Nuclear Material UO2

Reduces the Material block length for LWR elastic UO2 fuel within input files.

Description of Created Material Blocks

This NuclearMaterialUO2 action reduces BISON input file length by internally generating the Materials required for simulating elastic LWR nuclear fuel, specifically UO2.

warning:For LWR Use Only

This action is designed for use with only Light Water Reactor simulations which deal with Elastic stress calculations. Simulations with Inelastic models are not covered by this action.

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 2, Table 3, and Table 4. These blocks are created internally, based on the UO2 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 file length and complexity.

Fission Operation

note

This required parameter describes the characteristic type of fission study that will occur, i.e. Normal, LOCA, etc. This will also create both the AuxVariable and AuxKernel of the grain_radius that is used to model the grain evolution for fission. This must be placed under the NuclearMaterials block heading and cannot be placed under sub-blocks such as UO2. A description of the current different fission operation models can be found in Table 1.

Table 1: Fission Operation Descriptions

FissionOperation	Description
None	No fission occurs
Normal	Self-sustained nuclear chain reaction
HighBurnup	High Percentage of Fuel Burnup
RIA	Reactivity Initiated Accident
LOCA	Loss of Coolant Accident
BumpTest	Short-term reirradiation at increased power levels
HighInitial	High Initial Rating Test
PowerRamp	Ramp up of power output

The classes in Table 2 are automatically created when using NuclearMaterialUO2 depending on the UO2 Models and Fission operation used as well as what occurs under Physics conditions.

Table 2: Material classes created by the NuclearMaterialUO2 action

Created Material Classes	Pre-Set Parameters	Block Name	UO2 Models	Fission Operation
UO2ElasticityTensor	poissons_ratio = 0.345	fuel_elasticity_tensor	Elastic	All Fission Types
	youngs_modulus = 2.0e11
ComputeFiniteStrainElasticStress		fuel_elastic_stress	Elastic	All Fission Types
ComputeThermalExpansionEigenstrain	thermal_expansion_coeff = 10.0e-6	fuel_thermal_expansion \|ThermalExpansion	All Fission Types
	eigenstrain_name = fuel_thermal_strain
UO2VolumetricSwellingEigenstrain	burnup_function = burnup	fuel_volumetric_swelling	Swelling	All Fission Types
	initial_fuel_density = 10431.0
	eigenstrain_name = fuel_volumetric_strain
UO2RelocationEigenstrain	eigenstrain_name = fuel_relocation_strain	fuel_relocation	Relocation	All Fission Types
UO2Sifgrs	gbs_model = true	fuel_fission_gas_release	Fission Dependent\| All Fission Types
StrainAdjustedDensity	strain_free_density = 10431.0	fuel_density	all	All Fission Types
UO2Thermal		fuel_thermal	all	All Fission Types

The classes in Table 3 are only created when Thermal or if any Fission occurs under the Fission Operation conditions.

Table 3: Auxiliary classes created by the NuclearMaterialUO2 action

Created Auxiliary Classes	Type	Pre-Set Parameters	Block Name	Physics/Fission Operations
Temperature	Variable		temperature	Thermal
GrainRadiusAux	AuxKernel	variable = grain_radius	grain_radius	All Fission Types
		temp = temperature
		execute_on = LINEAR
HeatConduction	Kernel	variable = temperature	fuel_heat	Thermal
		extra_vector_tags = ref
HeatConductionTimeDerivative	Kernel	variable = temperature	fuel_heat_ie	Thermal
		extra_vector_tags = ref
NeutronHeatSource	Kernel	variable = temperature	heat_source	Thermal
		extra_vector_tags = ref

Table 4: Actions created by the NuclearMaterialUO2 action

Created Actions	Pre-Set Parameters	Block Name	Physics/UO2 Model Conditions
TensorMechanicsAction	volumetric_locking_correction = false	Physics/SolidMechanics/QuasiStatic	Mechanics
	automatic_eigenstrain_names = true
	decomposition_method = EigenSolution
	strain = FINITE

Burnup		Burnup	Burnup

Example Input Syntax `NuclearMaterials` can be used in multiple ways to simplify creation of various parts of the input file. In its most basic form, it can be used to automate the creation of the material models used to define the mechanical and thermal behavior of fuel and cladding materials. With additional options, it can also be used to automate the creation of the variables and kernels associated with mechanical and thermal physics, as well as the Burnup objects. Examples of these two different ways to use `NuclearMaterials` are provided below

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 NuclearMaterialUO2. 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.

UO2 Model Parameters

Elastic : Models elastic stress for an incremental formulation, both
incremental small and incremental finite strain formulations.
Relocation : Method to model the effect of UO2 cracking on gap width.
Swelling : Swelling due to solid fission products, gaseous fission products,
and densification all contribute to the change in volume of a UO2 fuel pellet
ThermalExpansion : Models isotropic thermal expansion with constant thermal
expansion coefficient.

