UPuZrAnisotropicSwellingEigenstrain

Accounts for the anisotropic swelling effect in UPuZr metal fuel.

Description

This model, UPuZrAnisotropicSwellingEigenstrain, computes a anisotropic strain based on the model originally proposed by Ogata and Yokoo (1999). The strain is computed based on an empirically derived anisotropy factor $var element = document.getElementById("moose-equation-91ceeaf4-ebbc-4817-8d54-d04de1a00540");katex.render("f_{crack}", element, {displayMode:false,throwOnError:false});$ which has been calibrated to a specific set of experimental data. Once that value is determined the radial eigenstrain imposed on the fuel is calculated as $var element = document.getElementById("moose-equation-925b2108-983b-43a1-b997-5f966fc84e7b");katex.render("\\varepsilon = \\ln \\left( f_{crack} \\frac{r_o^{gap}}{r_o^{fuel}} \\right)", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-e7279a1c-904b-49f1-82cc-468c57008200");katex.render("r_o^{gap}", element, {displayMode:false,throwOnError:false});$ is the initial gap between the clad and fuel and $var element = document.getElementById("moose-equation-3546dd14-7685-4fc9-a216-aab25fcd9bc8");katex.render("r_o^{fuel}", element, {displayMode:false,throwOnError:false});$ is the as-fabricated cold radius of pellet, both in meters.

Example Input Syntax

[Materials<<<{"href": "../../../syntax/Materials/index.html"}>>>]
  [fuel_anisotropic_swelling_strain]
    type = UPuZrAnisotropicSwellingEigenstrain<<<{"description": "Accounts for the anisotropic swelling effect in UPuZr metal fuel.", "href": "UPuZrAnisotropicSwellingEigenstrain.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = fuel
    fuel_pin_geometry<<<{"description": "Name of the UserObject that reads the pin geometry from the mesh."}>>> = fuel_pin_geometry
    anisotropy_factor<<<{"description": "Anisotropy factor as obtained from calibration plot"}>>> = 0.50
    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_anisotropic_swelling_strain
  []
[]

The eigenstrain name must also be passed to the strain calculator, and an example parameter setting is shown below:

[Physics<<<{"href": "../../../syntax/Physics/index.html"}>>>]
  [SolidMechanics<<<{"href": "../../../syntax/Physics/SolidMechanics/index.html"}>>>]
    [Layered1D<<<{"href": "../../../syntax/Physics/SolidMechanics/Layered1D/index.html"}>>>]
      [gps_fuel]
        add_scalar_variables<<<{"description": "Add the scalar_out_of_plane_strain variables."}>>> = true
        add_variables<<<{"description": "Add the displacement variables"}>>> = true
        out_of_plane_strain_name<<<{"description": "Name provided by user for aux variable to gather scalar_out_of_plane_strains."}>>> = strain_yy
        fuel_pin_geometry<<<{"description": "User object name which provides subblock index."}>>> = fuel_pin_geometry
        strain<<<{"description": "Strain formulation"}>>> = finite
        block<<<{"description": "The list of ids of the blocks (subdomain) that the stress divergence kernels will be applied to"}>>> = fuel
        eigenstrain_names<<<{"description": "List of eigenstrains to be applied in this strain calculation"}>>> = 'fuel_anisotropic_swelling_strain'
        decomposition_method<<<{"description": "Methods to calculate the finite strain and rotation increments"}>>> = EigenSolution
        mesh_generator<<<{"description": "The name of the generator to use as the prefix for mesh meta data properties."}>>> = layered1D_mesh
      []
    []
  []
[]

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.

Required Parameters

anisotropy_factor0Anisotropy factor as obtained from calibration plot
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Anisotropy factor as obtained from calibration plot
axial_directionyCoordinate axis of the axial direction of the fuel stack (0, 1, or 2 for x, y, or z
Default:y
C++ Type:MooseEnum
Options:x, y, z
Controllable:No
Description:Coordinate axis of the axial direction of the fuel stack (0, 1, or 2 for x, y, or z
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
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.
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.
pellet_diameterAs fabricated cold diameter of pellet in meters
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:As fabricated cold diameter of pellet in meters

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/anisotropic_swelling/anisotropic_swelling_eigenstrain.i)

References

T. Ogata and T. Yokoo. Devlopment and Validation of ALFUS: An Irradiation Behavior Analysis Code for Metallic Fast Reactor Fuels. Journal of Nuclear Technology, 128(1):113–123, 1999.

