PdPenetration

Penetration depth of palladium into the SiC layer of TRISO fuel particles

Description

The PdPenetration model computes the rate of palladium ingress into the silicon carbide (SiC) layer of a TRISO particle. Palladium is produced by fission and migrates towards the SiC layer and degrades it. The model proposed by Petti et al. (2004) was calculated by fitting in-reactor data to derive a correlation as a function of temperature. The correlation is given by:

$var element = document.getElementById("moose-equation-e2e857f0-b011-4191-9e01-d83d4d5c3d9a");katex.render(" \\dot{P}_{Pd} = 38.232 \\exp{ \\left(-\\frac{11342.3}{T_{K}} \\right) }", element, {displayMode:true,throwOnError:false});$

where $var element = document.getElementById("moose-equation-d3276042-b32a-4e33-b2ae-b1bd7bea32b5");katex.render("\\dot{P}_{Pd}", element, {displayMode:false,throwOnError:false});$ ( $var element = document.getElementById("moose-equation-639ef8b2-83de-477d-9dcc-777b02b155eb");katex.render("\\mu", element, {displayMode:false,throwOnError:false});$ $var element = document.getElementById("moose-equation-8aee8451-5387-4b8f-a1f5-6f1ec9f20240");katex.render("m/day", element, {displayMode:false,throwOnError:false});$ ) is the rate of penetration of Pd into the SiC layer and $var element = document.getElementById("moose-equation-c51b754b-06e2-4b4e-a36d-b80e7a1e45e0");katex.render("T_{K}", element, {displayMode:false,throwOnError:false});$ ( $var element = document.getElementById("moose-equation-adf0722d-c0e0-4e3d-a959-4c66551e7c91");katex.render("K", element, {displayMode:false,throwOnError:false});$ ) is the temperature of the SiC. Over a given timestep the average temperature is used for $var element = document.getElementById("moose-equation-a35156f7-74be-41cd-9066-62dd69cb0b0b");katex.render("T_{K}", element, {displayMode:false,throwOnError:false});$ :

$var element = document.getElementById("moose-equation-2064d8ab-468a-4a6c-9b68-809a65b716e3");katex.render(" T_{K} = \\frac{T_{current} + T_{old}}{2.0}", element, {displayMode:true,throwOnError:false});$

where $var element = document.getElementById("moose-equation-5b43939b-63cb-4e96-96f4-d38eee70f4f5");katex.render("T_{current}", element, {displayMode:false,throwOnError:false});$ is the temperature at the current timestep and $var element = document.getElementById("moose-equation-f2e13b88-5b29-41ff-b79b-b40e35d6e5d2");katex.render("T_{old}", element, {displayMode:false,throwOnError:false});$ is the temperature over the previous timestep. The total palladium penetration thickness is calculated as:

$var element = document.getElementById("moose-equation-35704433-31a7-4cb4-bf30-27e3e4dcded2");katex.render(" P_{Pd} = P_{PdOld} + \\dot{P}_{Pd} dt", element, {displayMode:true,throwOnError:false});$

warning

The correlation for Pd penetration is only temperature dependent and based on experiments with various amounts of initial Pd present. In reality a model for Pd should take into account the concentration of Pd available.

Range of Applicability

The palladium penetration model is assumed to be valid over all temperatures.

Example Input Syntax

[Postprocessors<<<{"href": "../../syntax/Postprocessors/index.html"}>>>]
  [pd_penetration]
    type = PdPenetration<<<{"description": "Penetration depth of palladium into the SiC layer of TRISO fuel particles", "href": "PdPenetration.html"}>>>
    boundary<<<{"description": "The list of boundary IDs from the mesh where this object applies"}>>> = 1
    variable<<<{"description": "The name of the variable which this postprocessor integrates"}>>> = temperature
    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'
  []
[]

Input Parameters

boundaryThe list of boundary IDs from the mesh where this object applies
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:The list of boundary IDs from the mesh where this object applies
variableThe name of the variable which this postprocessor integrates
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The name of the variable which this postprocessor integrates

Required 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, TRANSFER
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

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.
outputsVector of output names where you would like to restrict the output of variables(s) associated with this object
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
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

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

(examples/TRISO/failure_probability_monte_carlo/triso_1d_function.i)
(examples/TRISO/parfume/parfume.i)
(test/tests/SiCPdPenetration/palladium_penetration.i)
(test/tests/triso_failure/triso_failure_diffusivity.i)
(examples/TRISO/parfume/parfume_un.i)
(test/tests/triso_failure/triso_1d_kernel_migration.i)
(test/tests/triso_failure/triso_1d_pd_penetration.i)
(examples/TRISO/failure_probability_monte_carlo/triso_1d_constant.i)

References

David Petti, Phillipe Martin, Mayeul Phelip, and Ronald Ballinger. Development Of Improved Models And Designs For Coated-Particle Gas Reactor Fuels. Report INEEL/EXT-05-02615, Idaho National Laboratory for the International Nuclear Energy Research Initiative, December 2004.

@techreport{INERI2004,
    author = "Petti, David and Martin, Phillipe and Phelip, Mayeul and Ballinger, Ronald",
    title = "{Development Of Improved Models And Designs For Coated-Particle Gas Reactor Fuels}",
    institution = "Idaho National Laboratory for the International Nuclear Energy Research Initiative",
    year = "2004",
    month = "December",
    number = "INEEL/EXT-05-02615",
    type = "Report"
}

(test/tests/SiCPdPenetration/palladium_penetration.i)

# This test verifies the implementation of the palladium peneteration model
# for SiC in TRISO fuel particles.  The geometry is a 2D spherical shell of
# inner and outer diameters of 215 and 250 micrometers, respectively. The
# temperature is ramped linearly from 673.15 to 1673.15 K over 5.0e6 seconds
# using 5.0e5 second timesteps.
#
# The rate of palladium penetration (microns/day) is calculated by:
#
# P_{Pd}_dot = 38.232 * exp(-11342.3 / T) / 86400.0
#
# where T is the temperature. An incremental form is used to compute the total
# penetration thickness of the palladium.  Therefore, the average temperature
# over the timestep is used for T. The current penetration thickness is given by:
#
# P_{Pd} = P_{Pd}_old + P_{Pd}_dot * dt
#
# The palladium penetration for the 10 timesteps compared to the analytical
# calculation is provided below:
#
#     Current           BISON Pd        Analytical Pd
#  Temperature (K)   Penetration (m)   Penetration (m)
#     673.15              0                   0
#     773.15          3.4132E-11          3.4132E-11
#     873.15          2.6358E-10          2.6358E-10
#     973.15          1.2843E-09          1.2843E-09
#    1073.15          4.6762E-09          4.6762E-09
#    1173.15          1.3777E-08          1.3777E-08
#    1273.15          3.4558E-08          3.4558E-08
#    1373.15          7.6440E-08          7.6440E-08
#    1473.15          1.5293E-07          1.5293E-07
#    1573.15          2.8201E-07          2.8201E-07
#    1673.15          4.8624E-07          4.8624E-07

[Mesh]
  coord_type = RSPHERICAL
  [gen]
    type = TRISO1DMeshGenerator
    elem_type = EDGE2
    coordinates = '215e-6 250e-6'
    mesh_density = '4'
    block_names = 'sic'
  []
[]

[UserObjects]
  [particle_geometry]
    type = TRISOGeometry
    outer_OPyC = '1'
    outer_SiC = '1'
    outer_IPyC = '2'
    inner_IPyC = '1'
    outer_buffer = '1'
    outer_kernel = '1'
    include_particle = true
    include_pebble = false
  []
[]

[Variables]
  [temperature]
    order = FIRST
    family = LAGRANGE
    initial_condition = 673.15
  []
[]

[Functions]
  [temp_function]              # reads and interpolates input data defining amplitude curve for fill gas pressure
    type = PiecewiseLinear
    x = '0        5.0e6'
    y = '673.15 1673.15'
  []
[]

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

[BCs]
  [heat_removal]
    type = FunctionDirichletBC
    variable = temperature
    boundary = 2
    function = temp_function
  []
[]

[Materials]
  [thermal]
    type = MonolithicSiCThermal
    block = sic
    temperature = temperature
    thermal_conductivity_model = MILLER
  []

  [SiC_density]
    type = ParsedMaterial
    block = sic
    property_name = density
    expression = 3200.0
  []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -ksp_gmres_restart'
  petsc_options_value = 'lu       superlu_dist                  51'
  line_search = 'none'

  l_tol = 1e-5

  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-12

  start_time = 0.0
  end_time = 5.0e6
  num_steps = 10
  dt = 5.0e5
[]

[Postprocessors]
  [temperature]
    type = ElementExtremeValue
    block = sic
    value_type = 'max'
    variable = temperature
    execute_on = 'initial timestep_end'
  []
  [pd_penetration]
    type = PdPenetration
    boundary = 1
    variable = temperature
    execute_on = 'initial timestep_end'
  []
[]

[Outputs]
  csv = true
[]

(examples/TRISO/failure_probability_monte_carlo/triso_1d_function.i)


initial_fuel_density = 5

[GlobalParams]
  order = FIRST
  family = LAGRANGE
  displacements = 'disp_x'
  initial_enrichment = 0.14029 # [wt-]
  flux_conversion_factor = 1.0 # convert E>0.10 to E>0.18 MeV
  stress_free_temperature = 481 # used for thermal expansion
  energy_per_fission = 3.204e-11 # [J/fission]
  O_U = 1.428 # Initial Oxygen to Uranium atom ratio
  C_U = 0.392 # Initial Carbon to Uranium atom ratio
[]

[Mesh]
  coord_type = RSPHERICAL
  [gen]
    type = TRISO1DFiveLayerMeshGenerator
    elem_type = EDGE3
    kernel_radius = 213.35e-6
    buffer_thickness = 98.9e-6
    IPyC_thickness = 40.4e-6
    SiC_thickness = 35.2e-6
    OPyC_thickness = 43.4e-6
    kernel_mesh_density = ${initial_fuel_density}
    buffer_mesh_density = 3
    IPyC_mesh_density = 5
    SiC_mesh_density = 3
    OPyC_mesh_density = 4
  []
[]

[Problem]
  type = ReferenceResidualProblem
  reference_vector = 'ref'
  extra_tag_vectors = 'ref'
[]

[UserObjects]
  [particle_geometry]
    type = TRISOGeometry
    outer_OPyC = OPyC_outer_boundary
    outer_SiC = SiC_outer_boundary
    outer_IPyC = IPyC_outer_boundary
    inner_IPyC = IPyC_inner_boundary
    outer_buffer = buffer_outer_boundary
    outer_kernel = fuel_outer_boundary
    include_particle = true
    include_pebble = false
    IPyC_thickness_mean = 40.4e-6
    SiC_thickness_mean = 35.2e-6
    OPyC_thickness_mean = 43.4e-6
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [sic_failure_terminator]
    type = Terminator
    expression = 'sic_failure_overall > 0'
  []
[]

[Variables]
  [temperature]
    initial_condition = 481
  []
[]

[AuxVariables]
  [fission_rate]
    order = CONSTANT
    family = MONOMIAL
  []
  [burnup]
    order = CONSTANT
    family = MONOMIAL
  []
  [fast_neutron_flux]
    order = CONSTANT
    family = MONOMIAL
  []
  [fast_neutron_fluence]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [temp_bc]
    type = PiecewiseLinear
    data_file = outer_temp.csv
    x_index_in_file = 0
    y_index_in_file = 1
    format = columns
  []
  [fission_rate]
    type = ConstantFunction
    value = 5.75e19
  []
  [high_fidelity_strength_crackedIPyC]
    type = ConstantFunction
    value = '1403604095.0794'
  []
  [stress_correlation_crackedIPyC]
    type = TRISOStressCorrelationFunction
    triso_geometry = particle_geometry
    polynomial_coefficients_IPyC = '1 5.95176524e3 -2.25337303e8'
    polynomial_coefficients_SiC = '1 1.43220859e4 -5.17689523e7'
    polynomial_coefficients_OPyC = '1 -1.25870267e4 1.81620484e8'
    correlation_factor = -1.2447543093270736
  []
  [high_fidelity_strength_debonding]
    type = ConstantFunction
    value = '1705800293.3578'
  []
  [stress_correlation_debonding]
    type = TRISOStressCorrelationFunction
    triso_geometry = particle_geometry
    polynomial_coefficients_IPyC = '1 0 0'
    polynomial_coefficients_SiC = '1 0 0'
    polynomial_coefficients_OPyC = '1 0 0'
    correlation_factor = -0.14916368684964607
  []
  [high_fidelity_strength_asphericity]
    type = ConstantFunction
    value = '1371700806.9481'
  []
  [stress_correlation_asphericity]
    type = TRISOStressCorrelationFunction
    triso_geometry = particle_geometry
    polynomial_coefficients_IPyC = '1 1.00595402e3 1.43530004e7'
    polynomial_coefficients_SiC = '1 3.27925856e3 -2.02308753e8'
    polynomial_coefficients_OPyC = '1 2.07404580e3 -6.12612615e6'
    correlation_factor = 1.5191967993808713
  []
  [stress_change_correlation_asphericity]
    type = TRISOStressCorrelationFunction
    triso_geometry = particle_geometry
    polynomial_coefficients_IPyC = '1 -5.81891553e3 -2.81628655e7'
    polynomial_coefficients_SiC = '1 1.00990700e4 -5.55290343e8'
    polynomial_coefficients_OPyC = '1 -3.59151050e3 -2.65952373e7'
    correlation_factor = 1.3915168526633837
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  generate_output = 'stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz max_principal_stress'
  add_variables = true
  strain = FINITE
  incremental = true
  [fuel]
    block = fuel
    eigenstrain_names = 'UCO_swelling_eigenstrain UCO_TE_strain'
    extra_vector_tags = 'ref'
  []
  [buffer]
    block = buffer
    eigenstrain_names = 'Buffer_IIDC_strain Buffer_TE_strain'
    extra_vector_tags = 'ref'
  []
  [IPyC]
    block = IPyC
    eigenstrain_names = 'IPyC_IIDC_strain IPyC_TE_strain'
    extra_vector_tags = 'ref'
  []
  [SiC]
    block = SiC
    eigenstrain_names = 'SiC_thermal_eigenstrain'
    extra_vector_tags = 'ref'
  []
  [OPyC]
    block = OPyC
    eigenstrain_names = 'OPyC_IIDC_strain OPyC_TE_strain'
    extra_vector_tags = 'ref'
  []
[]

