UO2HotPressingCreepUpdate

Computes the secondary thermal and irradiation creep for UO2 LWR fuel. This material must be run in conjunction with ComputeMultipleInelasticStress.

Description

This model accounts for creep and, if selected, 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 $var element = document.getElementById("moose-equation-a46dae5a-0c9c-4699-9782-e8f9b02aa395");katex.render("_2", element, {displayMode:false,throwOnError:false});$ 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 with high creep rate or plastic deformations, and it is also referred to as hot-pressing.

The mathematical model of hot-pressing of ceramic UO $var element = document.getElementById("moose-equation-c88c06b2-e8b9-4c70-8f18-4c37c90e8972");katex.render("_2", element, {displayMode:false,throwOnError:false});$ was described by Rashid et al. (1974). By using an analogy of close-packed spherical shells in infinite media under hydrostatic compression, model on the stress-induced densification based on the mechanism of instantaneous plasticity and creep was derived. This section describes the implementation of the hot-pressing model based on the mechanisms of creep as follows. For the details of the instantaneous plasticity model implementation, see UO2HotPressingPlasticityUpdate.

Creep is modeling with a power-law form $var element = document.getElementById("moose-equation-a960a789-3366-4eda-b1d4-3a37d2acc205");katex.render(" \\dot{\\epsilon} = A\\sigma^{n}", element, {displayMode:true,throwOnError:false});$ The tangential creep rate of porous media, with density $var element = document.getElementById("moose-equation-decaf97a-434f-4eea-bdcb-b4d20b489745");katex.render("\\rho", element, {displayMode:false,throwOnError:false});$ , at the pore surface is given as in Rashid et al. (1974). $var element = document.getElementById("moose-equation-1e4c00fd-ca54-439c-a099-51b6ed759d7d");katex.render(" {\\dot{\\epsilon}}_{t} = \\frac{A}{2}\\left(\\frac{3}{2n}\\right)^{n}{\\left(\\frac{1}{(0.74(1-\\rho))^{1/n} -1}\\right)}^{n}P^{n}", element, {displayMode:true,throwOnError:false});$ And, the volumetric creep rate is $(1)var element = document.getElementById("moose-equation-5537200e-4b51-4ebf-94ba-1775697febaf");katex.render(" {\\dot{\\epsilon}}_{V} = 6 \\nu_{0}AP^{n}", element, {displayMode:true,throwOnError:false});$ Hot-pressing parameter $var element = document.getElementById("moose-equation-37de04f0-e2c2-4e83-9939-19e9284f46fb");katex.render("\\nu_{0}", element, {displayMode:false,throwOnError:false});$ is defined as $(2)var element = document.getElementById("moose-equation-7a9ddd3a-883d-4b97-9811-7fcaf0ce1165");katex.render(" \\nu_{0} = \\frac{1}{4}{\\left(\\frac{3}{2n}\\right)}^{n}{\\left(\\frac{1}{(0.74(1-\\rho))^{1/n}- 1}\\right)}^{n}P^n", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-b820f644-34d7-4ea6-8bd9-0dd397a71b86");katex.render("P", element, {displayMode:false,throwOnError:false});$ the hydrostatic pressure (Pa), $var element = document.getElementById("moose-equation-b1b7a06a-049d-4362-9d96-5b9a56918f0a");katex.render("n", element, {displayMode:false,throwOnError:false});$ is the exponent in the power law creep equation, $var element = document.getElementById("moose-equation-8718964f-c0b3-408e-9792-92728b830277");katex.render("A", element, {displayMode:false,throwOnError:false});$ is the leading coefficient in the power law creep equation, $var element = document.getElementById("moose-equation-d75c0f0c-3c67-4617-a05f-da9b71a01d89");katex.render("\\rho", element, {displayMode:false,throwOnError:false});$ is the fractional density (dimensionless), $var element = document.getElementById("moose-equation-5cdc5a58-27bd-4cbb-830f-51e44f09cac6");katex.render("\\dot{\\epsilon}", element, {displayMode:false,throwOnError:false});$ is the creep rate, and the subscripts $var element = document.getElementById("moose-equation-86ba3f66-708d-4794-a42d-53132237548d");katex.render("t", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-3f316d89-e5a6-4f57-a22a-03225dae837b");katex.render("V", element, {displayMode:false,throwOnError:false});$ represent tangential and volumetric components respectively.

Figure 1: Hot-pressing parameter $var element = document.getElementById("moose-equation-366a1138-3ff5-44ec-8a9a-0e9212551368");katex.render("\\nu_{0}", element, {displayMode:false,throwOnError:false});$ vs. fractional density

This material parameter $var element = document.getElementById("moose-equation-a0398080-03c6-4ff9-8c85-e665928f047c");katex.render("\\nu_{0}", element, {displayMode:false,throwOnError:false});$ is used in the hot-pressing model for the volumetric creep of UO $var element = document.getElementById("moose-equation-40b84598-1af0-47c3-8f0f-894349e0caa5");katex.render("_2", element, {displayMode:false,throwOnError:false});$ . The creep of UO $var element = document.getElementById("moose-equation-89e8d690-bc97-4c02-8ba8-d3c5240cf303");katex.render("_2", element, {displayMode:false,throwOnError:false});$ involves several mechanisms, and in their mathematical descriptions, different exponent $var element = document.getElementById("moose-equation-513f92b1-1449-40a5-885b-0f58e7cd7312");katex.render("n", element, {displayMode:false,throwOnError:false});$ could be used for the different mechanisms. The volumetric creep strain implemented in BISON code is assumed to be the combination of all the creep strains together. From Eq. (2), the hot-pressing parameter depends on the fuel density. With the increase of fuel density, the parameter $var element = document.getElementById("moose-equation-3880d304-b380-4133-b519-22624b90e97c");katex.render("\\nu_{0}", element, {displayMode:false,throwOnError:false});$ would be reduced; when fractional density approaches 1.0, the parameter $var element = document.getElementById("moose-equation-447264f8-5783-4041-8230-91b09825b67e");katex.render("\\nu_{0}", element, {displayMode:false,throwOnError:false});$ approaches zero, and the densification would essentially be terminated, i.e., the volumetric creep strain rate in Eq. (1) becomes zero. A plot of the hot-pressing parameter versus initial density at different $var element = document.getElementById("moose-equation-1ec9b0ed-43e7-4a33-a804-73326ad53a91");katex.render("n", element, {displayMode:false,throwOnError:false});$ is shown in Figure 1.