@article{ogata1999,
    author = "Ogata, T. and Yokoo, T.",
    title = "{D}evlopment and {V}alidation of {ALFUS}: {A}n {I}rradiation {B}ehavior {A}nalysis {C}ode for {M}etallic {F}ast {R}eactor {F}uels",
    journal = "Journal of Nuclear Technology",
    volume = "128",
    number = "1",
    pages = "113-123",
    year = "1999"
}

(test/tests/anisotropic_swelling/anisotropic_swelling_eigenstrain.i)

# The purpose of this test is to verify the calculation of the eigenstrain
# applied to the fuel to represent an anisotropic swelling behavior observed
# in metal fuels. The eigenstrain is used to move the outer radius of the fuel
# to close the fuel/cladding gap a specific amount to account for the
# anisotropic swelling. An anisotropy factor is used to determine the fraction
# of the initial fuel/cladding gap to remove via this eigenstrain. This
# empirical factor is determined from a curve fit of experimental data
# provided in a plot from a paper by Ogata and Yokoo. The initial
# implementation of this capability is being done using a 1.5D model for
# simplicity.
#
# The eigenstrain is calculated as:
#
# epsilon = ln (1.0 + delta_r / pellet_outer_radius)
#
# where delta_r = anisotropy_factor * clad_gap_width
#
# In this model the clad_gap_width is 3.50e-4 (350 microns) and the
# pellet_outer_radius is 2.0e-3 (2 mm). The anisotropy_factor for UZr fuel is
# taken as 0.5. Therefore, the anisotropic_swelling_eigenstrain is
#
# epsilon = ln (1.0 + 0.5 * 3.5e-4 / 2.0e-3)
#
# epsilon = 8.388148e-2
#
# The resulting displacement of the fuel closes the fuel/cladding gap from 350
# microns to 175 microns.
#
# These results are verified by Postprocessor output of the relevant
# quantities (anisotropic swelling strain, clad/fuel gap and the displacemnet
# of the fuel outer node).

[GlobalParams]
  order = FIRST
  family = LAGRANGE
  displacements = disp_x
  temperature = temperature
[]

[Mesh]
  coord_type = RZ
  [layered1D_mesh]
    type = Layered1DMeshGenerator
    slices_per_block = 1
    clad_gap_width = 3.5e-4
    clad_thickness = 3.8e-4
    fuel_height = 0.1
    include_clad = true
    include_plenum = false
    pellet_outer_radius = 2.0e-3
    elem_type = EDGE2
    pellet_mesh_density = 'customize'
    clad_mesh_density = 'customize'
    nx_p = 1
    nx_c = 1
  []
  patch_update_strategy = auto
  partitioner = centroid
  centroid_partitioner_direction = y
[]

[Variables]
  [temperature]
    order = FIRST
    family = LAGRANGE
    initial_condition = 580
  []
[]

[AuxVariables]
  [disp_y]
  []
  [disp_z]
  []
  [stress_xx]
    order = CONSTANT
    family = MONOMIAL
  []
  [strain_xx]
    order = CONSTANT
    family = MONOMIAL
  []
  [strain_zz]
    order = CONSTANT
    family = MONOMIAL
  []
  [anisotropic_swelling_strain]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = temperature
  []
[]

[Physics]
  [SolidMechanics]
    [Layered1D]
      [gps_fuel]
        add_scalar_variables = true
        add_variables = true
        out_of_plane_strain_name = strain_yy
        fuel_pin_geometry = fuel_pin_geometry
        strain = finite
        block = fuel
        eigenstrain_names = 'fuel_anisotropic_swelling_strain'
        decomposition_method = EigenSolution
        mesh_generator = layered1D_mesh
      []
      [gps_clad]
        add_scalar_variables = true
        add_variables = true
        out_of_plane_strain_name = strain_yy
        fuel_pin_geometry = fuel_pin_geometry
        strain = finite
        block = clad
        decomposition_method = EigenSolution
        mesh_generator = layered1D_mesh
      []
    []
  []
[]

