LayeredAxialRelocationEigenstrainUserObject

Determines and stores the eigenstrain to apply to move the mesh during axial relocation as a function of layer and azimuthal position.

Description

The LayeredAxialRelocationEigenstrainUserObject computes and stores an eigenstrain to applied to the fuel in crumbled layers during axial relocation as a function of layer and azimuthal position. The material UO2AxialRelocationEigenstrain then queries this User Object to determine the correct magnitude of the eigenstrain to apply given the layer and azimuthal position of the supplied quadrature point.

When a layer crumbles the effective diameter of the fuel moves into contact with the cladding. To ensure the domain on which the heat equation is applied is correct, the mesh must be moved. This is accommodated by this eigenstrain. Note that the inclusion of a ficticious strain does not affect the solution because after crumbling the stress and strain state within the fuel is meaningless. The eigenstrain is calculated by: $var element = document.getElementById("moose-equation-cd814f4a-8617-411d-82cf-c50472bc86a9");katex.render(" \\epsilon = \\ln\\left(1.0 + \\frac{R_{fcurr} + g_{width}- R_{fo} - g^r}{R_{fo}}\\right)", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-603d91e8-c58d-4904-8de3-f5dcc62bd68c");katex.render("R_{fcurr}", element, {displayMode:false,throwOnError:false});$ is the current fuel outer radius, $var element = document.getElementById("moose-equation-ec573f25-8c25-44db-90b6-5ce0ff6f88c7");katex.render("g_{width}", element, {displayMode:false,throwOnError:false});$ is the current fuel to clad gap, $var element = document.getElementById("moose-equation-0677285a-2d25-4209-a2ef-75664fd8a5c1");katex.render("g^r", element, {displayMode:false,throwOnError:false});$ is the residual gap size (default is 2 $var element = document.getElementById("moose-equation-fabdf6f6-fcd7-45ff-bff7-7766fc954006");katex.render("\\mu m", element, {displayMode:false,throwOnError:false});$ ), and $var element = document.getElementById("moose-equation-b1eee5c9-f272-4bc6-980f-0f864871141d");katex.render("R_{fo}", element, {displayMode:false,throwOnError:false});$ is the fuel outer radius at the time fuel mass gain is first calculated to occur. Since the current gap width can vary azimuthally, the eigenstrain is calculated and stored as a function of the azimuthal position. The definition of the residual gap is illustrated in Figure 1:

Figure 1: Change in fuel geometry and effective fuel density following fuel pellet collapse in the ballooned region of the cladding. A residual gap $var element = document.getElementById("moose-equation-ff1d95c2-3950-411a-a304-9888ede9a437");katex.render("g^r", element, {displayMode:false,throwOnError:false});$ is assumed to remain.

Example Input Syntax

[UserObjects<<<{"href": "../../syntax/UserObjects/index.html"}>>>]
  [layered_eigenstrain]
    type = LayeredAxialRelocationEigenstrainUserObject<<<{"description": "Determines and stores the eigenstrain to apply to move the mesh during axial relocation as a function of layer and azimuthal position.", "href": "LayeredAxialRelocationEigenstrainUserObject.html"}>>>
    pellet_outer_radius<<<{"description": "Aux variable holding the values of the pellet outer radius."}>>> = outer_fuel_radius
    axial_relocation_object<<<{"description": "Name of the AxialRelocationUserObject that determines whether the fuel has crumbled."}>>> = axial_relocation
    penetration<<<{"description": "Aux variable holding the values of the penetration distance between the fuel and clad."}>>> = penetration
    direction<<<{"description": "The direction of the layers."}>>> = y
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'initial timestep_end'
    boundary<<<{"description": "The list of boundaries (ids or names) from the mesh where this object applies"}>>> = 10
    layer_bounding_block<<<{"description": "List of block ids (SubdomainID) that are used to determine the upper and lower geometric bounds for all layers. If this is not specified, the ids specified in 'block' are used for this purpose."}>>> = fuel
    num_layers<<<{"description": "The number of layers."}>>> = 5
  []
[]

Input Parameters

axial_relocation_objectName of the AxialRelocationUserObject that determines whether the fuel has crumbled.
C++ Type:UserObjectName
Controllable:No
Description:Name of the AxialRelocationUserObject that determines whether the fuel has crumbled.
pellet_outer_radiusAux variable holding the values of the pellet outer radius.
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Aux variable holding the values of the pellet outer radius.
penetrationAux variable holding the values of the penetration distance between the fuel and clad.
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Aux variable holding the values of the penetration distance between the fuel and clad.

Required Parameters

blockThe list of block ids (SubdomainID) that this object will be applied
C++ Type:std::vector<SubdomainName>
Controllable:No
Description:The list of block ids (SubdomainID) 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
layer_bounding_blockList of block ids (SubdomainID) that are used to determine the upper and lower geometric bounds for all layers. If this is not specified, the ids specified in 'block' are used for this purpose.
C++ Type:std::vector<SubdomainName>
Controllable:No
Description:List of block ids (SubdomainID) that are used to determine the upper and lower geometric bounds for all layers. If this is not specified, the ids specified in 'block' are used for this purpose.
residual_gap_size2e-06The residual gap remaining in layers that have crumbled.
Default:2e-06
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The residual gap remaining in layers that have crumbled.
unique_node_executeFalseWhen false (default), block restricted objects will have the execute method called multiple times on a single node if the node lies on a interface between two subdomains.
Default:False
C++ Type:bool
Controllable:No
Description:When false (default), block restricted objects will have the execute method called multiple times on a single node if the node lies on a interface between two subdomains.

Optional Parameters

allow_duplicate_execution_on_initialFalseIn the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
Default:False
C++ Type:bool
Controllable:No
Description:In the case where this UserObject is depended upon by an initial condition, allow it to be executed twice during the initial setup (once before the IC and again after mesh adaptivity (if applicable).
execute_onTIMESTEP_ENDThe list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
Default:TIMESTEP_END
C++ Type:ExecFlagEnum
Options:XFEM_MARK, NONE, INITIAL, LINEAR, NONLINEAR_CONVERGENCE, NONLINEAR, POSTCHECK, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM
Controllable:No
Description:The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.
execution_order_group0Execution order groups are executed in increasing order (e.g., the lowest number is executed first). Note that negative group numbers may be used to execute groups before the default (0) group. Please refer to the user object documentation for ordering of user object execution within a group.
Default:0
C++ Type:int
Controllable:No
Description:Execution order groups are executed in increasing order (e.g., the lowest number is executed first). Note that negative group numbers may be used to execute groups before the default (0) group. Please refer to the user object documentation for ordering of user object execution within a group.
force_postauxFalseForces the UserObject to be executed in POSTAUX
Default:False
C++ Type:bool
Controllable:No
Description:Forces the UserObject to be executed in POSTAUX
force_preauxFalseForces the UserObject to be executed in PREAUX
Default:False
C++ Type:bool
Controllable:No
Description:Forces the UserObject to be executed in PREAUX
force_preicFalseForces the UserObject to be executed in PREIC during initial setup
Default:False
C++ Type:bool
Controllable:No
Description:Forces the UserObject to be executed in PREIC during initial setup

Execution Scheduling Parameters

average_radius1When using 'average' sampling this is how the number of values both above and below the layer that will be averaged.
Default:1
C++ Type:unsigned int
Controllable:No
Description:When using 'average' sampling this is how the number of values both above and below the layer that will be averaged.
cumulativeFalseWhen true the value in each layer is the sum of the values up to and including that layer
Default:False
C++ Type:bool
Controllable:No
Description:When true the value in each layer is the sum of the values up to and including that layer
positive_cumulative_directionTrueWhen 'cumulative' is true, whether the direction for summing the cumulative value is the positive direction or negative direction
Default:True
C++ Type:bool
Controllable:No
Description:When 'cumulative' is true, whether the direction for summing the cumulative value is the positive direction or negative direction
sample_typedirectHow to sample the layers. 'direct' means get the value of the layer the point falls in directly (or average if that layer has no value). 'interpolate' does a linear interpolation between the two closest layers. 'average' averages the two closest layers.
Default:direct
C++ Type:MooseEnum
Options:direct, interpolate, average
Controllable:No
Description:How to sample the layers. 'direct' means get the value of the layer the point falls in directly (or average if that layer has no value). 'interpolate' does a linear interpolation between the two closest layers. 'average' averages the two closest layers.