Example Input Syntax

[Materials<<<{"href": "../../../syntax/Materials/index.html"}>>>]
  [hotpressing]
    type = UO2HotPressingCreepUpdate<<<{"description": "Computes the secondary thermal and irradiation creep for UO2 LWR fuel. This material must be run in conjunction with ComputeMultipleInelasticStress.", "href": "UO2HotPressingCreepUpdate.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = 1
    base_name<<<{"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."}>>> = hp
    temperature<<<{"description": "Coupled temperature"}>>> = temp
    input_hotpressing<<<{"description": "Flag for using input hot pressing parameter"}>>> = true
    hotpressing_nu<<<{"description": "Input hot pressing parameter"}>>> = 0.01
    fission_rate<<<{"description": "Coupled fission rate"}>>> = fission_rate
    initial_grain_radius<<<{"description": "Fuel grain radius (m)"}>>> = 10.0e-6
    oxygen_to_metal_ratio<<<{"description": "Oxygen to metal ratio"}>>> = 2.0
    a7<<<{"description": "Coefficient on irradiation creep term"}>>> = 3.72264e-35
    q3<<<{"description": "Activation energy for irradiation creep, divided by gas constant (1/K)"}>>> = 2617
  []
[]

UO2HotPressingCreepUpdate 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
temperatureCoupled temperature
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Coupled temperature

Required Parameters

a77.78e-37Coefficient on irradiation creep term
Default:7.78e-37
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Coefficient on irradiation creep term
abs_error1e-06Absolute error in the iteration loop to compute trial pressure
Default:1e-06
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Absolute error in the iteration loop to compute trial pressure
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
burnup_functionBurnup function
C++ Type:BurnupFunctionName
Unit:(no unit assumed)
Controllable:No
Description:Burnup function
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.
fission_rateCoupled fission rate
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Coupled fission rate
has_hotpressing_plasticityFalseFlag to turn on instantaneous plasticity model
Default:False
C++ Type:bool
Controllable:No
Description:Flag to turn on instantaneous plasticity model
hotpressing_nu0Input hot pressing parameter
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Input hot pressing parameter
initial_grain_radius1e-05Fuel grain radius (m)
Default:1e-05
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Fuel grain radius (m)
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
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
max_iteration1000Maximum iteration number
Default:1000
C++ Type:int
Controllable:No
Description:Maximum iteration number
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.
oxygen_to_metal_ratio2Oxygen to metal ratio
Default:2
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Oxygen to metal ratio
po2_fraction0Weight fraction of PO2
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Weight fraction of PO2
q30Activation energy for irradiation creep, divided by gas constant (1/K)
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Activation energy for irradiation creep, divided by gas constant (1/K)
rel_error0.001Relative error in the iteration loop to computer trial pressure
Default:0.001
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Relative error in the iteration loop to computer trial pressure
relative_tolerance1e-08Relative convergence tolerance for Newton iteration
Default:1e-08
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Relative convergence tolerance for Newton iteration
use_substep_integration_errorFalseIf true, it establishes a substep size that will yield, at most,the creep numerical integration error given by substep_strain_tolerance.
Default:False
C++ Type:bool
Controllable:No
Description:If true, it establishes a substep size that will yield, at most,the creep numerical integration error given by substep_strain_tolerance.
use_substeppingNONEWhether and how to use substepping
Default:NONE
C++ Type:MooseEnum
Options:NONE, ERROR_BASED, INCREMENT_BASED
Controllable:No
Description:Whether and how to use substepping

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_hotpressing_strainName of the material property that stores the effective inelastic strain
Default:effective_hotpressing_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/fuelrodlinevaluesampler/example_problem_smeared_test2.i)
(test/tests/fuelrodlinevaluesampler/example_problem_smeared_test.i)
(test/tests/solid_mechanics/uo2_hotpressing/hotpressing_creep_plasticity.i)
(test/tests/example_problem_test/example_problem_test.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/fuelrodlinevaluesampler/example_problem_smeared_test2.i)

[GlobalParams]
  density = 10431.0
  displacements = 'disp_x disp_y'
  energy_per_fission = 3.2e-11 # J/fission
  temperature = temp
[]

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

[Mesh]
  coord_type = RZ
  patch_update_strategy = auto
  patch_size = 10
  partitioner = centroid
  centroid_partitioner_direction = y
  [mesh]
    type = FileMeshGenerator
    file = SmearedTwoPelletOneType2D.e
  []
[]

[Variables]
  [temp]
    initial_condition = 580.0
  []
[]

[AuxVariables]
  [fast_neutron_flux]
    block = clad
  []
  [fast_neutron_fluence]
    block = clad
  []
  [grain_radius]
    block = pellet_type_1
    initial_condition = 10e-6
  []
  [gap_cond]
    order = CONSTANT
    family = MONOMIAL
  []
  [coolant_htc]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [power_history]
    type = PiecewiseLinear
    data_file = powerhistory.csv
    scale_factor = 1
  []
  [axial_peaking_factors]
    type = ParsedFunction
    expression = 1
  []
  [pressure_ramp]
    type = PiecewiseLinear
    x = '-200 0'
    y = '0 1'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [fuel]
    block = pellet_type_1
    strain = FINITE
    incremental = true
    extra_vector_tags = 'ref'
    add_variables = true
    decomposition_method = EigenSolution
    eigenstrain_names = 'fuel_volumetric_swelling_eigenstrain
      fuel_relocation_eigenstrain fuel_thermal_eigenstrain'
    generate_output = 'stress_xx stress_yy stress_zz vonmises_stress'
  []
  [clad]
    block = clad
    strain = FINITE
    incremental = true
    extra_vector_tags = 'ref'
    add_variables = true
    decomposition_method = EigenSolution
    eigenstrain_names = 'clad_thermal_strain clad_irradiation_growth_eigenstrain'
    generate_output = 'stress_xx stress_yy stress_zz vonmises_stress'
  []
[]