[Kernels]
  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temperature
    extra_vector_tags = 'ref'
  []
  [heat]
    type = HeatConduction
    variable = temperature
    extra_vector_tags = 'ref'
  []
  [heat_source]
    type = NeutronHeatSource
    variable = temperature
    block = fuel
    fission_rate = fission_rate
    extra_vector_tags = 'ref'
  []
[]

[AuxKernels]
  [fissionrate]
    type = MaterialRealAux
    variable = fission_rate
    property = fission_rate
    block = fuel
    execute_on = timestep_begin
  []
  [burnup]
    type = MaterialRealAux
    variable = burnup
    property = burnup
    block = fuel
    execute_on = timestep_begin
  []
  [fast_neutron_flux]
    type = MaterialRealAux
    variable = fast_neutron_flux
    property = fast_neutron_flux
    execute_on = timestep_begin
  []
  [fast_neutron_fluence]
    type = MaterialRealAux
    variable = fast_neutron_fluence
    property = fast_neutron_fluence
    execute_on = timestep_begin
  []
[]

[ThermalContact]
  [thermal_contact]
    type = GasGapHeatTransfer
    variable = temperature
    primary = IPyC_inner_boundary
    secondary = buffer_outer_boundary
    initial_moles = initial_moles
    gas_released = 'fis_gas_released'
    released_gas_types = 'Kr Xe'
    released_fractions = '0.185 0.815'
    tangential_tolerance = 1e-6
    quadrature = false
    min_gap = 1e-7
    max_gap = 50e-6
    gap_geometry_type = sphere
  []
[]

[BCs]
  [no_disp_x]
    type = DirichletBC
    variable = disp_x
    boundary = xzero
    value = 0.0
  []
  [freesurf_temp]
    type = FunctionDirichletBC
    variable = temperature
    function = temp_bc
    boundary = exterior
  []
  [exterior_pressure_x]
    type = Pressure
    variable = disp_x
    boundary = exterior
    factor = 0.1e6
  []
  [PlenumPressure]
    [plenumPressure]
      boundary = buffer_IPyC_boundary
      startup_time = 1e4
      initial_pressure = 0
      R = 8.3145
      output_initial_moles = initial_moles
      temperature = ave_gas_temp
      volume = 'gap_volume buffer_void_volume kernel_void_volume'
      material_input = 'fis_gas_released'
      output = gas_pressure
    []
  []
[]

[Materials]
  [radial_stress]
    type = RankTwoCylindricalComponent
    rank_two_tensor = stress
    cylindrical_axis_point1 = '0 0 0'
    cylindrical_axis_point2 = '0 0 1'
    cylindrical_component = RadialStress
    property_name = radial_stress
    outputs = all
  []
  [fission_rate]
    type = GenericFunctionMaterial
    prop_names = fission_rate
    prop_values = fission_rate
    block = fuel
  []
  [fast_neutron_flux]
    type = FastNeutronFlux
    calculate_fluence = true
    factor = 6.2425e+17
  []
  [UCO_burnup]
    type = TRISOBurnup
    initial_density = 10966
    block = fuel
  []
  [UCO_thermal]
    type = UCOThermal
    block = fuel
    temperature = temperature
  []
  [UCO_elasticity_tensor]
    type = UCOElasticityTensor
    block = fuel
    temperature = temperature
  []
  [UCO_stress]
    type = ComputeFiniteStrainElasticStress
    block = fuel
  []
  [UCO_VolumetricSwellingEigenstrain]
    type = UCOVolumetricSwellingEigenstrain
    block = fuel
    eigenstrain_name = UCO_swelling_eigenstrain
  []
  [fuel_thermal_expansion]
    type = ComputeThermalExpansionEigenstrain
    block = fuel
    thermal_expansion_coeff = 10.0e-6
    temperature = temperature
    eigenstrain_name = UCO_TE_strain
  []
  [UCO_density]
    type = StrainAdjustedDensity
    block = fuel
    strain_free_density = 10966
  []
  [fission_gas_release]
    type = UCOFGR
    block = fuel
    average_grain_radius = 10e-6
    temperature = temperature
    triso_geometry = particle_geometry
    cutoff_neutron_flux = 0.0
  []
  [BAF_IPyC]
    type = BaconAnisotropyFactor
    initial_BAF = 1.0465
    block = IPyC
  []
  [BAF_OPyC]
    type = BaconAnisotropyFactor
    initial_BAF = 1.0429
    block = OPyC
  []
  [buffer_elasticity_tensor]
    type = BufferElasticityTensor
    block = buffer
    temperature = temperature
  []
  [buffer_stress]
    type = BufferCEGACreep
    block = buffer
    temperature = temperature
  []
  [buffer_thermal]
    type = BufferThermal
    block = buffer
    initial_density = 1050.0
  []
  [buffer_density]
    type = StrainAdjustedDensity
    block = buffer
    strain_free_density = 1050.0
  []
  [buffer_TE]
    type = BufferThermalExpansionEigenstrain
    block = buffer
    eigenstrain_name = Buffer_TE_strain
    temperature = temperature
  []
  [buffer_IIDC]
    type = BufferCEGAIrradiationEigenstrain
    block = buffer
    eigenstrain_name = Buffer_IIDC_strain
    temperature = temperature
  []
  [IPyC_elasticity_tensor]
    type = PyCElasticityTensor
    block = IPyC
    temperature = temperature
  []
  [IPyC_stress]
    type = PyCCEGACreep
    block = IPyC
    creep_rate_scale_factor = 1
    temperature = temperature
  []

  [IPyC_thermal]
    type = HeatConductionMaterial
    block = IPyC
    thermal_conductivity = 4.0
    specific_heat = 720.0
  []
  [IPyC_density]
    type = GenericConstantMaterial
    block = IPyC
    prop_names = 'density'
    prop_values = 1890
  []
  [normal_vectors_triso]
    type = NormalVectorsTRISO
    block = 'buffer IPyC OPyC'
  []
  [IPyC_IIDC]
    type = PyCCEGAIrradiationEigenstrain
    block = IPyC
    eigenstrain_name = IPyC_IIDC_strain
    temperature = temperature
    irradiation_eigenstrain_scale_factor = 1
  []
  [IPyC_TE]
    type = PyCThermalExpansionEigenstrain
    block = IPyC
    eigenstrain_name = IPyC_TE_strain
    temperature = temperature
  []
  [SiC_elasticity_tensor]
    type = MonolithicSiCElasticityTensor
    block = SiC
    temperature = temperature
    elastic_modulus_model = miller
  []
  [SiC_stress]
    type = ComputeFiniteStrainElasticStress
    block = SiC
  []
  [SiC_thermal]
    type = MonolithicSiCThermal
    block = SiC
    temperature = temperature
    thermal_conductivity_model = miller
  []
  [SiC_density]
    type = StrainAdjustedDensity
    block = SiC
    strain_free_density = 3200.0
  []
  [SiC_thermal_expansion]
    type = ComputeThermalExpansionEigenstrain
    block = SiC
    thermal_expansion_coeff = 4.9e-6
    temperature = temperature
    eigenstrain_name = SiC_thermal_eigenstrain
  []
  [OPyC_elasticity_tensor]
    type = PyCElasticityTensor
    block = OPyC
    temperature = temperature
    initial_BAF = 1.0
  []
  [OPyC_stress]
    type = PyCCEGACreep
    block = OPyC
    creep_rate_scale_factor = 1
    temperature = temperature
  []
  [OPyC_thermal_conductivity]
    type = HeatConductionMaterial
    block = OPyC
    thermal_conductivity = 4.0
    specific_heat = 720.0
  []
  [OPyC_density]
    type = GenericConstantMaterial
    block = OPyC
    prop_names = 'density'
    prop_values = 1900
  []
  [OPyC_IIDC]
    type = PyCCEGAIrradiationEigenstrain
    block = OPyC
    eigenstrain_name = OPyC_IIDC_strain
    temperature = temperature
    irradiation_eigenstrain_scale_factor = 1
  []
  [OPyC_TE]
    type = PyCThermalExpansionEigenstrain
    block = OPyC
    eigenstrain_name = OPyC_TE_strain
    temperature = temperature
  []
  [characteristic_strength_SiC]
    type = GenericConstantMaterial
    prop_values = '9640000'
    block = SiC
    prop_names = 'characteristic_strength'
  []
  [characteristic_strength_PyC]
    type = PyCCharacteristicStrength
    temperature = temperature
    X = 1.02
    block = 'IPyC OPyC'
  []
[]

[Dampers]
  [temp]
    type = MaxIncrement
    variable = temperature
    max_increment = 100
  []
[]

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

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'

  line_search = 'none'

  nl_rel_tol = 5e-6
  nl_abs_tol = 1e-8
  nl_max_its = 20

  l_tol = 1e-4
  l_max_its = 50

  start_time = 0.0
  end_time = 4.831315e7

  dtmin = 1e-4
  dt = 5e5
[]

