Nuclear Material Zirconium Alloy

Reduces the Material block length for LWR Zr-4 cladding within input files.

Description

This NuclearMaterialZirconiumAlloy action reduces BISON input file length by internally generating the Materials required for simulating elastic LWR nuclear cladding, specifically Zirconium Alloy.

warning:For LWR Use Only

This action is designed for use with only Light Water Reactor simulations which deal with UO2 fuel currently.

User-based Interface

To reduce the length and complexity of necessary blocks for simulations, an extensive standardization of operating conditions has been utilized within the NuclearMaterials.

All of the blocks, generated with the default parameter settings, are shown in Table 1, Table 2, and Table 3. These blocks are created internally, based on the Cladding Models and/or physics conditions shown. Additional parameters for each created class can be found below.

note

Certain parameters are determined internally to further reduce input length and complexity.

The classes in Table 1 are automatically created when using NuclearMaterialZirconiumAlloy depending on the Cladding Models and Fission operation used as well as what occurs under Physics conditions.

Table 1: Material classes created by the NuclearMaterialZirconiumAlloy action

Created Classes	Pre-Set Parameters	Block Name	Cladding Models
ComputeIsotropicElasticityTensor	poissons_ratio = 0.3	clad_elasticity_tensor	Elastic \|All Fission Types
	youngs_modulus = 7.5e10
ComputeMultipleInelasticStress	tangent_operator = elastic	clad_stress	Elastic \|All Fission Types
	inelastic_models = clad_zrycreep
ZryCreepLimbackHoppeUpdate	absolute_tolerance = 1e-10	clad_zrycreep	Creep \|All Fission Types
	max_iterations = 50
	fast_neutron_flux = fast_neutron_flux
	fast_neutron_fluence = fast_neutron_fluence
ZryThermalExpansionMATPROEigenstrain	burnup_function = burnup	clad_thermal_expansion	ThermalExpansion\|All Fission Types
	eigenstrain_name = clad_thermal_strain
ZryIrradiationGrowthEigenstrain	fast_neutron_fluence = fast_neutron_fluence	clad_irradiation_swelling \|IrradiationGrowth\|All Fission Types
	eigenstrain_name = fuel_irradiation_strain
StrainAdjustedDensity	strain_free_density = 6551.0	clad_density	\|All Fission Types
HeatConductionMaterial	thermal_conductivity = 16.0	clad_thermal	\|All Fission Types
	specific_heat = 330.0

The classes in Table 2 are only created when Thermal or if any Fission occurs under the Fission Operation conditions.

Table 2: Auxiliary classes created by the NuclearMaterialZirconiumAlloy action

Created Auxiliary Classes	Type	Pre-Set Parameters	Block Name	Physics/Cladding Models
Temperature	Variable		temperature	Thermal
Fast Neutron Flux	AuxVariable	\|fast_neutron_flux	Creep
Fast Neutron Fluence	AuxVariable	\|fast_neutron_fluence\| Creep
HeatConduction	Kernel	variable = temperature	fuel_heat	Thermal
		extra_vector_tags = ref
HeatConductionTimeDerivative	Kernel	variable = temperature	fuel_heat_ie	Thermal
		extra_vector_tags = ref

Table 3: Actions created by the NuclearMaterialZirconiumAlloy action

Created Actions	Pre-Set Parameters	Block Name	Physics/Cladding Model Conditions
TensorMechanicsAction	volumetric_locking_correction = false	Physics/SolidMechanics/QuasiStatic	Mechanics
	automatic_eigenstrain_names = true
	decomposition_method = EigenSolution
	strain = FINITE

## Example Simple Input Syntax

NuclearMaterials simplifies Material block inputs by applying standard parameter and classes depending on the simulation. It is possible to only replace the Materials blocks in an input file with the equivalent NuclearMaterialZirconiumAlloy. This procedure greatly reduces the length and complexity of the the necessary inputs while fully retaining the same functionality and end results. An example of this can be seen below.

Fission Operation

note

This required parameter describes the characteristic type of fission study that will occur, i.e. Normal, LOCA, etc. This must be placed under the NuclearMaterials block heading and cannot be placed under sub-blocks such as ZirconiumAlloy.

Cladding Model Parameters

Elastic : Models elastic stress for an incremental formulation, both
incremental small and incremental finite strain formulations.
Creep : Models secondary Hoppe irradiation creep and Limback-Andersson
secondary and primary thermal creep
IrradiationGrowth : Models strains due to irradiation growth.
ThermalExpansion : Models isotropic or anisotropic thermal expansion with
condition dependent thermal expansion coefficient.

Expanded Cladding Material Block

[Materials<<<{"href": "../../Materials/index.html"}>>>]
  [clad_thermal]
    type = HeatConductionMaterial<<<{"description": "General-purpose material model for heat conduction", "href": "../../../source/materials/HeatConductionMaterial.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = clad
    thermal_conductivity<<<{"description": "The thermal conductivity value"}>>> = 16.0
    specific_heat<<<{"description": "The specific heat value"}>>> = 330.0
  []
  [clad_elasticity_tensor]
    type = ZryElasticityTensor<<<{"description": "Either provides constant elasticity constants for Zircaloy cladding or calculates the Young's modulus and Poisson's ratio for Zircaloy cladding using MATPRO relations as a function of temperature and fast neutron fluence.", "href": "../../../source/materials/solid_mechanics/ZryElasticityTensor.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = clad
  []
  [clad_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": "../../../source/materials/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."}>>> = 'clad_zrycreep'
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = clad
  []
  [clad_zrycreep]
    type = ZryCreepLimbackHoppeUpdate<<<{"description": "Computes the Limback-Andersson thermal primary and secondary creep and the Hoppe irradiation creep for Zircaloy cladding.  This material must be run in conjunction with ComputeMultipleInelasticStress.", "href": "../../../source/materials/solid_mechanics/ZryCreepLimbackHoppeUpdate.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = clad
    temperature<<<{"description": "The coupled temperature (K)"}>>> = temp
    fast_neutron_flux<<<{"description": "The fast neutron flux"}>>> = fast_neutron_flux
    fast_neutron_fluence<<<{"description": "The fast neutron fluence"}>>> = fast_neutron_fluence
    model_irradiation_creep<<<{"description": "Set true to activate irradiation induced creep"}>>> = true
    model_primary_creep<<<{"description": "Set true to activate primary creep"}>>> = true
    model_thermal_creep<<<{"description": "Set true to activate steady state thermal creep"}>>> = true
  []
  [thermal_expansion]
    type = ZryThermalExpansionMATPROEigenstrain<<<{"description": "Computes eigenstrain due to anisotropic thermal expansion in Zircaloy cladding using Matpro correlations.", "href": "../../../source/materials/solid_mechanics/ZryThermalExpansionMATPROEigenstrain.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = clad
    temperature<<<{"description": "Coupled temperature"}>>> = temp
    stress_free_temperature<<<{"description": "Reference temperature at which there is no thermal expansion for thermal eigenstrain calculation"}>>> = 295.0
    eigenstrain_name<<<{"description": "Material property name for the eigenstrain tensor computed by this model. IMPORTANT: The name of this property must also be provided to the strain calculator."}>>> = clad_thermal_eigenstrain
  []
  [irradiation_swelling]
    type = ZryIrradiationGrowthEigenstrain<<<{"description": "Computes eigenstrain from irradiation growth in Zircaloy cladding using either the Franklin or ESCORE models.", "href": "../../../source/materials/solid_mechanics/ZryIrradiationGrowthEigenstrain.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = clad
    fast_neutron_fluence<<<{"description": "The fast neutron fluence"}>>> = fast_neutron_fluence
    zircaloy_material_type<<<{"description": "Type of irradiation growth volumetric swelling formulation."}>>> = stress_relief_annealed
    eigenstrain_name<<<{"description": "Material property name for the eigenstrain tensor computed by this model. IMPORTANT: The name of this property must also be provided to the strain calculator."}>>> = clad_irradiation_strain
  []
[]

Equivalent Simplified NuclearMaterial Cladding Block

[NuclearMaterials<<<{"href": "../index.html"}>>>]
  fission_operation<<<{"description": "Type of fission occuring in this simulation."}>>> = Normal
  [ZirconiumAlloy<<<{"href": "index.html"}>>>]
    [clad]
      block<<<{"description": "The list of ids of the blocks (subdomain) that the stress divergence kernels will be applied to"}>>> = clad
      cladding_models<<<{"description": "Type(s) of physics models used on this block.   The choices are: Creep Elastic Plasticity ZryOxidation IrradiationGrowth ThermalExpansion ZrPhase ZryCladdingFailure"}>>> = 'Elastic Creep ThermalExpansion IrradiationGrowth'
      stress_free_temperature<<<{"description": "Reference temperature for thermal eigenstrain calculation"}>>> = 295.0
      localized_initial_temperature<<<{"description": "Localized Initial temperature in Kelvins.  This allows individual blocks to have different temperature conditions apart from the global initial conditions."}>>> = 580.0
    []
  []
[]

Example Fully Reduced Input Syntax

Input file length and complexity can be reduced even further by use of additional Physics and/or CladdingModels block parameters, in addition to applying common parameters to sub-blocks under the NuclearMaterials header.

Physics parameters

Mechanics : This will create the TensorMechanicsAction block(s) under which it is listed. If listed under the NuclearMaterial block header, then this will be applied to all blocks under the header.
Thermal : This will create the temperature variable, the Kernel blocks HeatConduction and HeatConductionTimeDerivative needed to model thermal effects for ZirconiumAlloys.