[Kernels]
  [gravity]
    type = Gravity
    variable = disp_y
    value = -9.81
  []
  [heat]
    type = HeatConduction
    variable = temp
    extra_vector_tags = 'ref'
  []
  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temp
    extra_vector_tags = 'ref'
  []
  [heat_source]
    type = NeutronHeatSource
    variable = temp
    extra_vector_tags = 'ref'
    block = pellet_type_1
    burnup_function = burnup
  []
[]

[UserObjects]
  [pin_geometry]
    type = FuelPinGeometry
  []
[]

[Burnup]
  [burnup]
    block = pellet_type_1
    rod_ave_lin_pow = power_history # using the power function defined above
    axial_power_profile = axial_peaking_factors # using the axial power profile function defined above
    num_radial = 80
    num_axial = 11
    fuel_pin_geometry = 'pin_geometry'
    fuel_volume_ratio = 0.987775 # for use with dished pellets (ratio of actual volume to cylinder volume)
    order = CONSTANT
    family = MONOMIAL
    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_type_1
    variable = grain_radius
    temperature = temp
    execute_on = linear
  []
  [conductance]
    type = MaterialRealAux
    property = gap_conductance
    variable = gap_cond
    boundary = 10
    execute_on = 'initial timestep_end'
  []
  [coolant_htc]
    type = MaterialRealAux
    property = coolant_channel_htc
    variable = coolant_htc
    boundary = 2
    execute_on = 'initial timestep_end'
  []
[]

[Contact]
  [pellet_clad_mechanical]
    primary = 5
    secondary = 10
    formulation = KINEMATIC
    model = frictionless
    normalize_penalty = true
    penalty = 1e14
  []
[]

[ThermalContact]
  [thermal_contact]
    type = GasGapHeatTransfer
    variable = temp
    primary = 5
    secondary = 10
    initial_moles = initial_moles # coupling to a postprocessor which supplies the initial plenum/gap gas mass
    gas_released = fis_gas_released # coupling to a postprocessor which supplies the fission gas addition
    contact_pressure = contact_pressure
  []
[]

[BCs]
  [no_x_all] # pin pellets and clad along axis of symmetry (y)
    type = DirichletBC
    variable = disp_x
    boundary = 12
    value = 0.0
  []
  [no_y_clad_bottom] # pin clad bottom in the axial direction (y)
    type = DirichletBC
    variable = disp_y
    boundary = '1'
    value = 0.0
  []
  [no_y_fuel_bottom] # pin fuel bottom in the axial direction (y)
    type = DirichletBC
    variable = disp_y
    boundary = '1020'
    value = 0.0
  []
  [Pressure] #  apply coolant pressure on clad outer walls
    [coolantPressure]
      boundary = '1 2 3'
      factor = 15.5e6
      function = pressure_ramp # use the pressure_ramp function defined above
    []
  []
  [PlenumPressure] #  apply plenum pressure on clad inner walls and pellet surfaces
    [plenumPressure]
      boundary = 9
      initial_pressure = 2.0e6
      startup_time = -200
      R = 8.3143
      output_initial_moles = initial_moles # coupling to post processor to get initial fill gas mass
      temperature = ave_temp_interior # coupling to post processor to get gas temperature approximation
      volume = gas_volume # coupling to post processor to get gas volume
      material_input = fis_gas_released # coupling to post processor to get fission gas added
      output = plenum_pressure # coupling to post processor to output plenum/gap pressure
      displacements = 'disp_x disp_y'
      execute_on = 'initial linear'
    []
  []
[]

[CoolantChannel]
  [convective_clad_surface] # apply convective boundary to clad outer surface
    boundary = '1 2 3'
    variable = temp
    inlet_temperature = 580 # K
    inlet_pressure = 15.5e6 # Pa
    inlet_massflux = 3800 # kg/m^2-sec
    rod_diameter = 0.948e-2 # m
    rod_pitch = 1.26e-2 # m
    linear_heat_rate = power_history
    axial_power_profile = axial_peaking_factors
  []
[]

[Materials]
  [fuel_thermal]
    type = UO2Thermal
    block = pellet_type_1
    thermal_conductivity_model = NFIR
    initial_porosity = 0.0
    temperature = temp
    burnup_function = burnup
  []
  [fuel_volumetric_swelling]
    type = UO2VolumetricSwellingEigenstrain
    block = pellet_type_1
    burnup_function = burnup
    initial_fuel_density = 10431.0
    eigenstrain_name = 'fuel_volumetric_swelling_eigenstrain'
  []
  [fuel_elasticity_tensor]
    type = UO2ElasticityTensor
    block = pellet_type_1
  []
  [fuel_thermal_expansion]
    type = UO2ThermalExpansionMartinEigenstrain
    block = pellet_type_1
    stress_free_temperature = 295
    eigenstrain_name = 'fuel_thermal_eigenstrain'
  []
  [hotpressing]
    type = UO2HotPressingCreepUpdate
    block = pellet_type_1
    burnup_function = burnup
    initial_grain_radius = 10.0e-6
  []
  [radial_return_stress]
    type = ComputeMultipleInelasticStress
    tangent_operator = elastic
    inelastic_models = 'hotpressing'
    block = pellet_type_1
  []
  [fuel_relocation]
    type = UO2RelocationEigenstrain
    block = pellet_type_1
    burnup_function = burnup
    fuel_pin_geometry = 'pin_geometry'
    relocation_activation1 = 5000 #TM default value
    rod_ave_lin_pow = power_history
    axial_power_profile = axial_peaking_factors
    burnup_relocation_stop = 1.e20
    eigenstrain_name = fuel_relocation_eigenstrain
  []
  [clad_thermal]
    type = HeatConductionMaterial
    block = clad
    thermal_conductivity = 16.0
    specific_heat = 330.0
  []
  [clad_elasticity_tensor]
    type = ZryElasticityTensor
    block = clad
  []
  [clad_creep_model]
    type = ZryCreepHayesHoppeUpdate
    block = clad
    fast_neutron_flux = fast_neutron_flux
    model_irradiation_creep = true
    model_thermal_creep = true
  []
  [clad_inelastic_stress]
    type = ComputeMultipleInelasticStress
    block = clad
    tangent_operator = elastic
    inelastic_models = 'clad_creep_model'
  []
  [clad_thermal_expansion]
    type = ComputeThermalExpansionEigenstrain
    block = clad
    thermal_expansion_coeff = 5.0e-6
    stress_free_temperature = 295.0
    eigenstrain_name = clad_thermal_strain
  []
  [clad_irradiation_growth]
    type = ZryIrradiationGrowthEigenstrain
    block = clad
    fast_neutron_fluence = fast_neutron_fluence
    zircaloy_material_type = ESCORE_IrradiationGrowthZr4
    eigenstrain_name = clad_irradiation_growth_eigenstrain
  []
  [fission_gas_release]
    type = UO2Sifgrs
    block = pellet_type_1
    temperature = temp
    burnup_function = burnup
    grain_radius = grain_radius
    gbs_model = true
  []
  [clad_density]
    type = StrainAdjustedDensity
    block = clad
    strain_free_density = 6551.0
  []
  [fuel_density]
    type = StrainAdjustedDensity
    block = pellet_type_1
    strain_free_density = 10431.0
  []
[]

