Nuclear Material SS316

Reduces the Material block length for SS316 cladding within input files.

Description

This NuclearMaterialSS316 action reduces BISON input file length by internally generating the Materials required for simulating metallic nuclear cladding, specifically SS316.

The user may elect to use the nuclear_material_SS316_table action to generate the necessary material classes for common metallic fuel simulations. All of the material blocks, generated with the default parameter settings, are shown in Table 1.

Fission Operation

note

This required parameter describes the characteristic type of fission study that will occur. For metallic fuel type simulations, this is simply labeled as fission_operation = Normal. This must be placed under the NuclearMaterials block heading and cannot be placed under sub-blocks such as SS316.

Table 1: Material classes created by the NuclearMaterialSS316 action

Created Classes	Pre-Set Parameters	Block Name	SS316 models
ComputeIsotropicElasticityTensor	poissons_ratio = 0.265	clad_elasticity_tensor	Elastic (No Creep)
	youngs_modulus = 190e9
SS316ElasticityTensor		clad_elasticity_tensor	Elastic + Creep

ComputeLinearElasticStress	strain = SMALL	clad_stress	Elastic (No Creep)

ComputeFiniteStrainElasticStress	strain = FINITE	clad_stress	Elastic (No Creep)

ComputeMultipleInelasticStress		clad stress	Elastic + Creep

StrainAdjustedDensity	strain_free_density = 8000.0	clad_density

DerivativeParsedMaterial	density_expression = {user_input}	clad_density

SS316Thermal		clad_thermal	Thermal(Properties/Expansion)
			Elastic
SS316ThermalExpansionEigenstrain		clad_thermal_expansion	ThermalExpansion

FastNeutronFlux		fast_neutron_flux	Creep

SS316CreepUpdate		clad_creep	Creep

Example Input Syntax

Expanded Cladding Block

[Materials]
density = 13630.0
A_U = 0.238
A_Pu = 0.239
A_N = 0.014
X_Pu = 0.1
X_N = 0.5
avo = 6.0221408e23
M_avg = '${fparse X_N * A_N + X_Pu * A_Pu + (1.0 - X_N - X_Pu) * A_U}'
atoms = '${fparse density / M_avg * (1.0 - X_N) * avo}'

[GlobalParams]
  density = ${density}
  order = SECOND
  family = LAGRANGE
  energy_per_fission = 3.2e-11 # J/fission
  volumetric_locking_correction = false
  displacements = 'disp_x disp_y'

[]

[Problem]
  type = ReferenceResidualProblem
  reference_vector = 'ref'
  extra_tag_vectors = 'ref'
  group_variables = 'disp_x disp_y'
[]

[Mesh]
  coord_type = RZ
  use_displaced_mesh = false
  [smeared_pellet_mesh]
    type = FuelPinMeshGenerator
    clad_thickness = 0.51e-3
    pellet_outer_radius = 3.1e-3
    pellet_height = 343e-3
    clad_top_gap_height = 43.5e-3
    clad_gap_width = 0.325e-3
    bottom_clad_height = 8e-3
    top_clad_height = 8e-3
    clad_bot_gap_height = 0.2e-3 # unknown
    clad_mesh_density = customize
    pellet_mesh_density = customize
    nx_p = 6
    ny_p = 260
    nx_c = 4
    ny_c = 260
    ny_cu = 3
    ny_cl = 3
    pellet_quantity = 1
    elem_type = QUAD8
  []
  patch_size = 30
  patch_update_strategy = auto
  partitioner = centroid
  centroid_partitioner_direction = y
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [temp]
    initial_condition = 350
  []
[]

[AuxVariables]
  [pellet_wall_temp]
    order = CONSTANT
    family = MONOMIAL
  []
  [radial_heat_flux]
    order = CONSTANT
    family = MONOMIAL
  []
  [clad_inner_wall_temp]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [power_history]
    type = PiecewiseLinear
    x = '0 1e5   35e6 35100000' # unknown, final burnup was 9.6 %
    y = '0 1     1    0'
  []
  [axial_peaking_factors]
    type = PiecewiseLinear
    axis = y
    x = '0    46e-3 111e-3 200e-3 248e-3 313e-3 352e-3'
    y = '73e3 73e3  82e3   85e3   82e3   74e3   74e3'
  []
  [fission_func]
    type = ParsedFunction
    symbol_names = 'axial_peaking_factors power_history'
    symbol_values = 'axial_peaking_factors power_history'
    expression = 'linear_heating_rate := axial_peaking_factors * power_history;
             pellet_cross_sectional_area := 3.14159 * pow( 3.1e-3, 2 );
             volumetric_power := linear_heating_rate / pellet_cross_sectional_area;
             energy_per_fission := 3.2e-11;
             volumetric_power / energy_per_fission'
  []