Expanded Cladding Block

[Variables<<<{"href": "../../Variables/index.html"}>>>]
  # Define dependent variables and initial conditions
  [temp]
    initial_condition<<<{"description": "Specifies a constant initial condition for this variable"}>>> = 580.0 # set initial temp to coolant inlet
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable (additional orders not listed are allowed)"}>>> = FIRST
  []
[]

[AuxVariables<<<{"href": "../../AuxVariables/index.html"}>>>]
  [grain_radius]
    block = pellet_type_1
    initial_condition<<<{"description": "Specifies a constant initial condition for this variable"}>>> = 10e-6
  []
[]

[Kernels<<<{"href": "../../Kernels/index.html"}>>>]
  [heat]
    # gradient term in heat conduction equation
    type = HeatConduction<<<{"description": "Diffusive heat conduction term $-\\nabla\\cdot(k\\nabla T)$ of the thermal energy conservation equation", "href": "../../../source/kernels/HeatConduction.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = temp
    extra_vector_tags<<<{"description": "The extra tags for the vectors this Kernel should fill"}>>> = 'ref'
  []
  [heat_ie]
    # time term in heat conduction equation
    type = HeatConductionTimeDerivative<<<{"description": "Time derivative term $\\rho c_p \\frac{\\partial T}{\\partial t}$ of the thermal energy conservation equation.", "href": "../../../source/kernels/HeatConductionTimeDerivative.html"}>>>
    variable<<<{"description": "The name of the variable that this residual object operates on"}>>> = temp
    extra_vector_tags<<<{"description": "The extra tags for the vectors this Kernel should fill"}>>> = 'ref'
  []
[]
[Physics<<<{"href": "../../Physics/index.html"}>>>]
  [SolidMechanics<<<{"href": "../../Physics/SolidMechanics/index.html"}>>>]
    [QuasiStatic<<<{"href": "../../Physics/SolidMechanics/QuasiStatic/index.html"}>>>]
      [clad]
        block<<<{"description": "The list of ids of the blocks (subdomain) that the stress divergence kernels will be applied to"}>>> = clad
        add_variables<<<{"description": "Add the displacement variables"}>>> = true
        strain<<<{"description": "Strain formulation"}>>> = FINITE
        eigenstrain_names<<<{"description": "List of eigenstrains to be applied in this strain calculation"}>>> = 'clad_thermal_eigenstrain clad_irradiation_strain'
        generate_output<<<{"description": "Add scalar quantity output for stress and/or strain"}>>> = 'vonmises_stress stress_xx stress_yy stress_zz'
        extra_vector_tags<<<{"description": "The tag names for extra vectors that residual data should be saved into"}>>> = 'ref'
      []
    []
  []
[]

[Materials<<<{"href": "../../Materials/index.html"}>>>]
  # Define material behavior models and input material property data

  [clad_thermal]
    type = HeatConductionMaterial<<<{"description": "General-purpose material model for heat conduction", "href": "../../../source/materials/HeatConductionMaterial.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = clad
    thermal_conductivity<<<{"description": "The thermal conductivity value"}>>> = 16.0
    specific_heat<<<{"description": "The specific heat value"}>>> = 330.0
  []
  [clad_elasticity_tensor]
    type = ZryElasticityTensor<<<{"description": "Either provides constant elasticity constants for Zircaloy cladding or calculates the Young's modulus and Poisson's ratio for Zircaloy cladding using MATPRO relations as a function of temperature and fast neutron fluence.", "href": "../../../source/materials/solid_mechanics/ZryElasticityTensor.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = clad
  []
  [clad_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": "../../../source/materials/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."}>>> = 'clad_zrycreep'
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = clad
  []
  [clad_zrycreep]
    type = ZryCreepLimbackHoppeUpdate<<<{"description": "Computes the Limback-Andersson thermal primary and secondary creep and the Hoppe irradiation creep for Zircaloy cladding.  This material must be run in conjunction with ComputeMultipleInelasticStress.", "href": "../../../source/materials/solid_mechanics/ZryCreepLimbackHoppeUpdate.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = clad
    temperature<<<{"description": "The coupled temperature (K)"}>>> = temp
    fast_neutron_flux<<<{"description": "The fast neutron flux"}>>> = fast_neutron_flux
    fast_neutron_fluence<<<{"description": "The fast neutron fluence"}>>> = fast_neutron_fluence
    model_irradiation_creep<<<{"description": "Set true to activate irradiation induced creep"}>>> = true
    model_primary_creep<<<{"description": "Set true to activate primary creep"}>>> = true
    model_thermal_creep<<<{"description": "Set true to activate steady state thermal creep"}>>> = true
  []
  [thermal_expansion]
    type = ZryThermalExpansionMATPROEigenstrain<<<{"description": "Computes eigenstrain due to anisotropic thermal expansion in Zircaloy cladding using Matpro correlations.", "href": "../../../source/materials/solid_mechanics/ZryThermalExpansionMATPROEigenstrain.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = clad
    temperature<<<{"description": "Coupled temperature"}>>> = temp
    stress_free_temperature<<<{"description": "Reference temperature at which there is no thermal expansion for thermal eigenstrain calculation"}>>> = 295.0
    eigenstrain_name<<<{"description": "Material property name for the eigenstrain tensor computed by this model. IMPORTANT: The name of this property must also be provided to the strain calculator."}>>> = clad_thermal_eigenstrain
  []
  [irradiation_swelling]
    type = ZryIrradiationGrowthEigenstrain<<<{"description": "Computes eigenstrain from irradiation growth in Zircaloy cladding using either the Franklin or ESCORE models.", "href": "../../../source/materials/solid_mechanics/ZryIrradiationGrowthEigenstrain.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = clad
    fast_neutron_fluence<<<{"description": "The fast neutron fluence"}>>> = fast_neutron_fluence
    zircaloy_material_type<<<{"description": "Type of irradiation growth volumetric swelling formulation."}>>> = stress_relief_annealed
    eigenstrain_name<<<{"description": "Material property name for the eigenstrain tensor computed by this model. IMPORTANT: The name of this property must also be provided to the strain calculator."}>>> = clad_irradiation_strain
  []
  [clad_density]
    type = StrainAdjustedDensity<<<{"description": "Creates density material property", "href": "../../../source/materials/StrainAdjustedDensity.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = clad
    strain_free_density<<<{"description": "Material property for strain-free density"}>>> = 6551.0
  []
[]

[AuxKernels<<<{"href": "../../AuxKernels/index.html"}>>>]
  [grain_radius]
    type = GrainRadiusAux<<<{"description": "Computes grain evolution using an empirical model.", "href": "../../../source/auxkernels/GrainRadiusAux.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = pellet_type_1
    variable<<<{"description": "The name of the variable that this object applies to"}>>> = grain_radius
    temperature<<<{"description": "Coupled temperature (K)"}>>> = temp
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = linear
  []
[]

Fully Simplified Fuel Block

[NuclearMaterials<<<{"href": "../index.html"}>>>]
  generate_output<<<{"description": "Add scalar quantity output for stress and/or strain"}>>> = 'vonmises_stress stress_xx stress_yy stress_zz'
  fission_operation<<<{"description": "Type of fission occuring in this simulation."}>>> = Normal
  physics<<<{"description": "Type(s) of physics used on this block."}>>> = 'Mechanics Thermal'
  initial_temperature<<<{"description": "Initial temperature in Kelvins."}>>> = 580.0
  strain<<<{"description": "Strain formulation"}>>> = FINITE
  [ZirconiumAlloy<<<{"href": "index.html"}>>>]
    [clad]
      block<<<{"description": "The list of ids of the blocks (subdomain) that the stress divergence kernels will be applied to"}>>> = clad
      cladding_models<<<{"description": "Type(s) of physics models used on this block.   The choices are: Creep Elastic Plasticity ZryOxidation IrradiationGrowth ThermalExpansion ZrPhase ZryCladdingFailure"}>>> = 'Elastic Creep IrradiationGrowth ThermalExpansion'
      stress_free_temperature<<<{"description": "Reference temperature for thermal eigenstrain calculation"}>>> = 295.0
      extra_vector_tags<<<{"description": "The tag names for extra vectors that residual data should be saved into"}>>> = 'ref'
    []
  []
[]

The eigenstrain names must be included in the SolidMechanics QuasiStatic Action following the naming convention created by this class. The easiest method to ensure this continutity is to include Mechanics in the physics input parameter. By default, this will select automatic_eigenstrain_names = true.

warning

automatic_eigenstrain_names = true, the eigenstrain_names will be populated under restrictive conditions for classes such as CompositeEigenstrain, ComputeReducedOrderEigenstrain, and RankTwoTensorMaterialADConverter. The input components for these classes are not included in the eigenstrain_names passed to the TensorMechanicsAction. Set the automatic_eigenstrain_names = false and populate this list manually if these components need to be included.

