this model can be activated with the input parameter flag has_hotpressing_plasticity in UO2HotPressingCreepUpdate.

Description

This model accounts for instantaneous plastic flow surrounding pores in ceramic UO2 fuel pellet, which under pressure, can reduce pore volume and consequently reduce fuel porosity and increase fuel density. This is a densification mechanism of UO $var element = document.getElementById("moose-equation-5ad1220e-3cfd-403d-903c-fafde5d2a5c5");katex.render("_2", element, {displayMode:false,throwOnError:false});$ fuel under compressive stresses, which contributes to fuel densification in addition to the irradiation induced densification. Such mechanical densification process is more pronounced at high temperatures and is referred to as hot-pressing.

The mathematical model of hot-pressing of ceramic UO $var element = document.getElementById("moose-equation-6a0d560a-e695-42bf-9c95-45f0dbe17a74");katex.render("_2", element, {displayMode:false,throwOnError:false});$ was described by Rashid et al. (1974), using an analogy of close-packed spherical shells under hydrostatic pressure. The implementation of the hot-pressing model based on the instantaneous plasticity mechanism is describled here. For the details of the hot pressing creep model implementation, see UO2HotPressingCreepUpdate.

In Rashid et al. (1974), yield criterion of UO $var element = document.getElementById("moose-equation-25f7a4a9-b8ab-498d-8069-5df8acb50f3a");katex.render("_2", element, {displayMode:false,throwOnError:false});$ is described by a modified Mohr-coulomb criterion. Eq. (1) through Eq. (2) summarize the criterion: $(1)var element = document.getElementById("moose-equation-849f68b5-ab31-4301-918b-f3ad72a57c84");katex.render(" f= J_{2} + \\alpha J_{1}^{2} - K=0", element, {displayMode:true,throwOnError:false});$ The incremental plastic strain is given as: $var element = document.getElementById("moose-equation-63f3dbf6-0dc5-40cd-a8df-710935be0232");katex.render(" \\Delta \\epsilon_{ij}^{P} = \\lambda(S_{ij} + 2\\alpha J_{1} \\delta_{ij})", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-f303c771-0aa3-4c57-bc49-bd12cd23c936");katex.render("\\begin{aligned} J_1 = & \\sigma_{ii} \\\\ J_2 = & \\frac{1}{2}S_{ij}S_{ij} \\\\ S_{ij} = & \\sigma_{ij} - \\frac{1}{3} J_{1} \\delta_{ij}, i\\neq j \\end{aligned}", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-27ee50ff-147d-4c22-9fe4-0aa037b879f4");katex.render("\\delta_{ij}", element, {displayMode:false,throwOnError:false});$ is the Kronecker delta. The volumetric strain increment is $var element = document.getElementById("moose-equation-fc78d233-6f17-4869-9fd6-6008d6bbae65");katex.render(" \\Delta \\epsilon_{ii}^{P} = 6 \\lambda \\alpha J_1", element, {displayMode:true,throwOnError:false});$ $var element = document.getElementById("moose-equation-92007330-b3a1-4e27-81e2-1af90aebe49f");katex.render("\\alpha", element, {displayMode:false,throwOnError:false});$ defines a material parameter that relates to the yield stress of 100% UO $var element = document.getElementById("moose-equation-7a165f89-0910-4434-87b6-196ddd1459b6");katex.render("_2", element, {displayMode:false,throwOnError:false});$ density. $(2)var element = document.getElementById("moose-equation-1cc7392a-af64-4bdc-9483-2af98354645b");katex.render(" \\alpha = \\left(\\frac{Y(\\rho_0)/Y_s}{2/\\sqrt{3} \\ln(0.74/(1-\\rho))}\\right)^2", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-5146afbc-89ea-45a8-9875-24c915fbf7b6");katex.render("Y(\\rho_0)", element, {displayMode:false,throwOnError:false});$ is the yield stress of UO $var element = document.getElementById("moose-equation-2c48813b-b49d-4dfd-ac12-98ca8d9e42a0");katex.render("_2", element, {displayMode:false,throwOnError:false});$ at initial density $var element = document.getElementById("moose-equation-bb7b62ea-47d3-4ff6-9d29-1224e34732f2");katex.render("\\rho_0", element, {displayMode:false,throwOnError:false});$ , and $var element = document.getElementById("moose-equation-c42e9bc6-ce75-4e5d-a30f-35b752ba7837");katex.render("Y_s", element, {displayMode:false,throwOnError:false});$ is the yield stress at 100% UO $var element = document.getElementById("moose-equation-85f0164b-39fa-4e43-8711-66b686f59c28");katex.render("_2", element, {displayMode:false,throwOnError:false});$ density. The determination of $var element = document.getElementById("moose-equation-225654e0-d3f7-4963-8625-8411b9bba8c0");katex.render("\\alpha", element, {displayMode:false,throwOnError:false});$ needs experimental data on the yield stress of UO $var element = document.getElementById("moose-equation-be8e835b-2ccf-4f3d-b06b-231ced68f569");katex.render("_2", element, {displayMode:false,throwOnError:false});$ with different porosities, which is scarce in the literatures. Instead, an approximation is made in the code by using a constant ratio of $var element = document.getElementById("moose-equation-ccf03d63-5b85-4052-b01f-3587bf6430e0");katex.render("Y(\\rho_0)/Y_s", element, {displayMode:false,throwOnError:false});$ =0.95. The resultant equation of $var element = document.getElementById("moose-equation-0f409499-c95c-4310-8fb3-5ebbd9861993");katex.render("\\alpha", element, {displayMode:false,throwOnError:false});$ in BISON is $var element = document.getElementById("moose-equation-63f7e6a0-93ea-4a71-9d19-9d98a9b5ffe9");katex.render("\\alpha = \\frac{0.0752}{(\\ln(0.74/(1-\\rho))^2}", element, {displayMode:true,throwOnError:false});$