Expanded Fuel Material Block

[Materials<<<{"href": "../../Materials/index.html"}>>>]
  # Define material behavior models and input material property data
  [fuel_thermal] # temperature and burnup dependent thermal properties of UO2 (BISON kernel)
    type = UO2Thermal<<<{"description": "Computes thermal conductivity and specific heat capacity of uranium dioxide fuel.", "href": "../../../source/materials/UO2Thermal.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = pellet_type_1
    thermal_conductivity_model<<<{"description": "The thermal conductivity model."}>>> = NFIR
    temperature<<<{"description": "Coupled temperature"}>>> = temp
    burnup_function<<<{"description": "Burnup function"}>>> = burnup
  []
  [fuel_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor<<<{"description": "Compute a constant isotropic elasticity tensor.", "href": "../../../source/materials/ComputeIsotropicElasticityTensor.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = pellet_type_1
    youngs_modulus<<<{"description": "Young's modulus of the material."}>>> = 2.0e11
    poissons_ratio<<<{"description": "Poisson's ratio for the material."}>>> = 0.345
  []
  [fuel_elastic_stress]
    type = ComputeFiniteStrainElasticStress<<<{"description": "Compute stress using elasticity for finite strains", "href": "../../../source/materials/ComputeFiniteStrainElasticStress.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = pellet_type_1
  []
  [fuel_thermal_expansion]
    type = ComputeThermalExpansionEigenstrain<<<{"description": "Computes eigenstrain due to thermal expansion with a constant coefficient", "href": "../../../source/materials/ComputeThermalExpansionEigenstrain.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = pellet_type_1
    thermal_expansion_coeff<<<{"description": "Thermal expansion coefficient"}>>> = 10.0e-6
    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."}>>> = fuel_thermal_strain
  []
  [fuel_relocation]
    type = UO2RelocationEigenstrain<<<{"description": "Accounts for cracking and relocation of fuel pellet fragments in the radial direction and is necessary for accurate modeling of LWR fuel. The linear heat rate must either be a functionor a variable.", "href": "../../../source/materials/solid_mechanics/UO2RelocationEigenstrain.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = pellet_type_1
    burnup_function<<<{"description": "Burnup function"}>>> = burnup
    diameter<<<{"description": "As fabricated cold diameter of pellet in meters"}>>> = 0.0082
    rod_ave_lin_pow<<<{"description": "linear power function."}>>> = power_history
    axial_power_profile<<<{"description": "axial power peaking function."}>>> = axial_peaking_factors
    diametral_gap<<<{"description": "As fabricated cold diametral pellet-cladding gap in meters."}>>> = 160.0e-6
    burnup_relocation_stop<<<{"description": "Burnup at which relocation strain stops (in FIMA)"}>>> = 0.03
    relocation_activation1<<<{"description": "First activation linear power in W/m term in relocation model"}>>> = 5000
    relocation_model<<<{"description": "Type of relocation model formulation."}>>> = ESCORE_modified
    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."}>>> = fuel_relocation_strain
  []
  [fuel_volumetric_swelling]
    type = UO2VolumetricSwellingEigenstrain<<<{"description": "Computes and sums the change in fuel pellet volume due to densification and fission product release. This class applies a volumetric strain correction before adding the strain from this class to the diagonal entries of the eigenstrain tensor.", "href": "../../../source/materials/solid_mechanics/UO2VolumetricSwellingEigenstrain.html"}>>>
    gas_swelling_model_type<<<{"description": "Which type of model to use to calculate the gaseous swelling. Choices are SIFGRS MATPRO SIFGRS_IG. If you select SIFGRS or SIFGRS_IG, the SIFGRS model must be included in the input file."}>>> = SIFGRS
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = pellet_type_1
    temperature<<<{"description": "Coupled Temperature in Kelvin"}>>> = temp
    burnup_function<<<{"description": "Burnup function"}>>> = burnup
    initial_fuel_density<<<{"description": "Initial fuel density in kg-UO2/m^3"}>>> = 10431.0
    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."}>>> = fuel_volumetric_strain
  []
  [fission_gas_release]
    type = UO2Sifgrs<<<{"description": "Recommended fission gas model to account for generation of fission gasses in nuclear fuel", "href": "../../../source/materials/UO2Sifgrs.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = pellet_type_1
    temperature<<<{"description": "Coupled temperature"}>>> = temp
    burnup_function<<<{"description": "Burnup function"}>>> = burnup
    grain_radius<<<{"description": "Coupled grain Radius"}>>> = grain_radius
    gbs_model<<<{"description": "Activates the grain-boundary sweeping model"}>>> = true
  []
[]

Equivalent Simplified NuclearMaterial Fuel Block

[NuclearMaterials<<<{"href": "../index.html"}>>>]
  fission_operation<<<{"description": "Type of fission occuring in this simulation."}>>> = Normal
  [UO2<<<{"href": "index.html"}>>>]
    [fuel]
      block<<<{"description": "The list of ids of the blocks (subdomain) that the stress divergence kernels will be applied to"}>>> = pellet_type_1
      uo2_models<<<{"description": "Type(s) of physics models used on this block.   The choices are: Burnup Elastic Creep Relocation Swelling ThermalExpansion HighBurnupStructureFormation"}>>> = 'Elastic Relocation Swelling ThermalExpansion'
      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
      rod_ave_lin_pow<<<{"description": "The rod power history function."}>>> = power_history
      burnup_relocation_stop<<<{"description": "Burnup at which relocation strain stops (in FIMA)"}>>> = 0.03
    []
  []
[]

Example Fully Reduced Input Syntax

Input file length and complexity can be reduced even further by use of additional Physics and/or UO2Models 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, HeatConductionTimeDerivative, and NeutronHeatSource needed to model thermal effects for UO2.

UO2 Model Parameters

Burnup : This will create the Burnup block for UO2 fuel.