[Postprocessors]
  [ave_gas_temp]
    type = ElementAverageValue
    block = buffer
    variable = temperature
    execute_on = 'initial timestep_end'
  []
  [fis_gas_released]
    type = ElementIntegralMaterialProperty
    mat_prop = fis_gas_released
    block = fuel
    use_displaced_mesh = false
    execute_on = 'initial timestep_end'
  []
  [gap_volume]
    type = InternalVolume
    boundary = buffer_IPyC_boundary
    execute_on = 'initial linear'
    use_displaced_mesh = true
  []
  [buffer_void_volume]
    type = VoidVolume
    block = buffer
    theoretical_density = 2250
    execute_on = 'initial timestep_end'
    use_displaced_mesh = true
  []
  [kernel_th_density]
    type = UCOTheoreticalDensity
    execute_on = initial
  []
  [kernel_void_volume]
    type = VoidVolume
    block = fuel
    theoretical_density = kernel_th_density
    execute_on = 'initial timestep_end'
    use_displaced_mesh = true
  []
  [particle_power]
    type = ElementIntegralPower
    variable = temperature
    use_material_fission_rate = true
    fission_rate_material = fission_rate
    block = fuel
    execute_on = 'initial timestep_end'
  []
  [max_fluence]
    type = ElementExtremeValue
    variable = fast_neutron_fluence
    value_type = 'max'
    execute_on = 'initial timestep_end'
  []
  [max_burnup]
    type = ElementExtremeValue
    variable = burnup
    block = fuel
    value_type = 'max'
    execute_on = 'initial timestep_end'
  []
  [SiC_stress]
    type = ElementExtremeMaterialProperty
    block = SiC
    value_type = min
    mat_prop = stress_yy
  []
  [strength_SiC]
    type = WeibullEffectiveMeanStrength
    block = SiC
    weibull_modulus = 6
  []
  [failure_indicator_SiC]
    type = WeibullFailureOutputUsingCorrelation
    block = SiC
    weibull_modulus = 6
    stress_name = stress_yy
    high_fidelity_analysis_strength = 'high_fidelity_strength_asphericity'
    stress_correlation_function = 'stress_correlation_asphericity'
    stress_change_correlation_function = 'stress_change_correlation_asphericity'
  []
  [strength_IPyC]
    type = WeibullEffectiveMeanStrength
    block = IPyC
    weibull_modulus = 9.5
  []
  [failure_indicator_IPyC]
    type = WeibullFailureOutputUsingCorrelation
    block = IPyC
    weibull_modulus = 9.5
    stress_name = max_principal_stress
    effective_mean_strength = strength_IPyC
  []
  [failure_indicator_SiC_crackedIPyC]
    type = WeibullFailureOutputUsingCorrelation
    block = SiC
    weibull_modulus = 6
    stress_name = stress_yy
    high_fidelity_analysis_strength = 'high_fidelity_strength_crackedIPyC'
    stress_correlation_function = 'stress_correlation_crackedIPyC'
  []
  [failure_indicator_debonding]
    type = TRISODebondingFailureIndicator
    boundary = IPyC_outer_boundary
    bond_strength = 10e6
    stress_name = radial_stress
  []
  [failure_indicator_SiC_debonding]
    type = WeibullFailureOutputUsingCorrelation
    block = SiC
    weibull_modulus = 6
    stress_name = stress_yy
    high_fidelity_analysis_strength = 'high_fidelity_strength_debonding'
    stress_correlation_function = 'stress_correlation_debonding'
  []
  [sic_failure_overall]
    type = TRISOFailureEvaluation
    IPyC_failure = failure_indicator_IPyC
    SiC_failure_crackedIPyC = failure_indicator_SiC_crackedIPyC
    SiC_failure = failure_indicator_SiC
    SiC_failure_pd_penetration = failure_indicator_pd_penetration
    SiC_failure_kernel_migration = failure_indicator_kernel_migration
    failure_type = SIC_FAILURE_OVERALL
  []
  [ipyc_cracking]
    type = TRISOFailureEvaluation
    IPyC_failure = failure_indicator_IPyC
    SiC_failure_crackedIPyC = failure_indicator_SiC_crackedIPyC
    SiC_failure = failure_indicator_SiC
    failure_type = IPYC_CRACKING
  []
  [sic_failure_due_to_pressure]
    type = TRISOFailureEvaluation
    IPyC_failure = failure_indicator_IPyC
    SiC_failure_crackedIPyC = failure_indicator_SiC_crackedIPyC
    SiC_failure = failure_indicator_SiC
    failure_type = SIC_FAILURE_DUE_TO_PRESSURE
  []
  [sic_failure_due_to_ipyc_cracking]
    type = TRISOFailureEvaluation
    IPyC_failure = failure_indicator_IPyC
    SiC_failure_crackedIPyC = failure_indicator_SiC_crackedIPyC
    SiC_failure = failure_indicator_SiC
    failure_type = SIC_FAILURE_DUE_TO_IPYC_CRACKING
  []
  [debonding]
    type = TRISOFailureEvaluation
    IPyC_failure = failure_indicator_IPyC
    SiC_failure_crackedIPyC = failure_indicator_SiC_crackedIPyC
    SiC_failure = failure_indicator_SiC
    IPyC_SiC_debonding = failure_indicator_debonding
    SiC_failure_debonding = failure_indicator_SiC_debonding
    failure_type = IPYC_SIC_DEBONDING
  []
  [fluence_at_failure]
    type = TRISOFailureOccurrenceStatus
    failure_evaluation = ipyc_cracking
    failure_information = max_fluence
  []
  [weibull_failure_probability_IPyC]
    type = WeibullFailureProbability
    block = IPyC
    weibull_modulus = 9.5
    characteristic_strength = characteristic_strength
  []
  [weibull_failure_probability_SiC]
    type = WeibullFailureProbability
    block = SiC
    weibull_modulus = 6
    characteristic_strength = characteristic_strength
  []
  [pd_penetration]
    type = PdPenetration
    boundary = SiC_inner_boundary
    variable = temperature
    execute_on = 'initial timestep_end'
  []
  [failure_indicator_pd_penetration]
    type = PdPenetrationFailureIndicator
    triso_geometry = particle_geometry
    pd_penetration = pd_penetration
  []
  [kernel_migration_distance]
    type = KernelMigrationDistance
    block = 'fuel buffer IPyC SiC OPyC'
    variable = temperature
    temperature_gradient = 15000
    kernel_type = UCO
  []
  [failure_indicator_kernel_migration]
    type = KernelMigrationFailureIndicator
    kernel_migration_distance = kernel_migration_distance
    triso_geometry = particle_geometry
  []
[]

[Outputs]
  print_linear_residuals = false
  time_step_interval =  1
  csv = false
  exodus = false
  perf_graph = true
  print_linear_converged_reason = false
  print_nonlinear_converged_reason = false
[]

(examples/TRISO/parfume/parfume.i)

# UCO TRISO particle using several PARFUME models

initial_fuel_density = 10400

[GlobalParams]
  order = SECOND
  family = LAGRANGE
  displacements = 'disp_x'
  initial_enrichment = 0.1955 # [wt-]
  flux_conversion_factor = 1.0 # convert E>0.10 to E>0.18 MeV
  stress_free_temperature = 923.15 # used for thermal expansion
  energy_per_fission = 3.204e-11 # [J/fission]
  O_U = 1.5 # Initial Oxygen to Uranium atom ratio
  C_U = 0.4 # Initial Carbon to Uranium atom ratio
[]

[Mesh]
  coord_type = RSPHERICAL
  [gen]
    type = TRISO1DMeshGenerator
    elem_type = EDGE3
    coordinates = '0 2.125e-4 3.125e-4 3.125e-4 3.525e-4 3.875e-4 4.275e-4'
    mesh_density = '6 6 0 6 8 6'
    block_names = 'fuel buffer IPyC SiC OPyC'
  []
[]

[Problem]
  type = ReferenceResidualProblem
  reference_vector = 'ref'
  extra_tag_vectors = 'ref'
[]

[UserObjects]
  [particle_geometry]
    type = TRISOGeometry
  []
[]

[Variables]
  [temperature]
    initial_condition = 923.15
  []
  [conc]
    initial_condition = 0.0
    scaling = 1e18
  []
[]

[AuxVariables]
  [disp_y]
  []
  [disp_z]
  []

  [fission_rate]
    block = fuel
    order = CONSTANT
    family = MONOMIAL
  []

  [burnup]
    block = fuel
    order = CONSTANT
    family = MONOMIAL
  []

  [fast_neutron_flux]
    order = CONSTANT
    family = MONOMIAL
  []

  [fast_neutron_fluence]
    order = CONSTANT
    family = MONOMIAL
  []

  [gap_condSlave]
    order = CONSTANT
    family = MONOMIAL
  []

  [density]
    order = CONSTANT
    family = MONOMIAL
  []

  [thermal_conductivity]
    order = CONSTANT
    family = MONOMIAL
  []

  [swelling]
    order = CONSTANT
    family = MONOMIAL
  []

  [specific_heat]
    order = CONSTANT
    family = MONOMIAL
  []

  [volumetric_IIDC_strain]
    order = CONSTANT
    family = MONOMIAL
  []

  [radial_IIDC_strain]
    order = CONSTANT
    family = MONOMIAL
  []

  [tangential_IIDC_strain]
    order = CONSTANT
    family = MONOMIAL
  []

  [BAF]
    order = CONSTANT
    family = MONOMIAL
  []

  [fis_gas_produced]
    order = CONSTANT
    family = MONOMIAL
  []

  [fis_gas_released]
    order = CONSTANT
    family = MONOMIAL
  []

  [gap_HTC]
    order = CONSTANT
    family = MONOMIAL
  []

  [gap_distance]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [power_history]
    type = PiecewiseLinear
    x = '0 76e6 76.001e6'
    y = '1 1     0'
  []
  [fission_rate]
    type = LinearCombinationFunction
    functions = power_history
    w = 3.89e19
  []
  [temp_bc]
    type = PiecewiseLinear
    x = '0    76e6  76.001e6 84.641e6 84.6482e6'
    y = '1500 1500  300      300      2073'
  []
  [k_function]
    type = PiecewiseLinear
    x = '0     200e6'
    y = '4e-37 4e-37'
  []
  [d1_function]
    type = ParsedFunction
    expression = 'exp(t/4.5e25)'
  []
  [d_gap]
    type = PiecewiseLinear
    x = '1500  2100'
    y = '1e-14 1e-12'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [fuel]
    block = fuel
    add_variables = true
    strain = FINITE
    incremental = true
    generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz'
    eigenstrain_names = 'UCO_swelling_eigenstrain UCO_thermal_strain'
    extra_vector_tags = 'ref'
  []
  [buffer]
    block = buffer
    add_variables = true
    strain = FINITE
    incremental = true
    generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz'
    eigenstrain_names = 'buffer_IIDC_strain buffer_thermal_strain'
    extra_vector_tags = 'ref'
  []
  [IPyC]
    block = IPyC
    add_variables = true
    strain = FINITE
    incremental = true
    generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz'
    eigenstrain_names = 'IPyC_IIDC_strain IPyC_thermal_strain'
    extra_vector_tags = 'ref'
  []
  [SiC]
    block = SiC
    add_variables = true
    strain = FINITE
    incremental = true
    generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz'
    eigenstrain_names = 'SiC_thermal_eigenstrain'
    extra_vector_tags = 'ref'
  []
  [OPyC]
    block = OPyC
    add_variables = true
    strain = FINITE
    incremental = true
    generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz'
    eigenstrain_names = 'OPyC_IIDC_strain OPyC_thermal_strain'
    extra_vector_tags = 'ref'
  []
[]

[Kernels]
  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temperature
    extra_vector_tags = 'ref'
  []
  [heat]
    type = HeatConduction
    variable = temperature
    extra_vector_tags = 'ref'
  []
  [heat_source]
    type = NeutronHeatSource
    variable = temperature
    block = fuel
    fission_rate = fission_rate
    extra_vector_tags = 'ref'
  []
  [mass_ie]
    type = TimeDerivative
    variable = conc
    extra_vector_tags = 'ref'
  []
  [mass]
    type = ArrheniusDiffusion
    variable = conc
    extra_vector_tags = 'ref'
  []
  [mass_source]
    type = BodyForce
    variable = conc
    function = power_history
    value = 1.22e-5 # units of mol/m**3-s
    block = fuel
    extra_vector_tags = 'ref'
  []
  [mass_decay]
    type = Decay
    variable = conc
    radioactive_decay_constant = 7.297e-10 # units:(1/sec)  The constant for Cesium
    extra_vector_tags = 'ref'
  []
[]

[AuxKernels]
  [fissionrate]
    type = MaterialRealAux
    variable = fission_rate
    property = fission_rate
    block = fuel
    execute_on = timestep_begin
  []

  [burnup]
    type = MaterialRealAux
    variable = burnup
    property = burnup
    block = fuel
    execute_on = timestep_begin
  []

  [fast_neutron_flux]
    type = MaterialRealAux
    variable = fast_neutron_flux
    property = fast_neutron_flux
    block = 'fuel buffer IPyC SiC OPyC'
    execute_on = timestep_begin
  []

  [fast_neutron_fluence]
    type = MaterialRealAux
    variable = fast_neutron_fluence
    property = fast_neutron_fluence
    block = 'fuel buffer IPyC SiC OPyC'
    execute_on = timestep_begin
  []

  [conductanceSlave]
    type = MaterialRealAux
    property = gap_conductance
    variable = gap_condSlave
    boundary = buffer_outer_boundary
    execute_on = 'initial timestep_end'
  []

  [density]
    type = MaterialRealAux
    variable = density
    property = density
    block = 'fuel buffer IPyC SiC OPyC'
    execute_on = 'initial linear'
  []

  [thermal_conductivity]
    type = MaterialRealAux
    variable = thermal_conductivity
    property = thermal_conductivity
    block = 'fuel buffer IPyC SiC OPyC'
    execute_on = timestep_end
  []

  [specific_heat]
    type = MaterialRealAux
    variable = specific_heat
    property = specific_heat
    block = 'fuel buffer IPyC SiC OPyC'
    execute_on = timestep_end
  []

  [swelling]
    type = MaterialRealAux
    variable = swelling
    property = swelling
    block = fuel
    execute_on = linear
  []

  [volumetric_IIDC_strain]
    type = MaterialRealAux
    variable = volumetric_IIDC_strain
    property = volumetric_IIDC_strain
    block = 'IPyC OPyC'
    execute_on = timestep_end
  []

  [radial_IIDC_strain]
    type = MaterialRealAux
    variable = radial_IIDC_strain
    property = radial_IIDC_strain
    block = 'IPyC OPyC'
    execute_on = timestep_end
  []

  [tangential_IIDC_strain]
    type = MaterialRealAux
    variable = tangential_IIDC_strain
    property = tangential_IIDC_strain
    block = 'IPyC OPyC'
    execute_on = timestep_end
  []

  [BAF]
    type = MaterialRealAux
    variable = BAF
    property = BAF
    block = 'IPyC OPyC'
    execute_on = timestep_end
  []

  [fis_gas_produced]
    type = MaterialRealAux
    variable = fis_gas_produced
    property = fis_gas_produced
    block = fuel
    execute_on = linear
  []

  [fis_gas_released]
    type = MaterialRealAux
    variable = fis_gas_released
    property = fis_gas_released
    block = fuel
    execute_on = linear
  []

  [gap_HTC]
    type = MaterialRealAux
    property = gap_conductance
    variable = gap_HTC
    boundary = buffer_outer_boundary
    execute_on = 'initial timestep_end'
  []

  [gap_distance]
    type = PenetrationAux
    variable = gap_distance
    boundary = buffer_outer_boundary
    paired_boundary = IPyC_inner_boundary
    quantity = distance
    tangential_tolerance = 1e-6
    execute_on = 'initial timestep_end'
  []
[]

[Contact]
  [mechanical]
    primary = IPyC_inner_boundary
    secondary = buffer_outer_boundary
    penalty = 1e5
    model = frictionless
    formulation = kinematic
  []
[]