[AuxKernels]
  [stress_xx]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_xx
    index_i = 0
    index_j = 0
    execute_on = timestep_end
  []
  [anisotropic_swelling_strain]
    type = MaterialRealAux
    variable = anisotropic_swelling_strain
    block = fuel
    property = anisotropic_swelling_strain
    execute_on = timestep_end
  []
  [strain_xx]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = strain_xx
    index_i = 0
    index_j = 0
    execute_on = timestep_end
  []
  [strain_zz]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = strain_zz
    index_i = 2
    index_j = 2
    execute_on = timestep_end
  []
[]

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

[BCs]
  [temperature]
    type = DirichletBC
    boundary = '12 2'
    variable = temperature
    value = 580
  []
  [no_x_all]
    type = DirichletBC
    variable = disp_x
    boundary = 12
    value = 0.0
  []
[]

[Materials]
  [porotiy]
    type = GenericConstantMaterial
    block = fuel
    prop_names = porosity
    prop_values = 0.0
  []
  [fuel_thermal]
    type = HeatConductionMaterial
    block = fuel
    thermal_conductivity = 1.0
    specific_heat = 1.0
  []
  [fuel_elasticity_tensor]
    type = UPuZrElasticityTensor
    block = fuel
    X_Zr = 0.0
    X_Pu = 0.0
  []
  [fuel_stress]
    type = ComputeFiniteStrainElasticStress
    block = fuel
  []
  [fuel_anisotropic_swelling_strain]
    type = UPuZrAnisotropicSwellingEigenstrain
    block = fuel
    fuel_pin_geometry = fuel_pin_geometry
    anisotropy_factor = 0.50
    eigenstrain_name = fuel_anisotropic_swelling_strain
  []
  [clad_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = clad
    youngs_modulus = 7.5e10
    poissons_ratio = 0.3
  []
  [clad_stress]
    type = ComputeFiniteStrainElasticStress
    block = clad
  []
  [clad_thermal]
    type = HeatConductionMaterial
    block = clad
    thermal_conductivity = 16.0
    specific_heat = 330.0
  []
[]

[UserObjects]
  [fuel_pin_geometry]
    type = Layered1DFuelPinGeometry
    mesh_generator = layered1D_mesh
  []
[]

[Postprocessors]
  [_dt]
    type = TimestepSize
  []
  [aniso_swelling_strain]
    type = ElementAverageValue
    variable = anisotropic_swelling_strain
    block = fuel
    execute_on = 'initial timestep_end'
  []
  [clad_fuel_gap]
    type = NodalExtremeValue
    variable = penetration
    boundary = 10
    execute_on = 'initial timestep_end'
  []
  [disp_fuel_outer_node]
    type = NodalVariableValue
    variable = disp_x
    nodeid = 3
  []
[]

[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 = 25
  nl_rel_tol = 1e-6
  nl_abs_tol = 1e-8
  start_time = 0
  n_startup_steps = 1
  end_time = 6.0e2
  num_steps = 5000
  dtmax = 1e6
  dtmin = 1

  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 2e2
    optimal_iterations = 8
    iteration_window = 2
    linear_iteration_ratio = 100
    growth_factor = 2
    cutback_factor = .5
  []
[]

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

(test/tests/anisotropic_swelling/anisotropic_swelling_eigenstrain.i)

# The purpose of this test is to verify the calculation of the eigenstrain
# applied to the fuel to represent an anisotropic swelling behavior observed
# in metal fuels. The eigenstrain is used to move the outer radius of the fuel
# to close the fuel/cladding gap a specific amount to account for the
# anisotropic swelling. An anisotropy factor is used to determine the fraction
# of the initial fuel/cladding gap to remove via this eigenstrain. This
# empirical factor is determined from a curve fit of experimental data
# provided in a plot from a paper by Ogata and Yokoo. The initial
# implementation of this capability is being done using a 1.5D model for
# simplicity.
#
# The eigenstrain is calculated as:
#
# epsilon = ln (1.0 + delta_r / pellet_outer_radius)
#
# where delta_r = anisotropy_factor * clad_gap_width
#
# In this model the clad_gap_width is 3.50e-4 (350 microns) and the
# pellet_outer_radius is 2.0e-3 (2 mm). The anisotropy_factor for UZr fuel is
# taken as 0.5. Therefore, the anisotropic_swelling_eigenstrain is
#
# epsilon = ln (1.0 + 0.5 * 3.5e-4 / 2.0e-3)
#
# epsilon = 8.388148e-2
#
# The resulting displacement of the fuel closes the fuel/cladding gap from 350
# microns to 175 microns.
#
# These results are verified by Postprocessor output of the relevant
# quantities (anisotropic swelling strain, clad/fuel gap and the displacemnet
# of the fuel outer node).