Expanded Fuel 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'
  []
  [heat_source]
    # source term in heat conduction equation
    type = NeutronHeatSource<<<{"description": "Compute heat generation due to fission.", "href": "../../../source/kernels/NeutronHeatSource.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'
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = pellet_type_1 # fission rate applied to the fuel (block 2) only
    burnup_function<<<{"description": "Burnup function"}>>> = burnup
  []
[]
[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'
      []
    []
  []
[]

[Burnup<<<{"href": "../../Burnup/index.html"}>>>]
  [burnup]
    block<<<{"description": "The blocks where radial power factor should be computed."}>>> = pellet_type_1
    rod_ave_lin_pow<<<{"description": "Rod average linear power function."}>>> = power_history # using the power function defined above
    axial_power_profile<<<{"description": "Axial power peaking function."}>>> = axial_peaking_factors # using the axial power profile function defined above
    num_radial<<<{"description": "Number of radial divisions in secondary grid used to compute radial power profile."}>>> = 80
    num_axial<<<{"description": "Number of axial divisions in secondary grid used to compute radial power profile."}>>> = 11
    a_lower<<<{"description": "The lower axial coordinate of the fuel stack. Required if fuel_pin_geometry is not specified."}>>> = 0.00324 # mesh dependent!
    a_upper<<<{"description": "The upper axial coordinate of the fuel stack. Required if fuel_pin_geometry is not specified."}>>> = 0.12184 # mesh dependent!
    fuel_inner_radius<<<{"description": "The inner radius of the fuel."}>>> = 0
    fuel_outer_radius<<<{"description": "The outer radius of the fuel."}>>> = .0041
    fuel_volume_ratio<<<{"description": "Reduction factor for deviation from right circular cylinder fuel.  The ratio of actual volume to right circular cylinder volume."}>>> = 0.987775 # for use with dished pellets (ratio of actual volume to cylinder volume)
    order<<<{"description": "Specifies the order of the FE shape function to use for this variable."}>>> = CONSTANT
    family<<<{"description": "Specifies the family of FE shape functions to use for this variable."}>>> = MONOMIAL
    RPF<<<{"description": "Specifies that the radial power factor is required."}>>> = 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
  []
[]

[Materials<<<{"href": "../../Materials/index.html"}>>>]
  # Define material behavior models and input material property data
  [fuel_thermal]
    # temperature and burnup dependent thermal properties of UO2 (BISON kernel)
    type = UO2Thermal<<<{"description": "Computes thermal conductivity and specific heat capacity of uranium dioxide fuel.", "href": "../../../source/materials/UO2Thermal.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = pellet_type_1
    thermal_conductivity_model<<<{"description": "The thermal conductivity model."}>>> = NFIR
    temperature<<<{"description": "Coupled temperature"}>>> = temp
    burnup_function<<<{"description": "Burnup function"}>>> = burnup
  []
  [fuel_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor<<<{"description": "Compute a constant isotropic elasticity tensor.", "href": "../../../source/materials/ComputeIsotropicElasticityTensor.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = pellet_type_1
    youngs_modulus<<<{"description": "Young's modulus of the material."}>>> = 2.0e11
    poissons_ratio<<<{"description": "Poisson's ratio for the material."}>>> = 0.345
  []
  [fuel_elastic_stress]
    type = ComputeFiniteStrainElasticStress<<<{"description": "Compute stress using elasticity for finite strains", "href": "../../../source/materials/ComputeFiniteStrainElasticStress.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = pellet_type_1
  []
  [fuel_thermal_expansion]
    type = ComputeThermalExpansionEigenstrain<<<{"description": "Computes eigenstrain due to thermal expansion with a constant coefficient", "href": "../../../source/materials/ComputeThermalExpansionEigenstrain.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = pellet_type_1
    thermal_expansion_coeff<<<{"description": "Thermal expansion coefficient"}>>> = 10.0e-6
    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."}>>> = fuel_thermal_strain
  []
  [fuel_relocation]
    type = UO2RelocationEigenstrain<<<{"description": "Accounts for cracking and relocation of fuel pellet fragments in the radial direction and is necessary for accurate modeling of LWR fuel. The linear heat rate must either be a functionor a variable.", "href": "../../../source/materials/solid_mechanics/UO2RelocationEigenstrain.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = pellet_type_1
    burnup_function<<<{"description": "Burnup function"}>>> = burnup
    diameter<<<{"description": "As fabricated cold diameter of pellet in meters"}>>> = 0.0082
    rod_ave_lin_pow<<<{"description": "linear power function."}>>> = power_history
    axial_power_profile<<<{"description": "axial power peaking function."}>>> = axial_peaking_factors
    diametral_gap<<<{"description": "As fabricated cold diametral pellet-cladding gap in meters."}>>> = 160.0e-6
    burnup_relocation_stop<<<{"description": "Burnup at which relocation strain stops (in FIMA)"}>>> = 0.03
    relocation_activation1<<<{"description": "First activation linear power in W/m term in relocation model"}>>> = 5000
    relocation_model<<<{"description": "Type of relocation model formulation."}>>> = ESCORE_modified
    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."}>>> = fuel_relocation_strain
  []
  [fuel_volumetric_swelling]
    type = UO2VolumetricSwellingEigenstrain<<<{"description": "Computes and sums the change in fuel pellet volume due to densification and fission product release. This class applies a volumetric strain correction before adding the strain from this class to the diagonal entries of the eigenstrain tensor.", "href": "../../../source/materials/solid_mechanics/UO2VolumetricSwellingEigenstrain.html"}>>>
    gas_swelling_model_type<<<{"description": "Which type of model to use to calculate the gaseous swelling. Choices are SIFGRS MATPRO SIFGRS_IG. If you select SIFGRS or SIFGRS_IG, the SIFGRS model must be included in the input file."}>>> = SIFGRS
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = pellet_type_1
    temperature<<<{"description": "Coupled Temperature in Kelvin"}>>> = temp
    burnup_function<<<{"description": "Burnup function"}>>> = burnup
    initial_fuel_density<<<{"description": "Initial fuel density in kg-UO2/m^3"}>>> = 10431.0
    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."}>>> = fuel_volumetric_strain
  []
  [fission_gas_release]
    type = UO2Sifgrs<<<{"description": "Recommended fission gas model to account for generation of fission gasses in nuclear fuel", "href": "../../../source/materials/UO2Sifgrs.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = pellet_type_1
    temperature<<<{"description": "Coupled temperature"}>>> = temp
    burnup_function<<<{"description": "Burnup function"}>>> = burnup
    grain_radius<<<{"description": "Coupled grain Radius"}>>> = grain_radius
    gbs_model<<<{"description": "Activates the grain-boundary sweeping model"}>>> = true
  []