$var element = document.getElementById("moose-equation-ebd06962-7505-4540-8b79-634ad5da95bd");katex.render("\\lambda", element, {displayMode:false,throwOnError:false});$ however is not defined in Rashid et al. (1974). To implement the model in BISON, a new flow rule is used. The yield criterion is formulated as: $var element = document.getElementById("moose-equation-5b8eaae2-a27e-4056-82ca-5da121db8d20");katex.render(" f=\\sqrt{J_2+\\alpha J_{1} ^2 } = K", element, {displayMode:true,throwOnError:false});$ The effective stress is derived as: $var element = document.getElementById("moose-equation-c958460b-3bfe-491f-8aa5-d097ec2e2fb4");katex.render(" \\sigma_{eff} = \\sqrt{3(J_2 + \\alpha J_1 ^2 )}", element, {displayMode:true,throwOnError:false});$ The new flow rule used in BISON is provided in following equations. $var element = document.getElementById("moose-equation-2f608af0-4446-47a8-a54e-47403c9c516e");katex.render("\\Delta \\epsilon_{ij}^P = \\frac{3}{2} \\frac{S_{ij}}{\\sigma_{eff}} \\Delta \\epsilon^P, i \\neq j", element, {displayMode:true,throwOnError:false});$ $var element = document.getElementById("moose-equation-c9ead45a-8e4f-4c93-a0da-9e070861ad27");katex.render("\\Delta \\epsilon_{V}^P = 3 \\sqrt{\\frac{3 \\alpha}{2}} \\frac{J_1}{\\sigma_{eff}} \\Delta \\epsilon^P", element, {displayMode:true,throwOnError:false});$

Yield Stress Model

The hot-pressing or mechanical densification under instantaneous plastic flow depends on the yield strength of UO $var element = document.getElementById("moose-equation-4022f1ea-6fbb-4156-9e90-e2489668593b");katex.render("_2", element, {displayMode:false,throwOnError:false});$ , which is currently not available in BISON. A linear hardening material model is used for modeling the yield stress of UO $var element = document.getElementById("moose-equation-417bb26b-e2a5-4ef9-9993-72b3b0c5c346");katex.render("_2", element, {displayMode:false,throwOnError:false});$ . The yield stress for the linear hardening material is $var element = document.getElementById("moose-equation-d5c25fd2-d260-4e67-9d98-d694e20d8420");katex.render("\\sigma_{eff} = \\sigma_y + H\\Delta \\epsilon^P", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-a73bf417-2068-4e35-a80c-021d5930d4d3");katex.render("{\\sigma_y}", element, {displayMode:false,throwOnError:false});$ is the initial yield stress, $var element = document.getElementById("moose-equation-9cdb9788-7afa-4587-afc3-8b4e09f4305b");katex.render("{\\sigma_{eff}}", element, {displayMode:false,throwOnError:false});$ is the new yield stress (effective stress), $var element = document.getElementById("moose-equation-35710185-3b45-490a-ba08-11b06fc0fd1b");katex.render("{\\Delta \\epsilon^P }", element, {displayMode:false,throwOnError:false});$ is the effective incremental plastic strain, and $var element = document.getElementById("moose-equation-f5b46699-2144-48ab-b3ac-51be3ad3a812");katex.render("H", element, {displayMode:false,throwOnError:false});$ is the hardening modulus. The incremental effective plastic strain and new yield stress are computed in BISON using a radial return method.

Example Input Syntax

[Materials<<<{"href": "../../../syntax/Materials/index.html"}>>>]
  [plasticity]
    type = UO2HotPressingPlasticityUpdate<<<{"description": "Calculates the effective inelastic strain increment required to return the isotropic stress state to a J2 yield surface.  This class is intended to be a parent class for classes with specific constitutive models.", "href": "UO2HotPressingPlasticityUpdate.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = 1
    input_yield_stress<<<{"description": "Input UO2 yield stress"}>>> = 100e6
    input_hardening_modulus<<<{"description": "Input UO2 hardening modulus"}>>> = 0
    input_hotpressing<<<{"description": "Flag for using input hot pressing parameter"}>>> = true
    hotpressing_alpha<<<{"description": "Input hot pressing parameter alpha"}>>> = 0.0125
    model_hotpressing<<<{"description": "Flag to turn on hot pressing model; equivalent to CreepUO2 when set as false"}>>> = true
  []
[]

UO2HotPressingPlasticityUpdate must be run in conjunction with the inelastic strain return mapping stress calculator as shown below:

[Materials<<<{"href": "../../../syntax/Materials/index.html"}>>>]
  [radial_return_stress]
    type = ComputeMultipleInelasticStress<<<{"description": "Compute state (stress and internal parameters such as plastic strains and internal parameters) using an iterative process.  Combinations of creep models and plastic models may be used.", "href": "../ComputeMultipleInelasticStress.html"}>>>
    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."}>>> = 'creep hotpressing plasticity'
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = 1
    max_iterations<<<{"description": "Maximum number of the stress update iterations over the stress change after all update materials are called"}>>> = 30
    relative_tolerance<<<{"description": "Relative convergence tolerance for the stress update iterations over the stress change after all update materials are called"}>>> = 1e-7
    absolute_tolerance<<<{"description": "Absolute convergence tolerance for the stress update iterations over the stress change after all update materials are called"}>>> = 1e-7
  []
[]

Input Parameters

densityInitial fuel density
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Initial fuel density