Value Sampling / Aggregating Parameters

boundsThe 'bounding' positions of the layers i.e.: '0, 1.2, 3.7, 4.2' will mean 3 layers between those positions.
C++ Type:std::vector<double>
Unit:(no unit assumed)
Controllable:No
Description:The 'bounding' positions of the layers i.e.: '0, 1.2, 3.7, 4.2' will mean 3 layers between those positions.
directionThe direction of the layers.
C++ Type:MooseEnum
Options:x, y, z
Controllable:No
Description:The direction of the layers.
direction_maxMaximum coordinate along 'direction' that bounds the layers
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Maximum coordinate along 'direction' that bounds the layers
direction_minMinimum coordinate along 'direction' that bounds the layers
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Minimum coordinate along 'direction' that bounds the layers
num_layersThe number of layers.
C++ Type:unsigned int
Controllable:No
Description:The number of layers.

Layers Extent And Definition 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.
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

Input Files

(examples/axial_relocation/layered1D/twin_balloon.i)
(test/tests/axial_relocation/axial_relocation_volume_correction.i)
(examples/axial_relocation/layered1D/single_balloon.i)
(test/tests/axial_relocation/axial_relocation_eigenstrain.i)

(test/tests/axial_relocation/axial_relocation_eigenstrain.i)

# The purpose of this test is to verify the calculation of the eigenstrain
# applied to the fuel in the event that an axial layer has crumbled (accommodated
# additional mass) during axial relocation in Layered 1D. This eigenstrain is used
# to move the outer radius of the fuel to within a small residual gap size of the
# inside surface of the cladding.
#
# The eigenstrain is calculated as:
#
# epsilon = ln(1.0 + (R_fcurr + g_width - R_fo - g^r) / R_fo)
#
# where R_fcurr is the current outer radius of the pellet in the layer,
# g_width is the current fuel-to-clad gap width, g^r is the residual gap size
# (default of 2.0e-6 m), and R_fo is the fuel radius at the time the fuel begins
# to move to that layer.  In this test case since there is no thermal expansion
# or other radial displacements of the fuel, R_fo is the as-fabricated fuel radius.
#
# In this test crumbling of the middle layer of 5 (layer 2 since indexing of
# the layers begins at zero) occurs at the end of the simulation. Since only this
# layer is deemed crumbled it is only this layer to which the eigenstrain is applied.
# At this time the inner cladding radius is calculated to be 4.5e-3 + 0.00052 =
# 5.02e-3 m. Therefore, the axial relocation eigenstrain is calculated to be:
#
# epsilon = ln(1.0 + (5.02e-3 - 4.5e-3 - 2.0e-6) / 4.5e-3)
#
# epsilon = 0.108954
#
# This is verified by checking the value of the axial_relocation_strain column in the
# outputs vector postprocessor.

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

[Mesh]
  coord_type = RZ
  [layered1D_mesh]
    type = Layered1DMeshGenerator
    elem_type = EDGE2
    slices_per_block = 5
    pellet_outer_radius = 4.5e-3
    fuel_height = 0.5
    include_plenum = false
    nx_p = 10
    clad_gap_width = 0.0
    pellet_mesh_density = customize
    pellet_bottom_coor = 0.0
  []
  patch_update_strategy = auto
[]

[Variables]
  [temperature]
    order = FIRST
    family = LAGRANGE
    initial_condition = 1200
  []
[]

[AuxVariables]
  [disp_y]
  []
  [disp_z]
  []
  [burnup]
    order = FIRST
    family = LAGRANGE
  []
  [pulverized]
    order = CONSTANT
    family = MONOMIAL
  []
  [layered_average_contact_pressure]
    order = CONSTANT
    family = MONOMIAL
  []
  [layered_pulverized_fuel_volume]
    order = CONSTANT
    family = MONOMIAL
  []
  [layered_average_burnup]
    order = CONSTANT
    family = MONOMIAL
  []
  [layered_mass_fraction]
    order = CONSTANT
    family = MONOMIAL
  []
  [layered_packing_fraction]
    order = CONSTANT
    family = MONOMIAL
  []
  [inner_clad_radius]
    order = FIRST
    family = LAGRANGE
  []
  [layered_maximum_clad_radius]
    order = CONSTANT
    family = MONOMIAL
  []
  [layered_clad_internal_volume]
    order = CONSTANT
    family = MONOMIAL
  []
  [layered_average_gap_conductivity]
    order = CONSTANT
    family = MONOMIAL
  []
  [outer_fuel_radius]
    order = FIRST
    family = LAGRANGE
  []
  [axial_relocation_strain]
    order = CONSTANT
    family = MONOMIAL
  []
  [gap_thermal_conductivity]
    order = CONSTANT
    family = MONOMIAL
  []
  [strain_yy_0]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [burnup_function]
    type = ParsedFunction
    expression = 'x*100.0/4.275'
  []
  [power]
    type = PiecewiseLinear
    x = '0 100'
    y = '15000 15000'
  []
  [clad_displacement_function]
    type = ParsedFunction
    expression = '2.0e-5 * t * sin(pi * y / 0.5)'
  []
[]

[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 = 'axial_relocation'
        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]
  [burnup]
    type = FunctionAux
    variable = burnup
    function = burnup_function
    execute_on = 'initial linear'
  []
  [pulverized]
    type = MaterialRealAux
    block = fuel
    variable = pulverized
    property = pulverized
    execute_on = 'initial nonlinear'
  []
  [layered_average_contact_pressure]
    type = SpatialUserObjectAux
    variable = layered_average_contact_pressure
    execute_on = timestep_end
    block = fuel
    user_object = layered_average_contact_pressure
  []
  [layered_pulverized_fuel_volume]
    type = SpatialUserObjectAux
    variable = layered_pulverized_fuel_volume
    execute_on = timestep_end
    block = fuel
    user_object = layered_pulverized_fuel_volume
  []
  [layered_average_burnup]
    type = SpatialUserObjectAux
    variable = layered_average_burnup
    execute_on = timestep_end
    block = fuel
    user_object = layered_average_burnup
  []
  [layered_mass_fraction]
    type = AxialRelocationOutputAux
    variable = layered_mass_fraction
    execute_on = timestep_end
    block = fuel
    axial_relocation_user_object = axial_relocation
    output_option = MASS_FRACTION
  []
  [layered_packing_fraction]
    type = AxialRelocationOutputAux
    variable = layered_packing_fraction
    execute_on = timestep_end
    block = fuel
    axial_relocation_user_object = axial_relocation
    output_option = PACKING_FRACTION
  []
  [inner_clad_radius]
    type = Radius
    boundary = 5
    variable = inner_clad_radius
    execute_on = 'initial nonlinear'
  []
  [outer_fuel_radius]
    type = Radius
    boundary = 10
    variable = outer_fuel_radius
    execute_on = 'initial nonlinear'
  []
  [layered_maximum_clad_radius]
    type = SpatialUserObjectAux
    variable = layered_maximum_clad_radius
    execute_on = timestep_end
    block = fuel
    user_object = layered_maximum_clad_radius
  []
  [layered_clad_internal_volume]
    type = SpatialUserObjectAux
    variable = layered_clad_internal_volume
    execute_on = timestep_end
    block = fuel
    user_object = layered_clad_internal_volume
  []
  [layered_average_gap_conductivity]
    type = SpatialUserObjectAux
    variable = layered_average_gap_conductivity
    execute_on = timestep_end
    block = fuel
    user_object = layered_average_gap_conductivity
  []
  [axial_relocation_strain]
    type = MaterialRealAux
    variable = axial_relocation_strain
    block = fuel
    property = axial_relocation_strain
    execute_on = 'nonlinear timestep_end'
  []
  [gap_thermal_conductivity]
    type = MaterialRealAux
    variable = gap_thermal_conductivity
    property = gap_conductivity
    boundary = 10
    execute_on = 'initial linear'
  []
[]