[Physics<<<{"href": "../../Physics/index.html"}>>>]
  [SolidMechanics<<<{"href": "../../Physics/SolidMechanics/index.html"}>>>]
    [QuasiStatic<<<{"href": "../../Physics/SolidMechanics/QuasiStatic/index.html"}>>>]
      [pellets]
        block<<<{"description": "The list of ids of the blocks (subdomain) that the stress divergence kernels will be applied to"}>>> = pellet_type_1
        add_variables<<<{"description": "Add the displacement variables"}>>> = true
        strain<<<{"description": "Strain formulation"}>>> = FINITE
        eigenstrain_names<<<{"description": "List of eigenstrains to be applied in this strain calculation"}>>> = 'fuel_relocation_strain fuel_thermal_strain fuel_volumetric_strain'
        generate_output<<<{"description": "Add scalar quantity output for stress and/or strain"}>>> = 'vonmises_stress stress_xx stress_yy stress_zz'
        extra_vector_tags<<<{"description": "The tag names for extra vectors that residual data should be saved into"}>>> = 'ref'
      []
    []
  []
[]

(examples/2D-RZ_rodlet_10pellets/2D_discrete_finiteStrain/2D_discrete_finiteStrain.i)

# This model is a linear element, 10 discrete fuel pellet stack (pellet_type_1) with a fine mesh.


initial_fuel_density = 10431.0

[GlobalParams]
  # Set initial fuel density, other global parameters
  density = ${initial_fuel_density}
  initial_porosity = 0.05
  energy_per_fission = 3.2e-11 # J/fission
  volumetric_locking_correction = true
  displacements = 'disp_x disp_y'
[]

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

[Mesh]
  # Specify coordinate system type
  coord_type = RZ
  # Import mesh file
  patch_update_strategy = auto
  patch_size = 10 # For contact algorithm
  partitioner = centroid
  centroid_partitioner_direction = y
  [mesh]
    type = FileMeshGenerator
    file = ../fine10_rz.e
  []
[]

[Variables]
  # Define dependent variables and initial conditions
  [temp]
    initial_condition = 580.0 # set initial temp to coolant inlet
    order = FIRST
  []
[]

[AuxVariables]
  # Define auxilary variables
  [fast_neutron_flux]
    block = clad
  []
  [fast_neutron_fluence]
    block = clad
  []
  [grain_radius]
    block = pellet_type_1
    initial_condition = 10e-6
  []
  [creep_strain_rate]
    order = CONSTANT
    family = MONOMIAL
  []
  [effective_creep_strain]
    block = clad
    order = CONSTANT
    family = MONOMIAL
  []
  [gap_cond]
    order = CONSTANT
    family = MONOMIAL
  []
  [coolant_htc]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  # Define functions to control power and boundary conditions
  [power_history]
    type = PiecewiseLinear # reads and interpolates an input file containing rod average linear power vs time
    data_file = ../powerhistory.csv
    scale_factor = 1
  []
  [axial_peaking_factors] # reads and interpolates an input file containing the axial power profile vs time
    type = PiecewiseBilinear
    data_file = ../peakingfactors.csv
    scale_factor = 1
    axis = 1 # (0,1,2) => (x,y,z)
  []
  [pressure_ramp] # reads and interpolates input data defining amplitude curve for fill gas pressure
    type = PiecewiseLinear
    x = '-200 0'
    y = '0 1'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [pellets]
    block = pellet_type_1
    add_variables = true
    strain = FINITE
    eigenstrain_names = 'fuel_relocation_strain fuel_thermal_strain fuel_volumetric_strain'
    generate_output = 'vonmises_stress stress_xx stress_yy stress_zz'
    extra_vector_tags = 'ref'
  []
  [clad]
    block = clad
    add_variables = true
    strain = FINITE
    eigenstrain_names = 'clad_thermal_eigenstrain clad_irradiation_strain'
    generate_output = 'vonmises_stress stress_xx stress_yy stress_zz'
    extra_vector_tags = 'ref'
  []
[]

[Kernels]
  [gravity] # body force term in stress equilibrium equation
    type = Gravity
    variable = disp_y
    value = -9.81
  []
  [heat] # gradient term in heat conduction equation
    type = HeatConduction
    variable = temp
    extra_vector_tags = 'ref'
  []
  [heat_ie] # time term in heat conduction equation
    type = HeatConductionTimeDerivative
    variable = temp
    extra_vector_tags = 'ref'
  []
  [heat_source] # source term in heat conduction equation
    type = NeutronHeatSource
    variable = temp
    extra_vector_tags = 'ref'
    block = pellet_type_1 # fission rate applied to the fuel (block 2) only
    burnup_function = burnup
  []
[]

[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
    a_lower = 0.00324 # mesh dependent!
    a_upper = 0.12184 # mesh dependent!
    fuel_inner_radius = 0
    fuel_outer_radius = .0041
    fuel_volume_ratio = 0.987775 # for use with dished pellets (ratio of actual volume to cylinder volume)
    order = CONSTANT
    family = MONOMIAL
    RPF = RPF
    #N235 = N235 # Activate to write N235 concentration to output file
    #N238 = N238 # Activate to write N238 concentration to output file
    #N239 = N239 # Activate to write N239 concentration to output file
    #N240 = N240 # Activate to write N240 concentration to output file
    #N241 = N241 # Activate to write N241 concentration to output file
    #N242 = N242 # Activate to write N242 concentration to output file
  []
[]

[AuxKernels]
  # Define auxilliary kernels for each of the aux variables
  [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
  []
  [creep_strain_rate]
    type = MaterialRealAux
    property = creep_rate
    variable = creep_strain_rate
    block = clad
    execute_on = timestep_end
  []
  [effective_creep_strain]
    type = MaterialRealAux
    property = effective_creep_strain
    variable = effective_creep_strain
    block = clad
    execute_on = timestep_end
  []
  [conductance]
    type = MaterialRealAux
    property = gap_conductance
    variable = gap_cond
    boundary = 10
    execute_on = 'linear'
  []
  [coolant_htc]
    type = MaterialRealAux
    property = coolant_channel_htc
    variable = coolant_htc
    boundary = 2
    execute_on = 'linear'
  []
[]

[Contact]
  # Define mechanical contact between the fuel (sideset=10) and the clad (sideset=5)
  [pellet_clad_mechanical]
    primary = 5
    secondary = 10
    formulation = kinematic
    model = frictionless
    penalty = 1e7
  []
[]

[ThermalContact]
  # Define thermal contact between the fuel (sideset=10) and the clad (sideset=5)
  [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
    quadrature = true
  []
[]

[BCs]
  # Define boundary conditions
  [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 = 0
      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
    []
  []
[]

[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]
  # Define material behavior models and input material property data
  [fuel_thermal] # temperature and burnup dependent thermal properties of UO2 (BISON kernel)
    type = UO2Thermal
    block = pellet_type_1
    thermal_conductivity_model = NFIR
    temperature = temp
    burnup_function = burnup
  []
  [fuel_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = pellet_type_1
    youngs_modulus = 2.0e11
    poissons_ratio = 0.345
  []
  [fuel_elastic_stress]
    type = ComputeFiniteStrainElasticStress
    block = pellet_type_1
  []
  [fuel_thermal_expansion]
    type = ComputeThermalExpansionEigenstrain
    block = pellet_type_1
    thermal_expansion_coeff = 10.0e-6
    temperature = temp
    stress_free_temperature = 295.0
    eigenstrain_name = fuel_thermal_strain
  []
  [fuel_relocation]
    type = UO2RelocationEigenstrain
    block = pellet_type_1
    burnup_function = burnup
    diameter = 0.0082
    rod_ave_lin_pow = power_history
    axial_power_profile = axial_peaking_factors
    diametral_gap = 160.0e-6
    burnup_relocation_stop = 0.03
    relocation_activation1 = 5000
    relocation_model = ESCORE_modified
    eigenstrain_name = fuel_relocation_strain
  []
  [fuel_volumetric_swelling]
    type = UO2VolumetricSwellingEigenstrain
    gas_swelling_model_type = SIFGRS
    block = pellet_type_1
    temperature = temp
    burnup_function = burnup
    initial_fuel_density = 10431.0
    eigenstrain_name = fuel_volumetric_strain
  []
  [fission_gas_release]
    type = UO2Sifgrs
    block = pellet_type_1
    temperature = temp
    burnup_function = burnup
    grain_radius = grain_radius
    gbs_model = true
  []

  [clad_thermal]
    type = HeatConductionMaterial
    block = clad
    thermal_conductivity = 16.0
    specific_heat = 330.0
  []
  [clad_elasticity_tensor]
    type = ZryElasticityTensor
    block = clad
  []
  [clad_stress]
    type = ComputeMultipleInelasticStress
    tangent_operator = elastic
    inelastic_models = 'clad_zrycreep'
    block = clad
  []
  [clad_zrycreep]
    type = ZryCreepLimbackHoppeUpdate
    block = clad
    temperature = temp
    fast_neutron_flux = fast_neutron_flux
    fast_neutron_fluence = fast_neutron_fluence
    model_irradiation_creep = true
    model_primary_creep = true
    model_thermal_creep = true
  []
  [thermal_expansion]
    type = ZryThermalExpansionMATPROEigenstrain
    block = clad
    temperature = temp
    stress_free_temperature = 295.0
    eigenstrain_name = clad_thermal_eigenstrain
  []
  [irradiation_swelling]
    type = ZryIrradiationGrowthEigenstrain
    block = clad
    fast_neutron_fluence = fast_neutron_fluence
    zircaloy_material_type = stress_relief_annealed
    eigenstrain_name = clad_irradiation_strain
  []
  [clad_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]
  [limitT]
    type = MaxIncrement
    max_increment = 100.0
    variable = temp
  []
  [limitX]
    type = MaxIncrement
    max_increment = 1e-5
    variable = disp_x
  []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu       superlu_dist'

  line_search = 'none'

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

  start_time = -200
  n_startup_steps = 1
  end_time = 8.0e7

  dtmax = 2e6
  dtmin = 1

  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 2e2
    optimal_iterations = 8
    iteration_window = 2
    linear_iteration_ratio = 100
    growth_factor = 2
    cutback_factor = .5
  []
  [Quadrature]
    order = THIRD
    side_order = FIFTH
  []
[]

[Postprocessors]
  # Define postprocessors (some are required as specified above; others are optional; many others are available)
  [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 linear'
  []
  [ave_fuel_temp]
    type = ElementAverageValue
    block = pellet_type_1
    variable = temp
    execute_on = 'initial linear'
  []
  [fis_gas_produced] # fission gas produced (moles)
    type = ElementIntegralFisGasGeneratedSifgrs
    block = pellet_type_1
    execute_on = 'linear'
  []
  [fis_gas_released] # fission gas released to plenum (moles)
    type = ElementIntegralFisGasReleasedSifgrs
    block = pellet_type_1
    execute_on = 'linear'
  []
  [fis_gas_grain]
    type = ElementIntegralFisGasGrainSifgrs
    block = pellet_type_1
    outputs = exodus
    execute_on = 'linear'
  []
  [fis_gas_boundary]
    type = ElementIntegralFisGasBoundarySifgrs
    block = pellet_type_1
    outputs = exodus
    execute_on = 'linear'
  []
  [fission_gas_release]
    type = FGRPercent
    fission_gas_released = fis_gas_released
    fission_gas_generated = fis_gas_produced
    execute_on = 'linear'
  []

