MNVolumetricSwellingEigenstrain

Computes an eigenstrain due to volumetric swelling for UN (uranium mononitride) based on initial porosity and burnup.

Description

The MNVolumetricSwellingEigenstrain material model computes an eigenstrain tensor that accounts for volumetric swelling in uranium mononitride (UN). This correlation was developed for space nuclear power systems by Ross et al. (1990). The model computes the swelling increment by percent volume $var element = document.getElementById("moose-equation-2a803349-f809-42d8-bbf6-7a705eabe15e");katex.render("\\Delta V/V", element, {displayMode:false,throwOnError:false});$ (%): $var element = document.getElementById("moose-equation-5813be8b-e946-4c13-b352-926f5f020e1d");katex.render(" \\frac{\\Delta V}{V} = 4.7 \\times 10^{-11} T^{3.12} B^{0.83} \\phi^{0.5},", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-2a0c8a75-f34b-46c2-a412-29085131868f");katex.render("T", element, {displayMode:false,throwOnError:false});$ is the temperature (K), $var element = document.getElementById("moose-equation-ec8cbc7f-748b-4ff0-a2a8-a58caabc3cf4");katex.render("B", element, {displayMode:false,throwOnError:false});$ is the burnup (at.%), and $var element = document.getElementById("moose-equation-f2d6745c-d148-4f45-a418-1b48d65b8825");katex.render("\\phi", element, {displayMode:false,throwOnError:false});$ is the as-fabricated fuel density (% of theoretical). As specified in Ross et al. (1990), this swelling correlation is within $var element = document.getElementById("moose-equation-06611b3e-eb08-4260-937a-e57d44512ec2");katex.render("\\pm", element, {displayMode:false,throwOnError:false});$ 25\% of the data at burnups in excess of 1.12 a/o. However, the scatter of the data at lower burnups resulted in a deviation as high as $var element = document.getElementById("moose-equation-5a51fed4-bb4d-407e-8e09-a43c224b3513");katex.render("\\pm", element, {displayMode:false,throwOnError:false});$ 60\%. Note also that the original formulation is for the average temperature. The correlation was developed for an as-fabricated fuel density ranging from 90 to 98% of theoretical, a volume averaged fuel temperature ranging from 1200 to 1600 K, and a fuel burnup ranging from 0.05 to 4.58 at% Ross et al. (1990).

Example Input Syntax

[Materials<<<{"href": "../../../syntax/Materials/index.html"}>>>]
  [swelling]
    type = ADMNVolumetricSwellingEigenstrain<<<{"description": "Computes an eigenstrain due to volumetric swelling for UN (uranium mononitride) based on initial porosity and burnup.", "href": "MNVolumetricSwellingEigenstrain.html"}>>>
    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."}>>> = swelling
    temperature<<<{"description": "Coupled temperature (K)"}>>> = temp
    initial_porosity<<<{"description": "Initial (as-fabricated) fuel porosity (dimensionless)"}>>> = ${as_fabricated_porosity}
    burnup<<<{"description": "Coupled burnup material property."}>>> = burnup
    outputs<<<{"description": "Vector of output names where you would like to restrict the output of variables(s) associated with this object"}>>> = all
  []
[]

The eigenstrain name must also be passed to the strain calculator as shown below:

[Physics<<<{"href": "../../../syntax/Physics/index.html"}>>>]
  [SolidMechanics<<<{"href": "../../../syntax/Physics/SolidMechanics/index.html"}>>>]
    [QuasiStatic<<<{"href": "../../../syntax/Physics/SolidMechanics/QuasiStatic/index.html"}>>>]
      [all]
        strain<<<{"description": "Strain formulation"}>>> = SMALL
        decomposition_method<<<{"description": "Methods to calculate the finite strain and rotation increments"}>>> = EigenSolution
        add_variables<<<{"description": "Add the displacement variables"}>>> = true
        eigenstrain_names<<<{"description": "List of eigenstrains to be applied in this strain calculation"}>>> = swelling
        use_automatic_differentiation<<<{"description": "Flag to use automatic differentiation (AD) objects when possible"}>>> = true
      []
    []
  []
[]

Input Parameters

eigenstrain_nameMaterial property name for the eigenstrain tensor computed by this model. IMPORTANT: The name of this property must also be provided to the strain calculator.
C++ Type:std::string
Controllable:No
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.
temperatureCoupled temperature (K)
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Coupled temperature (K)