[ThermalContact]
  [thermal_contact]
    type = GasGapHeatTransfer
    variable = temperature
    primary = IPyC_inner_boundary
    secondary = buffer_outer_boundary
    initial_moles = initial_moles # coupling to a postprocessor which supplies the initial plenum/gap gas mass
    initial_gas_types = 'Kr Xe'
    initial_fractions = '0.185 0.815'
    gas_released = 'fis_gas_released'
    released_gas_types = 'Kr Xe'
    released_fractions = '0.185 0.815'
    tangential_tolerance = 1e-6
    roughness_primary = 0e-6
    roughness_secondary = 0e-6
    jumpdistance_primary = 0
    jumpdistance_secondary = 0
    quadrature = true
    emissivity_secondary = 0.0
    emissivity_primary = 0.0
    min_gap = 1e-7
    max_gap = 50e-6
    gap_geometry_type = sphere
  []

  [cesium_contact]
    type = GapHeatTransfer
    variable = conc
    primary = IPyC_inner_boundary
    secondary = buffer_outer_boundary
    tangential_tolerance = 1e-6
    gap_conductivity_function = d_gap
    gap_conductivity_function_variable = temperature
    appended_property_name = _conc
    quadrature = true
    gap_geometry_type = sphere
    emissivity_primary = 0.0
    emissivity_secondary = 0.0
    min_gap = 1e-7
  []
[]

[BCs]
  # pin particle along symmetry planes
  [no_disp_x]
    type = DirichletBC
    variable = disp_x
    boundary = xzero
    value = 0.0
  []

  # fix temperature on free surface
  [freesurf_temp]
    type = FunctionDirichletBC
    variable = temperature
    function = temp_bc
    boundary = exterior
  []

  # fix concentration on free surface
  [freesurf_conc]
    type = DirichletBC
    variable = conc
    boundary = exterior
    value = 0.0
  []

  # exterior and internal pressures
  [exterior_pressure_x]
    type = Pressure
    variable = disp_x
    boundary = exterior
    factor = 0.1e6
  []

  [PlenumPressure] #  apply gas pressure on buffer and IPyC boundaries
    [plenumPressure]
      boundary = buffer_IPyC_boundary
      initial_pressure = 100.0
      startup_time = 0
      R = 8.3145
      output_initial_moles = initial_moles
      temperature = ave_gas_temp
      volume = 'gap_volume buffer_void_volume kernel_void_volume'
      material_input = 'fis_gas_released'
      output = gas_pressure
    []
  []
[]

[Materials]

  [fission_rate]
    type = GenericFunctionMaterial
    prop_names = fission_rate
    prop_values = fission_rate
  []

  [fast_neutron_flux]
    type = FastNeutronFlux
    calculate_fluence = true
    flux_function = power_history
    factor = 5e17
  []

  [normal_vectors_triso]
    type = NormalVectorsTRISO
    block = 'buffer IPyC OPyC'
  []

  ### UCO properties

  [UCO_burnup]
    type = TRISOBurnup
    initial_density = ${initial_fuel_density}
  []

  [UCO_thermal]
    type = UCOThermal
    block = fuel
    temperature = temperature
  []

  [UCO_elasticity_tensor]
    type = UCOElasticityTensor
    block = fuel
    temperature = temperature
  []

  [UCO_stress]
    type = ComputeFiniteStrainElasticStress
    block = fuel
  []

  [UCO_VolumetricSwellingEigenstrain]
    type = UCOVolumetricSwellingEigenstrain
    block = fuel
    eigenstrain_name = UCO_swelling_eigenstrain
  []

  [UCO_thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    block = fuel
    thermal_expansion_coeff = 10e-6 # check this value for UCO
    eigenstrain_name = UCO_thermal_strain
    temperature = temperature
  []

  [UCO_density]
    type = StrainAdjustedDensity
    block = fuel
    strain_free_density = ${initial_fuel_density}
  []

  [fission_gas_release]
    type = UCOFGR
    block = fuel
    average_grain_radius = 10e-6
    temperature = temperature
    triso_geometry = particle_geometry
    cutoff_neutron_flux = 0.0
  []

  [fuel_conc]
    type = ArrheniusDiffusionCoef
    block = fuel
    d1 = 5.6e-8 # m^2/s
    q1 = 209.0e+3 # J/mol
    d2 = 5.2e-4 # m^2/s
    q2 = 362.0e+3 # J/mol
    temperature = temperature
  []

  ### Buffer Properties

  [buffer_elasticity_tensor]
    type = BufferElasticityTensor
    block = buffer
    temperature = temperature
  []

  [buffer_stress]
    type = BufferCEGACreep
    block = buffer
    temperature = temperature
  []

  [buffer_thermal]
    type = BufferThermal
    block = buffer
    initial_density = 1050.0
  []

  [buffer_density]
    type = StrainAdjustedDensity
    block = buffer
    strain_free_density = 1050.0
  []

  [buffer_thermal_strain]
    type = BufferThermalExpansionEigenstrain
    block = buffer
    eigenstrain_name = buffer_thermal_strain
    temperature = temperature
  []

  [buffer_IIDC_strain]
    type = BufferCEGAIrradiationEigenstrain
    block = buffer
    eigenstrain_name = buffer_IIDC_strain
    temperature = temperature
  []

  [buffer_conc]
    type = ArrheniusDiffusionCoef
    block = buffer
    d1 = 1.0e-12 # m^2/s
    q1 = 0.0
    d2 = 0.0
    q2 = 0.0
    temperature = temperature
  []

  ### IPyC  properties

  [IPyC_elasticity_tensor]
    type = PyCElasticityTensor
    block = IPyC
    temperature = temperature
    initial_BAF = 1.045
  []

  [IPyC_stress]
    type = PyCCEGACreep
    block = IPyC
    temperature = temperature
  []

  [IPyC_thermal]
    type = HeatConductionMaterial
    block = IPyC
    thermal_conductivity = 4.0
    specific_heat = 720.0
  []

  [IPyC_density]
    type = GenericConstantMaterial
    block = IPyC
    prop_names = 'density'
    prop_values = 1900.0
  []

  [IPyC_IIDC_strain]
    type = PyCCEGAIrradiationEigenstrain
    block = IPyC
    eigenstrain_name = IPyC_IIDC_strain
    temperature = temperature
  []

  [BAF_IPyC]
    type = BaconAnisotropyFactor
    initial_BAF = 1.045
    block = IPyC
  []

  [BAF_OPyC]
    type = BaconAnisotropyFactor
    initial_BAF = 1.045
    block = OPyC
  []

  [IPyC_thermal_strain]
    type = PyCThermalExpansionEigenstrain
    block = IPyC
    eigenstrain_name = IPyC_thermal_strain
    temperature = temperature
  []

  [IPyC_conc]
    type = ArrheniusDiffusionCoef
    block = IPyC
    d1 = 6.3e-8 # m^2/s
    q1 = 222.0e+3 # J/mol
    d2 = 0.0
    q2 = 0.0
    temperature = temperature
  []

  ### SiC properties

  [SiC_elasticity_tensor]
    type = MonolithicSiCElasticityTensor
    block = SiC
    temperature = temperature
    elastic_modulus_model = miller
  []

  [SiC_stress]
    type = ComputeFiniteStrainElasticStress
    block = SiC
  []

  [SiC_thermal]
    type = MonolithicSiCThermal
    block = SiC
    temperature = temperature
    thermal_conductivity_model = miller
  []

  [SiC_density]
    type = GenericConstantMaterial
    block = SiC
    prop_names = 'density'
    prop_values = 3200.0
  []

  [SiC_thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    block = SiC
    thermal_expansion_coeff = 4.9e-6
    temperature = temperature
    eigenstrain_name = SiC_thermal_eigenstrain
  []

  [SiC_conc]
    type = ArrheniusDiffusionCoef
    block = SiC
    d1 = 5.5e-14 # m^2/s
    d1_function = d1_function
    d1_function_variable = fast_neutron_fluence
    q1 = 125.0e+3 # J/mol
    d2 = 1.6e-2 # m^2/s
    q2 = 514.0e+3 # J/mol
    temperature = temperature
  []

  ###  OPyC properties

  [OPyC_elasticity_tensor]
    type = PyCElasticityTensor
    block = OPyC
    temperature = temperature
    initial_BAF = 1.045
  []

  [OPyC_stress]
    type = PyCCEGACreep
    block = OPyC
    temperature = temperature
  []

  [OPyC_thermal_conductivity]
    type = HeatConductionMaterial
    block = OPyC
    thermal_conductivity = 4.0
    specific_heat = 720.0
  []

  [OPyC_density]
    type = GenericConstantMaterial
    block = OPyC
    prop_names = 'density'
    prop_values = 1900.0
  []

  [OPyC_IIDC_strain]
    type = PyCCEGAIrradiationEigenstrain
    block = OPyC
    eigenstrain_name = OPyC_IIDC_strain
    temperature = temperature
  []

  [OPyC_thermal_strain]
    type = PyCThermalExpansionEigenstrain
    block = OPyC
    eigenstrain_name = OPyC_thermal_strain
    temperature = temperature
  []

  [OPyC_conc]
    type = ArrheniusDiffusionCoef
    block = OPyC
    d1 = 6.3e-8 # m^2/s
    q1 = 222.0e+3 # J/mol
    d2 = 0.0
    q2 = 0.0
    temperature = temperature
  []
[]

[Dampers]
  [temp]
    type = MaxIncrement
    variable = temperature
    max_increment = 50
  []
  [disp_x]
    type = MaxIncrement
    variable = disp_x
    max_increment = 1e-6
  []
[]

[Debug]
  show_var_residual_norms = true
  show_var_residual = 'disp_x temperature conc'
[]

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

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'

  line_search = 'none'

  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-7 #1e-12
  nl_max_its = 15

  l_tol = 1e-4 #1e-8
  l_max_its = 50

  start_time = 0.0
  end_time = 85.3682e6 #5.0e7
  num_steps = 1000

  dtmax = 2e6
  dtmin = 1

  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 20
    growth_factor = 1.5
    optimal_iterations = 8 #6
    linear_iteration_ratio = 100
    time_t = '0    76e6  76.001e6 84.641e6 84.6482e6'
    time_dt = '20  20     20      20       20'
  []

  [Quadrature]
    order = THIRD
  []
[]

[Postprocessors]
  [_dt]
    type = TimestepSize
    execute_on = timestep_end
  []
  [cs_release]
    type = SideIntegralMassFlux
    variable = conc
    boundary = exterior
  []
  [int_cs_release]
    type = TimeIntegratedPostprocessor
    value = cs_release
  []
  [cs_release_fuel]
    type = SideIntegralMassFlux
    variable = conc
    boundary = fuel_outer_boundary
  []
  [int_cs_release_fuel]
    type = TimeIntegratedPostprocessor
    value = cs_release_fuel
  []
  [cs_release_PyCGapBndry]
    type = SideIntegralMassFlux
    variable = conc
    boundary = IPyC_inner_boundary
  []
  [int_cs_release_PyCGapBndry]
    type = TimeIntegratedPostprocessor
    value = cs_release_PyCGapBndry
  []

  [ave_gas_temp]
    type = ElementAverageValue
    block = buffer
    variable = temperature
    execute_on = 'initial timestep_end'
  []

  [ave_gap_temp]
    type = SideAverageValue
    boundary = buffer_IPyC_boundary
    variable = temperature
    execute_on = 'initial timestep_end'
  []

  [fis_gas_produced]
    type = ElementIntegralMaterialProperty
    mat_prop = fis_gas_produced
    block = fuel
    execute_on = 'initial timestep_end'
  []

  [fis_gas_released]
    type = ElementIntegralMaterialProperty
    mat_prop = fis_gas_released
    block = fuel
    execute_on = 'initial timestep_end'
  []

  [gap_volume]
    type = InternalVolume
    boundary = buffer_IPyC_boundary
    execute_on = 'initial linear'
    use_displaced_mesh = true
  []

  [buffer_void_volume]
    type = VoidVolume
    block = buffer
    theoretical_density = 2250
    execute_on = 'initial timestep_end'
    use_displaced_mesh = true
  []

  [kernel_th_density]
    type = UCOTheoreticalDensity
    execute_on = initial
  []

  [kernel_void_volume]
    type = VoidVolume
    block = fuel
    theoretical_density = kernel_th_density
    execute_on = 'initial timestep_end'
    use_displaced_mesh = true
  []

  [volumeTotal]
    type = InternalVolume
    boundary = exterior
    execute_on = 'initial timestep_end'
    scale_factor = -1
  []
  [volumeFuel]
    type = InternalVolume
    boundary = fuel_outer_boundary
    execute_on = 'initial timestep_end'
    scale_factor = -1
  []
  [volumeGas]
    type = InternalVolume
    boundary = buffer_outer_boundary
    execute_on = 'initial timestep_end'
    scale_factor = -1
    addition = 4.67e-11
  []
  [volumeBufferShell]
    type = InternalVolume
    boundary = buffer_outer_boundary
    execute_on = 'initial timestep_end'
  []
  [ave_temp_interior]
    type = SideAverageValue
    boundary = buffer_outer_boundary
    variable = temperature
    execute_on = 'initial timestep_end'
  []

  [gap_HTC]
    type = ElementExtremeValue
    variable = gap_HTC
    block = buffer
    value_type = 'max'
    execute_on = 'initial timestep_end'
  []