  [gas_volume]
    type = InternalVolume
    boundary = 9
    execute_on = 'initial linear'
  []
  [flux_from_clad] # area integrated heat flux from the cladding
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 5
    diffusivity = thermal_conductivity
  []
  [flux_from_fuel] # area integrated heat flux from the fuel
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 10
    diffusivity = thermal_conductivity
  []

  [_dt] # time step
    type = TimestepSize
  []
  [num_lin_it]
    type = NumLinearIterations
  []
  [num_nonlin_it]
    type = NumNonlinearIterations
  []
  [tot_lin_it]
    type = CumulativeValuePostprocessor
    postprocessor = num_lin_it
  []
  [tot_nonlin_it]
    type = CumulativeValuePostprocessor
    postprocessor = num_nonlin_it
  []
  [alive_time]
    type = PerfGraphData
    section_name = Root
    data_type = TOTAL
  []

  [rod_total_power]
    type = ElementIntegralPower
    variable = temp
    burnup_function = burnup
    block = pellet_type_1
  []
  [rod_input_power]
    type = FunctionValuePostprocessor
    function = power_history
    scale_factor = 0.1186 # rod height
  []

  [mid_penetration]
    type = NodalVariableValue
    nodeid = 3781 #!!Mesh dependent!!
    variable = penetration
  []
  [central_fuel_temp]
    type = NodalVariableValue
    variable = temp
    nodeid = 3781 # !! Mesh dependent
  []
  [max_fuel_temp]
    type = NodalExtremeValue
    block = pellet_type_1
    value_type = max
    variable = temp
  []
  [max_clad_temp]
    type = NodalExtremeValue
    block = clad
    value_type = max
    variable = temp
  []
  [average_vonMises_fuel]
    type = ElementAverageValue
    variable = vonmises_stress
    block = pellet_type_1
  []
  [average_vonMises_clad]
    type = ElementAverageValue
    variable = vonmises_stress
    block = clad
  []
  [effective_creep_strain]
    type = ElementAverageValue
    block = clad
    variable = effective_creep_strain
  []
  [effective_creep_strain_rate]
    type = ElementAverageValue
    block = clad
    variable = creep_strain_rate
  []
[]

[VectorPostprocessors]
  [clad_dia]
    type = NodalValueSampler
    variable = disp_x
    boundary = 2
    sort_by = y
    outputs = 'outfile_clad_radial_displacement'
  []
  [pellet_dia]
    type = NodalValueSampler
    variable = disp_x
    boundary = 10
    sort_by = y
    outputs = 'outfile_fuel_radial_displacement'
  []
[]

[Outputs]
  perf_graph = true
  exodus = true
  color = false
  csv = true
  [console]
    type = Console
    max_rows = 25
  []
  [outfile_clad_radial_displacement]
    type = CSV
    execute_on = 'FINAL'
  []
  [outfile_fuel_radial_displacement]
    type = CSV
    execute_on = 'FINAL'
  []
[]

(examples/NuclearMaterialActions/LWR/Normal/2D_discrete_finiteStrain_action/2D_discrete_finiteStrain_action.i)

# This model is a linear element, 10 discrete fuel pellet stack (pellet_type_1) with a fine mesh.

[GlobalParams]
  # Set initial fuel density, other global parameters
  density = 10431.0
  initial_porosity = 0.05
  energy_per_fission = 3.2e-11 # J/fission
  volumetric_locking_correction = true
  displacements = 'disp_x disp_y'
  temperature = temperature
  grain_radius = grain_radius
  order = FIRST #Mesh element dictate this
  family = LAGRANGE
[]

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

[Mesh]
  # Specify coordinate system type
  coord_type = RZ
  # Import mesh file
  patch_update_strategy = auto
  patch_size = 10 # For contact algorithm
  partitioner = centroid
  centroid_partitioner_direction = y
  [mesh]
    type = FileMeshGenerator
    file = '../../../../2D-RZ_rodlet_10pellets/fine10_rz.e'
  []
[]

[Variables]
  # Define dependent variables and initial conditions
  [temperature]
    initial_condition = 580.0 # set initial temp to coolant inlet
  []
[]

[AuxVariables]
  # Define auxilary variables
  [creep_strain_rate]
    order = CONSTANT
    family = MONOMIAL
  []
  [effective_creep_strain]
    block = clad
    order = CONSTANT
    family = MONOMIAL
  []
  [gap_cond]
    order = CONSTANT
    family = MONOMIAL
  []
  [coolant_htc]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  # Define functions to control power and boundary conditions
  [power_history]
    type = PiecewiseLinear # reads and interpolates an input file containing rod average linear power vs time
    data_file = '../../../../2D-RZ_rodlet_10pellets/powerhistory.csv'
    scale_factor = 1
  []
  [axial_peaking_factors] # reads and interpolates an input file containing the axial power profile vs time
    type = PiecewiseBilinear
    data_file = '../../../../2D-RZ_rodlet_10pellets/peakingfactors.csv'
    scale_factor = 1
    axis = 1 # (0,1,2) => (x,y,z)
  []
  [pressure_ramp] # reads and interpolates input data defining amplitude curve for fill gas pressure
    type = PiecewiseLinear
    x = '-200 0'
    y = '0 1'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [pellets]
    block = pellet_type_1
    add_variables = true
    strain = FINITE
    eigenstrain_names = 'fuel_relocation_strain fuel_thermal_strain fuel_volumetric_strain'
    generate_output = 'vonmises_stress stress_xx stress_yy stress_zz'
    extra_vector_tags = 'ref'
  []
  [clad]
    block = clad
    add_variables = true
    strain = FINITE
    eigenstrain_names = 'clad_thermal_strain clad_irradiation_strain'
    generate_output = 'vonmises_stress stress_xx stress_yy stress_zz'
    extra_vector_tags = 'ref'
  []
[]

[Kernels]
  [gravity] # body force term in stress equilibrium equation
    type = Gravity
    variable = disp_y
    value = -9.81
  []
  [heat] # gradient term in heat conduction equation
    type = HeatConduction
    variable = temperature
    extra_vector_tags = 'ref'
  []
  [heat_ie] # time term in heat conduction equation
    type = HeatConductionTimeDerivative
    variable = temperature
    extra_vector_tags = 'ref'
  []
  [heat_source] # source term in heat conduction equation
    type = NeutronHeatSource
    variable = temperature
    extra_vector_tags = 'ref'
    block = pellet_type_1 # fission rate applied to the fuel (block 2) only
    burnup_function = burnup
  []
[]

[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
    a_lower = 0.00324 # mesh dependent!
    a_upper = 0.12184 # mesh dependent!
    fuel_inner_radius = 0
    fuel_outer_radius = .0041
    fuel_volume_ratio = 0.987775 # for use with dished pellets (ratio of actual volume to cylinder volume)
    order = CONSTANT
    family = MONOMIAL
    RPF = RPF
    #N235 = N235 # Activate to write N235 concentration to output file
    #N238 = N238 # Activate to write N238 concentration to output file
    #N239 = N239 # Activate to write N239 concentration to output file
    #N240 = N240 # Activate to write N240 concentration to output file
    #N241 = N241 # Activate to write N241 concentration to output file
    #N242 = N242 # Activate to write N242 concentration to output file
  []
[]

[AuxKernels]
  # Define auxilliary kernels for each of the aux variables
  [creep_strain_rate]
    type = MaterialRealAux
    property = creep_rate
    variable = creep_strain_rate
    block = clad
    execute_on = timestep_end
  []
  [conductance]
    type = MaterialRealAux
    property = gap_conductance
    variable = gap_cond
    boundary = 10
    execute_on = 'linear'
  []
  [coolant_htc]
    type = MaterialRealAux
    property = coolant_channel_htc
    variable = coolant_htc
    boundary = 2
    execute_on = 'linear'
  []
  [effective_creep_strain]
    type = MaterialRealAux
    property = effective_creep_strain
    variable = effective_creep_strain
    block = clad
  []
[]

[Contact]
  # Define mechanical contact between the fuel (sideset=10) and the clad (sideset=5)
  [pellet_clad_mechanical]
    primary = 5
    secondary = 10
    formulation = kinematic
    model = frictionless
    penalty = 1e7
  []
[]

[ThermalContact]
  # Define thermal contact between the fuel (sideset=10) and the clad (sideset=5)
  [thermal_contact]
    type = GasGapHeatTransfer
    variable = temperature
    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
    quadrature = true
  []
[]

[BCs]
  # Define boundary conditions
  [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 = 0
      R = 8.3143
      output_initial_moles = initial_moles # coupling to post processor to get initial fill gas mass
      temperature = ave_temperature_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
    []
  []
[]

[CoolantChannel]
  [convective_clad_surface] # apply convective boundary to clad outer surface
    boundary = '1 2 3'
    variable = temperature
    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
  []
[]

[NuclearMaterials]
  fission_operation = Normal
  [UO2]
    [fuel]
      block = pellet_type_1
      uo2_models = 'Elastic Relocation Swelling ThermalExpansion'
      stress_free_temperature = 295.0
      localized_initial_temperature = 580.0
      rod_ave_lin_pow = power_history
      burnup_relocation_stop = 0.03
    []
  []
  [ZirconiumAlloy]
    [clad]
      block = clad
      cladding_models = 'Elastic Creep ThermalExpansion IrradiationGrowth'
      stress_free_temperature = 295.0
      localized_initial_temperature = 580.0
    []
  []
[]