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

[ThermalContact]
  [thermal_contact]
    type = GasGapHeatTransfer
    variable = temperature
    primary = 5
    secondary = 10
    gap_conductivity = 1
  []
[]

[BCs]
  [temperature]
    type = DirichletBC
    boundary = '10 12 5 2'
    variable = temperature
    value = 1200
  []
  [no_x_all]
    type = DirichletBC
    variable = disp_x
    boundary = 12
    value = 0.0
  []
  [inner_clad_displacement]
    type = FunctionDirichletBC
    variable = disp_x
    boundary = '5'
    function = clad_displacement_function
  []
[]

[Materials]
  [uo2pulverization]
    type = UO2Pulverization
    block = fuel
    burnup = burnup
    layered_average_contact_pressure = layered_average_contact_pressure
    temperature = temperature
  []
  [fuel_thermal]
    type = HeatConductionMaterial
    block = fuel
    thermal_conductivity = 1.0
    specific_heat = 1.0
  []
  [fuel_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = fuel
    youngs_modulus = 2.e11
    poissons_ratio = .345
  []
  [fuel_stress]
    type = ComputeFiniteStrainElasticStress
    block = fuel
  []
  [axial_relocation_strain]
    type = UO2AxialRelocationEigenstrain
    block = fuel
    axial_relocation_eigenstrain_object = layered_eigenstrain
    eigenstrain_name = axial_relocation
  []
  [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
  []
  [layered_average_contact_pressure]
    type = LayeredSideAverage
    variable = contact_pressure
    direction = y
    execute_on = timestep_end
    boundary = 10
    num_layers = 5
  []
  [layered_average_gap_conductivity]
    type = LayeredSideAverage
    variable = gap_thermal_conductivity
    direction = y
    execute_on = timestep_end
    boundary = 10
    num_layers = 5
  []
  [layered_eigenstrain]
    type = LayeredAxialRelocationEigenstrainUserObject
    pellet_outer_radius = outer_fuel_radius
    axial_relocation_object = axial_relocation
    penetration = penetration
    direction = y
    execute_on = 'initial timestep_end'
    boundary = 10
    layer_bounding_block = fuel
    num_layers = 5
  []
  [layered_pulverized_fuel_volume]
    type = LayeredVariableIntegral
    variable = pulverized
    fuel_pin_geometry = fuel_pin_geometry
    direction = y
    execute_on = 'initial timestep_end'
    block = fuel
    num_layers = 5
  []
  [layered_average_burnup]
    type = LayeredAverage
    variable = burnup
    direction = y
    execute_on = 'initial timestep_end'
    block = fuel
    num_layers = 5
  []
  [layered_maximum_clad_radius]
    type = LayeredNodalExtremeValue
    variable = inner_clad_radius
    direction = y
    execute_on = 'initial timestep_end'
    boundary = 5
    layer_bounding_block = fuel
    num_layers = 5
  []
  [layered_clad_internal_volume]
    type = LayeredInternalVolume
    fuel_pin_geometry = fuel_pin_geometry
    out_of_plane_strain = 0
    direction = y
    execute_on = 'timestep_begin final'
    boundary = 5
    layer_bounding_block = fuel
    num_layers = 5
  []
  [axial_relocation]
    type = AxialRelocationUserObject
    block = fuel
    direction = y
    num_layers = 5
    layered_average_burnup = layered_average_burnup
    layered_pulverized_fuel_volume = layered_pulverized_fuel_volume
    layered_maximum_clad_radius = layered_maximum_clad_radius
    layered_clad_internal_volume = layered_clad_internal_volume
    max_linear_heat_generation_rate = maximum_power
    fuel_pin_geometry = fuel_pin_geometry
    execute_on = 'initial timestep_end'
  []
[]

[Postprocessors]
  [rod_input_power]
    type = FunctionValuePostprocessor
    function = power
    execute_on = timestep_end
  []
  [maximum_power]
    type = TimeExtremeValue
    postprocessor = rod_input_power
    value_type = max
    execute_on = timestep_end
  []
  [clad_volume]
    type = LayeredInternalVolumePostprocessor
    addition = 0
    boundary = 5
    component = 0
    execute_on = 'INITIAL LINEAR'
    fuel_pin_geometry = fuel_pin_geometry
    out_of_plane_strain = strain_yy_0
    use_displaced_mesh = true
  []
  [pellet_volume]
    type = LayeredCrumbledInternalVolumePostprocessor
    axial_relocation_object = axial_relocation
    boundary = 10
    component = 0
    execute_on = 'INITIAL LINEAR'
    fuel_pin_geometry = fuel_pin_geometry
    out_of_plane_strain = strain_yy_0
    use_displaced_mesh = true
  []
  [gas_volume]
    type = LinearCombinationPostprocessor
    execute_on = 'INITIAL LINEAR'
    pp_coefs = '1 1'
    pp_names = 'clad_volume pellet_volume'
  []
[]

[Executioner]
  type = Transient

  solve_type = PJFNK

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-ksp_gmres_restart'
  petsc_options_value = '101'

  line_search = 'none'

  l_max_its = 100
  nl_max_its = 100
  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-10
  l_tol = 1e-5
  start_time = 0.0
  num_steps = 14
  dt = 2
[]

[VectorPostprocessors]
  [vpp]
    type = LineValueSampler
    start_point = '2.25e-3 0.05 0'
    end_point = '2.25e-3 0.45 0'
    num_points = 5
    sort_by = y
    variable = 'axial_relocation_strain layered_packing_fraction'
    outputs = results
  []
[]

[Outputs]
  hide = penetration
  [results]
    type = CSV
    execute_on = final
    create_final_symlink = true
  []
[]

(examples/axial_relocation/layered1D/twin_balloon.i)


initial_fuel_density = 10431.0

[GlobalParams]
  density = ${initial_fuel_density}
  order = FIRST
  family = LAGRANGE
  displacements = disp_x
  temperature = temp
[]

[Mesh]
  coord_type = RZ
  patch_update_strategy = auto
  partitioner = centroid
  centroid_partitioner_direction = y
  [layered1D_mesh]
    type = Layered1DMeshGenerator
    elem_type = EDGE2
    slices_per_block = 36
    pellet_outer_radius = 4.5e-3
    clad_gap_width = 0.0
    clad_thickness = 0.56e-3
    fuel_height = 3.6
    include_plenum = false
    pellet_bottom_coor = 0.0
  []
[]

[Variables]
  [temp]
    initial_condition = 300.0
  []
[]

[Functions]
  [burnup_function]
    type = ParsedFunction
    expression = 0.07
  []
  [clad_displacement_function]
    type = ParsedFunction
    expression = '2.0e-5 * t * abs(sin(2*pi * y / 3.6))'
  []
  [power]
    type = PiecewiseLinear
    x = '0 100'
    y = '0 15000'
  []
[]

[AuxVariables]
  [disp_y]
  []
  [disp_z]
  []
  [layered_mass_fraction]
    order = CONSTANT
    family = MONOMIAL
  []
  [layered_average_contact_pressure]
    order = CONSTANT
    family = MONOMIAL
  []
  [layered_pulverized_fuel_volume]
    order = CONSTANT
    family = MONOMIAL
  []
  [layered_average_burnup]
    order = CONSTANT
    family = MONOMIAL
  []
  [burnup]
    order = FIRST
    family = LAGRANGE
  []
  [pulverized]
    order = CONSTANT
    family = MONOMIAL
  []
  [inner_clad_radius]
    order = FIRST
    family = LAGRANGE
  []
  [layered_maximum_clad_radius]
    order = CONSTANT
    family = MONOMIAL
  []
  [outer_fuel_radius]
    order = FIRST
    family = LAGRANGE
  []
  [axial_relocation_strain]
    order = CONSTANT
    family = MONOMIAL
  []
[]