  [coolant_press_ramp]
    type = PiecewiseLinear
    x = '0       35100000'
    y = '0.151e6 0.151e6' # unknown, Na coolant
  []
  [coolant_inlet_temp]
    type = PiecewiseLinear
    x = '0   1e5 35e6 35100000'
    y = '350 644 644  350'
  []
  [coolant_outlet_temp]
    type = PiecewiseLinear
    x = '0   1e5 35e6 35100000'
    y = '350 746 746  350'
  []
  [coolant_wall_temp]
    type = ParsedFunction
    symbol_values = 'coolant_inlet_temp coolant_outlet_temp'
    symbol_names = 'coolant_inlet_temp coolant_outlet_temp'
    expression = 'rod_length := 343e-3 + 43.5e-3 + 2 * 8e-3;
             delta_temp := coolant_outlet_temp - coolant_inlet_temp;
             interpolated_temp := coolant_inlet_temp + y * delta_temp / rod_length;
             max( min( interpolated_temp, coolant_outlet_temp ), coolant_inlet_temp )'
  []
  [radial_heat_flux]
    type = ParsedFunction
    symbol_values = 'coolant_wall_temp power_history axial_peaking_factors'
    symbol_names = 'coolant_wall_temp power_history axial_peaking_factors'
    expression = 'linear_heating_rate := axial_peaking_factors * power_history;
             pellet_radius := 3.1e-3;
             pellet_circumference := 3.14159 * pellet_radius * 2;
             linear_heating_rate / pellet_circumference'
  []
  [clad_inner_wall_temp]
    type = ParsedFunction
    symbol_values = 'radial_heat_flux coolant_wall_temp'
    symbol_names = 'radial_heat_flux coolant_wall_temp'
    expression = 'conductivity_316ss := 22;
             clad_thickness := 0.51e-3;
             coolant_wall_temp + radial_heat_flux / conductivity_316ss * clad_thickness'
  []
  [pellet_wall_temp]
    type = ParsedFunction
    symbol_values = 'radial_heat_flux coolant_wall_temp clad_inner_wall_temp'
    symbol_names = 'radial_heat_flux coolant_wall_temp clad_inner_wall_temp'
    expression = 'conductivity_gap := 100;
             gap_thickness := 0.325e-3;
             clad_inner_wall_temp + radial_heat_flux / conductivity_gap * gap_thickness'
  []

  [plenum_pressure]
    type = ConstantFunction
    value = 12.4e6 # initial fill
  []

  [porosity_ramp]
    type = PiecewiseLinear
    x = '0   1e5 35e6 35100000'
    y = '0.03 0.03 0.05  0.05' # Pellets start at 96.8% TD, but no data on final porosity.
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [fuel]
    block = pellet
    strain = SMALL
    incremental = true
    extra_vector_tags = 'ref'
    eigenstrain_names = 'fuel_thermal_expansion fuel_swelling'
    use_automatic_differentiation = true
  []
  [clad]
    block = clad
    strain = SMALL
    incremental = true
    extra_vector_tags = 'ref'
    use_automatic_differentiation = true
  []
[]

[Kernels]
  [gravity]
    type = ADGravity
    variable = disp_y
    value = -9.81
    extra_vector_tags = 'ref'
  []
  [heat]
    type = ADHeatConduction
    variable = temp
    extra_vector_tags = 'ref'
  []
  [heat_ie]
    type = ADHeatConductionTimeDerivative
    variable = temp
    extra_vector_tags = 'ref'
  []
  [heat_source]
    type = ADFissionRateHeatSource
    variable = temp
    block = pellet
    fission_rate = fission_rate
    extra_vector_tags = 'ref'
  []
[]

[AuxKernels]
  [pellet_wall_temp]
    type = FunctionAux
    variable = pellet_wall_temp
    function = pellet_wall_temp
  []
  [radial_heat_flux]
    type = FunctionAux
    variable = radial_heat_flux
    function = radial_heat_flux
  []
  [clad_inner_wall_temp]
    type = FunctionAux
    variable = clad_inner_wall_temp
    function = clad_inner_wall_temp
  []
[]