  [fuel_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"}>>> = pellet_type_1
    strain_free_density<<<{"description": "Material property for strain-free density"}>>> = ${initial_fuel_density}
  []
[]

[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
  [UO2<<<{"href": "index.html"}>>>]
    [fuel]
      block<<<{"description": "The list of ids of the blocks (subdomain) that the stress divergence kernels will be applied to"}>>> = pellet_type_1
      uo2_models<<<{"description": "Type(s) of physics models used on this block.   The choices are: Burnup Elastic Creep Relocation Swelling ThermalExpansion HighBurnupStructureFormation"}>>> = 'Burnup Elastic Relocation Swelling ThermalExpansion'
      stress_free_temperature<<<{"description": "Reference temperature for thermal eigenstrain calculation"}>>> = 295.0
      fuel_volume_ratio<<<{"description": "Reduction factor for deviation from right circular cylinder representation of the fuel mesh.  The ratio of actual volume to right circular cylinder volume."}>>> = 0.987787
      burnup_relocation_stop<<<{"description": "Burnup at which relocation strain stops (in FIMA)"}>>> = 0.03
      isotopes<<<{"description": "Fuel isotopes: Gd155 Gd157 U235 U238 Pu239 Pu240 Pu241 Pu242.  Number of entries must match number of entries in isotope_fractions."}>>> = 'U235 U238'
      isotope_fractions<<<{"description": "The isotope fractions associated with the 'isotopes' input line.  Must sum to 1.0."}>>> = '0.05 0.95'
      fuel_pin_geometry<<<{"description": "Name of the UserObject that reads the pin geometry from the mesh."}>>> = pin_geometry
      rod_ave_lin_pow<<<{"description": "The rod power history function."}>>> = power_history
      axial_power_profile<<<{"description": "The axial power peaking function."}>>> = axial_peaking_factors
      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'
      []
    []
  []
[]

Input Parameters

densityThe initial fuel density.
C++ Type:std::vector<double>
Unit:(no unit assumed)
Controllable:No
Description:The initial fuel density.
fragmentation_modelCOINDREAUThe model used to calculate the number of cracks in the fuel.
Default:COINDREAU
C++ Type:MooseEnum
Options:COINDREAU, WALTON, BARANI
Controllable:No
Description:The model used to calculate the number of cracks in the fuel.