[GlobalParams]
  order = FIRST
  family = LAGRANGE
  displacements = disp_x
  temperature = temperature
[]

[Mesh]
  coord_type = RZ
  [layered1D_mesh]
    type = Layered1DMeshGenerator
    slices_per_block = 1
    clad_gap_width = 3.5e-4
    clad_thickness = 3.8e-4
    fuel_height = 0.1
    include_clad = true
    include_plenum = false
    pellet_outer_radius = 2.0e-3
    elem_type = EDGE2
    pellet_mesh_density = 'customize'
    clad_mesh_density = 'customize'
    nx_p = 1
    nx_c = 1
  []
  patch_update_strategy = auto
  partitioner = centroid
  centroid_partitioner_direction = y
[]

[Variables]
  [temperature]
    order = FIRST
    family = LAGRANGE
    initial_condition = 580
  []
[]

[AuxVariables]
  [disp_y]
  []
  [disp_z]
  []
  [stress_xx]
    order = CONSTANT
    family = MONOMIAL
  []
  [strain_xx]
    order = CONSTANT
    family = MONOMIAL
  []
  [strain_zz]
    order = CONSTANT
    family = MONOMIAL
  []
  [anisotropic_swelling_strain]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = temperature
  []
[]

[Physics]
  [SolidMechanics]
    [Layered1D]
      [gps_fuel]
        add_scalar_variables = true
        add_variables = true
        out_of_plane_strain_name = strain_yy
        fuel_pin_geometry = fuel_pin_geometry
        strain = finite
        block = fuel
        eigenstrain_names = 'fuel_anisotropic_swelling_strain'
        decomposition_method = EigenSolution
        mesh_generator = layered1D_mesh
      []
      [gps_clad]
        add_scalar_variables = true
        add_variables = true
        out_of_plane_strain_name = strain_yy
        fuel_pin_geometry = fuel_pin_geometry
        strain = finite
        block = clad
        decomposition_method = EigenSolution
        mesh_generator = layered1D_mesh
      []
    []
  []
[]

[AuxKernels]
  [stress_xx]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_xx
    index_i = 0
    index_j = 0
    execute_on = timestep_end
  []
  [anisotropic_swelling_strain]
    type = MaterialRealAux
    variable = anisotropic_swelling_strain
    block = fuel
    property = anisotropic_swelling_strain
    execute_on = timestep_end
  []
  [strain_xx]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = strain_xx
    index_i = 0
    index_j = 0
    execute_on = timestep_end
  []
  [strain_zz]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = strain_zz
    index_i = 2
    index_j = 2
    execute_on = timestep_end
  []
[]

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

[BCs]
  [temperature]
    type = DirichletBC
    boundary = '12 2'
    variable = temperature
    value = 580
  []
  [no_x_all]
    type = DirichletBC
    variable = disp_x
    boundary = 12
    value = 0.0
  []
[]

[Materials]
  [porotiy]
    type = GenericConstantMaterial
    block = fuel
    prop_names = porosity
    prop_values = 0.0
  []
  [fuel_thermal]
    type = HeatConductionMaterial
    block = fuel
    thermal_conductivity = 1.0
    specific_heat = 1.0
  []
  [fuel_elasticity_tensor]
    type = UPuZrElasticityTensor
    block = fuel
    X_Zr = 0.0
    X_Pu = 0.0
  []
  [fuel_stress]
    type = ComputeFiniteStrainElasticStress
    block = fuel
  []
  [fuel_anisotropic_swelling_strain]
    type = UPuZrAnisotropicSwellingEigenstrain
    block = fuel
    fuel_pin_geometry = fuel_pin_geometry
    anisotropy_factor = 0.50
    eigenstrain_name = fuel_anisotropic_swelling_strain
  []
  [clad_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = clad
    youngs_modulus = 7.5e10
    poissons_ratio = 0.3
  []
  [clad_stress]
    type = ComputeFiniteStrainElasticStress
    block = clad
  []
  [clad_thermal]
    type = HeatConductionMaterial
    block = clad
    thermal_conductivity = 16.0
    specific_heat = 330.0
  []
[]