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

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu       superlu_dist'

  line_search = 'none'

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

  start_time = -200
  n_startup_steps = 1
  end_time = 8.0e7

  dtmax = 2e6
  dtmin = 1

  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 2e2
    optimal_iterations = 8
    iteration_window = 2
    linear_iteration_ratio = 100
    growth_factor = 2
    cutback_factor = .5
  []
  [Quadrature]
    order = THIRD
    side_order = FIFTH
  []
[]

[Postprocessors]
  # Define postprocessors (some are required as specified above; others are optional; many others are available)
  [ave_temperature_interior] # average temperature of the cladding interior and all pellet exteriors
    type = SideAverageValue
    boundary = 9
    variable = temperature
    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_temperature] # average temperature of cladding interior
    type = SideAverageValue
    boundary = 7
    variable = temperature
    execute_on = 'initial linear'
  []
  [ave_fuel_temperature]
    type = ElementAverageValue
    block = pellet_type_1
    variable = temperature
    execute_on = 'initial linear'
  []
  [fis_gas_produced] # fission gas produced (moles)
    type = ElementIntegralFisGasGeneratedSifgrs
    block = pellet_type_1
    execute_on = 'linear'
  []
  [fis_gas_released] # fission gas released to plenum (moles)
    type = ElementIntegralFisGasReleasedSifgrs
    block = pellet_type_1
    execute_on = 'linear'
  []
  [fis_gas_grain]
    type = ElementIntegralFisGasGrainSifgrs
    block = pellet_type_1
    outputs = exodus
    execute_on = 'linear'
  []
  [fis_gas_boundary]
    type = ElementIntegralFisGasBoundarySifgrs
    block = pellet_type_1
    outputs = exodus
    execute_on = 'linear'
  []
  [fission_gas_release]
    type = FGRPercent
    fission_gas_released = fis_gas_released
    fission_gas_generated = fis_gas_produced
    execute_on = 'linear'
  []

  [gas_volume]
    type = InternalVolume
    boundary = 9
    execute_on = 'initial linear'
  []
  [flux_from_clad] # area integrated heat flux from the cladding
    type = SideDiffusiveFluxIntegral
    variable = temperature
    boundary = 5
    diffusivity = thermal_conductivity
  []
  [flux_from_fuel] # area integrated heat flux from the fuel
    type = SideDiffusiveFluxIntegral
    variable = temperature
    boundary = 10
    diffusivity = thermal_conductivity
  []

  [_dt] # time step
    type = TimestepSize
  []
  [num_lin_it]
    type = NumLinearIterations
  []
  [num_nonlin_it]
    type = NumNonlinearIterations
  []
  [tot_lin_it]
    type = CumulativeValuePostprocessor
    postprocessor = num_lin_it
  []
  [tot_nonlin_it]
    type = CumulativeValuePostprocessor
    postprocessor = num_nonlin_it
  []
  [alive_time]
    type = PerfGraphData
    section_name = Root
    data_type = TOTAL
  []

  [rod_total_power]
    type = ElementIntegralPower
    variable = temperature
    burnup_function = burnup
    block = pellet_type_1
  []
  [rod_input_power]
    type = FunctionValuePostprocessor
    function = power_history
    scale_factor = 0.1186 # rod height
  []

  [mid_penetration]
    type = NodalVariableValue
    nodeid = 3781 #!!Mesh dependent!!
    variable = penetration
  []
  [central_fuel_temperature]
    type = NodalVariableValue
    variable = temperature
    nodeid = 3781 # !! Mesh dependent
  []
  [max_fuel_temperature]
    type = NodalExtremeValue
    block = pellet_type_1
    value_type = max
    variable = temperature
  []
  [max_clad_temperature]
    type = NodalExtremeValue
    block = clad
    value_type = max
    variable = temperature
  []
  [average_vonMises_fuel]
    type = ElementAverageValue
    variable = vonmises_stress
    block = pellet_type_1
  []
  [average_vonMises_clad]
    type = ElementAverageValue
    variable = vonmises_stress
    block = clad
  []
  [effective_creep_strain]
    type = ElementAverageValue
    block = clad
    variable = effective_creep_strain
  []
  [effective_creep_strain_rate]
    type = ElementAverageValue
    block = clad
    variable = creep_strain_rate
  []
[]

[VectorPostprocessors]
  [clad_dia]
    type = NodalValueSampler
    variable = disp_x
    boundary = 2
    sort_by = y
    outputs = 'outfile_clad_radial_displacement'
  []
  [pellet_dia]
    type = NodalValueSampler
    variable = disp_x
    boundary = 10
    sort_by = y
    outputs = 'outfile_fuel_radial_displacement'
  []
[]

[Outputs]
  perf_graph = true
  exodus = true
  color = false
  csv = true
  [console]
    type = Console
    max_rows = 25
  []
  [outfile_clad_radial_displacement]
    type = CSV
    execute_on = 'FINAL'
  []
  [outfile_fuel_radial_displacement]
    type = CSV
    execute_on = 'FINAL'
  []
[]

(examples/2D-RZ_rodlet_10pellets/2D_discrete_finiteStrain/2D_discrete_finiteStrain.i)

# This model is a linear element, 10 discrete fuel pellet stack (pellet_type_1) with a fine mesh.


initial_fuel_density = 10431.0

[GlobalParams]
  # Set initial fuel density, other global parameters
  density = ${initial_fuel_density}
  initial_porosity = 0.05
  energy_per_fission = 3.2e-11 # J/fission
  volumetric_locking_correction = true
  displacements = 'disp_x disp_y'
[]

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

[Mesh]
  # Specify coordinate system type
  coord_type = RZ
  # Import mesh file
  patch_update_strategy = auto
  patch_size = 10 # For contact algorithm
  partitioner = centroid
  centroid_partitioner_direction = y
  [mesh]
    type = FileMeshGenerator
    file = ../fine10_rz.e
  []
[]

[Variables]
  # Define dependent variables and initial conditions
  [temp]
    initial_condition = 580.0 # set initial temp to coolant inlet
    order = FIRST
  []
[]

[AuxVariables]
  # Define auxilary variables
  [fast_neutron_flux]
    block = clad
  []
  [fast_neutron_fluence]
    block = clad
  []
  [grain_radius]
    block = pellet_type_1
    initial_condition = 10e-6
  []
  [creep_strain_rate]
    order = CONSTANT
    family = MONOMIAL
  []
  [effective_creep_strain]
    block = clad
    order = CONSTANT
    family = MONOMIAL
  []
  [gap_cond]
    order = CONSTANT
    family = MONOMIAL
  []
  [coolant_htc]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  # Define functions to control power and boundary conditions
  [power_history]
    type = PiecewiseLinear # reads and interpolates an input file containing rod average linear power vs time
    data_file = ../powerhistory.csv
    scale_factor = 1
  []
  [axial_peaking_factors] # reads and interpolates an input file containing the axial power profile vs time
    type = PiecewiseBilinear
    data_file = ../peakingfactors.csv
    scale_factor = 1
    axis = 1 # (0,1,2) => (x,y,z)
  []
  [pressure_ramp] # reads and interpolates input data defining amplitude curve for fill gas pressure
    type = PiecewiseLinear
    x = '-200 0'
    y = '0 1'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [pellets]
    block = pellet_type_1
    add_variables = true
    strain = FINITE
    eigenstrain_names = 'fuel_relocation_strain fuel_thermal_strain fuel_volumetric_strain'
    generate_output = 'vonmises_stress stress_xx stress_yy stress_zz'
    extra_vector_tags = 'ref'
  []
  [clad]
    block = clad
    add_variables = true
    strain = FINITE
    eigenstrain_names = 'clad_thermal_eigenstrain clad_irradiation_strain'
    generate_output = 'vonmises_stress stress_xx stress_yy stress_zz'
    extra_vector_tags = 'ref'
  []
[]

[Kernels]
  [gravity] # body force term in stress equilibrium equation
    type = Gravity
    variable = disp_y
    value = -9.81
  []
  [heat] # gradient term in heat conduction equation
    type = HeatConduction
    variable = temp
    extra_vector_tags = 'ref'
  []
  [heat_ie] # time term in heat conduction equation
    type = HeatConductionTimeDerivative
    variable = temp
    extra_vector_tags = 'ref'
  []
  [heat_source] # source term in heat conduction equation
    type = NeutronHeatSource
    variable = temp
    extra_vector_tags = 'ref'
    block = pellet_type_1 # fission rate applied to the fuel (block 2) only
    burnup_function = burnup
  []
[]

[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
    a_lower = 0.00324 # mesh dependent!
    a_upper = 0.12184 # mesh dependent!
    fuel_inner_radius = 0
    fuel_outer_radius = .0041
    fuel_volume_ratio = 0.987775 # for use with dished pellets (ratio of actual volume to cylinder volume)
    order = CONSTANT
    family = MONOMIAL
    RPF = RPF
    #N235 = N235 # Activate to write N235 concentration to output file
    #N238 = N238 # Activate to write N238 concentration to output file
    #N239 = N239 # Activate to write N239 concentration to output file
    #N240 = N240 # Activate to write N240 concentration to output file
    #N241 = N241 # Activate to write N241 concentration to output file
    #N242 = N242 # Activate to write N242 concentration to output file
  []
[]