[Dampers]
  [BoundingValueNodalDamper]
    type = BoundingValueNodalDamper
    variable = temp
    max_value = 3200
    min_value = 300
  []
[]

[Preconditioning]
  [SMP]
    type = SMP
    coupled_groups = 'disp_x,disp_y'
  []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options = '-pc_type_asm'
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -ksp_gmres_restart'
  petsc_options_value = 'lu       superlu_dist                  51'

  line_search = 'none'

  verbose = true

  l_max_its = 100
  l_tol = 1e-5 #8e-3

  nl_max_its = 15

  nl_rel_tol = 1e-10

  nl_abs_tol = 1e-8

  start_time = -200
  num_steps = 2

  dtmax = 2e6
  dtmin = 1

  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 2.0e2
    optimal_iterations = 6
    iteration_window = 2
  []
[]

[Postprocessors]
  [ave_temp_interior] # average temperature of the cladding interior and all pellet exteriors
    type = SideAverageValue
    boundary = 9
    variable = temp
    execute_on = 'initial linear'
  []
  [clad_inner_vol] # volume inside of cladding
    type = InternalVolume
    boundary = 7
    outputs = exodus
    execute_on = 'initial timestep_end'
  []
  [pellet_volume] # fuel pellet total volume
    type = InternalVolume
    boundary = 8
    outputs = exodus
    execute_on = 'initial timestep_end'
  []
  [avg_clad_temp] # average temperature of cladding interior
    type = SideAverageValue
    boundary = 7
    variable = temp
    execute_on = 'initial timestep_end'
  []
  [fis_gas_produced] # fission gas produced (moles)
    type = ElementIntegralFisGasGeneratedSifgrs
    block = pellet_type_1
    execute_on = timestep_end
  []
  [fis_gas_released] # fission gas released to plenum (moles)
    type = ElementIntegralFisGasReleasedSifgrs
    block = pellet_type_1
    execute_on = timestep_end
  []
  [fis_gas_grain]
    type = ElementIntegralFisGasGrainSifgrs
    block = pellet_type_1
    outputs = exodus
    execute_on = timestep_end
  []
  [fis_gas_boundary]
    type = ElementIntegralFisGasBoundarySifgrs
    block = pellet_type_1
    outputs = exodus
    execute_on = timestep_end
  []
  [gas_volume] # gas volume
    type = InternalVolume
    boundary = 9
    component = 1
    execute_on = 'initial linear'
  []
  [flux_from_clad] # area integrated heat flux from the cladding
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 5
    diffusivity = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [flux_from_fuel] # area integrated heat flux from the fuel
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 10
    diffusivity = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [_dt] # time step
    type = TimestepSize
    execute_on = timestep_end
  []
  [nonlinear_its] # number of nonlinear iterations at each timestep
    type = NumNonlinearIterations
    execute_on = timestep_end
  []
  [rod_total_power]
    type = ElementIntegralPower
    variable = temp
    burnup_function = burnup
    block = pellet_type_1
    execute_on = 'initial timestep_end'
  []
  [rod_input_power]
    type = FunctionValuePostprocessor
    function = power_history
    scale_factor = 0.02372 # rod height
    execute_on = 'initial timestep_end'
  []
[]

[VectorPostprocessors]
  [fuel_vonmises]
    type = FuelRodLineValueSampler
    variable = vonmises_stress
    material = 'fuel'
    fraction = 0.51
    num_points = 20
    orientation = 'vertical'
    fuel_pin_geometry = 'pin_geometry'
    outputs = chkfile
  []
  [clad_vonmises]
    type = FuelRodLineValueSampler
    variable = vonmises_stress
    material = 'clad'
    fraction = 0.51
    num_points = 20
    orientation = 'vertical'
    fuel_pin_geometry = 'pin_geometry'
    outputs = chkfile
  []
[]

[Outputs]
  exodus = true
  color = false
  csv = true
  [console]
    type = Console
    output_linear = true
    max_rows = 25
  []
  [chkfile]
    type = CSV
    execute_on = 'FINAL'
  []
[]

(test/tests/fuelrodlinevaluesampler/example_problem_smeared_test.i)

initial_fuel_density = 10431.0

[GlobalParams]
  density = ${initial_fuel_density}
  displacements = 'disp_x disp_y'
  energy_per_fission = 3.2e-11 # J/fission
  temperature = temp
[]

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

[Mesh]
  coord_type = RZ
  displacements = 'disp_x disp_y'
  patch_update_strategy = auto
  patch_size = 10 # For contact algorithm
  partitioner = centroid
  centroid_partitioner_direction = y
  [mesh]
    type = FileMeshGenerator
    file = SmearedTwoPelletOneType2D.e
  []
[]