  ### Postprocessors for CO production
  [total_fission_rate]
    type = ElementIntegralPower
    variable = temperature
    fission_rate = fission_rate
    block = fuel
    energy_per_fission = 1.0
    outputs = exodus
    execute_on = 'initial timestep_end'
  []
  [total_fissions]
    type = TimeIntegratedPostprocessor
    value = total_fission_rate
    outputs = exodus
    execute_on = 'initial timestep_end'
  []
  [avg_surface_temp]
    type = SideAverageValue
    variable = temperature
    boundary = exterior
    outputs = exodus
    execute_on = 'initial timestep_end'
  []
  [time_int_surf_temp]
    type = TimeIntegratedPostprocessor
    value = avg_surface_temp
    outputs = exodus
    execute_on = 'initial timestep_end'
  []

  ##### irradiation conditions

  [particle_power]
    type = ElementIntegralPower
    variable = temperature
    use_material_fission_rate = true
    fission_rate_material = fission_rate
    block = fuel
    execute_on = 'initial timestep_end'
  []

  [max_fluence]
    type = ElementExtremeValue
    variable = fast_neutron_fluence
    block = 'fuel buffer IPyC SiC OPyC'
    value_type = 'max'
    execute_on = 'initial timestep_end'
  []

  [max_burnup]
    type = ElementExtremeValue
    variable = burnup
    block = fuel
    value_type = 'max'
    execute_on = 'initial timestep_end'
  []

  #### II strain

  [OPyC_radial_IIDC_strain]
    type = ElementExtremeValue
    variable = radial_IIDC_strain
    block = OPyC
    value_type = 'max'
    execute_on = 'initial timestep_end'
  []

  [OPyC_tangential_IIDC_strain]
    type = ElementExtremeValue
    variable = tangential_IIDC_strain
    block = OPyC
    value_type = 'max'
    execute_on = 'initial timestep_end'
  []

  [IPyC_radial_IIDC_strain]
    type = ElementExtremeValue
    variable = radial_IIDC_strain
    block = IPyC
    value_type = 'max'
    execute_on = 'initial timestep_end'
  []

  [IPyC_tangential_IIDC_strain]
    type = ElementExtremeValue
    variable = tangential_IIDC_strain
    block = IPyC
    value_type = 'max'
    execute_on = 'initial timestep_end'
  []

  #### temperatures

  [max_T_kernel]
    type = NodalExtremeValue
    variable = temperature
    block = fuel
    value_type = 'max'
    execute_on = 'initial timestep_end'
  []

  [max_T_buffer]
    type = NodalExtremeValue
    variable = temperature
    block = buffer
    value_type = 'max'
    execute_on = 'initial timestep_end'
  []

  [min_T_buffer]
    type = NodalExtremeValue
    variable = temperature
    block = buffer
    value_type = 'min'
    execute_on = 'initial timestep_end'
  []

  [max_T_IPyC]
    type = NodalExtremeValue
    variable = temperature
    block = IPyC
    value_type = 'max'
    execute_on = 'initial timestep_end'
  []

  [max_T_SiC]
    type = NodalExtremeValue
    variable = temperature
    block = SiC
    value_type = 'max'
    execute_on = 'initial timestep_end'
  []

  #### displacement BCs

  [max_disp_kernel]
    type = NodalExtremeValue
    variable = disp_x
    block = fuel
    value_type = 'max'
    execute_on = 'initial timestep_end'
  []

  [min_disp_buffer]
    type = NodalExtremeValue
    variable = disp_x
    block = buffer
    value_type = 'min'
    execute_on = 'initial timestep_end'
  []

  [max_disp_IPyC]
    type = NodalExtremeValue
    variable = disp_x
    block = IPyC
    value_type = 'max'
    execute_on = 'initial timestep_end'
  []

  #### hoop stresses

  [hoop_opyc_max]
    type = ElementExtremeValue
    variable = stress_yy
    block = OPyC
    execute_on = 'initial timestep_end'
  []

  [hoop_sic_max]
    type = ElementExtremeValue
    variable = stress_yy
    block = SiC
    execute_on = 'initial timestep_end'
  []

  [hoop_ipyc_max]
    type = ElementExtremeValue
    variable = stress_yy
    block = IPyC
    execute_on = 'initial timestep_end'
  []

  [hoop_buffer_max]
    type = ElementExtremeValue
    variable = stress_yy
    block = buffer
    execute_on = 'initial timestep_end'
  []

  [hoop_opyc_min]
    type = ElementExtremeValue
    variable = stress_yy
    block = OPyC
    value_type = min
    execute_on = 'initial timestep_end'
  []

  [hoop_sic_min]
    type = ElementExtremeValue
    variable = stress_yy
    block = SiC
    value_type = min
    execute_on = 'initial timestep_end'
  []

  [hoop_ipyc_min]
    type = ElementExtremeValue
    variable = stress_yy
    block = IPyC
    value_type = min
    execute_on = 'initial timestep_end'
  []

  [hoop_buffer_min]
    type = ElementExtremeValue
    variable = stress_yy
    block = buffer
    value_type = min
    execute_on = 'initial timestep_end'
  []

  ### Check warning for Density

  [oPyC_density]
    type = ElementExtremeValue
    variable = density
    block = OPyC
    execute_on = 'initial timestep_end'
  []

  [sic_density]
    type = ElementExtremeValue
    variable = density
    block = SiC
    execute_on = 'initial timestep_end'
  []

  [IPyC_density]
    type = ElementExtremeValue
    variable = density
    block = IPyC
    execute_on = 'initial timestep_end'
  []

  [buffer_density]
    type = ElementExtremeValue
    variable = density
    block = buffer
    execute_on = 'initial timestep_end'
  []

  [kernel_density]
    type = ElementExtremeValue
    variable = density
    block = fuel
    execute_on = 'initial timestep_end'
  []

  [pd_penetration]
    type = PdPenetration
    boundary = SiC_inner_boundary
    variable = temperature
    execute_on = 'initial timestep_end'
  []
[]

[Outputs]
  print_linear_residuals = true
  time_step_interval =  1
  exodus = true
  csv = true
  perf_graph = true
[]

(test/tests/SiCPdPenetration/palladium_penetration.i)

# This test verifies the implementation of the palladium peneteration model
# for SiC in TRISO fuel particles.  The geometry is a 2D spherical shell of
# inner and outer diameters of 215 and 250 micrometers, respectively. The
# temperature is ramped linearly from 673.15 to 1673.15 K over 5.0e6 seconds
# using 5.0e5 second timesteps.
#
# The rate of palladium penetration (microns/day) is calculated by:
#
# P_{Pd}_dot = 38.232 * exp(-11342.3 / T) / 86400.0
#
# where T is the temperature. An incremental form is used to compute the total
# penetration thickness of the palladium.  Therefore, the average temperature
# over the timestep is used for T. The current penetration thickness is given by:
#
# P_{Pd} = P_{Pd}_old + P_{Pd}_dot * dt
#
# The palladium penetration for the 10 timesteps compared to the analytical
# calculation is provided below:
#
#     Current           BISON Pd        Analytical Pd
#  Temperature (K)   Penetration (m)   Penetration (m)
#     673.15              0                   0
#     773.15          3.4132E-11          3.4132E-11
#     873.15          2.6358E-10          2.6358E-10
#     973.15          1.2843E-09          1.2843E-09
#    1073.15          4.6762E-09          4.6762E-09
#    1173.15          1.3777E-08          1.3777E-08
#    1273.15          3.4558E-08          3.4558E-08
#    1373.15          7.6440E-08          7.6440E-08
#    1473.15          1.5293E-07          1.5293E-07
#    1573.15          2.8201E-07          2.8201E-07
#    1673.15          4.8624E-07          4.8624E-07

[Mesh]
  coord_type = RSPHERICAL
  [gen]
    type = TRISO1DMeshGenerator
    elem_type = EDGE2
    coordinates = '215e-6 250e-6'
    mesh_density = '4'
    block_names = 'sic'
  []
[]

[UserObjects]
  [particle_geometry]
    type = TRISOGeometry
    outer_OPyC = '1'
    outer_SiC = '1'
    outer_IPyC = '2'
    inner_IPyC = '1'
    outer_buffer = '1'
    outer_kernel = '1'
    include_particle = true
    include_pebble = false
  []
[]

[Variables]
  [temperature]
    order = FIRST
    family = LAGRANGE
    initial_condition = 673.15
  []
[]

[Functions]
  [temp_function]              # reads and interpolates input data defining amplitude curve for fill gas pressure
    type = PiecewiseLinear
    x = '0        5.0e6'
    y = '673.15 1673.15'
  []
[]

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

[BCs]
  [heat_removal]
    type = FunctionDirichletBC
    variable = temperature
    boundary = 2
    function = temp_function
  []
[]

[Materials]
  [thermal]
    type = MonolithicSiCThermal
    block = sic
    temperature = temperature
    thermal_conductivity_model = MILLER
  []

  [SiC_density]
    type = ParsedMaterial
    block = sic
    property_name = density
    expression = 3200.0
  []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -ksp_gmres_restart'
  petsc_options_value = 'lu       superlu_dist                  51'
  line_search = 'none'

  l_tol = 1e-5

  nl_rel_tol = 1e-10
  nl_abs_tol = 1e-12

  start_time = 0.0
  end_time = 5.0e6
  num_steps = 10
  dt = 5.0e5
[]

[Postprocessors]
  [temperature]
    type = ElementExtremeValue
    block = sic
    value_type = 'max'
    variable = temperature
    execute_on = 'initial timestep_end'
  []
  [pd_penetration]
    type = PdPenetration
    boundary = 1
    variable = temperature
    execute_on = 'initial timestep_end'
  []
[]

[Outputs]
  csv = true
[]

(test/tests/triso_failure/triso_failure_diffusivity.i)

kernel_radius = 213.35e-6
buffer_thickness = 98.9e-6
IPyC_thickness = 40.4e-6
SiC_thickness = 35.2e-6
OPyC_thickness = 43.4e-6

coordinates1 = '${fparse kernel_radius}'
coordinates2 = '${fparse coordinates1+buffer_thickness}'
coordinates3 = '${fparse coordinates2+IPyC_thickness}'
coordinates4 = '${fparse coordinates3+SiC_thickness}'
coordinates5 = '${fparse coordinates4+OPyC_thickness}'

[GlobalParams]
  order = FIRST
  family = LAGRANGE
  displacements = 'disp_x'
  initial_enrichment = 0.14029 # [wt-]
  flux_conversion_factor = 1.0 # convert E>0.10 to E>0.18 MeV
  stress_free_temperature = 481 # used for thermal expansion
  energy_per_fission = 3.204e-11 # [J/fission]
  O_U = 1.428 # Initial Oxygen to Uranium atom ratio
  C_U = 0.392 # Initial Carbon to Uranium atom ratio
[]

[Mesh]
  coord_type = RSPHERICAL
  [mesh]
    type = TRISO1DMeshGenerator
    elem_type = EDGE2
    coordinates = '0 ${coordinates1} ${coordinates2} ${coordinates2} ${coordinates3} ${coordinates4} ${coordinates5}'
    mesh_density = '18 14 0 12 16 16'
    block_names = 'fuel buffer IPyC SiC OPyC'
  []
[]

[Problem]
  type = ReferenceResidualProblem
  reference_vector = 'ref'
  extra_tag_vectors = 'ref'
[]

[Physics/SolidMechanics/QuasiStatic]
  generate_output = 'stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz max_principal_stress'
  add_variables = true
  strain = FINITE
  incremental = true
  [fuel]
    block = fuel
    eigenstrain_names = 'UCO_swelling_eigenstrain UCO_TE_strain'
    extra_vector_tags = 'ref'
  []
  [buffer]
    block = buffer
    eigenstrain_names = 'Buffer_IIDC_strain Buffer_TE_strain'
    extra_vector_tags = 'ref'
  []
  [IPyC]
    block = IPyC
    eigenstrain_names = 'IPyC_IIDC_strain IPyC_TE_strain'
    extra_vector_tags = 'ref'
  []
  [SiC]
    block = SiC
    eigenstrain_names = 'SiC_thermal_eigenstrain'
    extra_vector_tags = 'ref'
  []
  [OPyC]
    block = OPyC
    eigenstrain_names = 'OPyC_IIDC_strain OPyC_TE_strain'
    extra_vector_tags = 'ref'
  []
[]

[UserObjects]
  [particle_geometry]
    type = TRISOGeometry
    outer_OPyC = OPyC_outer_boundary
    outer_SiC = SiC_outer_boundary
    outer_IPyC = IPyC_outer_boundary
    inner_IPyC = IPyC_inner_boundary
    outer_buffer = buffer_outer_boundary
    outer_kernel = fuel_outer_boundary
    include_particle = true
    include_pebble = false
    IPyC_thickness_mean = ${IPyC_thickness}
    SiC_thickness_mean = ${SiC_thickness}
    OPyC_thickness_mean = ${OPyC_thickness}
  []
[]

[Variables]
  [temperature]
    initial_condition = 873.15
  []
  [conc_Ag]
    initial_condition = 0.0
    scaling = 1e12
  []
[]