[BCs]
  [no_x_all]
    type = DirichletBC
    variable = disp_x
    boundary = 12
    value = 0.0
  []
  [no_y_fuel]
    type = DirichletBC
    variable = disp_y
    boundary = 20
    value = 0.0
  []
  [no_y_clad]
    type = DirichletBC
    variable = disp_y
    boundary = 1
    value = 0.0
  []
  [Pressure]
    [coolantPressure]
      boundary = '1 2 3'
      function = coolant_press_ramp
    []
    [plenumPressure]
      boundary = 9
      function = plenum_pressure
    []
  []
  [clad_outer_temp]
    type = FunctionDirichletBC
    boundary = '1 2 3'
    function = coolant_wall_temp
    variable = temp
  []
  [pellet_to_clad_cooling]
    type = FunctionDirichletBC
    boundary = 10
    function = pellet_wall_temp
    variable = temp
  []
[]

[Materials]
  [fission]
    type = ADGenericFunctionMaterial
    prop_names = fission_rate
    prop_values = fission_func
    outputs = all
  []

  [fuel_thermal]
    block = pellet
    type = ADMNThermal
    temperature = temp
    porosity = porosity
    outputs = all
  []
  [fuel_porosity]
    block = pellet
    type = ADGenericFunctionMaterial
    prop_names = porosity
    prop_values = porosity_ramp
    outputs = all
  []
  [fuel_elasticity_tensor]
    block = pellet
    type = ADMNElasticityTensor
    temperature = temp
    porosity = porosity
    output_properties = 'youngs_modulus poissons_ratio'
    outputs = all
  []
  [fuel_thermal_expansion]
    block = pellet
    type = ADMNThermalExpansionEigenstrain
    eigenstrain_name = fuel_thermal_expansion
    stress_free_temperature = 350
    temperature = temp

  []
  [fuel_creep]
    block = pellet
    type = ADMNCreepUpdate
    temperature = temp
    porosity = porosity
    fission_rate = fission_rate
    outputs = all
  []
  [burnup]
    type = ADBurnup
    block = pellet
    atoms_heavy_metal_per_volume = ${atoms}
    outputs = all
  []
  [fuel_swelling]
    block = pellet
    type = ADMNVolumetricSwellingEigenstrain
    eigenstrain_name = fuel_swelling
    temperature = temp
    initial_porosity = 0.03
    burnup = burnup
    outputs = all
  []
  [fuel_radial_return_stress]
    block = pellet
    type = ADComputeMultipleInelasticStress
    inelastic_models = 'fuel_creep'
  []
  [fuel_density]
    block = pellet
    type = ADStrainAdjustedDensity
    strain_free_density = ${density}
  []

  [clad_elasticity_tensor]
    block = clad
    type = ADComputeIsotropicElasticityTensor
    youngs_modulus = 190e9
    poissons_ratio = 0.265
  []
  [clad_stress]
    block = clad
    type = ADComputeLinearElasticStress
  []
  [clad_thermal]
    block = clad
    type = ADSS316Thermal
    temperature = temp
  []
  [clad_density]
    block = clad
    type = ADStrainAdjustedDensity
    strain_free_density = 8000
  []
[]

Simplified Cladding Block

[NuclearMaterials<<<{"href": "../index.html"}>>>]
  [SS316<<<{"href": "index.html"}>>>]
    [clad]
      block<<<{"description": "The list of ids of the blocks (subdomain) that the stress divergence kernels will be applied to"}>>> = clad
      incremental<<<{"description": "Use incremental or total strain"}>>> = true
      strain<<<{"description": "Strain formulation"}>>> = SMALL
      ss316_models<<<{"description": "Type(s) of physics models used on this block.   The choices are: Elastic Creep ThermalExpansion ThermalProperties"}>>> = 'Elastic'
    []
  []
[]

The eigenstrains have been automatically parsed and included by wrapping the SolidMechanics QuasiStatic Action inside the NuclearMaterials following the naming convention created by this class.

Input Parameters

ss316_modelsType(s) of physics models used on this block. The choices are: Elastic Creep ThermalExpansion ThermalProperties
C++ Type:MultiMooseEnum
Options:Elastic, Creep, ThermalExpansion, ThermalProperties
Controllable:No
Description:Type(s) of physics models used on this block. The choices are: Elastic Creep ThermalExpansion ThermalProperties