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

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

[AuxKernels]
  [layered_contact_pressure]
    type = SpatialUserObjectAux
    variable = layered_average_contact_pressure
    execute_on = timestep_end
    block = fuel
    user_object = average_contact_pressure
  []
  [layered_mass_fraction]
    type = AxialRelocationOutputAux
    variable = layered_mass_fraction
    execute_on = timestep_end
    block = fuel
    axial_relocation_user_object = axial_relocation
    output_option = MASS_FRACTION
  []
  [burnup]
    type = FunctionAux
    variable = burnup
    function = burnup_function
    execute_on = nonlinear
    block = fuel
  []
  [pulverized]
    type = MaterialRealAux
    property = pulverized
    variable = pulverized
    execute_on = timestep_end
    block = fuel
  []
  [inner_clad_radius]
    type = Radius
    boundary = 5
    variable = inner_clad_radius
    execute_on = 'initial nonlinear'
  []
  [outer_fuel_radius]
    type = Radius
    boundary = 10
    variable = outer_fuel_radius
    execute_on = 'initial nonlinear'
  []
  [layered_maximum_clad_radius]
    type = SpatialUserObjectAux
    variable = layered_maximum_clad_radius
    execute_on = timestep_end
    block = fuel
    user_object = layered_maximum_clad_radius
  []
  [axial_relocation_strain]
    type = MaterialRealAux
    variable = axial_relocation_strain
    block = fuel
    property = axial_relocation_strain
    execute_on = 'timestep_end'
  []
[]

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

[BCs]
  [no_x_all]
    type = DirichletBC
    variable = disp_x
    boundary = 12
    value = 0.0
  []
  [inner_clad_displacement]
    type = FunctionDirichletBC
    variable = disp_x
    boundary = '5'
    function = clad_displacement_function
  []
  [center]
    type = DirichletBC
    variable = temp
    boundary = 12
    value = 300
  []
  [clad_inner_surface]
    type = DirichletBC
    variable = temp
    boundary = 5
    value = 300
  []
  [clad_outer_surface]
    type = DirichletBC
    variable = temp
    boundary = 2
    value = 300
  []
[]

[UserObjects]
  [pin_geometry]
    type = Layered1DFuelPinGeometry
    mesh_generator = layered1D_mesh
  []
  [average_contact_pressure]
    type = LayeredSideAverage
    variable = contact_pressure
    direction = y
    execute_on = timestep_end
    boundary = 10
    num_layers = 36
  []
  [layered_eigenstrain]
    type = LayeredAxialRelocationEigenstrainUserObject
    pellet_outer_radius = outer_fuel_radius
    axial_relocation_object = axial_relocation
    penetration = penetration
    direction = y
    execute_on = 'initial nonlinear'
    boundary = 10
    layer_bounding_block = fuel
    num_layers = 36
  []
  [layered_maximum_clad_radius]
    type = LayeredNodalExtremeValue
    variable = inner_clad_radius
    direction = y
    execute_on = 'initial nonlinear'
    boundary = 5
    layer_bounding_block = fuel
    num_layers = 36
  []
  [layered_clad_internal_volume]
    type = LayeredInternalVolume
    fuel_pin_geometry = pin_geometry
    out_of_plane_strain = 0
    direction = y
    execute_on = 'initial nonlinear'
    boundary = 5
    layer_bounding_block = fuel
    num_layers = 36
  []
  [average_outer_fuel_radius]
    type = LayeredSideAverage
    variable = outer_fuel_radius
    direction = y
    execute_on = 'initial nonlinear'
    boundary = 10
    num_layers = 36
  []
  [layered_average_burnup]
    type = LayeredAverage
    variable = burnup
    direction = y
    execute_on = 'initial nonlinear'
    block = fuel
    num_layers = 36
  []
  [layered_pulverized_fuel_volume]
    type = LayeredVariableIntegral
    fuel_pin_geometry = pin_geometry
    variable = pulverized
    direction = y
    execute_on = 'initial nonlinear'
    block = fuel
    num_layers = 36
  []
  [axial_relocation]
    type = AxialRelocationUserObject
    direction = y
    num_layers = 36
    layered_average_burnup = layered_average_burnup
    layered_pulverized_fuel_volume = layered_pulverized_fuel_volume
    layered_maximum_clad_radius = layered_maximum_clad_radius
    layered_clad_internal_volume = layered_clad_internal_volume
    max_linear_heat_generation_rate = maximum_power
    fuel_pin_geometry = pin_geometry
    fragment_packing_fraction = 0.75 # Set to force overall packing fraction to be 0.75
    pulver_packing_fraction = 0.75 # Set to force overall packing fraction to be 0.75
    pulver_characteristic_length = 0.0001
    nonrelocatable_fuel_fraction = 0.01
    execute_on = 'initial nonlinear'
  []
[]

[Materials]
  [fuel_pulverization]
    type = UO2Pulverization
    burnup = burnup
    block = fuel
    temperature = temp
    layered_average_contact_pressure = layered_average_contact_pressure
  []

  [fuel_thermal]
    type = HeatConductionMaterial
    block = fuel
    thermal_conductivity = 3.0
    specific_heat = 260.0
  []

  [axial_relocation_strain]
    type = UO2AxialRelocationEigenstrain
    block = fuel
    axial_relocation_eigenstrain_object = layered_eigenstrain
    eigenstrain_name = axial_relocation
  []

  [fuel_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = fuel
    youngs_modulus = 2.e11
    poissons_ratio = .345
  []
  [fuel_stress]
    type = ComputeFiniteStrainElasticStress
    block = fuel
  []

  [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
  []
  [fuel_density]
    type = StrainAdjustedDensity
    block = fuel
    strain_free_density = ${initial_fuel_density}
  []
  [clad_density]
    type = StrainAdjustedDensity
    block = clad
    strain_free_density = 6551.0
  []
[]

[Postprocessors]
  [rod_input_power]
    type = FunctionValuePostprocessor
    function = power
    execute_on = timestep_end
  []
  [maximum_power]
    type = TimeExtremeValue
    postprocessor = rod_input_power
    value_type = max
    execute_on = timestep_end
  []
  [num_lin_it]
    type = NumLinearIterations
  []
  [num_nonlin_it]
    type = NumNonlinearIterations
  []
  [tot_lin_it]
    type = CumulativeValuePostprocessor
    postprocessor = num_lin_it
  []
  [tot_nonlin_it]
    type = CumulativeValuePostprocessor
    postprocessor = num_nonlin_it
  []
  [alive_time]
    type = PerfGraphData
    section_name = Root
    data_type = TOTAL
  []
[]

[VectorPostprocessors]
  [mass_fraction]
    type = LineValueSampler
    start_point = '0 0.05 0'
    end_point = '0 3.55 0'
    num_points = 36
    sort_by = y
    variable = layered_mass_fraction
    outputs = mass_fraction
  []
[]

[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'
  l_max_its = 60
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-10
  l_tol = 1e-5

  dt = 2
  start_time = 0.0
  end_time = 100
[]

[Outputs]
  perf_graph = true
  exodus = true
  [mass_fraction]
    type = CSV
    execute_on = 'final'
    create_final_symlink = true
  []
[]

(test/tests/axial_relocation/axial_relocation_volume_correction.i)