[AuxVariables]
  [bounds_dummy]
    order = FIRST
    family = LAGRANGE
  []
  [fission_rate]
    order = CONSTANT
    family = MONOMIAL
  []
  [burnup]
    order = CONSTANT
    family = MONOMIAL
  []
  [fast_neutron_flux]
    order = CONSTANT
    family = MONOMIAL
  []
  [fast_neutron_fluence]
    order = CONSTANT
    family = MONOMIAL
  []
  [fis_gas_produced]
    order = CONSTANT
    family = MONOMIAL
  []
  [fis_gas_released]
    order = CONSTANT
    family = MONOMIAL
  []
  [Ag_diff_coef]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [power_history]
    type = PiecewiseLinear
    x = '0 76e6'
    y = '1 1'
  []
  [fission_rate]
    type = LinearCombinationFunction
    functions = power_history
    w = 7.78e19
  []
  [high_fidelity_strength_crackedIPyC]
    type = ConstantFunction
    value = '1403604095.5707'
  []
  [stress_correlation_crackedIPyC]
    type = TRISOStressCorrelationFunction
    triso_geometry = particle_geometry
    polynomial_coefficients_IPyC = '1 0 0'
    polynomial_coefficients_SiC = '1 0 0'
    polynomial_coefficients_OPyC = '1 0 0'
    correlation_factor = -4.0
  []
  [high_fidelity_strength_asphericity]
    type = ConstantFunction
    value = '1371700766.8875'
  []
  [stress_correlation_asphericity]
    type = TRISOStressCorrelationFunction
    triso_geometry = particle_geometry
    polynomial_coefficients_IPyC = '1 0 0'
    polynomial_coefficients_SiC = '1 0 0'
    polynomial_coefficients_OPyC = '1 0 0'
    correlation_factor = 1.5191967987843993
  []
  [stress_change_correlation_asphericity]
    type = TRISOStressCorrelationFunction
    triso_geometry = particle_geometry
    polynomial_coefficients_IPyC = '1 0 0'
    polynomial_coefficients_SiC = '1 0 0'
    polynomial_coefficients_OPyC = '1 0 0'
    correlation_factor = 1.391516859626456
  []
  [d_gap]
    type = PiecewiseLinear
    x = '1500  2100'
    y = '1e-14 1e-12'
  []
  [ag_d1]
    type = ParsedFunction
    symbol_values = 'sic_failure_overall'
    symbol_names = 'failure'
    expression = 'if(failure > 0.5,1e-6,3.6e-9)'
  []
  [ag_q1]
    type = ParsedFunction
    symbol_values = 'sic_failure_overall'
    symbol_names = 'failure'
    expression = 'if(failure > 0.5,0,215e3)'
  []
[]

[Kernels]
  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temperature
    extra_vector_tags = 'ref'
  []
  [heat]
    type = HeatConduction
    variable = temperature
    extra_vector_tags = 'ref'
  []
  [heat_source]
    type = NeutronHeatSource
    variable = temperature
    block = fuel
    fission_rate = fission_rate
    extra_vector_tags = 'ref'
  []

  [mass_Ag_dt]
    type = TimeDerivative
    variable = conc_Ag
  []
  [mass_Ag]
    type = ArrheniusDiffusion
    variable = conc_Ag
    arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
    extra_vector_tags = 'ref'
  []
  [mass_source_Ag]
    type = SpeciesSourceRate
    variable = conc_Ag
    property_name = Ag_generation
    block = fuel
    extra_vector_tags = 'ref'
  []
[]

[AuxKernels]
  [fissionrate]
    type = MaterialRealAux
    variable = fission_rate
    property = fission_rate
    block = fuel
    execute_on = timestep_begin
  []
  [burnup]
    type = MaterialRealAux
    variable = burnup
    property = burnup
    block = fuel
    execute_on = timestep_begin
  []
  [fast_neutron_flux]
    type = MaterialRealAux
    variable = fast_neutron_flux
    property = fast_neutron_flux
    execute_on = timestep_begin
  []
  [fast_neutron_fluence]
    type = MaterialRealAux
    variable = fast_neutron_fluence
    property = fast_neutron_fluence
    execute_on = timestep_begin
  []
  [Ag_diff_coef]
    type = MaterialRealAux
    variable = Ag_diff_coef
    property = arrhenius_diffusion_coef_Ag
    execute_on = timestep_end
  []
[]

[BCs]
  [freesurf_temp]
    type = FunctionDirichletBC
    variable = temperature
    function = 873.15
    boundary = exterior
  []
  [freesurf_conc_Ag]
    type = DirichletBC
    variable = conc_Ag
    boundary = exterior
    value = 0.0
  []

  [no_disp_x]
    type = DirichletBC
    variable = disp_x
    boundary = xzero
    value = 0.0
  []

  [exterior_pressure_x]
    type = Pressure
    variable = disp_x
    boundary = exterior
    factor = 0.1e6
  []

  [PlenumPressure]
    [plenumPressure]
      boundary = buffer_IPyC_boundary
      startup_time = 1e4
      initial_pressure = 0
      output_initial_moles = initial_moles
      temperature = ave_gas_temp
      volume = 'gap_volume buffer_void_volume kernel_void_volume'
      material_input = 'fis_gas_released'
      output = gas_pressure
    []
  []
[]

[Controls]
  [ag_d1]
    type = RealFunctionControl
    parameter = 'Materials/SiC_conc_Ag/d1'
    function = 'ag_d1'
    execute_on = 'INITIAL TIMESTEP_BEGIN'
  []
  [ag_q1]
    type = RealFunctionControl
    parameter = 'Materials/SiC_conc_Ag/q1'
    function = 'ag_q1'
    execute_on = 'INITIAL TIMESTEP_BEGIN'
  []
[]

[Materials]
  [fission_rate]
    type = GenericFunctionMaterial
    prop_names = fission_rate
    prop_values = fission_rate
    #block = fuel
  []
  [fast_neutron_flux]
    type = FastNeutronFlux
    calculate_fluence = true
    flux_function = power_history
    factor = 1.16e18
  []

  # Arrhenius diffusion coefficients for kernel, PyC, and SiC
  #   come from IAEA TECDOC-978, French parameters.
  [fuel_conc_Ag]
    type = ArrheniusDiffusionCoef
    block = fuel
    d1 = 6.7e-9 # m^2/s
    q1 = 165e3 # J/mol
    temperature = temperature
    arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
  []

  [mass_source_Ag_property]
    type = SpeciesSourceMaterial
    property_name = Ag_generation
    kind = Ag
    block = fuel
  []

  ### Buffer Properties

  [buffer_conc_Ag]
    type = ArrheniusDiffusionCoef
    block = buffer
    d1 = 1e-8 # m^2/s
    q1 = 0.0
    temperature = temperature
    arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
  []

  ### IPyC  properties

  [IPyC_conc_Ag]
    type = ArrheniusDiffusionCoef
    block = IPyC
    d1 = 5.3e-9 # m^2/s
    q1 = 154e3 # J/mol
    temperature = temperature
    arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
  []

  ### SiC properties

  [SiC_conc_Ag]
    type = ArrheniusDiffusionCoef
    block = SiC
    d1 = 3.6e-9 # m^2/s
    q1 = 215e3 # J/mol
    temperature = temperature
    arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
  []

  ###  OPyC properties

  [OPyC_conc_Ag]
    type = ArrheniusDiffusionCoef
    block = OPyC
    d1 = 5.3e-9 # m^2/s
    q1 = 154e3 # J/mol
    temperature = temperature
    arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
  []

  [UCO_burnup]
    type = TRISOBurnup
    initial_density = 10966
    block = fuel
  []
  [UCO_thermal]
    type = UCOThermal
    block = fuel
    temperature = temperature
  []
  [UCO_elasticity_tensor]
    type = UCOElasticityTensor
    block = fuel
    temperature = temperature
  []
  [UCO_stress]
    type = ComputeFiniteStrainElasticStress
    block = fuel
  []
  [UCO_VolumetricSwellingEigenstrain]
    type = UCOVolumetricSwellingEigenstrain
    block = fuel
    eigenstrain_name = UCO_swelling_eigenstrain
  []
  [fuel_thermal_expansion]
    type = ComputeThermalExpansionEigenstrain
    block = fuel
    thermal_expansion_coeff = 10.0e-6
    temperature = temperature
    eigenstrain_name = UCO_TE_strain
  []
  [UCO_density]
    type = StrainAdjustedDensity
    block = fuel
    strain_free_density = 10966
  []
  [fission_gas_release]
    type = UCOFGR
    block = fuel
    average_grain_radius = 10e-6
    temperature = temperature
    triso_geometry = particle_geometry
    cutoff_neutron_flux = 0.0
  []
  [normal_vectors_triso]
    type = NormalVectorsTRISO
    block = 'buffer IPyC OPyC'
  []
  [BAF_IPyC]
    type = BaconAnisotropyFactor
    initial_BAF = 1.0465
    block = IPyC
  []
  [BAF_OPyC]
    type = BaconAnisotropyFactor
    initial_BAF = 1.0429
    block = OPyC
  []
  [buffer_elasticity_tensor]
    type = BufferElasticityTensor
    block = buffer
    temperature = temperature
  []
  [buffer_stress]
    type = BufferCEGACreep
    block = buffer
    temperature = temperature
  []
  [buffer_thermal]
    type = BufferThermal
    block = buffer
    initial_density = 1050.0
  []
  [buffer_density]
    type = StrainAdjustedDensity
    block = buffer
    strain_free_density = 1050.0
  []
  [buffer_TE]
    type = BufferThermalExpansionEigenstrain
    block = buffer
    eigenstrain_name = Buffer_TE_strain
    temperature = temperature
  []
  [buffer_IIDC]
    type = BufferCEGAIrradiationEigenstrain
    block = buffer
    eigenstrain_name = Buffer_IIDC_strain
    temperature = temperature
  []
  [IPyC_elasticity_tensor]
    type = PyCElasticityTensor
    block = IPyC
    temperature = temperature
  []
  [IPyC_stress]
    type = PyCCEGACreep
    block = IPyC
    creep_rate_scale_factor = 1
    temperature = temperature
  []

  [IPyC_thermal]
    type = HeatConductionMaterial
    block = IPyC
    thermal_conductivity = 4.0
    specific_heat = 720.0
  []
  [IPyC_density]
    type = GenericConstantMaterial
    block = IPyC
    prop_names = 'density'
    prop_values = 1890
  []
  [IPyC_IIDC]
    type = PyCCEGAIrradiationEigenstrain
    block = IPyC
    eigenstrain_name = IPyC_IIDC_strain
    temperature = temperature
    irradiation_eigenstrain_scale_factor = 1
  []
  [IPyC_TE]
    type = PyCThermalExpansionEigenstrain
    block = IPyC
    eigenstrain_name = IPyC_TE_strain
    temperature = temperature
  []
  [SiC_elasticity_tensor]
    type = MonolithicSiCElasticityTensor
    block = SiC
    temperature = temperature
    elastic_modulus_model = miller
  []
  [SiC_stress]
    type = ComputeFiniteStrainElasticStress
    block = SiC
  []
  [SiC_thermal]
    type = MonolithicSiCThermal
    block = SiC
    temperature = temperature
    thermal_conductivity_model = miller
  []
  [SiC_density]
    type = StrainAdjustedDensity
    block = SiC
    strain_free_density = 3200.0
  []
  [SiC_thermal_expansion]
    type = ComputeThermalExpansionEigenstrain
    block = SiC
    thermal_expansion_coeff = 4.9e-6
    temperature = temperature
    eigenstrain_name = SiC_thermal_eigenstrain
  []
  [OPyC_elasticity_tensor]
    type = PyCElasticityTensor
    block = OPyC
    temperature = temperature
    initial_BAF = 1.0
  []
  [OPyC_stress]
    type = PyCCEGACreep
    block = OPyC
    creep_rate_scale_factor = 1
    temperature = temperature
  []
  [OPyC_thermal_conductivity]
    type = HeatConductionMaterial
    block = OPyC
    thermal_conductivity = 4.0
    specific_heat = 720.0
  []
  [OPyC_density]
    type = GenericConstantMaterial
    block = OPyC
    prop_names = 'density'
    prop_values = 1900
  []
  [OPyC_IIDC]
    type = PyCCEGAIrradiationEigenstrain
    block = OPyC
    eigenstrain_name = OPyC_IIDC_strain
    temperature = temperature
    irradiation_eigenstrain_scale_factor = 1
  []
  [OPyC_TE]
    type = PyCThermalExpansionEigenstrain
    block = OPyC
    eigenstrain_name = OPyC_TE_strain
    temperature = temperature
  []
  [characteristic_strength_SiC]
    type = GenericConstantMaterial
    prop_values = '9640000'
    block = SiC
    prop_names = 'characteristic_strength'
  []
  [characteristic_strength_PyC]
    type = PyCCharacteristicStrength
    temperature = temperature
    X = 1.02
    block = 'IPyC OPyC'
  []
[]

[ThermalContact]
  [thermal_contact]
    type = GasGapHeatTransfer
    variable = temperature
    primary = IPyC_inner_boundary
    secondary = buffer_outer_boundary
    initial_moles = initial_moles # coupling to a postprocessor which supplies the initial plenum/gap gas mass
    initial_gas_types = 'Kr Xe'
    initial_fractions = '0.185 0.815'
    gas_released = 'fis_gas_released'
    released_gas_types = 'Kr Xe'
    released_fractions = '0.185 0.815'
    tangential_tolerance = 1e-6
    roughness_primary = 0e-6
    roughness_secondary = 0e-6
    jumpdistance_primary = 0
    jumpdistance_secondary = 0
    quadrature = true
    emissivity_secondary = 0.0
    emissivity_primary = 0.0
    min_gap = 1e-7
    max_gap = 50e-6
    gap_geometry_type = sphere
  []