Required Parameters

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
base_nameBase name for the MaterialProperties.
C++ Type:std::string
Controllable:No
Description:Base name for the MaterialProperties.
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.
density8000Clad density in kg-SS316/m^3.
Default:8000
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Clad density in kg-SS316/m^3.
density_expressionParsed function (see FParser) expression for the parsed density material
C++ Type:FunctionExpression
Unit:(no unit assumed)
Controllable:No
Description:Parsed function (see FParser) expression for the parsed density material
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
elastic_constants_modellegacy_ifrElastic constants model. Choices are: ornl legacy_ifr
Default:legacy_ifr
C++ Type:MooseEnum
Options:ornl, legacy_ifr
Controllable:No
Description:Elastic constants model. Choices are: ornl legacy_ifr
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_functionFunction which contains the neutron flux data.
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:Function which contains the neutron flux data.
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.
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
id_wastage_degradation_functionThe optional ID wastage degradation function that takes FCCI effect on cladding into consideration.
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:The optional ID wastage degradation function that takes FCCI effect on cladding into consideration.
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
od_wastage_degradation_functionThe optional OD wastage degradation function that takes CCCI effect on cladding into consideration.
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:The optional OD wastage degradation function that takes CCCI effect on cladding into consideration.
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_pressure0Function 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_ratio0.265Poisson's ratio for the material.
Default:0.265
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Poisson's ratio for the material.
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.
tangent_operatornonlinearType of tangent operator to return. 'elastic': return the elasticity tensor. 'nonlinear': return the full, general consistent tangent operator.
Default:nonlinear
C++ Type:MooseEnum
Options:elastic, nonlinear
Controllable:No
Description:Type of tangent operator to return. 'elastic': return the elasticity tensor. 'nonlinear': return the full, general consistent tangent operator.
temperatureCoupled temperature: Used in multiple models
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Coupled temperature: Used in multiple models
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_modulus1.9e+11Young's modulus of the material.
Default:1.9e+11
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`)
automatic_eigenstrain_namesTrueCollects all material eigenstrains and passes to required strain calculator within TMA internally.
Default:True
C++ Type:bool
Controllable:No
Description:Collects all material eigenstrains and passes to required strain calculator within TMA internally.
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
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
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

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

(assessment/nitride/EBRII/K4/analysis/base.i)

density = 13630.0
A_U = 0.238
A_Pu = 0.239
A_N = 0.014
X_Pu = 0.1
X_N = 0.5
avo = 6.0221408e23
M_avg = '${fparse X_N * A_N + X_Pu * A_Pu + (1.0 - X_N - X_Pu) * A_U}'
atoms = '${fparse density / M_avg * (1.0 - X_N) * avo}'

[GlobalParams]
  density = ${density}
  order = SECOND
  family = LAGRANGE
  energy_per_fission = 3.2e-11 # J/fission
  volumetric_locking_correction = false
  displacements = 'disp_x disp_y'

[]

[Problem]
  type = ReferenceResidualProblem
  reference_vector = 'ref'
  extra_tag_vectors = 'ref'
  group_variables = 'disp_x disp_y'
[]

[Mesh]
  coord_type = RZ
  use_displaced_mesh = false
  [smeared_pellet_mesh]
    type = FuelPinMeshGenerator
    clad_thickness = 0.51e-3
    pellet_outer_radius = 3.1e-3
    pellet_height = 343e-3
    clad_top_gap_height = 43.5e-3
    clad_gap_width = 0.325e-3
    bottom_clad_height = 8e-3
    top_clad_height = 8e-3
    clad_bot_gap_height = 0.2e-3 # unknown
    clad_mesh_density = customize
    pellet_mesh_density = customize
    nx_p = 6
    ny_p = 260
    nx_c = 4
    ny_c = 260
    ny_cu = 3
    ny_cl = 3
    pellet_quantity = 1
    elem_type = QUAD8
  []
  patch_size = 30
  patch_update_strategy = auto
  partitioner = centroid
  centroid_partitioner_direction = y
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [temp]
    initial_condition = 350
  []
[]

[AuxVariables]
  [pellet_wall_temp]
    order = CONSTANT
    family = MONOMIAL
  []
  [radial_heat_flux]
    order = CONSTANT
    family = MONOMIAL
  []
  [clad_inner_wall_temp]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [power_history]
    type = PiecewiseLinear
    x = '0 1e5   35e6 35100000' # unknown, final burnup was 9.6 %
    y = '0 1     1    0'
  []
  [axial_peaking_factors]
    type = PiecewiseLinear
    axis = y
    x = '0    46e-3 111e-3 200e-3 248e-3 313e-3 352e-3'
    y = '73e3 73e3  82e3   85e3   82e3   74e3   74e3'
  []
  [fission_func]
    type = ParsedFunction
    symbol_names = 'axial_peaking_factors power_history'
    symbol_values = 'axial_peaking_factors power_history'
    expression = 'linear_heating_rate := axial_peaking_factors * power_history;
             pellet_cross_sectional_area := 3.14159 * pow( 3.1e-3, 2 );
             volumetric_power := linear_heating_rate / pellet_cross_sectional_area;
             energy_per_fission := 3.2e-11;
             volumetric_power / energy_per_fission'
  []