# The purpose of this test is to verify the calculation of the internal gas volume
# in the rod when one or more axial layers have crumbled (accommodated
# additional mass) during axial relocation. This internal volume calculation
# takes into account that in crumbled layers the gas volume is intermixed with
# the porous bed of fuel fragments after the eigenstrain is applied to move the
# mesh to within a small residual gap size fo the inside surface of the cladding.
# In addition, in layers that have lost mass the packing fraction is calculated
# based upon the current mass in the layer via:
#
# phi = (m_frac * m_i) / (rho_f * V_c)
#
# where m_frac is the mass fraction in the layer, m_i is the initial mass in
# the layer, rho_f is the fuel density, and V_c is the internal volume of the
# cladding in the layer.
#
# In order to get the internal gas volume correct the volume of the pellet in
# the layers that have crumbled must be scaled by the packing fraction of that
# layer. This test consists of 5 layers and only the middle layer crumbles and
# experiences relocation.  At the end of the simulation the inner cladding radius
# is calculated ot be 4.5e-3 + 0.00052 = 5.02e-3 m.  Assuming a residual gap of
# 2.0e-6 m the fuel radius in this layer is 5.02e-3 - 2.0e-6 = 5.018e-3m. In all
# other layers the fuel radius remains as the as fabricated fuel radius (4.5e-3 m).
#
# Equal slice heights of 0.1 m are used giving a total pellet volume without the
# correction of:
#
# V_p = (0.1 * pi) * (4 * 4.5e-3^2 + 5.018e-3^2) = 3.335753e-5 m^3
#
# which is the value reported by the pellet_volume1 postprocessor (the postprocessor
# actually reports the negative of this value because of the direction of the normal
# of the pellet exterior). Adding the clad_volume and pellet_volume1 postprocessors
# give the value of postprocessor gas_volume1.
#
# However, the layer with a fuel radius of 5.018e-3 m must be multiplied by the
# packing fraction of 0.828912. In the layer that has lost mass the new packing
# fraction is given by:
#
# phi = (0.968449 * 0.0663592) / (10431.0 * 0.1 * pi * 4.92069e-3^2) = 0.80993
#
# These two corrections give a total pellet volume of:
#
# V_p = (0.1 * pi) * (3 * 4.5e-3^2 + 0.80993 * 4.5e-3^2 + 0.828912 * 5.018e-3^2)
#     = 3.079497e-05 m^3
#
# which is verified to be the negative of the value given by postprocessor
# pellet_volume2.  Adding the clad_volume and pellet_volum2 postprocessors gives
# the corrected gas volume given by the gas_volume2 postprocessor.

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

[Mesh]
  coord_type = RZ
  [layered1D_mesh]
    type = Layered1DMeshGenerator
    elem_type = EDGE2
    slices_per_block = 5
    pellet_outer_radius = 4.5e-3
    fuel_height = 0.5
    include_plenum = false
    nx_p = 10
    clad_gap_width = 0.0
    pellet_mesh_density = customize
    pellet_bottom_coor = 0.0
  []
  patch_update_strategy = auto
  partitioner = centroid
  centroid_partitioner_direction = y
[]

[Variables]
  [temperature]
    order = FIRST
    family = LAGRANGE
    initial_condition = 1200
  []
[]

[AuxVariables]
  [disp_y]
  []
  [disp_z]
  []
  [burnup]
    order = FIRST
    family = LAGRANGE
  []
  [pulverized]
    order = CONSTANT
    family = MONOMIAL
  []
  [layered_average_contact_pressure]
    order = CONSTANT
    family = MONOMIAL
  []
  [layered_pulverized_fuel_volume]
    order = CONSTANT
    family = MONOMIAL
  []
  [layered_average_burnup]
    order = CONSTANT
    family = MONOMIAL
  []
  [layered_mass_fraction]
    order = CONSTANT
    family = MONOMIAL
  []
  [inner_clad_radius]
    order = FIRST
    family = LAGRANGE
  []
  [layered_maximum_clad_radius]
    order = CONSTANT
    family = MONOMIAL
  []
  [outer_fuel_radius]
    order = FIRST
    family = LAGRANGE
  []
  [axial_relocation_strain]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [burnup_function]
    type = ParsedFunction
    expression = 'x*100.0/4.275'
  []
  [power]
    type = PiecewiseLinear
    x = '0 100'
    y = '15000 15000'
  []
  [clad_displacement_function]
    type = ParsedFunction
    expression = '2.0e-5 * t * sin(pi * y / 0.5)'
  []
  [gas_volume2]
    type = ParsedFunction
    expression = 'clad_volume + pellet_volume2'
    symbol_names = 'clad_volume pellet_volume2'
    symbol_values = 'clad_volume pellet_volume2'
  []
[]

[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 = 'axial_relocation'
        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]
  [burnup]
    type = FunctionAux
    variable = burnup
    function = burnup_function
    execute_on = 'initial linear'
  []
  [pulverized]
    type = MaterialRealAux
    block = fuel
    variable = pulverized
    property = pulverized
    execute_on = 'initial nonlinear'
  []
  [layered_average_contact_pressure]
    type = SpatialUserObjectAux
    variable = layered_average_contact_pressure
    execute_on = timestep_end
    block = fuel
    user_object = layered_average_contact_pressure
  []
  [layered_pulverized_fuel_volume]
    type = SpatialUserObjectAux
    variable = layered_pulverized_fuel_volume
    execute_on = timestep_end
    block = fuel
    user_object = layered_pulverized_fuel_volume
  []
  [layered_average_burnup]
    type = SpatialUserObjectAux
    variable = layered_average_burnup
    execute_on = timestep_end
    block = fuel
    user_object = layered_average_burnup
  []
  [layered_mass_fraction]
    type = AxialRelocationOutputAux
    variable = layered_mass_fraction
    execute_on = timestep_end
    block = fuel
    axial_relocation_user_object = axial_relocation
    output_option = MASS_FRACTION
  []
  [inner_clad_radius]
    type = Radius
    boundary = 5
    variable = inner_clad_radius
    execute_on = 'initial nonlinear'
  []
  [outer_fuel_radius]
    type = Radius
    boundary = 10
    variable = outer_fuel_radius
    execute_on = 'initial nonlinear'
  []
  [layered_maximum_clad_radius]
    type = SpatialUserObjectAux
    variable = layered_maximum_clad_radius
    execute_on = timestep_end
    block = fuel
    user_object = layered_maximum_clad_radius
  []
  [axial_relocation_strain]
    type = MaterialRealAux
    variable = axial_relocation_strain
    block = fuel
    property = axial_relocation_strain
    execute_on = 'nonlinear timestep_end'
  []
[]

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

[BCs]
  [temperature]
    type = DirichletBC
    boundary = '10 12 5 2'
    variable = temperature
    value = 1200
  []
  [no_x_all]
    type = DirichletBC
    variable = disp_x
    boundary = 12
    value = 0.0
  []
  [inner_clad_displacement]
    type = FunctionDirichletBC
    variable = disp_x
    boundary = '5'
    function = clad_displacement_function
  []
[]

[Materials]
  [uo2pulverization]
    type = UO2Pulverization
    block = fuel
    burnup = burnup
    layered_average_contact_pressure = layered_average_contact_pressure
    temperature = temperature
  []
  [fuel_thermal]
    type = HeatConductionMaterial
    block = fuel
    thermal_conductivity = 1.0
    specific_heat = 1.0
  []
  [fuel_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = fuel
    youngs_modulus = 2.e11
    poissons_ratio = .345
  []
  [fuel_stress]
    type = ComputeFiniteStrainElasticStress
    block = fuel
  []
  [axial_relocation_strain]
    type = UO2AxialRelocationEigenstrain
    block = fuel
    axial_relocation_eigenstrain_object = layered_eigenstrain
    eigenstrain_name = axial_relocation
  []
  [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
  []
  [layered_eigenstrain]
    type = LayeredAxialRelocationEigenstrainUserObject
    pellet_outer_radius = outer_fuel_radius
    axial_relocation_object = axial_relocation
    penetration = penetration
    direction = y
    execute_on = 'initial timestep_end'
    boundary = 10
    layer_bounding_block = fuel
    num_layers = 5
  []
  [layered_average_contact_pressure]
    type = LayeredSideAverage
    variable = contact_pressure
    direction = y
    execute_on = timestep_end
    boundary = 10
    num_layers = 5
  []
  [layered_pulverized_fuel_volume]
    type = LayeredVariableIntegral
    variable = pulverized
    fuel_pin_geometry = fuel_pin_geometry
    direction = y
    execute_on = 'initial timestep_end'
    block = fuel
    num_layers = 5
  []
  [layered_average_burnup]
    type = LayeredAverage
    variable = burnup
    direction = y
    execute_on = 'initial timestep_end'
    block = fuel
    num_layers = 5
  []
  [layered_maximum_clad_radius]
    type = LayeredNodalExtremeValue
    variable = inner_clad_radius
    direction = y
    execute_on = 'initial timestep_end'
    boundary = 5
    layer_bounding_block = fuel
    num_layers = 5
  []
  [layered_clad_internal_volume]
    type = LayeredInternalVolume
    fuel_pin_geometry = fuel_pin_geometry
    out_of_plane_strain = 0
    direction = y
    execute_on = 'initial timestep_end'
    boundary = 5
    layer_bounding_block = fuel
    num_layers = 5
  []
  [axial_relocation]
    type = AxialRelocationUserObject
    block = fuel
    direction = y
    num_layers = 5
    layered_average_burnup = layered_average_burnup
    layered_pulverized_fuel_volume = layered_pulverized_fuel_volume
    layered_maximum_clad_radius = layered_maximum_clad_radius
    layered_clad_internal_volume = layered_clad_internal_volume
    max_linear_heat_generation_rate = maximum_power
    fuel_pin_geometry = fuel_pin_geometry
    execute_on = 'initial timestep_end'
  []
[]