[Variables]
  [temp]
    initial_condition = 580.0 # set initial temp to coolant inlet
  []
[]

[AuxVariables]
  [fast_neutron_flux]
    block = clad
  []
  [fast_neutron_fluence]
    block = clad
  []
  [grain_radius]
    block = pellet_type_1
    initial_condition = 10e-6
  []
  [gap_cond]
    order = CONSTANT
    family = MONOMIAL
  []
  [coolant_htc]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [power_history]
    type = PiecewiseLinear
    data_file = powerhistory.csv
    scale_factor = 1
  []
  [axial_peaking_factors]
    type = ParsedFunction
    expression = 1
  []
  [pressure_ramp]
    type = PiecewiseLinear
    x = '-200 0'
    y = '0 1'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [fuel]
    block = pellet_type_1
    strain = FINITE
    incremental = true
    extra_vector_tags = 'ref'
    add_variables = true
    decomposition_method = EigenSolution
    eigenstrain_names = 'fuel_volumetric_swelling_eigenstrain
      fuel_relocation_eigenstrain fuel_thermal_eigenstrain'
    generate_output = 'stress_xx stress_yy stress_zz vonmises_stress'
  []
  [clad]
    block = clad
    strain = FINITE
    incremental = true
    extra_vector_tags = 'ref'
    add_variables = true
    decomposition_method = EigenSolution
    eigenstrain_names = 'clad_thermal_strain clad_irradiation_growth_eigenstrain'
    generate_output = 'stress_xx stress_yy stress_zz vonmises_stress'
  []
[]

[Kernels]
  [gravity]
    type = Gravity
    variable = disp_y
    value = -9.81
  []
  [heat]
    type = HeatConduction
    variable = temp
    extra_vector_tags = 'ref'
  []
  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temp
    extra_vector_tags = 'ref'
  []
  [heat_source]
    type = NeutronHeatSource
    variable = temp
    extra_vector_tags = 'ref'
    block = pellet_type_1
    burnup_function = burnup
  []
[]

[UserObjects]
  [pin_geometry]
    type = FuelPinGeometry
  []
[]

[Burnup]
  [burnup]
    block = pellet_type_1
    rod_ave_lin_pow = power_history # using the power function defined above
    axial_power_profile = axial_peaking_factors # using the axial power profile function defined above
    num_radial = 80
    num_axial = 11
    fuel_pin_geometry = 'pin_geometry'
    fuel_volume_ratio = 0.987775 # for use with dished pellets (ratio of actual volume to cylinder volume)
    order = CONSTANT
    family = MONOMIAL
    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_type_1
    variable = grain_radius
    temperature = temp
    execute_on = linear
  []
  [conductance]
    type = MaterialRealAux
    property = gap_conductance
    variable = gap_cond
    boundary = 10
    execute_on = 'initial timestep_end'
  []
  [coolant_htc]
    type = MaterialRealAux
    property = coolant_channel_htc
    variable = coolant_htc
    boundary = 2
    execute_on = 'initial timestep_end'
  []
[]

[Contact]
  [pellet_clad_mechanical]
    primary = 5
    secondary = 10
    formulation = KINEMATIC
    model = frictionless
    normalize_penalty = true
    penalty = 1e14
  []
[]

[ThermalContact]
  [thermal_contact]
    type = GasGapHeatTransfer
    variable = temp
    primary = 5
    secondary = 10
    initial_moles = initial_moles # coupling to a postprocessor which supplies the initial plenum/gap gas mass
    gas_released = fis_gas_released # coupling to a postprocessor which supplies the fission gas addition
    contact_pressure = contact_pressure
  []
[]

[BCs]
  [no_x_all] # pin pellets and clad along axis of symmetry (y)
    type = DirichletBC
    variable = disp_x
    boundary = 12
    value = 0.0
  []
  [no_y_clad_bottom] # pin clad bottom in the axial direction (y)
    type = DirichletBC
    variable = disp_y
    boundary = '1'
    value = 0.0
  []
  [no_y_fuel_bottom] # pin fuel bottom in the axial direction (y)
    type = DirichletBC
    variable = disp_y
    boundary = '1020'
    value = 0.0
  []
  [Pressure] #  apply coolant pressure on clad outer walls
    [coolantPressure]
      boundary = '1 2 3'
      factor = 15.5e6
      function = pressure_ramp # use the pressure_ramp function defined above
    []
  []
  [PlenumPressure] #  apply plenum pressure on clad inner walls and pellet surfaces
    [plenumPressure]
      boundary = 9
      initial_pressure = 2.0e6
      startup_time = -200
      R = 8.3143
      output_initial_moles = initial_moles # coupling to post processor to get initial fill gas mass
      temperature = ave_temp_interior # coupling to post processor to get gas temperature approximation
      volume = gas_volume # coupling to post processor to get gas volume
      material_input = fis_gas_released # coupling to post processor to get fission gas added
      output = plenum_pressure # coupling to post processor to output plenum/gap pressure
      displacements = 'disp_x disp_y'
      execute_on = 'initial linear'
    []
  []
[]

[CoolantChannel]
  [convective_clad_surface] # apply convective boundary to clad outer surface
    boundary = '1 2 3'
    variable = temp
    inlet_temperature = 580 # K
    inlet_pressure = 15.5e6 # Pa
    inlet_massflux = 3800 # kg/m^2-sec
    rod_diameter = 0.948e-2 # m
    rod_pitch = 1.26e-2 # m
    linear_heat_rate = power_history
    axial_power_profile = axial_peaking_factors
  []
[]