[AuxKernels]
  # Define auxilliary kernels for each of the aux variables
  [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
  []
  [creep_strain_rate]
    type = MaterialRealAux
    property = creep_rate
    variable = creep_strain_rate
    block = clad
    execute_on = timestep_end
  []
  [effective_creep_strain]
    type = MaterialRealAux
    property = effective_creep_strain
    variable = effective_creep_strain
    block = clad
    execute_on = timestep_end
  []
  [conductance]
    type = MaterialRealAux
    property = gap_conductance
    variable = gap_cond
    boundary = 10
    execute_on = 'linear'
  []
  [coolant_htc]
    type = MaterialRealAux
    property = coolant_channel_htc
    variable = coolant_htc
    boundary = 2
    execute_on = 'linear'
  []
[]

[Contact]
  # Define mechanical contact between the fuel (sideset=10) and the clad (sideset=5)
  [pellet_clad_mechanical]
    primary = 5
    secondary = 10
    formulation = kinematic
    model = frictionless
    penalty = 1e7
  []
[]

[ThermalContact]
  # Define thermal contact between the fuel (sideset=10) and the clad (sideset=5)
  [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
    quadrature = true
  []
[]

[BCs]
  # Define boundary conditions
  [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 = 0
      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
    []
  []
[]

[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]
  # Define material behavior models and input material property data
  [fuel_thermal] # temperature and burnup dependent thermal properties of UO2 (BISON kernel)
    type = UO2Thermal
    block = pellet_type_1
    thermal_conductivity_model = NFIR
    temperature = temp
    burnup_function = burnup
  []
  [fuel_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = pellet_type_1
    youngs_modulus = 2.0e11
    poissons_ratio = 0.345
  []
  [fuel_elastic_stress]
    type = ComputeFiniteStrainElasticStress
    block = pellet_type_1
  []
  [fuel_thermal_expansion]
    type = ComputeThermalExpansionEigenstrain
    block = pellet_type_1
    thermal_expansion_coeff = 10.0e-6
    temperature = temp
    stress_free_temperature = 295.0
    eigenstrain_name = fuel_thermal_strain
  []
  [fuel_relocation]
    type = UO2RelocationEigenstrain
    block = pellet_type_1
    burnup_function = burnup
    diameter = 0.0082
    rod_ave_lin_pow = power_history
    axial_power_profile = axial_peaking_factors
    diametral_gap = 160.0e-6
    burnup_relocation_stop = 0.03
    relocation_activation1 = 5000
    relocation_model = ESCORE_modified
    eigenstrain_name = fuel_relocation_strain
  []
  [fuel_volumetric_swelling]
    type = UO2VolumetricSwellingEigenstrain
    gas_swelling_model_type = SIFGRS
    block = pellet_type_1
    temperature = temp
    burnup_function = burnup
    initial_fuel_density = 10431.0
    eigenstrain_name = fuel_volumetric_strain
  []
  [fission_gas_release]
    type = UO2Sifgrs
    block = pellet_type_1
    temperature = temp
    burnup_function = burnup
    grain_radius = grain_radius
    gbs_model = true
  []

  [clad_thermal]
    type = HeatConductionMaterial
    block = clad
    thermal_conductivity = 16.0
    specific_heat = 330.0
  []
  [clad_elasticity_tensor]
    type = ZryElasticityTensor
    block = clad
  []
  [clad_stress]
    type = ComputeMultipleInelasticStress
    tangent_operator = elastic
    inelastic_models = 'clad_zrycreep'
    block = clad
  []
  [clad_zrycreep]
    type = ZryCreepLimbackHoppeUpdate
    block = clad
    temperature = temp
    fast_neutron_flux = fast_neutron_flux
    fast_neutron_fluence = fast_neutron_fluence
    model_irradiation_creep = true
    model_primary_creep = true
    model_thermal_creep = true
  []
  [thermal_expansion]
    type = ZryThermalExpansionMATPROEigenstrain
    block = clad
    temperature = temp
    stress_free_temperature = 295.0
    eigenstrain_name = clad_thermal_eigenstrain
  []
  [irradiation_swelling]
    type = ZryIrradiationGrowthEigenstrain
    block = clad
    fast_neutron_fluence = fast_neutron_fluence
    zircaloy_material_type = stress_relief_annealed
    eigenstrain_name = clad_irradiation_strain
  []
  [clad_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]
  [limitT]
    type = MaxIncrement
    max_increment = 100.0
    variable = temp
  []
  [limitX]
    type = MaxIncrement
    max_increment = 1e-5
    variable = disp_x
  []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu       superlu_dist'

  line_search = 'none'

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

  start_time = -200
  n_startup_steps = 1
  end_time = 8.0e7

  dtmax = 2e6
  dtmin = 1

  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 2e2
    optimal_iterations = 8
    iteration_window = 2
    linear_iteration_ratio = 100
    growth_factor = 2
    cutback_factor = .5
  []
  [Quadrature]
    order = THIRD
    side_order = FIFTH
  []
[]

[Postprocessors]
  # Define postprocessors (some are required as specified above; others are optional; many others are available)
  [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 linear'
  []
  [ave_fuel_temp]
    type = ElementAverageValue
    block = pellet_type_1
    variable = temp
    execute_on = 'initial linear'
  []
  [fis_gas_produced] # fission gas produced (moles)
    type = ElementIntegralFisGasGeneratedSifgrs
    block = pellet_type_1
    execute_on = 'linear'
  []
  [fis_gas_released] # fission gas released to plenum (moles)
    type = ElementIntegralFisGasReleasedSifgrs
    block = pellet_type_1
    execute_on = 'linear'
  []
  [fis_gas_grain]
    type = ElementIntegralFisGasGrainSifgrs
    block = pellet_type_1
    outputs = exodus
    execute_on = 'linear'
  []
  [fis_gas_boundary]
    type = ElementIntegralFisGasBoundarySifgrs
    block = pellet_type_1
    outputs = exodus
    execute_on = 'linear'
  []
  [fission_gas_release]
    type = FGRPercent
    fission_gas_released = fis_gas_released
    fission_gas_generated = fis_gas_produced
    execute_on = 'linear'
  []

  [gas_volume]
    type = InternalVolume
    boundary = 9
    execute_on = 'initial linear'
  []
  [flux_from_clad] # area integrated heat flux from the cladding
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 5
    diffusivity = thermal_conductivity
  []
  [flux_from_fuel] # area integrated heat flux from the fuel
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 10
    diffusivity = thermal_conductivity
  []

  [_dt] # time step
    type = TimestepSize
  []
  [num_lin_it]
    type = NumLinearIterations
  []
  [num_nonlin_it]
    type = NumNonlinearIterations
  []
  [tot_lin_it]
    type = CumulativeValuePostprocessor
    postprocessor = num_lin_it
  []
  [tot_nonlin_it]
    type = CumulativeValuePostprocessor
    postprocessor = num_nonlin_it
  []
  [alive_time]
    type = PerfGraphData
    section_name = Root
    data_type = TOTAL
  []

  [rod_total_power]
    type = ElementIntegralPower
    variable = temp
    burnup_function = burnup
    block = pellet_type_1
  []
  [rod_input_power]
    type = FunctionValuePostprocessor
    function = power_history
    scale_factor = 0.1186 # rod height
  []

  [mid_penetration]
    type = NodalVariableValue
    nodeid = 3781 #!!Mesh dependent!!
    variable = penetration
  []
  [central_fuel_temp]
    type = NodalVariableValue
    variable = temp
    nodeid = 3781 # !! Mesh dependent
  []
  [max_fuel_temp]
    type = NodalExtremeValue
    block = pellet_type_1
    value_type = max
    variable = temp
  []
  [max_clad_temp]
    type = NodalExtremeValue
    block = clad
    value_type = max
    variable = temp
  []
  [average_vonMises_fuel]
    type = ElementAverageValue
    variable = vonmises_stress
    block = pellet_type_1
  []
  [average_vonMises_clad]
    type = ElementAverageValue
    variable = vonmises_stress
    block = clad
  []
  [effective_creep_strain]
    type = ElementAverageValue
    block = clad
    variable = effective_creep_strain
  []
  [effective_creep_strain_rate]
    type = ElementAverageValue
    block = clad
    variable = creep_strain_rate
  []
[]

[VectorPostprocessors]
  [clad_dia]
    type = NodalValueSampler
    variable = disp_x
    boundary = 2
    sort_by = y
    outputs = 'outfile_clad_radial_displacement'
  []
  [pellet_dia]
    type = NodalValueSampler
    variable = disp_x
    boundary = 10
    sort_by = y
    outputs = 'outfile_fuel_radial_displacement'
  []
[]

[Outputs]
  perf_graph = true
  exodus = true
  color = false
  csv = true
  [console]
    type = Console
    max_rows = 25
  []
  [outfile_clad_radial_displacement]
    type = CSV
    execute_on = 'FINAL'
  []
  [outfile_fuel_radial_displacement]
    type = CSV
    execute_on = 'FINAL'
  []
[]

(examples/NuclearMaterialActions/LWR/Normal/2D_discrete_finiteStrain_nuc_mat_action_integrated/2D_discrete_finiteStrain_nuc_mat_action_integrated.i)

# This model is a linear element, 10 discrete fuel pellet stack (pellet_type_1) with a fine mesh.

[GlobalParams]
  # Set initial fuel density, other global parameters
  density = 10431.0
  initial_porosity = 0.05
  energy_per_fission = 3.2e-11 # J/fission
  volumetric_locking_correction = true
  displacements = 'disp_x disp_y'
  temperature = temperature
  grain_radius = grain_radius
  order = FIRST #Mesh element dictate this
  family = LAGRANGE
[]

[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 = '../../../../2D-RZ_rodlet_10pellets/fine10_rz.e'
  []
[]

[AuxVariables]
  [creep_strain_rate]
    order = CONSTANT
    family = MONOMIAL
  []
  [gap_cond]
    order = CONSTANT
    family = MONOMIAL
  []
  [coolant_htc]
    order = CONSTANT
    family = MONOMIAL
  []
  [effective_creep_strain]
    block = clad
    order = CONSTANT
    family = MONOMIAL
  []
[]