[Postprocessors]
  [rod_input_power]
    type = FunctionValuePostprocessor
    function = power
    execute_on = timestep_end
  []
  [maximum_power]
    type = TimeExtremeValue
    postprocessor = rod_input_power
    value_type = max
    execute_on = timestep_end
  []
  [pellet_volume1]
    type = LayeredInternalVolumePostprocessor
    boundary = 10
    component = 0
    fuel_pin_geometry = fuel_pin_geometry
    out_of_plane_strain = strain_yy
    execute_on = 'initial timestep_end'
  []
  [pellet_volume2]
    type = LayeredCrumbledInternalVolumePostprocessor
    boundary = 10
    component = 0
    fuel_pin_geometry = fuel_pin_geometry
    out_of_plane_strain = strain_yy
    axial_relocation_object = axial_relocation
    execute_on = 'initial timestep_end'
  []
  [clad_volume]
    type = LayeredInternalVolumePostprocessor
    boundary = 5
    component = 0
    fuel_pin_geometry = fuel_pin_geometry
    out_of_plane_strain = strain_yy
    execute_on = 'initial timestep_end'
  []
  [gas_volume]
    type = LayeredInternalVolumePostprocessor
    boundary = 9
    component = 0
    fuel_pin_geometry = fuel_pin_geometry
    out_of_plane_strain = strain_yy
    execute_on = 'initial timestep_end'
  []
  [gas_volume2]
    type = FunctionValuePostprocessor
    function = gas_volume2
    execute_on = 'initial timestep_end'
  []
[]

[Executioner]
  type = Transient

  solve_type = PJFNK

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-ksp_gmres_restart'
  petsc_options_value = '101'

  line_search = 'none'

  l_max_its = 100
  nl_max_its = 100
  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-10
  l_tol = 1e-5
  start_time = 0.0
  num_steps = 14
  dt = 2
[]

[Outputs]
  exodus = true
  hide = penetration
[]

(examples/axial_relocation/layered1D/single_balloon.i)


initial_fuel_density = 10431.0

[GlobalParams]
  density = ${initial_fuel_density}
  order = FIRST
  family = LAGRANGE
  displacements = disp_x
  temperature = temp
[]

[Mesh]
  coord_type = RZ
  patch_update_strategy = auto
  partitioner = centroid
  centroid_partitioner_direction = y
  [layered1D_mesh]
    type = Layered1DMeshGenerator
    elem_type = EDGE2
    slices_per_block = 36
    pellet_outer_radius = 4.5e-3
    clad_gap_width = 0.0
    clad_thickness = 0.56e-3
    fuel_height = 3.6
    include_plenum = false
    pellet_bottom_coor = 0.0
  []
[]

[Variables]
  [temp]
    initial_condition = 300.0
  []
[]

[Functions]
  [burnup_function]
    type = ParsedFunction
    expression = 0.07
  []
  [clad_displacement_function]
    type = ParsedFunction
    expression = '2.0e-5 * t * sin(pi * y / 3.6)'
  []
  [power]
    type = PiecewiseLinear
    x = '0 100'
    y = '0 15000'
  []
[]

[AuxVariables]
  [disp_y]
  []
  [disp_z]
  []
  [layered_mass_fraction]
    order = CONSTANT
    family = MONOMIAL
  []
  [layered_average_contact_pressure]
    order = CONSTANT
    family = MONOMIAL
  []
  [layered_pulverized_fuel_volume]
    order = CONSTANT
    family = MONOMIAL
  []
  [layered_average_burnup]
    order = CONSTANT
    family = MONOMIAL
  []
  [burnup]
    order = FIRST
    family = LAGRANGE
  []
  [pulverized]
    order = CONSTANT
    family = MONOMIAL
  []
  [inner_clad_radius]
    order = FIRST
    family = LAGRANGE
  []
  [layered_maximum_clad_radius]
    order = CONSTANT
    family = MONOMIAL
  []
  [outer_fuel_radius]
    order = FIRST
    family = LAGRANGE
  []
  [axial_relocation_strain]
    order = CONSTANT
    family = MONOMIAL
  []
[]

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

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

[AuxKernels]
  [layered_contact_pressure]
    type = SpatialUserObjectAux
    variable = layered_average_contact_pressure
    execute_on = timestep_end
    block = fuel
    user_object = average_contact_pressure
  []
  [layered_mass_fraction]
    type = AxialRelocationOutputAux
    variable = layered_mass_fraction
    execute_on = timestep_end
    block = fuel
    axial_relocation_user_object = axial_relocation
    output_option = MASS_FRACTION
  []
  [burnup]
    type = FunctionAux
    variable = burnup
    function = burnup_function
    execute_on = nonlinear
    block = fuel
  []
  [pulverized]
    type = MaterialRealAux
    property = pulverized
    variable = pulverized
    execute_on = 'initial timestep_end'
    block = fuel
  []
  [inner_clad_radius]
    type = Radius
    boundary = 5
    variable = inner_clad_radius
    execute_on = 'initial nonlinear'
  []
  [outer_fuel_radius]
    type = Radius
    boundary = 10
    variable = outer_fuel_radius
    execute_on = 'initial nonlinear'
  []
  [layered_maximum_clad_radius]
    type = SpatialUserObjectAux
    variable = layered_maximum_clad_radius
    execute_on = timestep_end
    block = fuel
    user_object = layered_maximum_clad_radius
  []
  [axial_relocation_strain]
    type = MaterialRealAux
    variable = axial_relocation_strain
    block = fuel
    property = axial_relocation_strain
    execute_on = 'timestep_end'
  []
[]

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

[BCs]
  [no_x_all]
    type = DirichletBC
    variable = disp_x
    boundary = 12
    value = 0.0
  []
  [inner_clad_displacement]
    type = FunctionDirichletBC
    variable = disp_x
    boundary = '5'
    function = clad_displacement_function
  []
  [center]
    type = DirichletBC
    variable = temp
    boundary = 12
    value = 300
  []
  [clad_inner_surface]
    type = DirichletBC
    variable = temp
    boundary = 5
    value = 300
  []
  [clad_outer_surface]
    type = DirichletBC
    variable = temp
    boundary = 2
    value = 300
  []
[]