[Materials]
  [fuel_thermal]
    type = UO2Thermal
    block = pellet_type_1
    thermal_conductivity_model = NFIR
    initial_porosity = 0.0
    temperature = temp
    burnup_function = burnup
  []
  [fuel_volumetric_swelling]
    type = UO2VolumetricSwellingEigenstrain
    block = pellet_type_1
    burnup_function = burnup
    initial_fuel_density = 10431.0
    eigenstrain_name = 'fuel_volumetric_swelling_eigenstrain'
  []
  [fuel_elasticity_tensor]
    type = UO2ElasticityTensor
    block = pellet_type_1
  []
  [fuel_thermal_expansion]
    type = UO2ThermalExpansionMartinEigenstrain
    block = pellet_type_1
    stress_free_temperature = 295
    eigenstrain_name = 'fuel_thermal_eigenstrain'
  []
  [hotpressing]
    type = UO2HotPressingCreepUpdate
    block = pellet_type_1
    burnup_function = burnup
    initial_grain_radius = 10.0e-6
  []
  [radial_return_stress]
    type = ComputeMultipleInelasticStress
    tangent_operator = elastic
    inelastic_models = 'hotpressing'
    block = pellet_type_1
  []
  [fuel_relocation]
    type = UO2RelocationEigenstrain
    block = pellet_type_1
    burnup_function = burnup
    fuel_pin_geometry = 'pin_geometry'
    relocation_activation1 = 5000 #TM default value
    rod_ave_lin_pow = power_history
    axial_power_profile = axial_peaking_factors
    burnup_relocation_stop = 1.e20
    eigenstrain_name = 'fuel_relocation_eigenstrain'
  []
  [clad_thermal]
    type = HeatConductionMaterial
    block = clad
    thermal_conductivity = 16.0
    specific_heat = 330.0
  []
  [clad_elasticity_tensor]
    type = ZryElasticityTensor
    block = clad
  []
  [clad_creep_model]
    type = ZryCreepHayesHoppeUpdate
    block = clad
    fast_neutron_flux = fast_neutron_flux
    model_irradiation_creep = true
    model_thermal_creep = true
  []
  [clad_inelastic_stress]
    type = ComputeMultipleInelasticStress
    block = clad
    tangent_operator = elastic
    inelastic_models = 'clad_creep_model'
  []
  [clad_thermal_expansion]
    type = ComputeThermalExpansionEigenstrain
    block = clad
    thermal_expansion_coeff = 5.0e-6
    stress_free_temperature = 295.0
    eigenstrain_name = clad_thermal_strain
  []
  [clad_irradiation_growth]
    type = ZryIrradiationGrowthEigenstrain
    block = clad
    fast_neutron_fluence = fast_neutron_fluence
    zircaloy_material_type = ESCORE_IrradiationGrowthZr4
    eigenstrain_name = clad_irradiation_growth_eigenstrain
  []
  [fission_gas_release]
    type = UO2Sifgrs
    block = pellet_type_1
    temperature = temp
    burnup_function = burnup
    grain_radius = grain_radius
    gbs_model = true
  []
  [clad_density]
    type = StrainAdjustedDensity
    block = clad
    strain_free_density = 6551.0
  []
  [fuel_density]
    type = StrainAdjustedDensity
    block = pellet_type_1
    strain_free_density = ${initial_fuel_density}
  []
[]

[Dampers]
  [BoundingValueNodalDamper]
    type = BoundingValueNodalDamper
    variable = temp
    max_value = 3200
    min_value = 300
  []
[]

[Preconditioning]
  [SMP]
    type = SMP
    coupled_groups = 'disp_x,disp_y'
  []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options = '-pc_type_asm'
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -ksp_gmres_restart'
  petsc_options_value = 'lu       superlu_dist                  51'

  line_search = 'none'

  verbose = true

  l_max_its = 100
  l_tol = 1e-5 #8e-3

  nl_max_its = 15

  nl_rel_tol = 1e-10

  nl_abs_tol = 1e-8

  start_time = -200
  num_steps = 2

  dtmax = 2e6
  dtmin = 1

  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 2.0e2
    optimal_iterations = 6
    iteration_window = 2
  []
[]

[Postprocessors]
  [ave_temp_interior] # average temperature of the cladding interior and all pellet exteriors
    type = SideAverageValue
    boundary = 9
    variable = temp
    execute_on = 'initial linear'
  []
  [clad_inner_vol] # volume inside of cladding
    type = InternalVolume
    boundary = 7
    outputs = exodus
    execute_on = 'initial timestep_end'
  []
  [pellet_volume] # fuel pellet total volume
    type = InternalVolume
    boundary = 8
    outputs = exodus
    execute_on = 'initial timestep_end'
  []
  [avg_clad_temp] # average temperature of cladding interior
    type = SideAverageValue
    boundary = 7
    variable = temp
    execute_on = 'initial timestep_end'
  []
  [fis_gas_produced] # fission gas produced (moles)
    type = ElementIntegralFisGasGeneratedSifgrs
    block = pellet_type_1
    execute_on = timestep_end
  []
  [fis_gas_released] # fission gas released to plenum (moles)
    type = ElementIntegralFisGasReleasedSifgrs
    block = pellet_type_1
    execute_on = timestep_end
  []
  [fis_gas_grain]
    type = ElementIntegralFisGasGrainSifgrs
    block = pellet_type_1
    outputs = exodus
    execute_on = timestep_end
  []
  [fis_gas_boundary]
    type = ElementIntegralFisGasBoundarySifgrs
    block = pellet_type_1
    outputs = exodus
    execute_on = timestep_end
  []
  [gas_volume] # gas volume
    type = InternalVolume
    boundary = 9
    component = 1
    execute_on = 'initial linear'
  []
  [flux_from_clad] # area integrated heat flux from the cladding
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 5
    diffusivity = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [flux_from_fuel] # area integrated heat flux from the fuel
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 10
    diffusivity = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [_dt] # time step
    type = TimestepSize
    execute_on = timestep_end
  []
  [nonlinear_its] # number of nonlinear iterations at each timestep
    type = NumNonlinearIterations
    execute_on = timestep_end
  []
  [rod_total_power]
    type = ElementIntegralPower
    variable = temp
    burnup_function = burnup
    block = pellet_type_1
    execute_on = 'initial timestep_end'
  []
  [rod_input_power]
    type = FunctionValuePostprocessor
    function = power_history
    scale_factor = 0.02372 # rod height
    execute_on = 'initial timestep_end'
  []
[]