Required Parameters

base_nameOptional parameter that allows the user to define multiple mechanics material systems on the same block, i.e. for multiple phases
C++ Type:std::string
Controllable:No
Description:Optional parameter that allows the user to define multiple mechanics material systems on the same block, i.e. for multiple phases
blockThe list of blocks (ids or names) that this object will be applied
C++ Type:std::vector<SubdomainName>
Controllable:No
Description:The list of blocks (ids or names) that this object will be applied
boundaryThe list of boundaries (ids or names) from the mesh where this object applies
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:The list of boundaries (ids or names) from the mesh where this object applies
burnupburnupCoupled burnup material property.
Default:burnup
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:Coupled burnup material property.
computeTrueWhen false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
Default:True
C++ Type:bool
Controllable:No
Description:When false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
constant_onNONEWhen ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
Default:NONE
C++ Type:MooseEnum
Options:NONE, ELEMENT, SUBDOMAIN
Controllable:No
Description:When ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
declare_suffixAn optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:An optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.
initial_porosity0.05Initial (as-fabricated) fuel porosity (dimensionless)
Default:0.05
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Initial (as-fabricated) fuel porosity (dimensionless)

Optional 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.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:Yes
Description:Set the enabled status of the MooseObject.
implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Controllable:No
Description:Determines whether this object is calculated using an implicit or explicit form
seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Controllable:No
Description:The seed for the master random number generator
use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:False
C++ Type:bool
Controllable:No
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

Advanced Parameters

output_propertiesList of material properties, from this material, to output (outputs must also be defined to an output type)
C++ Type:std::vector<std::string>
Controllable:No
Description:List of material properties, from this material, to output (outputs must also be defined to an output type)
outputsnone Vector of output names where you would like to restrict the output of variables(s) associated with this object
Default:none
C++ Type:std::vector<OutputName>
Controllable:No
Description:Vector of output names where you would like to restrict the output of variables(s) associated with this object

Outputs Parameters

prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
use_interpolated_stateFalseFor the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.
Default:False
C++ Type:bool
Controllable:No
Description:For the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.

Material Property Retrieval Parameters

Input Files

(test/tests/solid_mechanics/mn_volumetric_swelling/exact.i)
(assessment/nitride/EBRII/K4/analysis/base.i)

References

Steven B. Ross, Mohamed S. El-Genk, and R.Bruce Matthews. Uranium nitride fuel swelling correlation. Journal of Nuclear Materials, 170(2):169 – 177, 1990. URL: http://www.sciencedirect.com/science/article/pii/002231159090409G, doi:https://doi.org/10.1016/0022-3115(90)90409-G.

@ARTICLE{ross1990,
    author = "Ross, Steven B. and El-Genk, Mohamed S. and Matthews, R.Bruce",
    title = "Uranium nitride fuel swelling correlation",
    journal = "Journal of Nuclear Materials",
    volume = "170",
    number = "2",
    pages = "169 - 177",
    year = "1990",
    issn = "0022-3115",
    doi = "https://doi.org/10.1016/0022-3115(90)90409-G",
    url = "http://www.sciencedirect.com/science/article/pii/002231159090409G"
}

(test/tests/solid_mechanics/mn_volumetric_swelling/exact.i)

# This tests ADMNVolumetricSwellingEigenstrain due to changing temperature, porosity, and burnup.
# Exact solution is calculated as a function in the input file.

as_fabricated_porosity = 0.07

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
[]

[Mesh]
  use_displaced_mesh = false
  [gen]
    type = ExamplePatchMeshGenerator
    dim = 3
  []
[]

[AuxVariables]
  [temp]
  []
  [volumetric_strain]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [temp_ramp]
    type = PiecewiseLinear
    x = '0 1'
    y = '500 1100' # The model changes at 700 C, so bracket it.
  []
  [burnup_ramp]
    type = PiecewiseLinear
    x = '0 1'
    y = '0 0.1'
  []
[]

[AuxKernels]
  [temp_aux]
    type = FunctionAux
    variable = temp
    function = temp_ramp
  []
  [volumetric_strain]
    type = ADRankTwoScalarAux
    rank_two_tensor = total_strain
    variable = volumetric_strain
    scalar_type = VolumetricStrain
  []
[]