Required Parameters

RIA_initial_burnupInitial burnup function used in RIA for SIFGRS and UO2Thermal.
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:Initial burnup function used in RIA for SIFGRS and UO2Thermal.
a_lowerThe lower axial coordinate of the fuel stack. Required if fuel_pin_geometry is not specified.
C++ Type:std::vector<double>
Unit:(no unit assumed)
Controllable:No
Description:The lower axial coordinate of the fuel stack. Required if fuel_pin_geometry is not specified.
a_upperThe upper axial coordinate of the fuel stack. Required if fuel_pin_geometry is not specified.
C++ Type:std::vector<double>
Unit:(no unit assumed)
Controllable:No
Description:The upper axial coordinate of the fuel stack. Required if fuel_pin_geometry is not specified.
active__all__ If specified only the blocks named will be visited and made active
Default:__all__
C++ Type:std::vector<std::string>
Controllable:No
Description:If specified only the blocks named will be visited and made active
add_variablesFalseAdd the displacement variables
Default:False
C++ Type:bool
Controllable:No
Description:Add the displacement variables
additional_physicsType(s) of physics used on this block. The choices are: Mechanics Thermal
C++ Type:MultiMooseEnum
Options:Mechanics, Thermal
Controllable:No
Description:Type(s) of physics used on this block. The choices are: Mechanics Thermal
automatic_eigenstrain_namesTrueCollects all material eigenstrains and passes to required strain calculator within the solid mechanics physics internally.
Default:True
C++ Type:bool
Controllable:No
Description:Collects all material eigenstrains and passes to required strain calculator within the solid mechanics physics internally.
burnup_functionBurnup function
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:Burnup function
crumbling_scale_factor0.0001Scaling factor to apply to the Young's modulus in layers that have crumbled during axial relocation.
Default:0.0001
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Scaling factor to apply to the Young's modulus in layers that have crumbled during axial relocation.
d1_functionFunction to be multiplied by d1
C++ Type:std::vector<FunctionName>
Unit:(no unit assumed)
Controllable:No
Description:Function to be multiplied by d1
d1_function_variableVariable to be used when evaluating d1_function. If not given, time will be used.
C++ Type:std::vector<std::string>
Controllable:No
Description:Variable to be used when evaluating d1_function. If not given, time will be used.
decomposition_methodEigenSolutionMethods to calculate the finite strain and rotation increments
Default:EigenSolution
C++ Type:MooseEnum
Options:TaylorExpansion, EigenSolution, HughesWinget
Controllable:No
Description:Methods to calculate the finite strain and rotation increments
diffusion_1st_activation_energiesDiffusion activation energies.
C++ Type:std::vector<double>
Unit:(no unit assumed)
Controllable:No
Description:Diffusion activation energies.
diffusion_1st_coefficients1st diffusion coefficient.
C++ Type:std::vector<double>
Unit:(no unit assumed)
Controllable:No
Description:1st diffusion coefficient.
diffusion_2nd_activation_energiesSecond diffusion activation energy
C++ Type:std::vector<double>
Unit:(no unit assumed)
Controllable:No
Description:Second diffusion activation energy
diffusion_2nd_coefficients2nd diffusion coefficient
C++ Type:std::vector<double>
Unit:(no unit assumed)
Controllable:No
Description:2nd diffusion coefficient
element_decay_constantsRadioactive decay constant for elements tracked
C++ Type:std::vector<double>
Unit:(no unit assumed)
Controllable:No
Description:Radioactive decay constant for elements tracked
element_scalingRelative scaling of element percentages
C++ Type:std::vector<double>
Unit:(no unit assumed)
Controllable:No
Description:Relative scaling of element percentages
elements_initial_concentrationRelative ratio of element concentration
C++ Type:std::vector<double>
Unit:(no unit assumed)
Controllable:No
Description:Relative ratio of element concentration
elements_trackedThe elements tracked within TRISO simulations.
C++ Type:MultiMooseEnum
Options:Ag, Cs, Sr
Controllable:No
Description:The elements tracked within TRISO simulations.
extra_vector_tagsThe tag names for extra vectors that residual data should be saved into
C++ Type:std::vector<TagName>
Controllable:No
Description:The tag names for extra vectors that residual data should be saved into
familyLAGRANGESpecifies the family of FE shape functions to use for this variable.
Default:LAGRANGE
C++ Type:MooseEnum
Options:LAGRANGE, MONOMIAL, SCALAR, LAGRANGE_VEC, MONOMIAL_VEC, L2_HIERARCHIC, L2_HIERARCHIC_VEC, L2_LAGRANGE, L2_LAGRANGE_VEC, L2_RAVIART_THOMAS
Controllable:No
Description:Specifies the family of FE shape functions to use for this variable.
flux_factor1Constant multiplied against the function, rod average linear power, or q_variable.
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Constant multiplied against the function, rod average linear power, or q_variable.
flux_functionThe function that describes the fast neutron flux
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:The function that describes the fast neutron flux
fraction_of_neutron_heat_source1Fraction of neutron heat source power applied
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Fraction of neutron heat source power applied
fuel_inner_radius0The inner radius of the fuel.
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The inner radius of the fuel.
fuel_outer_radius0.0041The outer radius of the fuel.
Default:0.0041
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The outer radius of the fuel.
fuel_volume_ratioReduction factor for deviation from right circular cylinder representation of the fuel mesh. The ratio of actual volume to right circular cylinder volume.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Reduction factor for deviation from right circular cylinder representation of the fuel mesh. The ratio of actual volume to right circular cylinder volume.
generate_outputAdd scalar quantity output for stress and/or strain
C++ Type:MultiMooseEnum
Options:cauchy_stress_xx, cauchy_stress_xy, cauchy_stress_xz, cauchy_stress_yx, cauchy_stress_yy, cauchy_stress_yz, cauchy_stress_zx, cauchy_stress_zy, cauchy_stress_zz, creep_strain_xx, creep_strain_xy, creep_strain_xz, creep_strain_yx, creep_strain_yy, creep_strain_yz, creep_strain_zx, creep_strain_zy, creep_strain_zz, creep_stress_xx, creep_stress_xy, creep_stress_xz, creep_stress_yx, creep_stress_yy, creep_stress_yz, creep_stress_zx, creep_stress_zy, creep_stress_zz, deformation_gradient_xx, deformation_gradient_xy, deformation_gradient_xz, deformation_gradient_yx, deformation_gradient_yy, deformation_gradient_yz, deformation_gradient_zx, deformation_gradient_zy, deformation_gradient_zz, elastic_strain_xx, elastic_strain_xy, elastic_strain_xz, elastic_strain_yx, elastic_strain_yy, elastic_strain_yz, elastic_strain_zx, elastic_strain_zy, elastic_strain_zz, mechanical_strain_xx, mechanical_strain_xy, mechanical_strain_xz, mechanical_strain_yx, mechanical_strain_yy, mechanical_strain_yz, mechanical_strain_zx, mechanical_strain_zy, mechanical_strain_zz, pk1_stress_xx, pk1_stress_xy, pk1_stress_xz, pk1_stress_yx, pk1_stress_yy, pk1_stress_yz, pk1_stress_zx, pk1_stress_zy, pk1_stress_zz, pk2_stress_xx, pk2_stress_xy, pk2_stress_xz, pk2_stress_yx, pk2_stress_yy, pk2_stress_yz, pk2_stress_zx, pk2_stress_zy, pk2_stress_zz, plastic_strain_xx, plastic_strain_xy, plastic_strain_xz, plastic_strain_yx, plastic_strain_yy, plastic_strain