[VectorPostprocessors]
  [fuel_vonmises]
    type = FuelRodLineValueSampler
    variable = vonmises_stress
    material = 'fuel'
    fraction = 0.51
    num_points = 20
    orientation = 'horizontal'
    fuel_pin_geometry = 'pin_geometry'
    outputs = chkfile
  []
  [clad_vonmises]
    type = FuelRodLineValueSampler
    variable = vonmises_stress
    material = 'clad'
    fraction = 0.51
    num_points = 9
    orientation = 'horizontal'
    fuel_pin_geometry = 'pin_geometry'
    outputs = chkfile
  []
[]

[Outputs]
  exodus = true
  color = false
  csv = true
  [console]
    type = Console
    output_linear = true
    max_rows = 25
  []
  [chkfile]
    type = CSV
    execute_on = 'FINAL'
  []
[]

(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/example_problem_test/example_problem_test.i)

[GlobalParams]
  density = 10431.0
  displacements = 'disp_x disp_y'
  energy_per_fission = 3.2e-11 # J/fission
  temperature = temp
  volumetric_locking_correction = false
[]

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

[Mesh]
  coord_type = RZ
  patch_update_strategy = auto
  patch_size = 10 # For contact algorithm
  partitioner = centroid
  centroid_partitioner_direction = y
  [mesh]
    type = FileMeshGenerator
    file = 2_pellet_discrete.e
  []
[]

[Variables]
  [temp]
    initial_condition = 580.0
  []
[]

[AuxVariables]
  [fast_neutron_flux]
    block = clad
  []
  [fast_neutron_fluence]
    block = clad
  []
  [grain_radius]
    block = pellet_type_1
    initial_condition = 10e-6
  []
  [gap_cond]
    order = CONSTANT
    family = MONOMIAL
  []
  [coolant_htc]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [power_history]
    type = PiecewiseLinear
    data_file = powerhistory.csv
    scale_factor = 1
  []
  [axial_peaking_factors]
    type = ParsedFunction
    expression = 1
  []
  [pressure_ramp]
    type = PiecewiseLinear
    x = '-200 0'
    y = '0 1'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [fuel]
    block = pellet_type_1
    strain = FINITE
    incremental = true
    extra_vector_tags = 'ref'
    add_variables = true
    decomposition_method = EigenSolution
    eigenstrain_names = 'fuel_volumetric_swelling_eigenstrain
      fuel_relocation_eigenstrain fuel_thermal_eigenstrain'
    generate_output = 'stress_xx stress_yy stress_zz vonmises_stress'
  []
  [clad]
    block = clad
    strain = FINITE
    incremental = true
    extra_vector_tags = 'ref'
    add_variables = true
    decomposition_method = EigenSolution
    eigenstrain_names = 'clad_thermal_strain clad_irradiation_growth_eigenstrain'
    generate_output = 'stress_xx stress_yy stress_zz vonmises_stress'
  []
[]

[Kernels]
  [gravity]
    type = Gravity
    variable = disp_y
    value = -9.81
  []
  [heat]
    type = HeatConduction
    variable = temp
    extra_vector_tags = 'ref'
  []
  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temp
    extra_vector_tags = 'ref'
  []
  [heat_source]
    type = NeutronHeatSource
    variable = temp
    extra_vector_tags = 'ref'
    block = pellet_type_1
    burnup_function = burnup
  []
[]

[UserObjects]
  [pin_geometry]
    type = FuelPinGeometry
  []
[]

[Burnup]
  [burnup]
    block = pellet_type_1
    rod_ave_lin_pow = power_history
    axial_power_profile = axial_peaking_factors
    num_radial = 80
    num_axial = 11
    fuel_pin_geometry = 'pin_geometry'
    fuel_volume_ratio = 0.987775
    order = CONSTANT
    family = MONOMIAL
    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_type_1
    variable = grain_radius
    temperature = temp
    execute_on = linear
  []
  [conductance]
    type = MaterialRealAux
    property = gap_conductance
    variable = gap_cond
    boundary = 10
    execute_on = 'initial timestep_end'
  []
  [coolant_htc]
    type = MaterialRealAux
    property = coolant_channel_htc
    variable = coolant_htc
    boundary = 2
    execute_on = 'initial timestep_end'
  []
[]

[Contact]
  [pellet_clad_mechanical]
    primary = 5
    secondary = 10
    formulation = KINEMATIC
    model = frictionless
    normalize_penalty = true
    penalty = 1e14
  []
[]

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

[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'
      factor = 15.5e6
      function = pressure_ramp
    []
  []
  [PlenumPressure]
    [plenumPressure]
      boundary = 9
      initial_pressure = 2.0e6
      startup_time = -200
      R = 8.3143
      output_initial_moles = initial_moles
      temperature = ave_temp_interior
      volume = gas_volume
      material_input = fis_gas_released
      output = plenum_pressure
      displacements = 'disp_x disp_y'
      execute_on = 'initial linear'
    []
  []
[]

[CoolantChannel]
  [convective_clad_surface]
    boundary = '1 2 3'
    variable = temp
    inlet_temperature = 580 # K
    inlet_pressure = 15.5e6 # Pa
    inlet_massflux = 3800 # kg/m^2-sec
    rod_diameter = 0.948e-2 # m
    rod_pitch = 1.26e-2 # m
    linear_heat_rate = power_history
    axial_power_profile = axial_peaking_factors
  []
[]