Required Parameters

absolute_tolerance1e-11Absolute convergence tolerance for Newton iteration
Default:1e-11
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Absolute convergence tolerance for Newton iteration
acceptable_multiplier10Factor applied to relative and absolute tolerance for acceptable convergence if iterations are no longer making progress
Default:10
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Factor applied to relative and absolute tolerance for acceptable convergence if iterations are no longer making progress
adaptive_substeppingFalseUse adaptive substepping, where the number of substeps is successively doubled until the return mapping model successfully converges or the maximum number of substeps is reached.
Default:False
C++ Type:bool
Controllable:No
Description:Use adaptive substepping, where the number of substeps is successively doubled until the return mapping model successfully converges or the maximum number of substeps is reached.
automatic_differentiation_return_mappingFalseWhether to use automatic differentiation to compute the derivative.
Default:False
C++ Type:bool
Controllable:No
Description:Whether to use automatic differentiation to compute the derivative.
base_nameOptional parameter that defines a prefix for all material properties related to this stress update model. This allows for multiple models of the same type to be used without naming conflicts.
C++ Type:std::string
Controllable:No
Description:Optional parameter that defines a prefix for all material properties related to this stress update model. This allows for multiple models of the same type to be used without naming conflicts.
blockThe list of blocks (ids or names) that this object will be applied
C++ Type:std::vector<SubdomainName>
Controllable:No
Description:The list of blocks (ids or names) that this object will be applied
boundaryThe list of boundaries (ids or names) from the mesh where this object applies
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:The list of boundaries (ids or names) from the mesh where this object applies
constant_onNONEWhen ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
Default:NONE
C++ Type:MooseEnum
Options:NONE, ELEMENT, SUBDOMAIN
Controllable:No
Description:When ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
debug_outputFalseFlag for turn on debug output
Default:False
C++ Type:bool
Controllable:No
Description:Flag for turn on debug output
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.
hotpressing_alpha0Input hot pressing parameter alpha
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Input hot pressing parameter alpha
input_hardening_modulus0Input UO2 hardening modulus
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Input UO2 hardening modulus
input_hotpressingFalseFlag for using input hot pressing parameter
Default:False
C++ Type:bool
Controllable:No
Description:Flag for using input hot pressing parameter
input_yield_stress0Input UO2 yield stress
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Input UO2 yield stress
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.
model_hotpressingTrueFlag to turn on hot pressing model; equivalent to CreepUO2 when set as false
Default:True
C++ Type:bool
Controllable:No
Description:Flag to turn on hot pressing model; equivalent to CreepUO2 when set as false
relative_tolerance1e-08Relative convergence tolerance for Newton iteration
Default:1e-08
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Relative convergence tolerance for Newton iteration
use_flow_ruleTrueUse modifed flow rule for modified Mohr-Columnb yield function
Default:True
C++ Type:bool
Controllable:No
Description:Use modifed flow rule for modified Mohr-Columnb yield function
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

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

Input Files

(test/tests/solid_mechanics/uo2_hotpressing/hotpressing_creep_plasticity.i)
(test/tests/solid_mechanics/uo2_hotpressing/creep_plasticity.i)
(test/tests/solid_mechanics/uo2_hotpressing/plasticity.i)

References

Y. R. Rashid, H. T. Tang, and E. B. Johansson. Mathematical treatment of hot pressing of reactor fuel. Nuclear Engineering Design, 29:1–6, 1974.

@ARTICLE{rashid1974a,
    author = "Rashid, Y. R. and Tang, H. T. and Johansson, E. B.",
    title = "Mathematical Treatment of Hot Pressing of Reactor Fuel",
    journal = "Nuclear Engineering Design",
    year = "1974",
    volume = "29",
    pages = "1-6",
    affiliation = "Nuclear Energy Division, General Electric Company, San Jose, CA 95114, USA",
    publisher = "North-Holland Publishing Company"
}

(test/tests/solid_mechanics/uo2_hotpressing/hotpressing_creep_plasticity.i)

#=============================================================================================
# This case is prepared for testing hotpressing driven by combined creep and plasticity for UO2
#
#
# The test is a single element with an initial inner radius of 1, outer radius of 2,
# and a height of 1 under RZ coordinate system.
#
# Input condition
# ===============
#
# Fission density =  2e18 fissios/m**3-s
# Const. temperature = 1500 K
#
# Material property
# =================
#     Fuel density = 95% TD
#     Fuel grain radius = 10 micron
#
# B.C.
# ====
#     Top surface of the element is compressed.
#     Roller at the bottom with zero axial displacement.
#
#
# Results:
#
#
#                             Analytical           BISON
#     --------------------------------------------------------
#     Axial creep strain      -5.40e-4             -5.4024e-4
#     Axial elastic strain    -4.9088e-4           -4.90915e-4
#     Axial plastic strain    -4.46912e-3          -4.467369e-3
#     Axial stress (Pa)       -9.8176e7            -9.8183e7
#     Plastic volumetric strain 1.61e76e-3         -1.611369e-3
#
# Notes: uniaxial load, sigma_y   = sigma_y/sqrt(1+3*alpha)
#                       ep_v / (ep_y - ep_v/3) = 1.5*sqrt(6*alpha)
#        sigma_y --> ec, ee
#        ep = et - ec - ee
#
#==============================================================================================

[GlobalParams]
  density = 10431.0
  displacements = 'disp_r disp_z'
[]

[Mesh]
  coord_type = RZ
  use_displaced_mesh = false
  [mesh]
    type = FileMeshGenerator
    file = 1x1_rz_rev1.e
  []
[]

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

  [disp_z]
    order = FIRST
    family = LAGRANGE
  []

  [temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 1500.0
  []
[]

[AuxVariables]
  [fission_rate]
    order = FIRST
    family = LAGRANGE
  []

  [stress_yy]
    order = CONSTANT
    family = MONOMIAL
  []

  [yield_stress]
    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
  []

  [plastic_strain_xy]
    order = CONSTANT
    family = MONOMIAL
  []

  [plastic_strain_yz]
    order = CONSTANT
    family = MONOMIAL
  []

  [plastic_strain_zx]
    order = CONSTANT
    family = MONOMIAL
  []

  [creep_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []

  [elastic_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []

  [total_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [top_pull]
    type = PiecewiseLinear
    x = '0   100000'
    y = '-0.5e-3 -5.5e-3'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    incremental = true
    strain = small
  []
[]

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

  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temp
  []
[]


[AuxKernels]
  [fissionrate]
    type = FissionRateGeneral
    fission_rate_formulation = GENERIC
    variable = fission_rate
    value = 2.0e18
  []

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

  [yield_stress]
    type = MaterialRealAux
    variable = yield_stress
    property = yield_stress
  []

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

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

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

  [plastic_strain_xy]
    type = RankTwoAux
    variable = plastic_strain_xy
    rank_two_tensor = plastic_strain
    index_i = 0
    index_j = 1
  []

  [plastic_strain_yz]
    type = RankTwoAux
    variable = plastic_strain_yz
    rank_two_tensor = plastic_strain
    index_i = 1
    index_j = 2
  []

  [plastic_strain_zx]
    type = RankTwoAux
    variable = plastic_strain_zx
    rank_two_tensor = plastic_strain
    index_i = 2
    index_j = 0
  []