  [coolant_press_ramp]
    type = PiecewiseLinear
    x = '0       35100000'
    y = '0.151e6 0.151e6' # unknown, Na coolant
  []
  [coolant_inlet_temp]
    type = PiecewiseLinear
    x = '0   1e5 35e6 35100000'
    y = '350 644 644  350'
  []
  [coolant_outlet_temp]
    type = PiecewiseLinear
    x = '0   1e5 35e6 35100000'
    y = '350 746 746  350'
  []
  [coolant_wall_temp]
    type = ParsedFunction
    symbol_values = 'coolant_inlet_temp coolant_outlet_temp'
    symbol_names = 'coolant_inlet_temp coolant_outlet_temp'
    expression = 'rod_length := 343e-3 + 43.5e-3 + 2 * 8e-3;
             delta_temp := coolant_outlet_temp - coolant_inlet_temp;
             interpolated_temp := coolant_inlet_temp + y * delta_temp / rod_length;
             max( min( interpolated_temp, coolant_outlet_temp ), coolant_inlet_temp )'
  []
  [radial_heat_flux]
    type = ParsedFunction
    symbol_values = 'coolant_wall_temp power_history axial_peaking_factors'
    symbol_names = 'coolant_wall_temp power_history axial_peaking_factors'
    expression = 'linear_heating_rate := axial_peaking_factors * power_history;
             pellet_radius := 3.1e-3;
             pellet_circumference := 3.14159 * pellet_radius * 2;
             linear_heating_rate / pellet_circumference'
  []
  [clad_inner_wall_temp]
    type = ParsedFunction
    symbol_values = 'radial_heat_flux coolant_wall_temp'
    symbol_names = 'radial_heat_flux coolant_wall_temp'
    expression = 'conductivity_316ss := 22;
             clad_thickness := 0.51e-3;
             coolant_wall_temp + radial_heat_flux / conductivity_316ss * clad_thickness'
  []
  [pellet_wall_temp]
    type = ParsedFunction
    symbol_values = 'radial_heat_flux coolant_wall_temp clad_inner_wall_temp'
    symbol_names = 'radial_heat_flux coolant_wall_temp clad_inner_wall_temp'
    expression = 'conductivity_gap := 100;
             gap_thickness := 0.325e-3;
             clad_inner_wall_temp + radial_heat_flux / conductivity_gap * gap_thickness'
  []

  [plenum_pressure]
    type = ConstantFunction
    value = 12.4e6 # initial fill
  []

  [porosity_ramp]
    type = PiecewiseLinear
    x = '0   1e5 35e6 35100000'
    y = '0.03 0.03 0.05  0.05' # Pellets start at 96.8% TD, but no data on final porosity.
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [fuel]
    block = pellet
    strain = SMALL
    incremental = true
    extra_vector_tags = 'ref'
    eigenstrain_names = 'fuel_thermal_expansion fuel_swelling'
    use_automatic_differentiation = true
  []
  [clad]
    block = clad
    strain = SMALL
    incremental = true
    extra_vector_tags = 'ref'
    use_automatic_differentiation = true
  []
[]

[Kernels]
  [gravity]
    type = ADGravity
    variable = disp_y
    value = -9.81
    extra_vector_tags = 'ref'
  []
  [heat]
    type = ADHeatConduction
    variable = temp
    extra_vector_tags = 'ref'
  []
  [heat_ie]
    type = ADHeatConductionTimeDerivative
    variable = temp
    extra_vector_tags = 'ref'
  []
  [heat_source]
    type = ADFissionRateHeatSource
    variable = temp
    block = pellet
    fission_rate = fission_rate
    extra_vector_tags = 'ref'
  []
[]

[AuxKernels]
  [pellet_wall_temp]
    type = FunctionAux
    variable = pellet_wall_temp
    function = pellet_wall_temp
  []
  [radial_heat_flux]
    type = FunctionAux
    variable = radial_heat_flux
    function = radial_heat_flux
  []
  [clad_inner_wall_temp]
    type = FunctionAux
    variable = clad_inner_wall_temp
    function = clad_inner_wall_temp
  []
[]