  [conc_Ag]
    type = GapHeatTransfer
    variable = conc_Ag
    primary = IPyC_inner_boundary
    secondary = buffer_outer_boundary
    tangential_tolerance = 1e-6
    gap_conductivity_function = d_gap
    gap_conductivity_function_variable = temperature
    appended_property_name = _conc_Ag
    quadrature = true
    gap_geometry_type = sphere
    emissivity_primary = 0.0
    emissivity_secondary = 0.0
    min_gap = 1e-7
  []
[]

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

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'

  line_search = 'none'

  nl_rel_tol = 1e-7
  nl_abs_tol = 1e-7
  nl_max_its = 20

  l_tol = 1e-4
  l_max_its = 50

  start_time = 0.0
  end_time = 4.831315e7

  dtmin = 1e-4

  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 20
    growth_factor = 1.5
    optimal_iterations = 8 #6
    linear_iteration_ratio = 100
    time_t = '0    76e6  76.001e6 84.641e6 84.6482e6'
    time_dt = '20  20     20      20       20'
  []
[]

[Postprocessors]
  [ave_gas_temp]
    type = ElementAverageValue
    block = buffer
    variable = temperature
    execute_on = 'initial timestep_end'
  []
  [gap_volume]
    type = InternalVolume
    boundary = buffer_IPyC_boundary
    execute_on = 'initial linear'
    use_displaced_mesh = true
  []
  [buffer_void_volume]
    type = VoidVolume
    block = buffer
    theoretical_density = 2250
    execute_on = 'initial timestep_end'
    use_displaced_mesh = true
  []
  [kernel_th_density]
    type = UCOTheoreticalDensity
    execute_on = initial
  []
  [kernel_void_volume]
    type = VoidVolume
    block = fuel
    theoretical_density = kernel_th_density
    execute_on = 'initial timestep_end'
    use_displaced_mesh = true
  []
  [release_heat_inc]
    type = SideIntegralMassFlux
    variable = temperature
    boundary = exterior
    arrhenius_prpty_name = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [release_Ag_inc]
    type = SideIntegralMassFlux
    variable = conc_Ag
    boundary = exterior
    arrhenius_prpty_name = arrhenius_diffusion_coef_Ag
    execute_on = 'initial timestep_end'
  []
  [released_Ag]
    type = TimeIntegratedPostprocessor # computes time integration of value
    value = release_Ag_inc
    execute_on = 'initial timestep_end'
  []
  [total_Ag]
    type = ElementIntegralMaterialProperty
    mat_prop = Ag_generation_total
    block = fuel
    execute_on = 'initial timestep_end'
  []
  [x_Ag_released]
    type = FractionalRelease
    released = released_Ag
    total = total_Ag
  []
  [retained_Ag]
    type = ElementIntegralVariablePostprocessor
    variable = conc_Ag
  []

  [fis_gas_produced]
    type = ElementIntegralMaterialProperty
    mat_prop = fis_gas_produced
    block = fuel
    execute_on = 'initial timestep_end'
  []

  [fis_gas_released]
    type = ElementIntegralMaterialProperty
    mat_prop = fis_gas_released
    block = fuel
    execute_on = 'initial linear timestep_end'
  []

  ### Postprocessors for CO production
  [total_fission_rate]
    type = ElementIntegralPower
    variable = temperature
    fission_rate = fission_rate
    block = fuel
    energy_per_fission = 1.0
    execute_on = 'initial timestep_end'
  []
  [total_fissions]
    type = TimeIntegratedPostprocessor
    value = total_fission_rate
    execute_on = 'initial timestep_end'
  []

  ##### irradiation conditions

  [particle_power]
    type = ElementIntegralPower
    variable = temperature
    use_material_fission_rate = true
    fission_rate_material = fission_rate
    block = fuel
    execute_on = 'initial timestep_end'
  []

  [max_fluence]
    type = ElementExtremeValue
    variable = fast_neutron_fluence
    value_type = 'max'
    execute_on = 'initial timestep_end'
  []

  [max_burnup]
    type = ElementExtremeValue
    variable = burnup
    block = fuel
    value_type = 'max'
    execute_on = 'initial timestep_end'
  []

  [SiC_stress]
    type = ElementExtremeMaterialProperty
    block = SiC
    value_type = min
    mat_prop = stress_yy
  []
  [strength_SiC]
    type = WeibullEffectiveMeanStrength
    block = SiC
    weibull_modulus = 6
  []
  [failure_indicator_SiC]
    type = WeibullFailureOutputUsingCorrelation
    block = SiC
    weibull_modulus = 6
    stress_name = stress_yy
    high_fidelity_analysis_strength = 'high_fidelity_strength_asphericity'
    stress_correlation_function = 'stress_correlation_asphericity'
    stress_change_correlation_function = 'stress_change_correlation_asphericity'
  []
  [strength_IPyC]
    type = WeibullEffectiveMeanStrength
    block = IPyC
    weibull_modulus = 9.5
  []
  [failure_indicator_IPyC]
    type = WeibullFailureOutputUsingCorrelation
    block = IPyC
    weibull_modulus = 9.5
    stress_name = max_principal_stress
    effective_mean_strength = strength_IPyC
  []
  [failure_indicator_SiC_crackedIPyC]
    type = WeibullFailureOutputUsingCorrelation
    block = SiC
    weibull_modulus = 6
    stress_name = stress_yy
    high_fidelity_analysis_strength = 'high_fidelity_strength_crackedIPyC'
    stress_correlation_function = 'stress_correlation_crackedIPyC'
  []
  [sic_failure_overall]
    type = TRISOFailureEvaluation
    IPyC_failure = failure_indicator_IPyC
    SiC_failure_crackedIPyC = failure_indicator_SiC_crackedIPyC
    SiC_failure = failure_indicator_SiC
    SiC_failure_pd_penetration = failure_indicator_pd_penetration
    failure_type = SIC_FAILURE_OVERALL
  []
  [ipyc_cracking]
    type = TRISOFailureEvaluation
    IPyC_failure = failure_indicator_IPyC
    SiC_failure_crackedIPyC = failure_indicator_SiC_crackedIPyC
    SiC_failure = failure_indicator_SiC
    failure_type = IPYC_CRACKING
  []
  [sic_failure_due_to_pressure]
    type = TRISOFailureEvaluation
    IPyC_failure = failure_indicator_IPyC
    SiC_failure_crackedIPyC = failure_indicator_SiC_crackedIPyC
    SiC_failure = failure_indicator_SiC
    failure_type = SIC_FAILURE_DUE_TO_PRESSURE
  []
  [sic_failure_due_to_ipyc_cracking]
    type = TRISOFailureEvaluation
    IPyC_failure = failure_indicator_IPyC
    SiC_failure_crackedIPyC = failure_indicator_SiC_crackedIPyC
    SiC_failure = failure_indicator_SiC
    failure_type = SIC_FAILURE_DUE_TO_IPYC_CRACKING
  []
  [weibull_failure_probability_IPyC]
    type = WeibullFailureProbability
    block = IPyC
    weibull_modulus = 9.5
    characteristic_strength = characteristic_strength
  []
  [weibull_failure_probability_SiC]
    type = WeibullFailureProbability
    block = SiC
    weibull_modulus = 6
    characteristic_strength = characteristic_strength
  []
  [pd_penetration]
    type = PdPenetration
    boundary = SiC_inner_boundary
    variable = temperature
    execute_on = 'initial timestep_end'
  []
  [failure_indicator_pd_penetration]
    type = PdPenetrationFailureIndicator
    triso_geometry = particle_geometry
    pd_penetration = pd_penetration
  []
[]

[Outputs]
  csv = true
[]

(examples/TRISO/parfume/parfume_un.i)

# UN TRISO particle using several PARFUME models

[GlobalParams]
  order = SECOND
  family = LAGRANGE
  displacements = 'disp_x'
  initial_enrichment = 0.1955 # [wt-]
  flux_conversion_factor = 1.0 # convert E>0.10 to E>0.18 MeV
  stress_free_temperature = 923.15 # used for thermal expansion
  energy_per_fission = 3.204e-11 # [J/fission]
  O_U = 1.5 # Initial Oxygen to Uranium atom ratio
  C_U = 0.4 # Initial Carbon to Uranium atom ratio
[]

[Mesh]
  coord_type = RSPHERICAL
  [gen]
    type = TRISO1DMeshGenerator
    elem_type = EDGE3
    coordinates = '0 2.125e-4 3.125e-4 3.125e-4 3.525e-4 3.875e-4 4.275e-4'
    mesh_density = '6 6 0 6 8 6'
    block_names = 'fuel buffer IPyC SiC OPyC'
  []
[]

[Problem]
  type = ReferenceResidualProblem
  reference_vector = 'ref'
  extra_tag_vectors = 'ref'
[]

[UserObjects]
  [particle_geometry]
    type = TRISOGeometry
  []
[]

[Variables]
  [temperature]
    initial_condition = 923.15
  []
  [conc]
    initial_condition = 0.0
    scaling = 1e18
  []
[]

[AuxVariables]
  [disp_y]
  []
  [disp_z]
  []

  [fission_rate]
    block = fuel
    order = CONSTANT
    family = MONOMIAL
  []

  [burnup]
    block = fuel
    order = CONSTANT
    family = MONOMIAL
  []

  [fast_neutron_flux]
    order = CONSTANT
    family = MONOMIAL
  []

  [fast_neutron_fluence]
    order = CONSTANT
    family = MONOMIAL
  []

  [gap_condSlave]
    order = CONSTANT
    family = MONOMIAL
  []

  [density]
    order = CONSTANT
    family = MONOMIAL
  []

  [thermal_conductivity]
    order = CONSTANT
    family = MONOMIAL
  []

  [swelling]
    order = CONSTANT
    family = MONOMIAL
  []

  [specific_heat]
    order = CONSTANT
    family = MONOMIAL
  []

  [volumetric_IIDC_strain]
    order = CONSTANT
    family = MONOMIAL
  []

  [radial_IIDC_strain]
    order = CONSTANT
    family = MONOMIAL
  []

  [tangential_IIDC_strain]
    order = CONSTANT
    family = MONOMIAL
  []

  [BAF]
    order = CONSTANT
    family = MONOMIAL
  []

  [fis_gas_produced]
    order = CONSTANT
    family = MONOMIAL
  []

  [fis_gas_released]
    order = CONSTANT
    family = MONOMIAL
  []

  [gap_HTC]
    order = CONSTANT
    family = MONOMIAL
  []

  [gap_distance]
    order = CONSTANT
    family = MONOMIAL
  []

[]

[Functions]
  [power_history]
    type = PiecewiseLinear
    x = '0 76e6 76.001e6'
    y = '1 1     0'
  []
  [fission_rate]
    type = LinearCombinationFunction
    functions = power_history
    w = 3.89e19
  []
  [temp_bc]
    type = PiecewiseLinear
    # A final temperature ramp is not possible with the UNThermal model since
    # its range of applicability ends at 1800 K
    # To use the model beyond its limit but get a warning, add
    # value_range_behavior = WARN in the GlobalParams block.
    x = '0    76e6  76.001e6 84.641e6 84.6482e6'
    y = '1500 1500  300      300      2073'
  []
  [k_function]
    type = PiecewiseLinear
    x = '0     200e6'
    y = '4e-37 4e-37'
  []
  [d1_function]
    type = ParsedFunction
    expression = 'exp(t/4.5e25)'
  []
  [d_gap]
    type = PiecewiseLinear
    x = '1500  2100'
    y = '1e-14 1e-12'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [fuel]
    block = fuel
    add_variables = true
    strain = FINITE
    incremental = true
    generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz'
    eigenstrain_names = 'UN_swelling_eigenstrain UN_thermal_strain'
    extra_vector_tags = 'ref'
  []
  [buffer]
    block = buffer
    add_variables = true
    strain = FINITE
    incremental = true
    generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz'
    eigenstrain_names = 'buffer_IIDC_strain buffer_thermal_strain'
    extra_vector_tags = 'ref'
  []
  [IPyC]
    block = IPyC
    add_variables = true
    strain = FINITE
    incremental = true
    generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz'
    eigenstrain_names = 'IPyC_IIDC_strain IPyC_thermal_strain'
    extra_vector_tags = 'ref'
  []
  [SiC]
    block = SiC
    add_variables = true
    strain = FINITE
    incremental = true
    generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz'
    eigenstrain_names = 'SiC_thermal_eigenstrain'
    extra_vector_tags = 'ref'
  []
  [OPyC]
    block = OPyC
    add_variables = true
    strain = FINITE
    incremental = true
    generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz'
    eigenstrain_names = 'OPyC_IIDC_strain OPyC_thermal_strain'
    extra_vector_tags = 'ref'
  []
[]