  [creep_strain_yy]
    type = RankTwoAux
    variable = creep_strain_yy
    rank_two_tensor = creep_strain
    index_i = 1
    index_j = 1
  []

  [elastic_strain_yy]
    type = RankTwoAux
    variable = elastic_strain_yy
    rank_two_tensor = elastic_strain
    index_i = 1
    index_j = 1
  []

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


[BCs]
  [u_top_pull]
    type = FunctionDirichletBC
    variable = disp_z
    boundary = '2 3'
    function = top_pull
  []
  [u_bottom_fix]
    type = DirichletBC
    variable = disp_z
    boundary = '1 4'
    value = 0.0
  []
  [temp_fix]
    type = DirichletBC
    variable = temp
    boundary = '1 2 3 4'
    value = 1500.0
  []
[]

[Materials]
  [plasticity]
    type = UO2HotPressingPlasticityUpdate
    block = 1
    input_yield_stress = 100e6
    input_hardening_modulus  = 0
    input_hotpressing = true
    hotpressing_alpha = 0.0125
    model_hotpressing = true
  []
  [creep]
    type = UO2CreepUpdate
    block = 1
    temperature = temp
    fission_rate = fission_rate
    initial_grain_radius = 10.0e-6
    oxygen_to_metal_ratio = 2.0
    a7 = 3.72264e-35
    q3 = 2617
  []
  [hotpressing]
    type = UO2HotPressingCreepUpdate
    block = 1
    base_name = hp
    temperature = temp
    input_hotpressing = true
    hotpressing_nu = 0.01
    fission_rate = fission_rate
    initial_grain_radius = 10.0e-6
    oxygen_to_metal_ratio = 2.0
    a7 = 3.72264e-35
    q3 = 2617
  []
  [radial_return_stress]
    type = ComputeMultipleInelasticStress
    tangent_operator = elastic
    inelastic_models = 'creep hotpressing plasticity'
    block = 1
    max_iterations = 30
    relative_tolerance = 1e-7
    absolute_tolerance = 1e-7
  []
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = 1
    youngs_modulus = 2.0e11
    poissons_ratio = 0.319
  []
  [thermal]
    type = HeatConductionMaterial
    block = 1
    specific_heat = 1.0
    thermal_conductivity = 100.
  []
  [density]
    type = StrainAdjustedDensity
    block = 1
    strain_free_density = 6550
  []
[]

[Postprocessors]
   [elem_yield_stress]
    type = ElementalVariableValue
    variable = yield_stress
    elementid = 0
  []

  [elem_stress_yy]
    type = ElementalVariableValue
    variable = stress_yy
    elementid = 0
  []

  [elem_plastic_strain_xx]
    type = ElementalVariableValue
    variable = plastic_strain_xx
    elementid = 0
  []

  [elem_plastic_strain_yy]
    type = ElementalVariableValue
    variable = plastic_strain_yy
    elementid = 0
  []

  [elem_creep_strain_yy]
    type = ElementalVariableValue
    variable = creep_strain_yy
    elementid = 0
  []

  [elem_total_strain_yy]
    type = ElementalVariableValue
    variable = total_strain_yy
    elementid = 0
  []

  [elem_elastic_strain_yy]
    type = ElementalVariableValue
    variable = elastic_strain_yy
    elementid = 0
  []

  [elem_plastic_strain_zz]
    type = ElementalVariableValue
    variable = plastic_strain_zz
    elementid = 0
  []
[]

[Executioner]
  type = Transient

  solve_type = PJFNK

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-ksp_gmres_restart'
  petsc_options_value = '101'

  line_search = 'none'

  l_max_its = 100
  nl_max_its = 20
  nl_rel_tol = 1e-16
  nl_abs_tol = 1e-5
  l_tol = 1e-5
  start_time = 0.0
  num_steps = 10
  dtmin = 10000
  dt = 10000
[]

[Outputs]
  csv = true
  [out]
    type = Exodus
  []
[]

(test/tests/solid_mechanics/uo2_hotpressing/hotpressing_creep_plasticity.i)

#=============================================================================================
# This case is prepared for testing hotpressing driven by combined creep and plasticity for UO2
#
#
# The test is a single element with an initial inner radius of 1, outer radius of 2,
# and a height of 1 under RZ coordinate system.
#
# Input condition
# ===============
#
# Fission density =  2e18 fissios/m**3-s
# Const. temperature = 1500 K
#
# Material property
# =================
#     Fuel density = 95% TD
#     Fuel grain radius = 10 micron
#
# B.C.
# ====
#     Top surface of the element is compressed.
#     Roller at the bottom with zero axial displacement.
#
#
# Results:
#
#
#                             Analytical           BISON
#     --------------------------------------------------------
#     Axial creep strain      -5.40e-4             -5.4024e-4
#     Axial elastic strain    -4.9088e-4           -4.90915e-4
#     Axial plastic strain    -4.46912e-3          -4.467369e-3
#     Axial stress (Pa)       -9.8176e7            -9.8183e7
#     Plastic volumetric strain 1.61e76e-3         -1.611369e-3
#
# Notes: uniaxial load, sigma_y   = sigma_y/sqrt(1+3*alpha)
#                       ep_v / (ep_y - ep_v/3) = 1.5*sqrt(6*alpha)
#        sigma_y --> ec, ee
#        ep = et - ec - ee
#
#==============================================================================================

[GlobalParams]
  density = 10431.0
  displacements = 'disp_r disp_z'
[]

[Mesh]
  coord_type = RZ
  use_displaced_mesh = false
  [mesh]
    type = FileMeshGenerator
    file = 1x1_rz_rev1.e
  []
[]

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

  [disp_z]
    order = FIRST
    family = LAGRANGE
  []

  [temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 1500.0
  []
[]

[AuxVariables]
  [fission_rate]
    order = FIRST
    family = LAGRANGE
  []

  [stress_yy]
    order = CONSTANT
    family = MONOMIAL
  []

  [yield_stress]
    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
  []

  [plastic_strain_xy]
    order = CONSTANT
    family = MONOMIAL
  []

  [plastic_strain_yz]
    order = CONSTANT
    family = MONOMIAL
  []