[UserObjects]
  [pin_geometry]
    type = Layered1DFuelPinGeometry
    mesh_generator = layered1D_mesh
  []
  [average_contact_pressure]
    type = LayeredSideAverage
    variable = contact_pressure
    direction = y
    execute_on = 'initial nonlinear'
    boundary = 10
    num_layers = 36
  []
  [layered_eigenstrain]
    type = LayeredAxialRelocationEigenstrainUserObject
    pellet_outer_radius = outer_fuel_radius
    axial_relocation_object = axial_relocation
    penetration = penetration
    direction = y
    execute_on = 'initial nonlinear'
    boundary = 10
    layer_bounding_block = fuel
    num_layers = 36
  []
  [layered_maximum_clad_radius]
    type = LayeredNodalExtremeValue
    variable = inner_clad_radius
    direction = y
    execute_on = 'initial nonlinear'
    boundary = 5
    layer_bounding_block = fuel
    num_layers = 36
  []
  [layered_clad_internal_volume]
    type = LayeredInternalVolume
    fuel_pin_geometry = pin_geometry
    out_of_plane_strain = 0
    direction = y
    execute_on = 'initial nonlinear'
    boundary = 5
    layer_bounding_block = fuel
    num_layers = 36
  []
  [average_outer_fuel_radius]
    type = LayeredSideAverage
    variable = outer_fuel_radius
    direction = y
    execute_on = 'initial nonlinear'
    boundary = 10
    num_layers = 36
  []
  [layered_average_burnup]
    type = LayeredAverage
    variable = burnup
    direction = y
    execute_on = 'initial nonlinear'
    block = fuel
    num_layers = 36
  []
  [layered_pulverized_fuel_volume]
    type = LayeredVariableIntegral
    fuel_pin_geometry = pin_geometry
    variable = pulverized
    direction = y
    execute_on = 'initial nonlinear'
    block = fuel
    num_layers = 36
  []
  [axial_relocation]
    type = AxialRelocationUserObject
    direction = y
    num_layers = 36
    layered_average_burnup = layered_average_burnup
    layered_pulverized_fuel_volume = layered_pulverized_fuel_volume
    layered_maximum_clad_radius = layered_maximum_clad_radius
    layered_clad_internal_volume = layered_clad_internal_volume
    max_linear_heat_generation_rate = maximum_power
    fuel_pin_geometry = pin_geometry
    fragment_packing_fraction = 0.75 # Set to force overall packing fraction to be 0.75
    pulver_packing_fraction = 0.75 # Set to force overall packing fraction to be 0.75
    pulver_characteristic_length = 0.0001
    nonrelocatable_fuel_fraction = 0.01
    execute_on = 'initial nonlinear'
  []
[]

[Materials]
  [fuel_pulverization]
    type = UO2Pulverization
    burnup = burnup
    block = fuel
    temperature = temp
    layered_average_contact_pressure = layered_average_contact_pressure
  []

  [fuel_thermal]
    type = HeatConductionMaterial
    block = fuel
    thermal_conductivity = 3.0
    specific_heat = 260.0
  []

  [axial_relocation_strain]
    type = UO2AxialRelocationEigenstrain
    block = fuel
    axial_relocation_eigenstrain_object = layered_eigenstrain
    eigenstrain_name = axial_relocation
  []

  [fuel_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = fuel
    youngs_modulus = 2.e11
    poissons_ratio = .345
  []
  [fuel_stress]
    type = ComputeFiniteStrainElasticStress
    block = fuel
  []

  [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
  []
  [fuel_density]
    type = StrainAdjustedDensity
    block = fuel
    strain_free_density = ${initial_fuel_density}
  []
  [clad_density]
    type = StrainAdjustedDensity
    block = clad
    strain_free_density = 6551.0
  []
[]

[Postprocessors]
  [rod_input_power]
    type = FunctionValuePostprocessor
    function = power
    execute_on = 'timestep_end'
  []
  [maximum_power]
    type = TimeExtremeValue
    postprocessor = rod_input_power
    value_type = max
    execute_on = 'timestep_end'
  []
  [num_lin_it]
    type = NumLinearIterations
  []
  [num_nonlin_it]
    type = NumNonlinearIterations
  []
  [tot_lin_it]
    type = CumulativeValuePostprocessor
    postprocessor = num_lin_it
  []
  [tot_nonlin_it]
    type = CumulativeValuePostprocessor
    postprocessor = num_nonlin_it
  []
  [alive_time]
    type = PerfGraphData
    section_name = Root
    data_type = TOTAL
  []
[]

[VectorPostprocessors]
  [mass_fraction]
    type = LineValueSampler
    start_point = '0 0.05 0'
    end_point = '0 3.55 0'
    num_points = 36
    sort_by = y
    variable = layered_mass_fraction
    outputs = mass_fraction
  []
[]

[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'
  l_max_its = 60
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-10
  l_tol = 1e-5

  dt = 2
  start_time = 0.0
  end_time = 100
[]

[Outputs]
  perf_graph = true
  exodus = true
  [mass_fraction]
    type = CSV
    execute_on = 'final'
    create_final_symlink = true
  []
[]

(test/tests/axial_relocation/axial_relocation_eigenstrain.i)

# The purpose of this test is to verify the calculation of the eigenstrain
# applied to the fuel in the event that an axial layer has crumbled (accommodated
# additional mass) during axial relocation in Layered 1D. This eigenstrain is used
# to move the outer radius of the fuel to within a small residual gap size of the
# inside surface of the cladding.
#
# The eigenstrain is calculated as:
#
# epsilon = ln(1.0 + (R_fcurr + g_width - R_fo - g^r) / R_fo)
#
# where R_fcurr is the current outer radius of the pellet in the layer,
# g_width is the current fuel-to-clad gap width, g^r is the residual gap size
# (default of 2.0e-6 m), and R_fo is the fuel radius at the time the fuel begins
# to move to that layer.  In this test case since there is no thermal expansion
# or other radial displacements of the fuel, R_fo is the as-fabricated fuel radius.
#
# In this test crumbling of the middle layer of 5 (layer 2 since indexing of
# the layers begins at zero) occurs at the end of the simulation. Since only this
# layer is deemed crumbled it is only this layer to which the eigenstrain is applied.
# At this time the inner cladding radius is calculated to be 4.5e-3 + 0.00052 =
# 5.02e-3 m. Therefore, the axial relocation eigenstrain is calculated to be:
#
# epsilon = ln(1.0 + (5.02e-3 - 4.5e-3 - 2.0e-6) / 4.5e-3)
#
# epsilon = 0.108954
#
# This is verified by checking the value of the axial_relocation_strain column in the
# outputs vector postprocessor.

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

[Mesh]
  coord_type = RZ
  [layered1D_mesh]
    type = Layered1DMeshGenerator
    elem_type = EDGE2
    slices_per_block = 5
    pellet_outer_radius = 4.5e-3
    fuel_height = 0.5
    include_plenum = false
    nx_p = 10
    clad_gap_width = 0.0
    pellet_mesh_density = customize
    pellet_bottom_coor = 0.0
  []
  patch_update_strategy = auto
[]

[Variables]
  [temperature]
    order = FIRST
    family = LAGRANGE
    initial_condition = 1200
  []
[]

[AuxVariables]
  [disp_y]
  []
  [disp_z]
  []
  [burnup]
    order = FIRST
    family = LAGRANGE
  []
  [pulverized]
    order = CONSTANT
    family = MONOMIAL
  []
  [layered_average_contact_pressure]
    order = CONSTANT
    family = MONOMIAL
  []
  [layered_pulverized_fuel_volume]
    order = CONSTANT
    family = MONOMIAL
  []
  [layered_average_burnup]
    order = CONSTANT
    family = MONOMIAL
  []
  [layered_mass_fraction]
    order = CONSTANT
    family = MONOMIAL
  []
  [layered_packing_fraction]
    order = CONSTANT
    family = MONOMIAL
  []
  [inner_clad_radius]
    order = FIRST
    family = LAGRANGE
  []
  [layered_maximum_clad_radius]
    order = CONSTANT
    family = MONOMIAL
  []
  [layered_clad_internal_volume]
    order = CONSTANT
    family = MONOMIAL
  []
  [layered_average_gap_conductivity]
    order = CONSTANT
    family = MONOMIAL
  []
  [outer_fuel_radius]
    order = FIRST
    family = LAGRANGE
  []
  [axial_relocation_strain]
    order = CONSTANT
    family = MONOMIAL
  []
  [gap_thermal_conductivity]
    order = CONSTANT
    family = MONOMIAL
  []
  [strain_yy_0]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [burnup_function]
    type = ParsedFunction
    expression = 'x*100.0/4.275'
  []
  [power]
    type = PiecewiseLinear
    x = '0 100'
    y = '15000 15000'
  []
  [clad_displacement_function]
    type = ParsedFunction
    expression = '2.0e-5 * t * sin(pi * y / 0.5)'
  []
[]