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

[Functions]
  [power_history]
    type = PiecewiseLinear
    data_file = '../../../../2D-RZ_rodlet_10pellets/powerhistory.csv'
    scale_factor = 1
  []
  [axial_peaking_factors]
    type = PiecewiseBilinear
    data_file = '../../../../2D-RZ_rodlet_10pellets/peakingfactors.csv'
    scale_factor = 1
    axis = 1 # (0,1,2) => (x,y,z)
  []
  [pressure_ramp]
    type = PiecewiseLinear
    x = '-200 0'
    y = '0 1'
  []
[]

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

[AuxKernels]
  [creep_strain_rate]
    type = MaterialRealAux
    property = creep_rate
    variable = creep_strain_rate
    block = clad
    execute_on = timestep_end
  []
  [conductance]
    type = MaterialRealAux
    property = gap_conductance
    variable = gap_cond
    boundary = 10
    execute_on = 'linear'
  []
  [coolant_htc]
    type = MaterialRealAux
    property = coolant_channel_htc
    variable = coolant_htc
    boundary = 2
    execute_on = 'linear'
  []
  [effective_creep_strain]
    type = MaterialRealAux
    property = effective_creep_strain
    variable = effective_creep_strain
    block = clad
  []
[]

[Contact]
  [pellet_clad_mechanical]
    primary = 5
    secondary = 10
    formulation = kinematic
    model = frictionless
    penalty = 1e7
  []
[]

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

[BCs]
  [no_x_all]
    type = DirichletBC
    variable = disp_x
    boundary = 12
    value = 0.0
  []
  [no_y_clad_bottom]
    type = DirichletBC
    variable = disp_y
    boundary = '1'
    value = 0.0
  []
  [no_y_fuel_bottom]
    type = DirichletBC
    variable = disp_y
    boundary = '1020'
    value = 0.0
  []
  [Pressure]
    [coolantPressure]
      boundary = '1 2 3'
      factor = 15.5e6
      function = pressure_ramp
    []
  []
  [PlenumPressure]
    [plenumPressure]
      boundary = 9
      initial_pressure = 2.0e6
      startup_time = 0
      R = 8.3143
      output_initial_moles = initial_moles
      temperature = ave_temperature_interior
      volume = gas_volume
      material_input = fis_gas_released
      output = plenum_pressure
    []
  []
[]

[CoolantChannel]
  [convective_clad_surface]
    boundary = '1 2 3'
    variable = temperature
    inlet_temperature = 580 # 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
  []
[]

[NuclearMaterials]
  generate_output = 'vonmises_stress stress_xx stress_yy stress_zz'
  fission_operation = Normal
  physics = 'Mechanics Thermal'
  initial_temperature = 580.0
  strain = FINITE
  [UO2]
    [fuel]
      block = pellet_type_1
      uo2_models = 'Burnup Elastic Relocation Swelling ThermalExpansion'
      stress_free_temperature = 295.0
      fuel_volume_ratio = 0.987787
      burnup_relocation_stop = 0.03
      isotopes = 'U235 U238'
      isotope_fractions = '0.05 0.95'
      fuel_pin_geometry = pin_geometry
      rod_ave_lin_pow = power_history
      axial_power_profile = axial_peaking_factors
      extra_vector_tags = 'ref'
    []
  []
  [ZirconiumAlloy]
    [clad]
      block = clad
      cladding_models = 'Elastic Creep IrradiationGrowth ThermalExpansion'
      stress_free_temperature = 295.0
      extra_vector_tags = 'ref'
    []
  []
[]

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

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu       superlu_dist'

  line_search = 'none'

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

  start_time = -200
  n_startup_steps = 1
  end_time = 8.0e7

  dtmax = 2e6
  dtmin = 1

  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 2e2
    optimal_iterations = 8
    iteration_window = 2
    linear_iteration_ratio = 100
    growth_factor = 2
    cutback_factor = .5
  []
  [Quadrature]
    order = THIRD
    side_order = FIFTH
  []
[]

[Postprocessors]
  [ave_temperature_interior]
    type = SideAverageValue
    boundary = 9
    variable = temperature
    execute_on = 'initial linear'
  []
  [clad_inner_vol]
    type = InternalVolume
    boundary = 7
    #outputs = exodus
    execute_on = 'initial timestep_end'
  []
  [pellet_volume]
    type = InternalVolume
    boundary = 8
    #outputs = exodus
    execute_on = 'initial timestep_end'
  []
  [avg_clad_temperature]
    type = SideAverageValue
    boundary = 7
    variable = temperature
    execute_on = 'initial linear'
  []
  [ave_fuel_temperature]
    type = ElementAverageValue
    block = pellet_type_1
    variable = temperature
    execute_on = 'initial linear'
  []
  [fis_gas_produced]
    type = ElementIntegralFisGasGeneratedSifgrs
    block = pellet_type_1
    execute_on = 'linear'
  []
  [fis_gas_released]
    type = ElementIntegralFisGasReleasedSifgrs
    block = pellet_type_1
    execute_on = 'linear'
  []
  [fis_gas_grain]
    type = ElementIntegralFisGasGrainSifgrs
    block = pellet_type_1
    outputs = exodus
    execute_on = 'linear'
  []
  [fis_gas_boundary]
    type = ElementIntegralFisGasBoundarySifgrs
    block = pellet_type_1
    outputs = exodus
    execute_on = 'linear'
  []
  [fission_gas_release]
    type = FGRPercent
    fission_gas_released = fis_gas_released
    fission_gas_generated = fis_gas_produced
    execute_on = 'linear'
  []

  [gas_volume]
    type = InternalVolume
    boundary = 9
    execute_on = 'initial linear'
  []
  [flux_from_clad]
    type = SideDiffusiveFluxIntegral
    variable = temperature
    boundary = 5
    diffusivity = thermal_conductivity
  []
  [flux_from_fuel]
    type = SideDiffusiveFluxIntegral
    variable = temperature
    boundary = 10
    diffusivity = thermal_conductivity
  []

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

  [rod_total_power]
    type = ElementIntegralPower
    variable = temperature
    burnup_function = burnup
    block = pellet_type_1
  []
  [rod_input_power]
    type = FunctionValuePostprocessor
    function = power_history
    scale_factor = 0.1186 # rod height
  []

  [mid_penetration]
    type = NodalVariableValue
    nodeid = 3781 #!!Mesh dependent!!
    variable = penetration
  []
  [central_fuel_temperature]
    type = NodalVariableValue
    variable = temperature
    nodeid = 3781 # !! Mesh dependent
  []
  [max_fuel_temperature]
    type = NodalExtremeValue
    block = pellet_type_1
    value_type = max
    variable = temperature
  []
  [max_clad_temperature]
    type = NodalExtremeValue
    block = clad
    value_type = max
    variable = temperature
  []
  [average_vonMises_fuel]
    type = ElementAverageValue
    variable = vonmises_stress
    block = pellet_type_1
  []
  [average_vonMises_clad]
    type = ElementAverageValue
    variable = vonmises_stress
    block = clad
  []
  [effective_creep_strain]
    type = ElementAverageValue
    block = clad
    variable = effective_creep_strain
  []
  [effective_creep_strain_rate]
    type = ElementAverageValue
    block = clad
    variable = creep_strain_rate
  []
[]

[VectorPostprocessors]
  [clad_dia]
    type = NodalValueSampler
    variable = disp_x
    boundary = 2
    sort_by = y
    outputs = 'outfile_clad_radial_displacement'
  []
  [pellet_dia]
    type = NodalValueSampler
    variable = disp_x
    boundary = 10
    sort_by = y
    outputs = 'outfile_fuel_radial_displacement'
  []
[]

[Outputs]
  perf_graph = true
  exodus = true
  color = false
  csv = true
  [console]
    type = Console
    max_rows = 25
  []
  [outfile_clad_radial_displacement]
    type = CSV
    execute_on = 'FINAL'
  []
  [outfile_fuel_radial_displacement]
    type = CSV
    execute_on = 'FINAL'
  []
[]

(examples/NuclearMaterialActions/LWR/Normal/2D_discrete_finiteStrain_action/2D_discrete_finiteStrain_action.i)

# This model is a linear element, 10 discrete fuel pellet stack (pellet_type_1) with a fine mesh.

[GlobalParams]
  # Set initial fuel density, other global parameters
  density = 10431.0
  initial_porosity = 0.05
  energy_per_fission = 3.2e-11 # J/fission
  volumetric_locking_correction = true
  displacements = 'disp_x disp_y'
  temperature = temperature
  grain_radius = grain_radius
  order = FIRST #Mesh element dictate this
  family = LAGRANGE
[]

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

[Mesh]
  # Specify coordinate system type
  coord_type = RZ
  # Import mesh file
  patch_update_strategy = auto
  patch_size = 10 # For contact algorithm
  partitioner = centroid
  centroid_partitioner_direction = y
  [mesh]
    type = FileMeshGenerator
    file = '../../../../2D-RZ_rodlet_10pellets/fine10_rz.e'
  []
[]

[Variables]
  # Define dependent variables and initial conditions
  [temperature]
    initial_condition = 580.0 # set initial temp to coolant inlet
  []
[]