  [plastic_strain_zx]
    order = CONSTANT
    family = MONOMIAL
  []

  [creep_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []

  [elastic_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []

  [total_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [top_pull]
    type = PiecewiseLinear
    x = '0   100000'
    y = '-0.5e-3 -5.5e-3'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    incremental = true
    strain = small
  []
[]

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

  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temp
  []
[]


[AuxKernels]
  [fissionrate]
    type = FissionRateGeneral
    fission_rate_formulation = GENERIC
    variable = fission_rate
    value = 2.0e18
  []

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

  [yield_stress]
    type = MaterialRealAux
    variable = yield_stress
    property = yield_stress
  []

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

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

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

  [plastic_strain_xy]
    type = RankTwoAux
    variable = plastic_strain_xy
    rank_two_tensor = plastic_strain
    index_i = 0
    index_j = 1
  []

  [plastic_strain_yz]
    type = RankTwoAux
    variable = plastic_strain_yz
    rank_two_tensor = plastic_strain
    index_i = 1
    index_j = 2
  []

  [plastic_strain_zx]
    type = RankTwoAux
    variable = plastic_strain_zx
    rank_two_tensor = plastic_strain
    index_i = 2
    index_j = 0
  []

  [creep_strain_yy]
    type = RankTwoAux
    variable = creep_strain_yy
    rank_two_tensor = creep_strain
    index_i = 1
    index_j = 1
  []

  [elastic_strain_yy]
    type = RankTwoAux
    variable = elastic_strain_yy
    rank_two_tensor = elastic_strain
    index_i = 1
    index_j = 1
  []

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


[BCs]
  [u_top_pull]
    type = FunctionDirichletBC
    variable = disp_z
    boundary = '2 3'
    function = top_pull
  []
  [u_bottom_fix]
    type = DirichletBC
    variable = disp_z
    boundary = '1 4'
    value = 0.0
  []
  [temp_fix]
    type = DirichletBC
    variable = temp
    boundary = '1 2 3 4'
    value = 1500.0
  []
[]

[Materials]
  [plasticity]
    type = UO2HotPressingPlasticityUpdate
    block = 1
    input_yield_stress = 100e6
    input_hardening_modulus  = 0
    input_hotpressing = true
    hotpressing_alpha = 0.0125
    model_hotpressing = true
  []
  [creep]
    type = UO2CreepUpdate
    block = 1
    temperature = temp
    fission_rate = fission_rate
    initial_grain_radius = 10.0e-6
    oxygen_to_metal_ratio = 2.0
    a7 = 3.72264e-35
    q3 = 2617
  []
  [hotpressing]
    type = UO2HotPressingCreepUpdate
    block = 1
    base_name = hp
    temperature = temp
    input_hotpressing = true
    hotpressing_nu = 0.01
    fission_rate = fission_rate
    initial_grain_radius = 10.0e-6
    oxygen_to_metal_ratio = 2.0
    a7 = 3.72264e-35
    q3 = 2617
  []
  [radial_return_stress]
    type = ComputeMultipleInelasticStress
    tangent_operator = elastic
    inelastic_models = 'creep hotpressing plasticity'
    block = 1
    max_iterations = 30
    relative_tolerance = 1e-7
    absolute_tolerance = 1e-7
  []
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = 1
    youngs_modulus = 2.0e11
    poissons_ratio = 0.319
  []
  [thermal]
    type = HeatConductionMaterial
    block = 1
    specific_heat = 1.0
    thermal_conductivity = 100.
  []
  [density]
    type = StrainAdjustedDensity
    block = 1
    strain_free_density = 6550
  []
[]

[Postprocessors]
   [elem_yield_stress]
    type = ElementalVariableValue
    variable = yield_stress
    elementid = 0
  []

  [elem_stress_yy]
    type = ElementalVariableValue
    variable = stress_yy
    elementid = 0
  []

  [elem_plastic_strain_xx]
    type = ElementalVariableValue
    variable = plastic_strain_xx
    elementid = 0
  []

  [elem_plastic_strain_yy]
    type = ElementalVariableValue
    variable = plastic_strain_yy
    elementid = 0
  []

  [elem_creep_strain_yy]
    type = ElementalVariableValue
    variable = creep_strain_yy
    elementid = 0
  []

  [elem_total_strain_yy]
    type = ElementalVariableValue
    variable = total_strain_yy
    elementid = 0
  []

  [elem_elastic_strain_yy]
    type = ElementalVariableValue
    variable = elastic_strain_yy
    elementid = 0
  []

  [elem_plastic_strain_zz]
    type = ElementalVariableValue
    variable = plastic_strain_zz
    elementid = 0
  []
[]

[Executioner]
  type = Transient

  solve_type = PJFNK

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-ksp_gmres_restart'
  petsc_options_value = '101'

  line_search = 'none'

  l_max_its = 100
  nl_max_its = 20
  nl_rel_tol = 1e-16
  nl_abs_tol = 1e-5
  l_tol = 1e-5
  start_time = 0.0
  num_steps = 10
  dtmin = 10000
  dt = 10000
[]

[Outputs]
  csv = true
  [out]
    type = Exodus
  []
[]

(test/tests/solid_mechanics/uo2_hotpressing/hotpressing_creep_plasticity.i)

#=============================================================================================
# This case is prepared for testing hotpressing driven by combined creep and plasticity for UO2
#
#
# The test is a single element with an initial inner radius of 1, outer radius of 2,
# and a height of 1 under RZ coordinate system.
#
# Input condition
# ===============
#
# Fission density =  2e18 fissios/m**3-s
# Const. temperature = 1500 K
#
# Material property
# =================
#     Fuel density = 95% TD
#     Fuel grain radius = 10 micron
#
# B.C.
# ====
#     Top surface of the element is compressed.
#     Roller at the bottom with zero axial displacement.
#
#
# Results:
#
#
#                             Analytical           BISON
#     --------------------------------------------------------
#     Axial creep strain      -5.40e-4             -5.4024e-4
#     Axial elastic strain    -4.9088e-4           -4.90915e-4
#     Axial plastic strain    -4.46912e-3          -4.467369e-3
#     Axial stress (Pa)       -9.8176e7            -9.8183e7
#     Plastic volumetric strain 1.61e76e-3         -1.611369e-3
#
# Notes: uniaxial load, sigma_y   = sigma_y/sqrt(1+3*alpha)
#                       ep_v / (ep_y - ep_v/3) = 1.5*sqrt(6*alpha)
#        sigma_y --> ec, ee
#        ep = et - ec - ee
#
#==============================================================================================