[UserObjects]
  [fuel_pin_geometry]
    type = Layered1DFuelPinGeometry
    mesh_generator = layered1D_mesh
  []
[]

[Postprocessors]
  [_dt]
    type = TimestepSize
  []
  [aniso_swelling_strain]
    type = ElementAverageValue
    variable = anisotropic_swelling_strain
    block = fuel
    execute_on = 'initial timestep_end'
  []
  [clad_fuel_gap]
    type = NodalExtremeValue
    variable = penetration
    boundary = 10
    execute_on = 'initial timestep_end'
  []
  [disp_fuel_outer_node]
    type = NodalVariableValue
    variable = disp_x
    nodeid = 3
  []
[]

[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 = 25
  nl_rel_tol = 1e-6
  nl_abs_tol = 1e-8
  start_time = 0
  n_startup_steps = 1
  end_time = 6.0e2
  num_steps = 5000
  dtmax = 1e6
  dtmin = 1

  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 2e2
    optimal_iterations = 8
    iteration_window = 2
    linear_iteration_ratio = 100
    growth_factor = 2
    cutback_factor = .5
  []
[]

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

(test/tests/anisotropic_swelling/anisotropic_swelling_eigenstrain.i)

# The purpose of this test is to verify the calculation of the eigenstrain
# applied to the fuel to represent an anisotropic swelling behavior observed
# in metal fuels. The eigenstrain is used to move the outer radius of the fuel
# to close the fuel/cladding gap a specific amount to account for the
# anisotropic swelling. An anisotropy factor is used to determine the fraction
# of the initial fuel/cladding gap to remove via this eigenstrain. This
# empirical factor is determined from a curve fit of experimental data
# provided in a plot from a paper by Ogata and Yokoo. The initial
# implementation of this capability is being done using a 1.5D model for
# simplicity.
#
# The eigenstrain is calculated as:
#
# epsilon = ln (1.0 + delta_r / pellet_outer_radius)
#
# where delta_r = anisotropy_factor * clad_gap_width
#
# In this model the clad_gap_width is 3.50e-4 (350 microns) and the
# pellet_outer_radius is 2.0e-3 (2 mm). The anisotropy_factor for UZr fuel is
# taken as 0.5. Therefore, the anisotropic_swelling_eigenstrain is
#
# epsilon = ln (1.0 + 0.5 * 3.5e-4 / 2.0e-3)
#
# epsilon = 8.388148e-2
#
# The resulting displacement of the fuel closes the fuel/cladding gap from 350
# microns to 175 microns.
#
# These results are verified by Postprocessor output of the relevant
# quantities (anisotropic swelling strain, clad/fuel gap and the displacemnet
# of the fuel outer node).

[GlobalParams]
  order = FIRST
  family = LAGRANGE
  displacements = disp_x
  temperature = temperature
[]

[Mesh]
  coord_type = RZ
  [layered1D_mesh]
    type = Layered1DMeshGenerator
    slices_per_block = 1
    clad_gap_width = 3.5e-4
    clad_thickness = 3.8e-4
    fuel_height = 0.1
    include_clad = true
    include_plenum = false
    pellet_outer_radius = 2.0e-3
    elem_type = EDGE2
    pellet_mesh_density = 'customize'
    clad_mesh_density = 'customize'
    nx_p = 1
    nx_c = 1
  []
  patch_update_strategy = auto
  partitioner = centroid
  centroid_partitioner_direction = y
[]

[Variables]
  [temperature]
    order = FIRST
    family = LAGRANGE
    initial_condition = 580
  []
[]

[AuxVariables]
  [disp_y]
  []
  [disp_z]
  []
  [stress_xx]
    order = CONSTANT
    family = MONOMIAL
  []
  [strain_xx]
    order = CONSTANT
    family = MONOMIAL
  []
  [strain_zz]
    order = CONSTANT
    family = MONOMIAL
  []
  [anisotropic_swelling_strain]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = temperature
  []
[]