[AuxVariables]
  # Define auxilary variables
  [creep_strain_rate]
    order = CONSTANT
    family = MONOMIAL
  []
  [effective_creep_strain]
    block = clad
    order = CONSTANT
    family = MONOMIAL
  []
  [gap_cond]
    order = CONSTANT
    family = MONOMIAL
  []
  [coolant_htc]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  # Define functions to control power and boundary conditions
  [power_history]
    type = PiecewiseLinear # reads and interpolates an input file containing rod average linear power vs time
    data_file = '../../../../2D-RZ_rodlet_10pellets/powerhistory.csv'
    scale_factor = 1
  []
  [axial_peaking_factors] # reads and interpolates an input file containing the axial power profile vs time
    type = PiecewiseBilinear
    data_file = '../../../../2D-RZ_rodlet_10pellets/peakingfactors.csv'
    scale_factor = 1
    axis = 1 # (0,1,2) => (x,y,z)
  []
  [pressure_ramp] # reads and interpolates input data defining amplitude curve for fill gas pressure
    type = PiecewiseLinear
    x = '-200 0'
    y = '0 1'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [pellets]
    block = pellet_type_1
    add_variables = true
    strain = FINITE
    eigenstrain_names = 'fuel_relocation_strain fuel_thermal_strain fuel_volumetric_strain'
    generate_output = 'vonmises_stress stress_xx stress_yy stress_zz'
    extra_vector_tags = 'ref'
  []
  [clad]
    block = clad
    add_variables = true
    strain = FINITE
    eigenstrain_names = 'clad_thermal_strain clad_irradiation_strain'
    generate_output = 'vonmises_stress stress_xx stress_yy stress_zz'
    extra_vector_tags = 'ref'
  []
[]

[Kernels]
  [gravity] # body force term in stress equilibrium equation
    type = Gravity
    variable = disp_y
    value = -9.81
  []
  [heat] # gradient term in heat conduction equation
    type = HeatConduction
    variable = temperature
    extra_vector_tags = 'ref'
  []
  [heat_ie] # time term in heat conduction equation
    type = HeatConductionTimeDerivative
    variable = temperature
    extra_vector_tags = 'ref'
  []
  [heat_source] # source term in heat conduction equation
    type = NeutronHeatSource
    variable = temperature
    extra_vector_tags = 'ref'
    block = pellet_type_1 # fission rate applied to the fuel (block 2) only
    burnup_function = burnup
  []
[]

[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
    a_lower = 0.00324 # mesh dependent!
    a_upper = 0.12184 # mesh dependent!
    fuel_inner_radius = 0
    fuel_outer_radius = .0041
    fuel_volume_ratio = 0.987775 # for use with dished pellets (ratio of actual volume to cylinder volume)
    order = CONSTANT
    family = MONOMIAL
    RPF = RPF
    #N235 = N235 # Activate to write N235 concentration to output file
    #N238 = N238 # Activate to write N238 concentration to output file
    #N239 = N239 # Activate to write N239 concentration to output file
    #N240 = N240 # Activate to write N240 concentration to output file
    #N241 = N241 # Activate to write N241 concentration to output file
    #N242 = N242 # Activate to write N242 concentration to output file
  []
[]

[AuxKernels]
  # Define auxilliary kernels for each of the aux variables
  [creep_strain_rate]
    type = MaterialRealAux
    property = creep_rate
    variable = creep_strain_rate
    block = clad
    execute_on = timestep_end
  []
  [conductance]
    type = MaterialRealAux
    property = gap_conductance
    variable = gap_cond
    boundary = 10
    execute_on = 'linear'
  []
  [coolant_htc]
    type = MaterialRealAux
    property = coolant_channel_htc
    variable = coolant_htc
    boundary = 2
    execute_on = 'linear'
  []
  [effective_creep_strain]
    type = MaterialRealAux
    property = effective_creep_strain
    variable = effective_creep_strain
    block = clad
  []
[]

[Contact]
  # Define mechanical contact between the fuel (sideset=10) and the clad (sideset=5)
  [pellet_clad_mechanical]
    primary = 5
    secondary = 10
    formulation = kinematic
    model = frictionless
    penalty = 1e7
  []
[]

[ThermalContact]
  # Define thermal contact between the fuel (sideset=10) and the clad (sideset=5)
  [thermal_contact]
    type = GasGapHeatTransfer
    variable = temperature
    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
    quadrature = true
  []
[]

[BCs]
  # Define boundary conditions
  [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 = 0
      R = 8.3143
      output_initial_moles = initial_moles # coupling to post processor to get initial fill gas mass
      temperature = ave_temperature_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
    []
  []
[]

[CoolantChannel]
  [convective_clad_surface] # apply convective boundary to clad outer surface
    boundary = '1 2 3'
    variable = temperature
    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
  []
[]

[NuclearMaterials]
  fission_operation = Normal
  [UO2]
    [fuel]
      block = pellet_type_1
      uo2_models = 'Elastic Relocation Swelling ThermalExpansion'
      stress_free_temperature = 295.0
      localized_initial_temperature = 580.0
      rod_ave_lin_pow = power_history
      burnup_relocation_stop = 0.03
    []
  []
  [ZirconiumAlloy]
    [clad]
      block = clad
      cladding_models = 'Elastic Creep ThermalExpansion IrradiationGrowth'
      stress_free_temperature = 295.0
      localized_initial_temperature = 580.0
    []
  []
[]

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

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu       superlu_dist'

  line_search = 'none'

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

  start_time = -200
  n_startup_steps = 1
  end_time = 8.0e7

  dtmax = 2e6
  dtmin = 1

  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 2e2
    optimal_iterations = 8
    iteration_window = 2
    linear_iteration_ratio = 100
    growth_factor = 2
    cutback_factor = .5
  []
  [Quadrature]
    order = THIRD
    side_order = FIFTH
  []
[]

[Postprocessors]
  # Define postprocessors (some are required as specified above; others are optional; many others are available)
  [ave_temperature_interior] # average temperature of the cladding interior and all pellet exteriors
    type = SideAverageValue
    boundary = 9
    variable = temperature
    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_temperature] # average temperature of cladding interior
    type = SideAverageValue
    boundary = 7
    variable = temperature
    execute_on = 'initial linear'
  []
  [ave_fuel_temperature]
    type = ElementAverageValue
    block = pellet_type_1
    variable = temperature
    execute_on = 'initial linear'
  []
  [fis_gas_produced] # fission gas produced (moles)
    type = ElementIntegralFisGasGeneratedSifgrs
    block = pellet_type_1
    execute_on = 'linear'
  []
  [fis_gas_released] # fission gas released to plenum (moles)
    type = ElementIntegralFisGasReleasedSifgrs
    block = pellet_type_1
    execute_on = 'linear'
  []
  [fis_gas_grain]
    type = ElementIntegralFisGasGrainSifgrs
    block = pellet_type_1
    outputs = exodus
    execute_on = 'linear'
  []
  [fis_gas_boundary]
    type = ElementIntegralFisGasBoundarySifgrs
    block = pellet_type_1
    outputs = exodus
    execute_on = 'linear'
  []
  [fission_gas_release]
    type = FGRPercent
    fission_gas_released = fis_gas_released
    fission_gas_generated = fis_gas_produced
    execute_on = 'linear'
  []

  [gas_volume]
    type = InternalVolume
    boundary = 9
    execute_on = 'initial linear'
  []
  [flux_from_clad] # area integrated heat flux from the cladding
    type = SideDiffusiveFluxIntegral
    variable = temperature
    boundary = 5
    diffusivity = thermal_conductivity
  []
  [flux_from_fuel] # area integrated heat flux from the fuel
    type = SideDiffusiveFluxIntegral
    variable = temperature
    boundary = 10
    diffusivity = thermal_conductivity
  []

  [_dt] # time step
    type = TimestepSize
  []
  [num_lin_it]
    type = NumLinearIterations
  []
  [num_nonlin_it]
    type = NumNonlinearIterations
  []
  [tot_lin_it]
    type = CumulativeValuePostprocessor
    postprocessor = num_lin_it
  []
  [tot_nonlin_it]
    type = CumulativeValuePostprocessor
    postprocessor = num_nonlin_it
  []
  [alive_time]
    type = PerfGraphData
    section_name = Root
    data_type = TOTAL
  []

  [rod_total_power]
    type = ElementIntegralPower
    variable = temperature
    burnup_function = burnup
    block = pellet_type_1
  []
  [rod_input_power]
    type = FunctionValuePostprocessor
    function = power_history
    scale_factor = 0.1186 # rod height
  []

  [mid_penetration]
    type = NodalVariableValue
    nodeid = 3781 #!!Mesh dependent!!
    variable = penetration
  []
  [central_fuel_temperature]
    type = NodalVariableValue
    variable = temperature
    nodeid = 3781 # !! Mesh dependent
  []
  [max_fuel_temperature]
    type = NodalExtremeValue
    block = pellet_type_1
    value_type = max
    variable = temperature
  []
  [max_clad_temperature]
    type = NodalExtremeValue
    block = clad
    value_type = max
    variable = temperature
  []
  [average_vonMises_fuel]
    type = ElementAverageValue
    variable = vonmises_stress
    block = pellet_type_1
  []
  [average_vonMises_clad]
    type = ElementAverageValue
    variable = vonmises_stress
    block = clad
  []
  [effective_creep_strain]
    type = ElementAverageValue
    block = clad
    variable = effective_creep_strain
  []
  [effective_creep_strain_rate]
    type = ElementAverageValue
    block = clad
    variable = creep_strain_rate
  []
[]

[VectorPostprocessors]
  [clad_dia]
    type = NodalValueSampler
    variable = disp_x
    boundary = 2
    sort_by = y
    outputs = 'outfile_clad_radial_displacement'
  []
  [pellet_dia]
    type = NodalValueSampler
    variable = disp_x
    boundary = 10
    sort_by = y
    outputs = 'outfile_fuel_radial_displacement'
  []
[]

[Outputs]
  perf_graph = true
  exodus = true
  color = false
  csv = true
  [console]
    type = Console
    max_rows = 25
  []
  [outfile_clad_radial_displacement]
    type = CSV
    execute_on = 'FINAL'
  []
  [outfile_fuel_radial_displacement]
    type = CSV
    execute_on = 'FINAL'
  []
[]

Description
User - based Interface
Example Fully Reduced Input Syntax