[GlobalParams]
  density = 10431.0
  displacements = 'disp_r disp_z'
[]

[Mesh]
  coord_type = RZ
  use_displaced_mesh = false
  [mesh]
    type = FileMeshGenerator
    file = 1x1_rz_rev1.e
  []
[]

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

  [disp_z]
    order = FIRST
    family = LAGRANGE
  []

  [temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 1500.0
  []
[]

[AuxVariables]
  [fission_rate]
    order = FIRST
    family = LAGRANGE
  []

  [stress_yy]
    order = CONSTANT
    family = MONOMIAL
  []

  [yield_stress]
    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
  []

  [plastic_strain_xy]
    order = CONSTANT
    family = MONOMIAL
  []

  [plastic_strain_yz]
    order = CONSTANT
    family = MONOMIAL
  []

  [plastic_strain_zx]
    order = CONSTANT
    family = MONOMIAL
  []

  [creep_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []

  [elastic_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []

  [total_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [top_pull]
    type = PiecewiseLinear
    x = '0   100000'
    y = '-0.5e-3 -5.5e-3'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    incremental = true
    strain = small
  []
[]

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

  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temp
  []
[]


[AuxKernels]
  [fissionrate]
    type = FissionRateGeneral
    fission_rate_formulation = GENERIC
    variable = fission_rate
    value = 2.0e18
  []

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

  [yield_stress]
    type = MaterialRealAux
    variable = yield_stress
    property = yield_stress
  []

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

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

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

  [plastic_strain_xy]
    type = RankTwoAux
    variable = plastic_strain_xy
    rank_two_tensor = plastic_strain
    index_i = 0
    index_j = 1
  []

  [plastic_strain_yz]
    type = RankTwoAux
    variable = plastic_strain_yz
    rank_two_tensor = plastic_strain
    index_i = 1
    index_j = 2
  []

  [plastic_strain_zx]
    type = RankTwoAux
    variable = plastic_strain_zx
    rank_two_tensor = plastic_strain
    index_i = 2
    index_j = 0
  []

  [creep_strain_yy]
    type = RankTwoAux
    variable = creep_strain_yy
    rank_two_tensor = creep_strain
    index_i = 1
    index_j = 1
  []

  [elastic_strain_yy]
    type = RankTwoAux
    variable = elastic_strain_yy
    rank_two_tensor = elastic_strain
    index_i = 1
    index_j = 1
  []

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


[BCs]
  [u_top_pull]
    type = FunctionDirichletBC
    variable = disp_z
    boundary = '2 3'
    function = top_pull
  []
  [u_bottom_fix]
    type = DirichletBC
    variable = disp_z
    boundary = '1 4'
    value = 0.0
  []
  [temp_fix]
    type = DirichletBC
    variable = temp
    boundary = '1 2 3 4'
    value = 1500.0
  []
[]

[Materials]
  [plasticity]
    type = UO2HotPressingPlasticityUpdate
    block = 1
    input_yield_stress = 100e6
    input_hardening_modulus  = 0
    input_hotpressing = true
    hotpressing_alpha = 0.0125
    model_hotpressing = true
  []
  [creep]
    type = UO2CreepUpdate
    block = 1
    temperature = temp
    fission_rate = fission_rate
    initial_grain_radius = 10.0e-6
    oxygen_to_metal_ratio = 2.0
    a7 = 3.72264e-35
    q3 = 2617
  []
  [hotpressing]
    type = UO2HotPressingCreepUpdate
    block = 1
    base_name = hp
    temperature = temp
    input_hotpressing = true
    hotpressing_nu = 0.01
    fission_rate = fission_rate
    initial_grain_radius = 10.0e-6
    oxygen_to_metal_ratio = 2.0
    a7 = 3.72264e-35
    q3 = 2617
  []
  [radial_return_stress]
    type = ComputeMultipleInelasticStress
    tangent_operator = elastic
    inelastic_models = 'creep hotpressing plasticity'
    block = 1
    max_iterations = 30
    relative_tolerance = 1e-7
    absolute_tolerance = 1e-7
  []
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = 1
    youngs_modulus = 2.0e11
    poissons_ratio = 0.319
  []
  [thermal]
    type = HeatConductionMaterial
    block = 1
    specific_heat = 1.0
    thermal_conductivity = 100.
  []
  [density]
    type = StrainAdjustedDensity
    block = 1
    strain_free_density = 6550
  []
[]

[Postprocessors]
   [elem_yield_stress]
    type = ElementalVariableValue
    variable = yield_stress
    elementid = 0
  []

  [elem_stress_yy]
    type = ElementalVariableValue
    variable = stress_yy
    elementid = 0
  []

  [elem_plastic_strain_xx]
    type = ElementalVariableValue
    variable = plastic_strain_xx
    elementid = 0
  []

  [elem_plastic_strain_yy]
    type = ElementalVariableValue
    variable = plastic_strain_yy
    elementid = 0
  []

  [elem_creep_strain_yy]
    type = ElementalVariableValue
    variable = creep_strain_yy
    elementid = 0
  []

  [elem_total_strain_yy]
    type = ElementalVariableValue
    variable = total_strain_yy
    elementid = 0
  []

  [elem_elastic_strain_yy]
    type = ElementalVariableValue
    variable = elastic_strain_yy
    elementid = 0
  []

  [elem_plastic_strain_zz]
    type = ElementalVariableValue
    variable = plastic_strain_zz
    elementid = 0
  []
[]

[Executioner]
  type = Transient

  solve_type = PJFNK

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-ksp_gmres_restart'
  petsc_options_value = '101'

  line_search = 'none'

  l_max_its = 100
  nl_max_its = 20
  nl_rel_tol = 1e-16
  nl_abs_tol = 1e-5
  l_tol = 1e-5
  start_time = 0.0
  num_steps = 10
  dtmin = 10000
  dt = 10000
[]