_yz, plastic_strain_zx, plastic_strain_zy, plastic_strain_zz, small_stress_xx, small_stress_xy, small_stress_xz, small_stress_yx, small_stress_yy, small_stress_yz, small_stress_zx, small_stress_zy, small_stress_zz, strain_xx, strain_xy, strain_xz, strain_yx, strain_yy, strain_yz, strain_zx, strain_zy, strain_zz, stress_xx, stress_xy, stress_xz, stress_yx, stress_yy, stress_yz, stress_zx, stress_zy, stress_zz, effective_plastic_strain, effective_creep_strain, firstinv_stress, firstinv_cauchy_stress, firstinv_pk1_stress, firstinv_pk2_stress, firstinv_small_stress, firstinv_strain, hydrostatic_stress, hydrostatic_cauchy_stress, hydrostatic_pk1_stress, hydrostatic_pk2_stress, hydrostatic_small_stress, intensity_stress, intensity_cauchy_stress, intensity_pk1_stress, intensity_pk2_stress, intensity_small_stress, l2norm_mechanical_strain, l2norm_stress, l2norm_cauchy_stress, l2norm_pk1_stress, l2norm_strain, l2norm_elastic_strain, l2norm_plastic_strain, l2norm_creep_strain, max_principal_mechanical_strain, max_principal_stress, max_principal_cauchy_stress, max_principal_pk1_stress, max_principal_pk2_stress, max_principal_small_stress, max_principal_strain, maxshear_stress, maxshear_cauchy_stress, maxshear_pk1_stress, maxshear_pk2_stress, maxshear_small_stress, mid_principal_mechanical_strain, mid_principal_stress, mid_principal_cauchy_stress, mid_principal_pk1_stress, mid_principal_pk2_stress, mid_principal_small_stress, mid_principal_strain, min_principal_mechanical_strain, min_principal_stress, min_principal_cauchy_stress, min_principal_pk1_stress, min_principal_pk2_stress, min_principal_small_stress, min_principal_strain, secondinv_stress, secondinv_cauchy_stress, secondinv_pk1_stress, secondinv_pk2_stress, secondinv_small_stress, secondinv_strain, thirdinv_stress, thirdinv_cauchy_stress, thirdinv_pk1_stress, thirdinv_pk2_stress, thirdinv_small_stress, thirdinv_strain, triaxiality_stress, triaxiality_cauchy_stress, triaxiality_pk1_stress, triaxiality_pk2_stress, triaxiality_small_stress, volumetric_mechanical_strain, volumetric_strain, vonmises_stress, vonmises_cauchy_stress, vonmises_pk1_stress, vonmises_pk2_stress, directional_stress, directional_strain, axial_stress, axial_strain, axial_plastic_strain, axial_creep_strain, axial_elastic_strain, hoop_stress, hoop_strain, hoop_plastic_strain, hoop_creep_strain, hoop_elastic_strain, radial_stress, radial_strain, spherical_hoop_stress, spherical_hoop_strain, spherical_hoop_plastic_strain, spherical_hoop_creep_strain, spherical_hoop_elastic_strain, spherical_radial_stress, spherical_radial_strain
Controllable:No
Description:Add scalar quantity output for stress and/or strain
inactiveIf specified blocks matching these identifiers will be skipped.
C++ Type:std::vector<std::string>
Controllable:No
Description:If specified blocks matching these identifiers will be skipped.
incrementalFalseUse incremental or total strain
Default:False
C++ Type:bool
Controllable:No
Description:Use incremental or total strain
initial_fuel_densityInitial fuel density in kg-UO2/m^3
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Initial fuel density in kg-UO2/m^3
isotope_fractionsThe isotope fractions associated with the 'isotopes' input line. Must sum to 1.0.
C++ Type:std::vector<std::vector<double>>
Unit:(no unit assumed)
Controllable:No
Description:The isotope fractions associated with the 'isotopes' input line. Must sum to 1.0.
isotopesU235 U238 Fuel isotopes: Gd155 Gd157 U235 U238 Pu239 Pu240 Pu241 Pu242. Number of entries must match number of entries in isotope_fractions.
Default:U235 U238
C++ Type:std::vector<MultiMooseEnum>
Options:Gd155, Gd157, U235, U238, Pu239, Pu240, Pu241, Pu242
Controllable:No
Description:Fuel isotopes: Gd155 Gd157 U235 U238 Pu239 Pu240 Pu241 Pu242. Number of entries must match number of entries in isotope_fractions.
localized_initial_temperatureLocalized Initial temperature in Kelvins. This allows individual blocks to have different temperature conditions apart from the global initial conditions.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Localized Initial temperature in Kelvins. This allows individual blocks to have different temperature conditions apart from the global initial conditions.
localized_temperature_functionFunction that describes localized temperature within the block.
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:Function that describes localized temperature within the block.
num_axial20Number of axial divisions in secondary grid used to compute radial power profile.
Default:20
C++ Type:unsigned int
Controllable:No
Description:Number of axial divisions in secondary grid used to compute radial power profile.
num_radial80Number of radial divisions in secondary grid used to compute radial power profile.
Default:80
C++ Type:unsigned int
Controllable:No
Description:Number of radial divisions in secondary grid used to compute radial power profile.
orderSECONDSpecifies the order of the FE shape function to use for this variable.
Default:SECOND
C++ Type:MooseEnum
Options:CONSTANT, FIRST, SECOND, THIRD, FOURTH, FIFTH, SIXTH, SEVENTH, EIGHTH, NINTH
Controllable:No
Description:Specifies the order of the FE shape function to use for this variable.
out_of_plane_pressure_function0Function used to prescribe pressure in the out-of-plane direction (y for 1D Axisymmetric or z for 2D Cartesian problems)
Default:0
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:Function used to prescribe pressure in the out-of-plane direction (y for 1D Axisymmetric or z for 2D Cartesian problems)
physicsType(s) of physics used on this block.
C++ Type:MultiMooseEnum
Options:Mechanics, Thermal
Controllable:No
Description:Type(s) of physics used on this block.
poissons_ratioPoisson's ratio for the material.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Poisson's ratio for the material.
rpf_inputThe radial power profile function. Used to specify the rpf from input
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:The radial power profile function. Used to specify the rpf from input
strainSMALLStrain formulation
Default:SMALL
C++ Type:MooseEnum
Options:SMALL, FINITE
Controllable:No
Description:Strain formulation
stress_free_temperatureReference temperature for thermal eigenstrain calculation
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Reference temperature for thermal eigenstrain calculation
system_pressure_functionThe function to use for the pressure on the exterior of the cladding.
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:The function to use for the pressure on the exterior of the cladding.
temperatureCoupled temperature: Used in multiple models
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Coupled temperature: Used in multiple models
uo2_modelsType(s) of physics models used on this block. The choices are: Burnup Elastic Creep Relocation Swelling ThermalExpansion HighBurnupStructureFormation
C++ Type:MultiMooseEnum
Options:Burnup, Elastic, Creep, Relocation, Swelling, ThermalExpansion, HighBurnupStructureFormation
Controllable:No
Description:Type(s) of physics models used on this block. The choices are: Burnup Elastic Creep Relocation Swelling ThermalExpansion HighBurnupStructureFormation
use_automatic_differentiationFalseFlag to use automatic differentiation (AD) objects when possible
Default:False
C++ Type:bool
Controllable:No
Description:Flag to use automatic differentiation (AD) objects when possible
youngs_modulusYoung's modulus of the material.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Young's modulus of the material.