[BCs]
  [no_x_all]
    type = DirichletBC
    variable = disp_x
    boundary = 12
    value = 0.0
  []
  [no_y_fuel]
    type = DirichletBC
    variable = disp_y
    boundary = 20
    value = 0.0
  []
  [no_y_clad]
    type = DirichletBC
    variable = disp_y
    boundary = 1
    value = 0.0
  []
  [Pressure]
    [coolantPressure]
      boundary = '1 2 3'
      function = coolant_press_ramp
    []
    [plenumPressure]
      boundary = 9
      function = plenum_pressure
    []
  []
  [clad_outer_temp]
    type = FunctionDirichletBC
    boundary = '1 2 3'
    function = coolant_wall_temp
    variable = temp
  []
  [pellet_to_clad_cooling]
    type = FunctionDirichletBC
    boundary = 10
    function = pellet_wall_temp
    variable = temp
  []
[]

[Materials]
  [fission]
    type = ADGenericFunctionMaterial
    prop_names = fission_rate
    prop_values = fission_func
    outputs = all
  []

  [fuel_thermal]
    block = pellet
    type = ADMNThermal
    temperature = temp
    porosity = porosity
    outputs = all
  []
  [fuel_porosity]
    block = pellet
    type = ADGenericFunctionMaterial
    prop_names = porosity
    prop_values = porosity_ramp
    outputs = all
  []
  [fuel_elasticity_tensor]
    block = pellet
    type = ADMNElasticityTensor
    temperature = temp
    porosity = porosity
    output_properties = 'youngs_modulus poissons_ratio'
    outputs = all
  []
  [fuel_thermal_expansion]
    block = pellet
    type = ADMNThermalExpansionEigenstrain
    eigenstrain_name = fuel_thermal_expansion
    stress_free_temperature = 350
    temperature = temp

  []
  [fuel_creep]
    block = pellet
    type = ADMNCreepUpdate
    temperature = temp
    porosity = porosity
    fission_rate = fission_rate
    outputs = all
  []
  [burnup]
    type = ADBurnup
    block = pellet
    atoms_heavy_metal_per_volume = ${atoms}
    outputs = all
  []
  [fuel_swelling]
    block = pellet
    type = ADMNVolumetricSwellingEigenstrain
    eigenstrain_name = fuel_swelling
    temperature = temp
    initial_porosity = 0.03
    burnup = burnup
    outputs = all
  []
  [fuel_radial_return_stress]
    block = pellet
    type = ADComputeMultipleInelasticStress
    inelastic_models = 'fuel_creep'
  []
  [fuel_density]
    block = pellet
    type = ADStrainAdjustedDensity
    strain_free_density = ${density}
  []

  [clad_elasticity_tensor]
    block = clad
    type = ADComputeIsotropicElasticityTensor
    youngs_modulus = 190e9
    poissons_ratio = 0.265
  []
  [clad_stress]
    block = clad
    type = ADComputeLinearElasticStress
  []
  [clad_thermal]
    block = clad
    type = ADSS316Thermal
    temperature = temp
  []
  [clad_density]
    block = clad
    type = ADStrainAdjustedDensity
    strain_free_density = 8000
  []
[]

[Preconditioning]
  [SMP]
    type = SMP
    full = true
  []
[]

[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 -ksp_gmres_restart'
  petsc_options_value = 'lu       superlu_dist                  51'
  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 = 35100000
  dtmin = 1
  dtmax = 2e6

  [Quadrature]
    order = fifth
    side_order = seventh
  []

  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 2e2
    time_t = ' 0   1e5 35e6 35100000'
    time_dt = '1e2 1e2 1e2  1e2'
    optimal_iterations = 10
    growth_factor = 2
    cutback_factor = 0.5
    iteration_window = 1
    linear_iteration_ratio = 100
  []
[]

[Postprocessors]
  [peak_burnup]
    type = ElementExtremeValue
    block = pellet
    value_type = max
    variable = burnup
  []

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

[PerformanceMetricOutputs]
  outputs = performance_metrics
[]

[Outputs]
  color = true
  exodus = true
  perf_graph = true
  [console]
    type = Console
    max_rows = 25
    time_step_interval =  1
    output_linear = true
  []
  [out]
    type = CSV
    show = 'peak_burnup'
  []
  [performance_metrics]
    type = CSV
    show = 'peak_burnup num_lin_it num_nonlin_it alive_time'
  []
[]

(assessment/nitride/EBRII/K4/analysis/base_action.i)

  density = 13630.0
  A_U = 0.238
  A_Pu = 0.239
  A_N = 0.014
  X_Pu = 0.1
  X_N = 0.5
  avo = 6.0221408e23
  M_avg = '${fparse X_N * A_N + X_Pu * A_Pu + (1.0 - X_N - X_Pu) * A_U}'
  atoms_heavy_metal_per_volume = '${fparse density / M_avg * (1.0 - X_N) * avo}'