[Outputs]
  csv = true
  [out]
    type = Exodus
  []
[]

(test/tests/solid_mechanics/uo2_hotpressing/creep_plasticity.i)

#===========================================================================================
# This case is prepared for testing combined creep and plasticity for UO2.
#
# The test is a single element with an initial inner radius of 1, outer radius of 2,
# and a height of 1 under RZ coordinate system.
#
# Input condition
# ===============
#
# Fission density =  2e18 fissios/m**3-s
# Const. temperature = 1500 K
#
# Material property
# =================
#     Fuel density = 95% TD
#     Fuel grain radius = 10 micron
#
# B.C.
# ====
#     Top surface of the element is pulled.
#     Roller at the bottom with zero axial displacement.
#
#
# Results:
#
#
#                    Analytical           BISON
#     -------------------------------------------------
#     Creep strain   5.67e-4              5.666737e-4
#     Elastic strain 5.0e-4               5.000000e-4
#     Plastic strain 4.43e-3              4.433326e-4
#
#
#============================================================================================

[GlobalParams]
  density = 10431.0
  displacements = 'disp_r disp_z'
[]

[Mesh]
  coord_type = RZ
  use_displaced_mesh = false
  [mesh]
    type = FileMeshGenerator
    file = 1x1_rz_rev1.e
  []
[]

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

  [disp_z]
    order = FIRST
    family = LAGRANGE
  []

  [temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 1500.0
  []
[]

[AuxVariables]
  [fission_rate]
    order = FIRST
    family = LAGRANGE
  []

  [stress_yy]
    order = CONSTANT
    family = MONOMIAL
  []

  [yield_stress]
    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
  []

  [plastic_strain_xy]
    order = CONSTANT
    family = MONOMIAL
  []

  [plastic_strain_yz]
    order = CONSTANT
    family = MONOMIAL
  []

  [plastic_strain_zx]
    order = CONSTANT
    family = MONOMIAL
  []

  [creep_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []

  [elastic_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []

  [total_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [top_pull]
    type = PiecewiseLinear
    x = '0   100000'
    y = '0.5e-3    5.5e-3'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    incremental = true
    strain = small
  []
[]

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

  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temp
  []
[]


[AuxKernels]
  [fissionrate]
    type = FissionRateGeneral
    fission_rate_formulation = GENERIC
    variable = fission_rate
    value = 2.0e18
  []

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

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

  [plastic_strain_yy]
    type = RankTwoAux
    variable = plastic_strain_yy
    rank_two_tensor = plastic_strain
    index_i = 1
    index_j = 1
  []
  [plastic_strain_zz]
    type = RankTwoAux
    variable = plastic_strain_zz
    rank_two_tensor = plastic_strain
    index_i = 2
    index_j = 2
  []

  [plastic_strain_xy]
    type = RankTwoAux
    variable = plastic_strain_xy
    rank_two_tensor = plastic_strain
    index_i = 0
    index_j = 1
  []
  [plastic_strain_yz]
    type = RankTwoAux
    variable = plastic_strain_yz
    rank_two_tensor = plastic_strain
    index_i = 1
    index_j = 2
  []

  [plastic_strain_zx]
    type = RankTwoAux
    variable = plastic_strain_zx
    rank_two_tensor = plastic_strain
    index_i = 2
    index_j = 0
  []

  [creep_strain_yy]
    type = RankTwoAux
    variable = creep_strain_yy
    rank_two_tensor = creep_strain
    index_i = 1
    index_j = 1
  []

  [elastic_strain_yy]
    type = RankTwoAux
    variable = elastic_strain_yy
    rank_two_tensor = elastic_strain
    index_i = 1
    index_j = 1
  []

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

[BCs]
  [u_top_pull]
    type = FunctionDirichletBC
    variable = disp_z
    boundary = '2 3'
    function = top_pull
  []

  [u_bottom_fix]
    type = DirichletBC
    variable = disp_z
    boundary = '1 4'
    value = 0.0
  []

  [temp_fix]
    type = DirichletBC
    variable = temp
    boundary = '1 2 3 4'
    value = 1500.0
  []
[]

[Materials]
  [plasticity]
    type = UO2HotPressingPlasticityUpdate
    block = 1
    input_yield_stress = 100e6
    input_hardening_modulus  = 0
    model_hotpressing = false
  []
  [creep]
    type = UO2CreepUpdate
    block = 1
    temperature = temp
    fission_rate = fission_rate
    initial_grain_radius = 10.0e-6
    oxygen_to_metal_ratio = 2.0
    a7 = 3.72264e-35
    q3 = 2617
  []

  [radial_return_stress]
    type = ComputeMultipleInelasticStress
    tangent_operator = elastic
    inelastic_models = 'creep plasticity'
    block = 1
    relative_tolerance = 1e-7
    absolute_tolerance = 1e-7
  []
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = 1
    youngs_modulus = 2.0e11
    poissons_ratio = 0.3
  []
  [thermal]
    type = HeatConductionMaterial
    block = 1
    specific_heat = 1.0
    thermal_conductivity = 100.
  []
  [density]
    type = StrainAdjustedDensity
    block = 1
    strain_free_density = 6550
  []
[]

[Postprocessors]
   [elem_yield_stress]
    type = ElementalVariableValue
    variable = yield_stress
    elementid = 0
  []

  [elem_stress_yy]
    type = ElementalVariableValue
    variable = stress_yy
    elementid = 0
  []

  [elem_plastic_strain_xx]
    type = ElementalVariableValue
    variable = plastic_strain_xx
    elementid = 0
  []

  [elem_plastic_strain_yy]
    type = ElementalVariableValue
    variable = plastic_strain_yy
    elementid = 0
  []

  [elem_creep_strain_yy]
    type = ElementalVariableValue
    variable = creep_strain_yy
    elementid = 0
  []

  [elem_total_strain_yy]
    type = ElementalVariableValue
    variable = total_strain_yy
    elementid = 0
  []

  [elem_elastic_strain_yy]
    type = ElementalVariableValue
    variable = elastic_strain_yy
    elementid = 0
  []

  [elem_plastic_strain_zz]
    type = ElementalVariableValue
    variable = plastic_strain_zz
    elementid = 0
  []
[]