[Physics/SolidMechanics/QuasiStatic/all]
  strain = SMALL
  decomposition_method = EigenSolution
  add_variables = true
  eigenstrain_names = swelling
  use_automatic_differentiation = true
[]

[BCs]
  [left]
    type = ADDirichletBC
    variable = disp_x
    value = 0
    boundary = left
  []
  [bottom]
    type = ADDirichletBC
    variable = disp_y
    value = 0
    boundary = bottom
  []
  [back]
    type = ADDirichletBC
    variable = disp_z
    value = 0
    boundary = back
  []
[]

[Materials]
  [elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    youngs_modulus = 1
    poissons_ratio = 0.3
  []
  [swelling]
    type = ADMNVolumetricSwellingEigenstrain
    eigenstrain_name = swelling
    temperature = temp
    initial_porosity = ${as_fabricated_porosity}
    burnup = burnup
    outputs = all
  []
  [stress]
    type = ADComputeLinearElasticStress
  []
  [burnup]
    type = ADGenericFunctionMaterial
    prop_names = 'burnup'
    prop_values = 'burnup_ramp'
    outputs = all
  []
[]

[Executioner]
  type = Transient
  num_steps = 10
  dt = 0.1
[]

[Postprocessors]
  [temp]
    type = ElementAverageValue
    variable = temp
  []
  [burnup_avg]
    type = ElementAverageValue
    variable = burnup
  []
  [volumetric_strain]
    type = ElementAverageValue
    variable = volumetric_strain
  []
  [swelling_exact]
    type = ParsedPostprocessor
    pp_names = 'temp burnup_avg '
    expression = '4.7e-11 * temp^3.12 * (burnup_avg * 100)^0.83 * (100.0 * (1.0 - ${as_fabricated_porosity}))^0.5 / 100.0'
  []
  [swelling_diff]
    type = ParsedPostprocessor
    pp_names = 'volumetric_strain swelling_exact'
    expression = '(volumetric_strain - swelling_exact) / swelling_exact'
    outputs = none
  []
  [swelling_max_diff]
    type = TimeExtremeValue
    postprocessor = swelling_diff
    value_type = abs_max
  []
[]

[Outputs]
  csv = true
[]

(test/tests/solid_mechanics/mn_volumetric_swelling/exact.i)

# This tests ADMNVolumetricSwellingEigenstrain due to changing temperature, porosity, and burnup.
# Exact solution is calculated as a function in the input file.

as_fabricated_porosity = 0.07

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
[]

[Mesh]
  use_displaced_mesh = false
  [gen]
    type = ExamplePatchMeshGenerator
    dim = 3
  []
[]

[AuxVariables]
  [temp]
  []
  [volumetric_strain]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [temp_ramp]
    type = PiecewiseLinear
    x = '0 1'
    y = '500 1100' # The model changes at 700 C, so bracket it.
  []
  [burnup_ramp]
    type = PiecewiseLinear
    x = '0 1'
    y = '0 0.1'
  []
[]

[AuxKernels]
  [temp_aux]
    type = FunctionAux
    variable = temp
    function = temp_ramp
  []
  [volumetric_strain]
    type = ADRankTwoScalarAux
    rank_two_tensor = total_strain
    variable = volumetric_strain
    scalar_type = VolumetricStrain
  []
[]

[Physics/SolidMechanics/QuasiStatic/all]
  strain = SMALL
  decomposition_method = EigenSolution
  add_variables = true
  eigenstrain_names = swelling
  use_automatic_differentiation = true
[]

[BCs]
  [left]
    type = ADDirichletBC
    variable = disp_x
    value = 0
    boundary = left
  []
  [bottom]
    type = ADDirichletBC
    variable = disp_y
    value = 0
    boundary = bottom
  []
  [back]
    type = ADDirichletBC
    variable = disp_z
    value = 0
    boundary = back
  []
[]

[Materials]
  [elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    youngs_modulus = 1
    poissons_ratio = 0.3
  []
  [swelling]
    type = ADMNVolumetricSwellingEigenstrain
    eigenstrain_name = swelling
    temperature = temp
    initial_porosity = ${as_fabricated_porosity}
    burnup = burnup
    outputs = all
  []
  [stress]
    type = ADComputeLinearElasticStress
  []
  [burnup]
    type = ADGenericFunctionMaterial
    prop_names = 'burnup'
    prop_values = 'burnup_ramp'
    outputs = all
  []
[]

[Executioner]
  type = Transient
  num_steps = 10
  dt = 0.1
[]