[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 = 'axial_relocation'
        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]
  [burnup]
    type = FunctionAux
    variable = burnup
    function = burnup_function
    execute_on = 'initial linear'
  []
  [pulverized]
    type = MaterialRealAux
    block = fuel
    variable = pulverized
    property = pulverized
    execute_on = 'initial nonlinear'
  []
  [layered_average_contact_pressure]
    type = SpatialUserObjectAux
    variable = layered_average_contact_pressure
    execute_on = timestep_end
    block = fuel
    user_object = layered_average_contact_pressure
  []
  [layered_pulverized_fuel_volume]
    type = SpatialUserObjectAux
    variable = layered_pulverized_fuel_volume
    execute_on = timestep_end
    block = fuel
    user_object = layered_pulverized_fuel_volume
  []
  [layered_average_burnup]
    type = SpatialUserObjectAux
    variable = layered_average_burnup
    execute_on = timestep_end
    block = fuel
    user_object = layered_average_burnup
  []
  [layered_mass_fraction]
    type = AxialRelocationOutputAux
    variable = layered_mass_fraction
    execute_on = timestep_end
    block = fuel
    axial_relocation_user_object = axial_relocation
    output_option = MASS_FRACTION
  []
  [layered_packing_fraction]
    type = AxialRelocationOutputAux
    variable = layered_packing_fraction
    execute_on = timestep_end
    block = fuel
    axial_relocation_user_object = axial_relocation
    output_option = PACKING_FRACTION
  []
  [inner_clad_radius]
    type = Radius
    boundary = 5
    variable = inner_clad_radius
    execute_on = 'initial nonlinear'
  []
  [outer_fuel_radius]
    type = Radius
    boundary = 10
    variable = outer_fuel_radius
    execute_on = 'initial nonlinear'
  []
  [layered_maximum_clad_radius]
    type = SpatialUserObjectAux
    variable = layered_maximum_clad_radius
    execute_on = timestep_end
    block = fuel
    user_object = layered_maximum_clad_radius
  []
  [layered_clad_internal_volume]
    type = SpatialUserObjectAux
    variable = layered_clad_internal_volume
    execute_on = timestep_end
    block = fuel
    user_object = layered_clad_internal_volume
  []
  [layered_average_gap_conductivity]
    type = SpatialUserObjectAux
    variable = layered_average_gap_conductivity
    execute_on = timestep_end
    block = fuel
    user_object = layered_average_gap_conductivity
  []
  [axial_relocation_strain]
    type = MaterialRealAux
    variable = axial_relocation_strain
    block = fuel
    property = axial_relocation_strain
    execute_on = 'nonlinear timestep_end'
  []
  [gap_thermal_conductivity]
    type = MaterialRealAux
    variable = gap_thermal_conductivity
    property = gap_conductivity
    boundary = 10
    execute_on = 'initial linear'
  []
[]

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

[ThermalContact]
  [thermal_contact]
    type = GasGapHeatTransfer
    variable = temperature
    primary = 5
    secondary = 10
    gap_conductivity = 1
  []
[]

[BCs]
  [temperature]
    type = DirichletBC
    boundary = '10 12 5 2'
    variable = temperature
    value = 1200
  []
  [no_x_all]
    type = DirichletBC
    variable = disp_x
    boundary = 12
    value = 0.0
  []
  [inner_clad_displacement]
    type = FunctionDirichletBC
    variable = disp_x
    boundary = '5'
    function = clad_displacement_function
  []
[]

[Materials]
  [uo2pulverization]
    type = UO2Pulverization
    block = fuel
    burnup = burnup
    layered_average_contact_pressure = layered_average_contact_pressure
    temperature = temperature
  []
  [fuel_thermal]
    type = HeatConductionMaterial
    block = fuel
    thermal_conductivity = 1.0
    specific_heat = 1.0
  []
  [fuel_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = fuel
    youngs_modulus = 2.e11
    poissons_ratio = .345
  []
  [fuel_stress]
    type = ComputeFiniteStrainElasticStress
    block = fuel
  []
  [axial_relocation_strain]
    type = UO2AxialRelocationEigenstrain
    block = fuel
    axial_relocation_eigenstrain_object = layered_eigenstrain
    eigenstrain_name = axial_relocation
  []
  [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
  []
  [layered_average_contact_pressure]
    type = LayeredSideAverage
    variable = contact_pressure
    direction = y
    execute_on = timestep_end
    boundary = 10
    num_layers = 5
  []
  [layered_average_gap_conductivity]
    type = LayeredSideAverage
    variable = gap_thermal_conductivity
    direction = y
    execute_on = timestep_end
    boundary = 10
    num_layers = 5
  []
  [layered_eigenstrain]
    type = LayeredAxialRelocationEigenstrainUserObject
    pellet_outer_radius = outer_fuel_radius
    axial_relocation_object = axial_relocation
    penetration = penetration
    direction = y
    execute_on = 'initial timestep_end'
    boundary = 10
    layer_bounding_block = fuel
    num_layers = 5
  []
  [layered_pulverized_fuel_volume]
    type = LayeredVariableIntegral
    variable = pulverized
    fuel_pin_geometry = fuel_pin_geometry
    direction = y
    execute_on = 'initial timestep_end'
    block = fuel
    num_layers = 5
  []
  [layered_average_burnup]
    type = LayeredAverage
    variable = burnup
    direction = y
    execute_on = 'initial timestep_end'
    block = fuel
    num_layers = 5
  []
  [layered_maximum_clad_radius]
    type = LayeredNodalExtremeValue
    variable = inner_clad_radius
    direction = y
    execute_on = 'initial timestep_end'
    boundary = 5
    layer_bounding_block = fuel
    num_layers = 5
  []
  [layered_clad_internal_volume]
    type = LayeredInternalVolume
    fuel_pin_geometry = fuel_pin_geometry
    out_of_plane_strain = 0
    direction = y
    execute_on = 'timestep_begin final'
    boundary = 5
    layer_bounding_block = fuel
    num_layers = 5
  []
  [axial_relocation]
    type = AxialRelocationUserObject
    block = fuel
    direction = y
    num_layers = 5
    layered_average_burnup = layered_average_burnup
    layered_pulverized_fuel_volume = layered_pulverized_fuel_volume
    layered_maximum_clad_radius = layered_maximum_clad_radius
    layered_clad_internal_volume = layered_clad_internal_volume
    max_linear_heat_generation_rate = maximum_power
    fuel_pin_geometry = fuel_pin_geometry
    execute_on = 'initial timestep_end'
  []
[]

[Postprocessors]
  [rod_input_power]
    type = FunctionValuePostprocessor
    function = power
    execute_on = timestep_end
  []
  [maximum_power]
    type = TimeExtremeValue
    postprocessor = rod_input_power
    value_type = max
    execute_on = timestep_end
  []
  [clad_volume]
    type = LayeredInternalVolumePostprocessor
    addition = 0
    boundary = 5
    component = 0
    execute_on = 'INITIAL LINEAR'
    fuel_pin_geometry = fuel_pin_geometry
    out_of_plane_strain = strain_yy_0
    use_displaced_mesh = true
  []
  [pellet_volume]
    type = LayeredCrumbledInternalVolumePostprocessor
    axial_relocation_object = axial_relocation
    boundary = 10
    component = 0
    execute_on = 'INITIAL LINEAR'
    fuel_pin_geometry = fuel_pin_geometry
    out_of_plane_strain = strain_yy_0
    use_displaced_mesh = true
  []
  [gas_volume]
    type = LinearCombinationPostprocessor
    execute_on = 'INITIAL LINEAR'
    pp_coefs = '1 1'
    pp_names = 'clad_volume pellet_volume'
  []
[]

[Executioner]
  type = Transient

  solve_type = PJFNK

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-ksp_gmres_restart'
  petsc_options_value = '101'

  line_search = 'none'

  l_max_its = 100
  nl_max_its = 100
  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-10
  l_tol = 1e-5
  start_time = 0.0
  num_steps = 14
  dt = 2
[]

[VectorPostprocessors]
  [vpp]
    type = LineValueSampler
    start_point = '2.25e-3 0.05 0'
    end_point = '2.25e-3 0.45 0'
    num_points = 5
    sort_by = y
    variable = 'axial_relocation_strain layered_packing_fraction'
    outputs = results
  []
[]

[Outputs]
  hide = penetration
  [results]
    type = CSV
    execute_on = final
    create_final_symlink = true
  []
[]

Description
Example Input Syntax
Input Parameters
Input Files