Optional Parameters

additional_generate_outputAdd scalar quantity output for stress and/or strain (will be appended to the list in `generate_output`)
C++ Type:MultiMooseEnum
Options:cauchy_stress_xx, cauchy_stress_xy, cauchy_stress_xz, cauchy_stress_yx, cauchy_stress_yy, cauchy_stress_yz, cauchy_stress_zx, cauchy_stress_zy, cauchy_stress_zz, creep_strain_xx, creep_strain_xy, creep_strain_xz, creep_strain_yx, creep_strain_yy, creep_strain_yz, creep_strain_zx, creep_strain_zy, creep_strain_zz, creep_stress_xx, creep_stress_xy, creep_stress_xz, creep_stress_yx, creep_stress_yy, creep_stress_yz, creep_stress_zx, creep_stress_zy, creep_stress_zz, deformation_gradient_xx, deformation_gradient_xy, deformation_gradient_xz, deformation_gradient_yx, deformation_gradient_yy, deformation_gradient_yz, deformation_gradient_zx, deformation_gradient_zy, deformation_gradient_zz, elastic_strain_xx, elastic_strain_xy, elastic_strain_xz, elastic_strain_yx, elastic_strain_yy, elastic_strain_yz, elastic_strain_zx, elastic_strain_zy, elastic_strain_zz, mechanical_strain_xx, mechanical_strain_xy, mechanical_strain_xz, mechanical_strain_yx, mechanical_strain_yy, mechanical_strain_yz, mechanical_strain_zx, mechanical_strain_zy, mechanical_strain_zz, pk1_stress_xx, pk1_stress_xy, pk1_stress_xz, pk1_stress_yx, pk1_stress_yy, pk1_stress_yz, pk1_stress_zx, pk1_stress_zy, pk1_stress_zz, pk2_stress_xx, pk2_stress_xy, pk2_stress_xz, pk2_stress_yx, pk2_stress_yy, pk2_stress_yz, pk2_stress_zx, pk2_stress_zy, pk2_stress_zz, plastic_strain_xx, plastic_strain_xy, plastic_strain_xz, plastic_strain_yx, plastic_strain_yy, plastic_strain_yz, plastic_strain_zx, plastic_strain_zy, plastic_strain_zz, small_stress_xx, small_stress_xy, small_stress_xz, small_stress_yx, small_stress_yy, small_stress_yz, small_stress_zx, small_stress_zy, small_stress_zz, strain_xx, strain_xy, strain_xz, strain_yx, strain_yy, strain_yz, strain_zx, strain_zy, strain_zz, stress_xx, stress_xy, stress_xz, stress_yx, stress_yy, stress_yz, stress_zx, stress_zy, stress_zz, effective_plastic_strain, effective_creep_strain, firstinv_stress, firstinv_cauchy_stress, firstinv_pk1_stress, firstinv_pk2_stress, firstinv_small_stress, firstinv_strain, hydrostatic_stress, hydrostatic_cauchy_stress, hydrostatic_pk1_stress, hydrostatic_pk2_stress, hydrostatic_small_stress, intensity_stress, intensity_cauchy_stress, intensity_pk1_stress, intensity_pk2_stress, intensity_small_stress, l2norm_mechanical_strain, l2norm_stress, l2norm_cauchy_stress, l2norm_pk1_stress, l2norm_strain, l2norm_elastic_strain, l2norm_plastic_strain, l2norm_creep_strain, max_principal_mechanical_strain, max_principal_stress, max_principal_cauchy_stress, max_principal_pk1_stress, max_principal_pk2_stress, max_principal_small_stress, max_principal_strain, maxshear_stress, maxshear_cauchy_stress, maxshear_pk1_stress, maxshear_pk2_stress, maxshear_small_stress, mid_principal_mechanical_strain, mid_principal_stress, mid_principal_cauchy_stress, mid_principal_pk1_stress, mid_principal_pk2_stress, mid_principal_small_stress, mid_principal_strain, min_principal_mechanical_strain, min_principal_stress, min_principal_cauchy_stress, min_principal_pk1_stress, min_principal_pk2_stress, min_principal_small_stress, min_principal_strain, secondinv_stress, secondinv_cauchy_stress, secondinv_pk1_stress, secondinv_pk2_stress, secondinv_small_stress, secondinv_strain, thirdinv_stress, thirdinv_cauchy_stress, thirdinv_pk1_stress, thirdinv_pk2_stress, thirdinv_small_stress, thirdinv_strain, triaxiality_stress, triaxiality_cauchy_stress, triaxiality_pk1_stress, triaxiality_pk2_stress, triaxiality_small_stress, volumetric_mechanical_strain, volumetric_strain, vonmises_stress, vonmises_cauchy_stress, vonmises_pk1_stress, vonmises_pk2_stress, directional_stress, directional_strain, axial_stress, axial_strain, axial_plastic_strain, axial_creep_strain, axial_elastic_strain, hoop_stress, hoop_strain, hoop_plastic_strain, hoop_creep_strain, hoop_elastic_strain, radial_stress, radial_strain, spherical_hoop_stress, spherical_hoop_strain, spherical_hoop_plastic_strain, spherical_hoop_creep_strain, spherical_hoop_elastic_strain, spherical_radial_stress, spherical_radial_strain
Controllable:No
Description:Add scalar quantity output for stress and/or strain (will be appended to the list in `generate_output`)
blockThe list of ids of the blocks (subdomain) that the stress divergence kernels will be applied to
C++ Type:std::vector<SubdomainName>
Controllable:No
Description:The list of ids of the blocks (subdomain) that the stress divergence kernels will be applied to
displacementsThe displacements appropriate for the simulation geometry and coordinate system: Used in density and strain models
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The displacements appropriate for the simulation geometry and coordinate system: Used in density and strain models
volumetric_locking_correctionFalseFlag to correct volumetric locking
Default:False
C++ Type:bool
Controllable:No
Description:Flag to correct volumetric locking