[Postprocessors]
  [temp]
    type = ElementAverageValue
    variable = temp
  []
  [burnup_avg]
    type = ElementAverageValue
    variable = burnup
  []
  [volumetric_strain]
    type = ElementAverageValue
    variable = volumetric_strain
  []
  [swelling_exact]
    type = ParsedPostprocessor
    pp_names = 'temp burnup_avg '
    expression = '4.7e-11 * temp^3.12 * (burnup_avg * 100)^0.83 * (100.0 * (1.0 - ${as_fabricated_porosity}))^0.5 / 100.0'
  []
  [swelling_diff]
    type = ParsedPostprocessor
    pp_names = 'volumetric_strain swelling_exact'
    expression = '(volumetric_strain - swelling_exact) / swelling_exact'
    outputs = none
  []
  [swelling_max_diff]
    type = TimeExtremeValue
    postprocessor = swelling_diff
    value_type = abs_max
  []
[]

[Outputs]
  csv = true
[]

(test/tests/solid_mechanics/mn_volumetric_swelling/exact.i)

# This tests ADMNVolumetricSwellingEigenstrain due to changing temperature, porosity, and burnup.
# Exact solution is calculated as a function in the input file.

as_fabricated_porosity = 0.07

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
[]

[Mesh]
  use_displaced_mesh = false
  [gen]
    type = ExamplePatchMeshGenerator
    dim = 3
  []
[]

[AuxVariables]
  [temp]
  []
  [volumetric_strain]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [temp_ramp]
    type = PiecewiseLinear
    x = '0 1'
    y = '500 1100' # The model changes at 700 C, so bracket it.
  []
  [burnup_ramp]
    type = PiecewiseLinear
    x = '0 1'
    y = '0 0.1'
  []
[]

[AuxKernels]
  [temp_aux]
    type = FunctionAux
    variable = temp
    function = temp_ramp
  []
  [volumetric_strain]
    type = ADRankTwoScalarAux
    rank_two_tensor = total_strain
    variable = volumetric_strain
    scalar_type = VolumetricStrain
  []
[]

[Physics/SolidMechanics/QuasiStatic/all]
  strain = SMALL
  decomposition_method = EigenSolution
  add_variables = true
  eigenstrain_names = swelling
  use_automatic_differentiation = true
[]

[BCs]
  [left]
    type = ADDirichletBC
    variable = disp_x
    value = 0
    boundary = left
  []
  [bottom]
    type = ADDirichletBC
    variable = disp_y
    value = 0
    boundary = bottom
  []
  [back]
    type = ADDirichletBC
    variable = disp_z
    value = 0
    boundary = back
  []
[]

[Materials]
  [elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    youngs_modulus = 1
    poissons_ratio = 0.3
  []
  [swelling]
    type = ADMNVolumetricSwellingEigenstrain
    eigenstrain_name = swelling
    temperature = temp
    initial_porosity = ${as_fabricated_porosity}
    burnup = burnup
    outputs = all
  []
  [stress]
    type = ADComputeLinearElasticStress
  []
  [burnup]
    type = ADGenericFunctionMaterial
    prop_names = 'burnup'
    prop_values = 'burnup_ramp'
    outputs = all
  []
[]

[Executioner]
  type = Transient
  num_steps = 10
  dt = 0.1
[]

[Postprocessors]
  [temp]
    type = ElementAverageValue
    variable = temp
  []
  [burnup_avg]
    type = ElementAverageValue
    variable = burnup
  []
  [volumetric_strain]
    type = ElementAverageValue
    variable = volumetric_strain
  []
  [swelling_exact]
    type = ParsedPostprocessor
    pp_names = 'temp burnup_avg '
    expression = '4.7e-11 * temp^3.12 * (burnup_avg * 100)^0.83 * (100.0 * (1.0 - ${as_fabricated_porosity}))^0.5 / 100.0'
  []
  [swelling_diff]
    type = ParsedPostprocessor
    pp_names = 'volumetric_strain swelling_exact'
    expression = '(volumetric_strain - swelling_exact) / swelling_exact'
    outputs = none
  []
  [swelling_max_diff]
    type = TimeExtremeValue
    postprocessor = swelling_diff
    value_type = abs_max
  []
[]

[Outputs]
  csv = true
[]

(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'
  []
[]

Description
Example Input Syntax
Input Parameters
Input Files
References