[Materials]
  [fuel_thermal]
    type = UO2Thermal
    block = pellet_type_1
    thermal_conductivity_model = NFIR
    initial_porosity = 0.0
    temperature = temp
    burnup_function = burnup
  []
  [fuel_volumetric_swelling]
    type = UO2VolumetricSwellingEigenstrain
    block = pellet_type_1
    burnup = burnup
    initial_fuel_density = 10431.0
    eigenstrain_name = 'fuel_volumetric_swelling_eigenstrain'
  []
  [fuel_elasticity_tensor]
    type = UO2ElasticityTensor
    block = pellet_type_1
  []
  [fuel_thermal_expansion]
    type = UO2ThermalExpansionMartinEigenstrain
    block = pellet_type_1
    stress_free_temperature = 295
    eigenstrain_name = 'fuel_thermal_eigenstrain'
  []
  [hotpressing]
    type = UO2HotPressingCreepUpdate
    block = pellet_type_1
    burnup_function = burnup
    initial_grain_radius = 10.0e-6
  []
  [radial_return_stress]
    type = ComputeMultipleInelasticStress
    tangent_operator = elastic
    inelastic_models = ' hotpressing'
    block = pellet_type_1
  []
  [fuel_relocation]
    type = UO2RelocationEigenstrain
    block = pellet_type_1
    burnup_function = burnup
    fuel_pin_geometry = 'pin_geometry'
    rod_ave_lin_pow = power_history
    axial_power_profile = axial_peaking_factors
    relocation_activation1 = 5000 #TM default value
    burnup_relocation_stop = 1.e20
    eigenstrain_name = 'fuel_relocation_eigenstrain'
  []
  [clad_thermal]
    type = HeatConductionMaterial
    block = clad
    thermal_conductivity = 16.0
    specific_heat = 330.0
  []
  [clad_elasticity_tensor]
    type = ZryElasticityTensor
    block = clad
  []
  [clad_creep_model]
    type = ZryCreepHayesHoppeUpdate
    block = clad
    fast_neutron_flux = fast_neutron_flux
    model_irradiation_creep = true
    model_thermal_creep = true
  []
  [clad_inelastic_stress]
    type = ComputeMultipleInelasticStress
    block = clad
    tangent_operator = elastic
    inelastic_models = 'clad_creep_model'
  []
  [clad_thermal_expansion]
    type = ComputeThermalExpansionEigenstrain
    block = clad
    thermal_expansion_coeff = 5.0e-6
    stress_free_temperature = 295.0
    eigenstrain_name = clad_thermal_strain
  []
  [clad_irradiation_growth]
    type = ZryIrradiationGrowthEigenstrain
    block = clad
    fast_neutron_fluence = fast_neutron_fluence
    zircaloy_material_type = ESCORE_IrradiationGrowthZr4
    eigenstrain_name = clad_irradiation_growth_eigenstrain
  []
  [fission_gas_release]
    type = UO2Sifgrs
    block = pellet_type_1
    temperature = temp
    burnup_function = burnup
    grain_radius = grain_radius
    gbs_model = true
  []
  [clad_density]
    type = StrainAdjustedDensity
    block = clad
    strain_free_density = 6551.0
  []
  [fuel_density]
    type = StrainAdjustedDensity
    block = pellet_type_1
    strain_free_density = 10431.0
  []
[]

[Dampers]
  [BoundingValueNodalDamper]
    type = BoundingValueNodalDamper
    variable = temp
    max_value = 3200
    min_value = 300
  []
[]

[Preconditioning]
  [SMP]
    type = SMP
    coupled_groups = 'disp_x,disp_y'
  []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options = '-pc_type_asm'
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -ksp_gmres_restart'
  petsc_options_value = 'lu       superlu_dist                  51'

  line_search = 'none'

  verbose = true

  l_max_its = 100
  l_tol = 1e-5 #8e-3

  nl_max_its = 15

  nl_rel_tol = 1e-10

  nl_abs_tol = 1e-8

  start_time = -200
  num_steps = 2

  dtmax = 2e6
  dtmin = 1

  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 2.0e2
    optimal_iterations = 6
    iteration_window = 2
  []
[]

[Postprocessors]
  [ave_temp_interior] # average temperature of the cladding interior and all pellet exteriors
    type = SideAverageValue
    boundary = 9
    variable = temp
    execute_on = 'initial linear'
  []
  [clad_inner_vol] # volume inside of cladding
    type = InternalVolume
    boundary = 7
    outputs = exodus
    execute_on = 'initial timestep_end'
  []
  [pellet_volume] # fuel pellet total volume
    type = InternalVolume
    boundary = 8
    outputs = exodus
    execute_on = 'initial timestep_end'
  []
  [avg_clad_temp] # average temperature of cladding interior
    type = SideAverageValue
    boundary = 7
    variable = temp
    execute_on = 'initial timestep_end'
  []
  [fis_gas_produced] # fission gas produced (moles)
    type = ElementIntegralFisGasGeneratedSifgrs
    block = pellet_type_1
    execute_on = timestep_end
  []
  [fis_gas_released] # fission gas released to plenum (moles)
    type = ElementIntegralFisGasReleasedSifgrs
    block = pellet_type_1
    execute_on = timestep_end
  []
  [fis_gas_grain]
    type = ElementIntegralFisGasGrainSifgrs
    block = pellet_type_1
    outputs = exodus
    execute_on = timestep_end
  []
  [fis_gas_boundary]
    type = ElementIntegralFisGasBoundarySifgrs
    block = pellet_type_1
    outputs = exodus
    execute_on = timestep_end
  []
  [gas_volume] # gas volume
    type = InternalVolume
    boundary = 9
    component = 1
    execute_on = 'initial linear'
  []
  [flux_from_clad] # area integrated heat flux from the cladding
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 5
    diffusivity = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [flux_from_fuel] # area integrated heat flux from the fuel
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 10
    diffusivity = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [_dt] # time step
    type = TimestepSize
    execute_on = timestep_end
  []
  [nonlinear_its] # number of nonlinear iterations at each timestep
    type = NumNonlinearIterations
    execute_on = timestep_end
  []
  [rod_total_power]
    type = ElementIntegralPower
    variable = temp
    burnup_function = burnup
    block = pellet_type_1
    execute_on = 'initial timestep_end'
  []
  [rod_input_power]
    type = FunctionValuePostprocessor
    function = power_history
    scale_factor = 0.02372 # rod height
    execute_on = 'initial timestep_end'
  []
[]

[Outputs]
  exodus = true
  color = false
  [console]
    type = Console
    output_linear = true
    max_rows = 25
  []
[]

Description
Example Input Syntax
Input Parameters
Input Files
References