[Physics]
  [SolidMechanics]
    [Layered1D]
      [gps_fuel]
        add_scalar_variables = true
        add_variables = true
        out_of_plane_strain_name = strain_yy
        fuel_pin_geometry = fuel_pin_geometry
        strain = finite
        block = fuel
        eigenstrain_names = 'fuel_anisotropic_swelling_strain'
        decomposition_method = EigenSolution
        mesh_generator = layered1D_mesh
      []
      [gps_clad]
        add_scalar_variables = true
        add_variables = true
        out_of_plane_strain_name = strain_yy
        fuel_pin_geometry = fuel_pin_geometry
        strain = finite
        block = clad
        decomposition_method = EigenSolution
        mesh_generator = layered1D_mesh
      []
    []
  []
[]

[AuxKernels]
  [stress_xx]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_xx
    index_i = 0
    index_j = 0
    execute_on = timestep_end
  []
  [anisotropic_swelling_strain]
    type = MaterialRealAux
    variable = anisotropic_swelling_strain
    block = fuel
    property = anisotropic_swelling_strain
    execute_on = timestep_end
  []
  [strain_xx]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = strain_xx
    index_i = 0
    index_j = 0
    execute_on = timestep_end
  []
  [strain_zz]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = strain_zz
    index_i = 2
    index_j = 2
    execute_on = timestep_end
  []
[]

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

[BCs]
  [temperature]
    type = DirichletBC
    boundary = '12 2'
    variable = temperature
    value = 580
  []
  [no_x_all]
    type = DirichletBC
    variable = disp_x
    boundary = 12
    value = 0.0
  []
[]

[Materials]
  [porotiy]
    type = GenericConstantMaterial
    block = fuel
    prop_names = porosity
    prop_values = 0.0
  []
  [fuel_thermal]
    type = HeatConductionMaterial
    block = fuel
    thermal_conductivity = 1.0
    specific_heat = 1.0
  []
  [fuel_elasticity_tensor]
    type = UPuZrElasticityTensor
    block = fuel
    X_Zr = 0.0
    X_Pu = 0.0
  []
  [fuel_stress]
    type = ComputeFiniteStrainElasticStress
    block = fuel
  []
  [fuel_anisotropic_swelling_strain]
    type = UPuZrAnisotropicSwellingEigenstrain
    block = fuel
    fuel_pin_geometry = fuel_pin_geometry
    anisotropy_factor = 0.50
    eigenstrain_name = fuel_anisotropic_swelling_strain
  []
  [clad_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = clad
    youngs_modulus = 7.5e10
    poissons_ratio = 0.3
  []
  [clad_stress]
    type = ComputeFiniteStrainElasticStress
    block = clad
  []
  [clad_thermal]
    type = HeatConductionMaterial
    block = clad
    thermal_conductivity = 16.0
    specific_heat = 330.0
  []
[]

[UserObjects]
  [fuel_pin_geometry]
    type = Layered1DFuelPinGeometry
    mesh_generator = layered1D_mesh
  []
[]

[Postprocessors]
  [_dt]
    type = TimestepSize
  []
  [aniso_swelling_strain]
    type = ElementAverageValue
    variable = anisotropic_swelling_strain
    block = fuel
    execute_on = 'initial timestep_end'
  []
  [clad_fuel_gap]
    type = NodalExtremeValue
    variable = penetration
    boundary = 10
    execute_on = 'initial timestep_end'
  []
  [disp_fuel_outer_node]
    type = NodalVariableValue
    variable = disp_x
    nodeid = 3
  []
[]

[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 = 25
  nl_rel_tol = 1e-6
  nl_abs_tol = 1e-8
  start_time = 0
  n_startup_steps = 1
  end_time = 6.0e2
  num_steps = 5000
  dtmax = 1e6
  dtmin = 1

  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 2e2
    optimal_iterations = 8
    iteration_window = 2
    linear_iteration_ratio = 100
    growth_factor = 2
    cutback_factor = .5
  []
[]

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

Description
Example Input Syntax
Input Parameters
Input Files
References