[Executioner]
  type = Transient

  solve_type = PJFNK

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-ksp_gmres_restart'
  petsc_options_value = '101'

  line_search = 'none'

  l_max_its = 100
  nl_max_its = 20
  nl_rel_tol = 1e-16
  nl_abs_tol = 1e-5
  l_tol = 1e-5
  start_time = 0.0
  num_steps = 10
  dtmin = 10000
  dt = 10000
[]

[Outputs]
  csv = true
  [out]
    type = Exodus
  []
[]

(test/tests/solid_mechanics/uo2_hotpressing/plasticity.i)

#===========================================================================================
# Tests plasticity in material model UO2HotPressingPlasticityUpdate
#
# The test is a single element with an initial inner radius of 1, outer radius of 2, and
# a height of 1 under RZ coordinate system.
#
# Two nodes on the top surface of the element are pulled.
# Temperature = 1500 K
# Fission density =  2e18 fissios/m**3-s
# Initial fuel density = 95% TD
#
# Linear hardening material is used.
#
#============================================================================================

[GlobalParams]
  density = 10431.0
  displacements = 'disp_r disp_z'
[]

[Mesh]
  coord_type = RZ
  use_displaced_mesh = false
  [mesh]
    type = FileMeshGenerator
    file = 1x1_rz_rev1.e
  []
[]

[Variables]
  [disp_r]
    order = FIRST
    family = LAGRANGE
  []
  [disp_z]
    order = FIRST
    family = LAGRANGE
  []
  [temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 1500.0
  []
[]

[AuxVariables]
  [fission_rate]
    order = FIRST
    family = LAGRANGE
  []
  [stress_yy]
    order = CONSTANT
    family = MONOMIAL
  []
  [yield_stress]
    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
  []
  [plastic_strain_xy]
    order = CONSTANT
    family = MONOMIAL
  []
  [plastic_strain_yz]
    order = CONSTANT
    family = MONOMIAL
  []
  [plastic_strain_zx]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [top_pull]
    type = PiecewiseLinear
    x = '0    50000  100000'
    y = '0    0.5e-3 5.5e-3'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    incremental = true
    strain = small
  []
[]

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

[AuxKernels]
  [fissionrate]
    type = FissionRateGeneral
    fission_rate_formulation = GENERIC
    variable = fission_rate
    value = 2.0e18
  []
  [stress_yy]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_yy
    index_i = 1
    index_j = 1
  []
  [yield_stress]
    type = MaterialRealAux
    variable = yield_stress
    property = yield_stress
  []
  [plastic_strain_xx]
    type = RankTwoAux
    variable = plastic_strain_xx
    rank_two_tensor = plastic_strain
    index_i = 0
    index_j = 0
  []
  [plastic_strain_yy]
    type = RankTwoAux
    variable = plastic_strain_yy
    rank_two_tensor = plastic_strain
    index_i = 1
    index_j = 1
  []
  [plastic_strain_zz]
    type = RankTwoAux
    variable = plastic_strain_zz
    rank_two_tensor = plastic_strain
    index_i = 2
    index_j = 2
  []
  [plastic_strain_xy]
    type = RankTwoAux
    variable = plastic_strain_xy
    rank_two_tensor = plastic_strain
    index_i = 0
    index_j = 1
  []
  [plastic_strain_yz]
    type = RankTwoAux
    variable = plastic_strain_yz
    rank_two_tensor = plastic_strain
    index_i = 1
    index_j = 2
  []
  [plastic_strain_zx]
    type = RankTwoAux
    variable = plastic_strain_zx
    rank_two_tensor = plastic_strain
    index_i = 2
    index_j = 0
  []
[]

[BCs]
  [u_top_pull]
    type = FunctionDirichletBC
    variable = disp_z
    boundary = '2 3'
    function = top_pull
  []
  [u_bottom_fix]
    type = DirichletBC
    variable = disp_z
    boundary = '1 4'
    value = 0.0
  []
  [temp_fix]
    type = DirichletBC
    variable = temp
    boundary = '1 2 3 4'
    value = 1500.0
  []
[]

[Materials]
  [hotpressing_plasticity]
    type = UO2HotPressingPlasticityUpdate
    block = 1
    input_yield_stress = 100
    input_hardening_modulus  = 1000
    model_hotpressing = true
    input_hotpressing = true
    hotpressing_alpha = 0.01
    debug_output = true
  []
  [radial_return_stress]
    type = ComputeMultipleInelasticStress
    tangent_operator = elastic
    inelastic_models = 'hotpressing_plasticity'
    block = 1
  []
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = 1
    youngs_modulus = 2.e5
    poissons_ratio = 0.3
  []
  [thermal]
    type = HeatConductionMaterial
    block = 1
    specific_heat = 1.0
    thermal_conductivity = 100.
  []
  [density]
    type = StrainAdjustedDensity
    block = 1
    strain_free_density = 6550
  []
[]

[Postprocessors]
   [elem_yield_stress]
    type = ElementalVariableValue
    variable = yield_stress
    elementid = 0
  []

  [elem_stress_yy]
    type = ElementalVariableValue
    variable = stress_yy
    elementid = 0
  []

  [elem_plastic_strain_xx]
    type = ElementalVariableValue
    variable = plastic_strain_xx
    elementid = 0
  []

  [elem_plastic_strain_yy]
    type = ElementalVariableValue
    variable = plastic_strain_yy
    elementid = 0
  []

  [elem_plastic_strain_zz]
    type = ElementalVariableValue
    variable = plastic_strain_zz
    elementid = 0
  []
[]

[Executioner]
  type = Transient
  solve_type = PJFNK

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-ksp_gmres_restart'
  petsc_options_value = '101'

  line_search = 'none'

  l_max_its = 100
  nl_max_its = 10
  nl_rel_tol = 1e-16
  nl_abs_tol = 1e-9
  l_tol = 1e-5
  start_time = 0.0
  num_steps = 10
  dtmin = 10000
  dt = 10000
 []

[Outputs]
  csv = true
  [out]
    type = Exodus
  []
[]

Description
Yield Stress Model
Example Input Syntax
Input Parameters
Input Files
References