[GlobalParams]
  order = SECOND
  family = LAGRANGE
  energy_per_fission = 3.2e-11 # J/fission
  volumetric_locking_correction = false
  displacements = 'disp_x disp_y'
  temperature = temperature
[]

[Problem]
  type = ReferenceResidualProblem
  reference_vector = 'ref'
  extra_tag_vectors = 'ref'
  group_variables = 'disp_x disp_y'
[]

[Mesh]
  coord_type = RZ
  use_displaced_mesh = false
  [smeared_pellet_mesh]
    type = FuelPinMeshGenerator
    clad_thickness = 0.51e-3
    pellet_outer_radius = 3.1e-3
    pellet_height = 343e-3
    clad_top_gap_height = 43.5e-3
    clad_gap_width = 0.325e-3
    bottom_clad_height = 8e-3
    top_clad_height = 8e-3
    clad_bot_gap_height = 0.2e-3 # unknown
    clad_mesh_density = customize
    pellet_mesh_density = customize
    nx_p = 6
    ny_p = 260
    nx_c = 4
    ny_c = 260
    ny_cu = 3
    ny_cl = 3
    pellet_quantity = 1
    elem_type = QUAD8
  []
  patch_size = 30
  patch_update_strategy = auto
  partitioner = centroid
  centroid_partitioner_direction = y
[]

[AuxVariables]
  [pellet_wall_temp]
    order = CONSTANT
    family = MONOMIAL
  []
  [radial_heat_flux]
    order = CONSTANT
    family = MONOMIAL
  []
  [clad_inner_wall_temp]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [power_history]
    type = PiecewiseLinear
    x = '0 1e5   35e6 35100000' # unknown, final burnup was 9.6 %
    y = '0 1     1    0'
  []
  [axial_peaking_factors]
    type = PiecewiseLinear
    axis = y
    x = '0    46e-3 111e-3 200e-3 248e-3 313e-3 352e-3'
    y = '73e3 73e3  82e3   85e3   82e3   74e3   74e3'
  []
  [fission_func]
    type = ParsedFunction
    symbol_names = 'axial_peaking_factors power_history'
    symbol_values = 'axial_peaking_factors power_history'
    expression = 'linear_heating_rate := axial_peaking_factors * power_history;
             pellet_cross_sectional_area := 3.14159 * pow( 3.1e-3, 2 );
             volumetric_power := linear_heating_rate / pellet_cross_sectional_area;
             energy_per_fission := 3.2e-11;
             volumetric_power / energy_per_fission'
  []

  [coolant_press_ramp]
    type = PiecewiseLinear
    x = '0       35100000'
    y = '0.151e6 0.151e6' # unknown, Na coolant
  []
  [coolant_inlet_temp]
    type = PiecewiseLinear
    x = '0   1e5 35e6 35100000'
    y = '350 644 644  350'
  []
  [coolant_outlet_temp]
    type = PiecewiseLinear
    x = '0   1e5 35e6 35100000'
    y = '350 746 746  350'
  []
  [coolant_wall_temp]
    type = ParsedFunction
    symbol_values = 'coolant_inlet_temp coolant_outlet_temp'
    symbol_names = 'coolant_inlet_temp coolant_outlet_temp'
    expression = 'rod_length := 343e-3 + 43.5e-3 + 2 * 8e-3;
             delta_temp := coolant_outlet_temp - coolant_inlet_temp;
             interpolated_temp := coolant_inlet_temp + y * delta_temp / rod_length;
             max( min( interpolated_temp, coolant_outlet_temp ), coolant_inlet_temp )'
  []
  [radial_heat_flux]
    type = ParsedFunction
    symbol_values = 'coolant_wall_temp power_history axial_peaking_factors'
    symbol_names = 'coolant_wall_temp power_history axial_peaking_factors'
    expression = 'linear_heating_rate := axial_peaking_factors * power_history;
             pellet_radius := 3.1e-3;
             pellet_circumference := 3.14159 * pellet_radius * 2;
             linear_heating_rate / pellet_circumference'
  []
  [clad_inner_wall_temp]
    type = ParsedFunction
    symbol_values = 'radial_heat_flux coolant_wall_temp'
    symbol_names = 'radial_heat_flux coolant_wall_temp'
    expression = 'conductivity_316ss := 22;
             clad_thickness := 0.51e-3;
             coolant_wall_temp + radial_heat_flux / conductivity_316ss * clad_thickness'
  []
  [pellet_wall_temp]
    type = ParsedFunction
    symbol_values = 'radial_heat_flux coolant_wall_temp clad_inner_wall_temp'
    symbol_names = 'radial_heat_flux coolant_wall_temp clad_inner_wall_temp'
    expression = 'conductivity_gap := 100;
             gap_thickness := 0.325e-3;
             clad_inner_wall_temp + radial_heat_flux / conductivity_gap * gap_thickness'
  []