Mechanics Parameters

axial_power_profileThe axial power peaking function.
C++ Type:std::vector<FunctionName>
Unit:(no unit assumed)
Controllable:No
Description:The axial power peaking function.
energy_per_fission3.28451e-11Energy released per fission (J/fission).
Default:3.28451e-11
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Energy released per fission (J/fission).
fuel_pin_geometryName of the UserObject that reads the pin geometry from the mesh.
C++ Type:UserObjectName
Controllable:No
Description:Name of the UserObject that reads the pin geometry from the mesh.
rod_ave_lin_powThe rod power history function.
C++ Type:std::vector<FunctionName>
Unit:(no unit assumed)
Controllable:No
Description:The rod power history function.

Burnup Parameters

burnupCoupled Burnup: Used in fuel creep, fission gas, relocation, swelling, and thermal models
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Coupled Burnup: Used in fuel creep, fission gas, relocation, swelling, and thermal models
fission_rateCoupled Fission rate: Used in fuel burnup, creep, densification, fission gas, relocation, swelling, and thermal models
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Coupled Fission rate: Used in fuel burnup, creep, densification, fission gas, relocation, swelling, and thermal models
grain_radiusCoupled Grain Radius: Used in fuel creep, densification, fission gas, swelling, and thermal models
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Coupled Grain Radius: Used in fuel creep, densification, fission gas, swelling, and thermal models
initial_grain_radius1e-05Initial grain radius
Default:1e-05
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Initial grain radius

Fission Parameters

burnup_relocation_stop1e+12Burnup at which relocation strain stops (in FIMA)
Default:1e+12
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Burnup at which relocation strain stops (in FIMA)

Relocation Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.

Advanced Parameters

initial_porosityInitial fuel porosity (dimensionless): Used in fission gas, porosity, swelling, and thermal models
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Initial fuel porosity (dimensionless): Used in fission gas, porosity, swelling, and thermal models
total_densification0.01The densification that will occur given as a fraction of theoretical density
Default:0.01
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The densification that will occur given as a fraction of theoretical density

Swelling Parameters

(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 of Created Material Blocks
User - based Interface
Example Input Syntax can be used in multiple ways to simplify creation of various parts of the input file . In its most basic form , it can be used to automate the creation of the material models used to define the mechanical and thermal behavior of fuel and cladding materials . With additional options , it can also be used to automate the creation of the variables and kernels associated with mechanical and thermal physics , as well as the Burnup objects . Examples of these two different ways to use are provided below NuclearMaterials NuclearMaterials
Example Simple Input Syntax
Example Fully Reduced Input Syntax
Input Parameters