  [plenum_pressure]
    type = ConstantFunction
    value = 12.4e6 # initial fill
  []

  [porosity_ramp]
    type = PiecewiseLinear
    x = '0   1e5 35e6 35100000'
    y = '0.03 0.03 0.05  0.05' # Pellets start at 96.8% TD, but no data on final porosity.
  []
[]

[Kernels]
  [gravity]
    type = ADGravity
    variable = disp_y
    value = -9.81
    extra_vector_tags = 'ref'
  []
[]

[AuxKernels]
  [pellet_wall_temp]
    type = FunctionAux
    variable = pellet_wall_temp
    function = pellet_wall_temp
  []
  [radial_heat_flux]
    type = FunctionAux
    variable = radial_heat_flux
    function = radial_heat_flux
  []
  [clad_inner_wall_temp]
    type = FunctionAux
    variable = clad_inner_wall_temp
    function = clad_inner_wall_temp
  []
[]

[BCs]
  [no_x_all]
    type = DirichletBC
    variable = disp_x
    boundary = 12
    value = 0.0
  []
  [no_y_fuel]
    type = DirichletBC
    variable = disp_y
    boundary = 20
    value = 0.0
  []
  [no_y_clad]
    type = DirichletBC
    variable = disp_y
    boundary = 1
    value = 0.0
  []
  [Pressure]
    [coolantPressure]
      boundary = '1 2 3'
      function = coolant_press_ramp
    []
    [plenumPressure]
      boundary = 9
      function = plenum_pressure
    []
  []
  [clad_outer_temp]
    type = FunctionDirichletBC
    boundary = '1 2 3'
    function = coolant_wall_temp
    variable = temperature
  []
  [pellet_to_clad_cooling]
    type = FunctionDirichletBC
    boundary = 10
    function = pellet_wall_temp
    variable = temperature
  []
[]

[NuclearMaterials]
  stress_free_temperature = 350
  initial_temperature = 350
  fission_operation = 'HighBurnup'
  add_variables = true
  physics = 'Mechanics Thermal'
  extra_vector_tags = 'ref'
  automatic_eigenstrain_names = true
  use_automatic_differentiation = true
  decomposition_method = TaylorExpansion
  [UN]
    [fuel]
      block = pellet
      density = ${density}
      atoms_heavy_metal_per_volume = ${atoms_heavy_metal_per_volume}
      fission_function = fission_func
      incremental = true
      strain = SMALL
      un_models = 'Burnup Elastic Creep Swelling ThermalExpansion'
      properties_to_output = 'youngs_modulus poissons_ratio'
      initial_porosity = 0.03
      porosity_function = porosity_ramp
      stress_free_temperature = 350
    []
  []
  [SS316]
    [clad]
      block = clad
      incremental = true
      strain = SMALL
      ss316_models = 'Elastic'
    []
  []
[]

[Preconditioning]
  [SMP]
    type = SMP
    full = true
  []
[]

[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 -ksp_gmres_restart'
  petsc_options_value = 'lu       superlu_dist                  51'
  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 = 35100000
  dtmin = 1
  dtmax = 2e6

  [Quadrature]
    order = fifth
    side_order = seventh
  []

  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 2e2
    time_t = ' 0   1e5 35e6 35100000'
    time_dt = '1e2 1e2 1e2  1e2'
    optimal_iterations = 10
    growth_factor = 2
    cutback_factor = 0.5
    iteration_window = 1
    linear_iteration_ratio = 100
  []
[]

[Postprocessors]
  [peak_burnup]
    type = ElementExtremeValue
    block = pellet
    value_type = max
    variable = burnup
  []

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

[PerformanceMetricOutputs]
  outputs = performance_metrics
[]

[Outputs]
  color = true
  exodus = true
  perf_graph = true
  [console]
    type = Console
    max_rows = 25
    time_step_interval =  1
    output_linear = true
  []
  [out]
    type = CSV
    show = 'peak_burnup'
  []
  [performance_metrics]
    type = CSV
    show = 'peak_burnup num_lin_it num_nonlin_it alive_time'
  []
[]

Description
Example Input Syntax
Input Parameters