[Kernels]
  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temperature
    extra_vector_tags = 'ref'
  []
  [heat]
    type = HeatConduction
    variable = temperature
    extra_vector_tags = 'ref'
  []
  [heat_source]
    type = NeutronHeatSource
    variable = temperature
    block = fuel
    fission_rate = fission_rate
    extra_vector_tags = 'ref'
  []
  [mass_ie]
    type = TimeDerivative
    variable = conc
    extra_vector_tags = 'ref'
  []
  [mass]
    type = ArrheniusDiffusion
    variable = conc
    extra_vector_tags = 'ref'
  []
  [mass_source]
    type = BodyForce
    variable = conc
    function = power_history
    value = 1.22e-5 # units of mol/m**3-s
    block = fuel
    extra_vector_tags = 'ref'
  []
  [mass_decay]
    type = Decay
    variable = conc
    radioactive_decay_constant = 7.297e-10 # units:(1/sec)  The constant for Cesium
    extra_vector_tags = 'ref'
  []
[]

[AuxKernels]
  [fissionrate]
    type = MaterialRealAux
    variable = fission_rate
    property = fission_rate
    block = fuel
    execute_on = timestep_begin
  []

  [burnup]
    type = MaterialRealAux
    variable = burnup
    property = burnup
    block = fuel
    execute_on = timestep_begin
  []

  [fast_neutron_flux]
    type = MaterialRealAux
    variable = fast_neutron_flux
    property = fast_neutron_flux
    block = 'fuel buffer IPyC SiC OPyC'
    execute_on = timestep_begin
  []

  [fast_neutron_fluence]
    type = MaterialRealAux
    variable = fast_neutron_fluence
    property = fast_neutron_fluence
    block = 'fuel buffer IPyC SiC OPyC'
    execute_on = timestep_begin
  []

  [conductanceSlave]
    type = MaterialRealAux
    property = gap_conductance
    variable = gap_condSlave
    boundary = buffer_outer_boundary
    execute_on = 'initial timestep_end'
  []

  [density]
    type = MaterialRealAux
    variable = density
    property = density
    block = 'fuel buffer IPyC SiC OPyC'
    execute_on = 'initial linear'
  []

  [thermal_conductivity]
    type = MaterialRealAux
    variable = thermal_conductivity
    property = thermal_conductivity
    block = 'fuel buffer IPyC SiC OPyC'
    execute_on = timestep_end
  []

  [specific_heat]
    type = MaterialRealAux
    variable = specific_heat
    property = specific_heat
    block = 'fuel buffer IPyC SiC OPyC'
    execute_on = timestep_end
  []

  [swelling]
    type = MaterialRealAux
    variable = swelling
    property = swelling
    block = fuel
    execute_on = linear
  []

  [volumetric_IIDC_strain]
    type = MaterialRealAux
    variable = volumetric_IIDC_strain
    property = volumetric_IIDC_strain
    block = 'IPyC OPyC'
    execute_on = timestep_end
  []

  [radial_IIDC_strain]
    type = MaterialRealAux
    variable = radial_IIDC_strain
    property = radial_IIDC_strain
    block = 'IPyC OPyC'
    execute_on = timestep_end
  []

  [tangential_IIDC_strain]
    type = MaterialRealAux
    variable = tangential_IIDC_strain
    property = tangential_IIDC_strain
    block = 'IPyC OPyC'
    execute_on = timestep_end
  []

  [BAF]
    type = MaterialRealAux
    variable = BAF
    property = BAF
    block = 'IPyC OPyC'
    execute_on = timestep_end
  []

  [fis_gas_produced]
    type = MaterialRealAux
    variable = fis_gas_produced
    property = fis_gas_produced
    block = fuel
    execute_on = linear
  []

  [fis_gas_released]
    type = MaterialRealAux
    variable = fis_gas_released
    property = fis_gas_released
    block = fuel
    execute_on = linear
  []

  [gap_HTC]
    type = MaterialRealAux
    property = gap_conductance
    variable = gap_HTC
    boundary = buffer_outer_boundary
    execute_on = 'initial timestep_end'
  []

  [gap_distance]
    type = PenetrationAux
    variable = gap_distance
    boundary = buffer_outer_boundary
    paired_boundary = IPyC_inner_boundary
    quantity = distance
    tangential_tolerance = 1e-6
    execute_on = 'initial timestep_end'
  []
[]

[Contact]
  [mechanical]
    primary = IPyC_inner_boundary
    secondary = buffer_outer_boundary
    penalty = 1e5
    model = frictionless
    formulation = kinematic
  []
[]

[ThermalContact]
  [thermal_contact]
    type = GasGapHeatTransfer
    variable = temperature
    primary = IPyC_inner_boundary
    secondary = buffer_outer_boundary
    initial_moles = initial_moles # coupling to a postprocessor which supplies the initial plenum/gap gas mass
    initial_gas_types = 'Kr Xe'
    initial_fractions = '0.185 0.815'
    gas_released = 'fis_gas_released'
    released_gas_types = 'Kr Xe'
    released_fractions = '0.185 0.815'
    tangential_tolerance = 1e-6
    roughness_primary = 0e-6
    roughness_secondary = 0e-6
    jumpdistance_primary = 0
    jumpdistance_secondary = 0
    quadrature = true
    emissivity_secondary = 0.0
    emissivity_primary = 0.0
    min_gap = 1e-7
    max_gap = 50e-6
    gap_geometry_type = sphere
  []

  [cesium_contact]
    type = GapHeatTransfer
    variable = conc
    primary = IPyC_inner_boundary
    secondary = buffer_outer_boundary
    tangential_tolerance = 1e-6
    gap_conductivity_function = d_gap
    gap_conductivity_function_variable = temperature
    appended_property_name = _conc
    quadrature = true
    gap_geometry_type = sphere
    emissivity_primary = 0.0
    emissivity_secondary = 0.0
    min_gap = 1e-7
  []
[]

[BCs]
  # pin particle along symmetry planes
  [no_disp_x]
    type = DirichletBC
    variable = disp_x
    boundary = xzero
    value = 0.0
  []

  # fix temperature on free surface
  [freesurf_temp]
    type = FunctionDirichletBC
    variable = temperature
    function = temp_bc
    boundary = exterior
  []

  # fix concentration on free surface
  [freesurf_conc]
    type = DirichletBC
    variable = conc
    boundary = exterior
    value = 0.0
  []

  # exterior and internal pressures
  [exterior_pressure_x]
    type = Pressure
    variable = disp_x
    boundary = exterior
    factor = 0.1e6
  []

  [PlenumPressure] #  apply gas pressure on buffer and IPyC boundaries
    [plenumPressure]
      boundary = buffer_IPyC_boundary
      initial_pressure = 100.0
      startup_time = 0
      R = 8.3145
      output_initial_moles = initial_moles
      temperature = ave_gas_temp
      volume = 'gap_volume buffer_void_volume kernel_void_volume'
      material_input = 'fis_gas_released'
      output = gas_pressure
    []
  []
[]

[Materials]

  [fission_rate]
    type = GenericFunctionMaterial
    prop_names = fission_rate
    prop_values = fission_rate
  []

  [fast_neutron_flux]
    type = FastNeutronFlux
    calculate_fluence = true
    flux_function = power_history
    factor = 5e17
  []

  [normal_vectors_triso]
    type = NormalVectorsTRISO
    block = 'buffer IPyC OPyC'
  []

  ### UN properties

  [UN_burnup]
    type = TRISOBurnup
    initial_density = 13760.0
    kernel_type = UN
  []

  [UN_thermal]
    type = MNThermal
    block = fuel
    temperature = temperature
    formulation = COLLIN_BAUER
  []

  [UN_elasticity_tensor]
    type = UNElasticityTensor
    block = fuel
    temperature = temperature
  []

  [UN_stress]
    type = ComputeFiniteStrainElasticStress
    block = fuel
  []

  [UN_VolumetricSwellingEigenstrain]
    type = BurnupDependentEigenstrain
    block = fuel
    swelling_name = swelling
    eigenstrain_name = UN_swelling_eigenstrain
    swelling_factor = 0.8
  []

  [UN_thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    block = fuel
    thermal_expansion_coeff = 10e-6 # check this value for UN
    eigenstrain_name = UN_thermal_strain
    temperature = temperature
  []

  [UN_density]
    type = StrainAdjustedDensity
    block = fuel
    strain_free_density = 13760.0
  []

  [fission_gas_release]
    type = UNFGR
    block = fuel
    average_grain_radius = 10e-6
    temperature = temperature
    triso_geometry = particle_geometry
  []

  [fuel_conc]
    type = ArrheniusDiffusionCoef
    block = fuel
    d1 = 5.6e-8 # m^2/s
    q1 = 209.0e+3 # J/mol
    d2 = 5.2e-4 # m^2/s
    q2 = 362.0e+3 # J/mol
    temperature = temperature
  []

  ### Buffer Properties

  [buffer_elasticity_tensor]
    type = BufferElasticityTensor
    block = buffer
    temperature = temperature
  []

  [buffer_stress]
    type = BufferCEGACreep
    block = buffer
    temperature = temperature
  []

  [buffer_thermal]
    type = BufferThermal
    block = buffer
    initial_density = 1050.0
  []

  [buffer_density]
    type = StrainAdjustedDensity
    block = buffer
    strain_free_density = 1050.0
  []

  [buffer_thermal_strain]
    type = BufferThermalExpansionEigenstrain
    block = buffer
    eigenstrain_name = buffer_thermal_strain
    temperature = temperature
  []

  [buffer_IIDC_strain]
    type = BufferCEGAIrradiationEigenstrain
    block = buffer
    eigenstrain_name = buffer_IIDC_strain
    temperature = temperature
  []

  [buffer_conc]
    type = ArrheniusDiffusionCoef
    block = buffer
    d1 = 1.0e-12 # m^2/s
    q1 = 0.0
    d2 = 0.0
    q2 = 0.0
    temperature = temperature
  []

  ### IPyC  properties

  [IPyC_elasticity_tensor]
    type = PyCElasticityTensor
    block = IPyC
    temperature = temperature
    initial_BAF = 1.045
    poissons_ratio = 0.23
  []

  [IPyC_stress]
    type = PyCCEGACreep
    block = IPyC
    temperature = temperature
  []

  [IPyC_thermal]
    type = HeatConductionMaterial
    block = IPyC
    thermal_conductivity = 4.0
    specific_heat = 720.0
  []

  [IPyC_density]
    type = GenericConstantMaterial
    block = IPyC
    prop_names = 'density'
    prop_values = 1900.0
  []

  [IPyC_IIDC_strain]
    type = PyCCEGAIrradiationEigenstrain
    block = IPyC
    eigenstrain_name = IPyC_IIDC_strain
    temperature = temperature
  []

  [BAF_IPyC]
    type = BaconAnisotropyFactor
    initial_BAF = 1.045
    block = IPyC
  []

  [BAF_OPyC]
    type = BaconAnisotropyFactor
    initial_BAF = 1.045
    block = OPyC
  []

  [IPyC_thermal_strain]
    type = PyCThermalExpansionEigenstrain
    block = IPyC
    eigenstrain_name = IPyC_thermal_strain
    temperature = temperature
  []

  [IPyC_conc]
    type = ArrheniusDiffusionCoef
    block = IPyC
    d1 = 6.3e-8 # m^2/s
    q1 = 222.0e+3 # J/mol
    d2 = 0.0
    q2 = 0.0
    temperature = temperature
  []

  ### SiC properties

  [SiC_elasticity_tensor]
    type = MonolithicSiCElasticityTensor
    block = SiC
    temperature = temperature
    elastic_modulus_model = miller
  []

  [SiC_stress]
    type = ComputeFiniteStrainElasticStress
    block = SiC
  []

  [SiC_thermal]
    type = MonolithicSiCThermal
    block = SiC
    temperature = temperature
    thermal_conductivity_model = miller
  []

  [SiC_density]
    type = GenericConstantMaterial
    block = SiC
    prop_names = 'density'
    prop_values = 3200.0
  []

  [SiC_thermal_strain]
    type = MonolithicSiCThermalExpansionEigenstrain
    block = SiC
    temperature = temperature
    eigenstrain_name = SiC_thermal_eigenstrain
  []

  [SiC_conc]
    type = ArrheniusDiffusionCoef
    block = SiC
    d1 = 5.5e-14 # m^2/s
    d1_function = d1_function
    d1_function_variable = fast_neutron_fluence
    q1 = 125.0e+3 # J/mol
    d2 = 1.6e-2 # m^2/s
    q2 = 514.0e+3 # J/mol
    temperature = temperature
  []

  ###  OPyC properties

  [OPyC_elasticity_tensor]
    type = PyCElasticityTensor
    block = OPyC
    temperature = temperature
    initial_BAF = 1.045
    poissons_ratio = 0.23
  []

  [OPyC_stress]
    type = PyCCEGACreep
    block = OPyC
    temperature = temperature
  []

  [OPyC_thermal_conductivity]
    type = HeatConductionMaterial
    block = OPyC
    thermal_conductivity = 4.0
    specific_heat = 720.0
  []

  [OPyC_density]
    type = GenericConstantMaterial
    block = OPyC
    prop_names = 'density'
    prop_values = 1900.0
  []

  [OPyC_IIDC_strain]
    type = PyCCEGAIrradiationEigenstrain
    block = OPyC
    eigenstrain_name = OPyC_IIDC_strain
    temperature = temperature
  []

  [OPyC_thermal_strain]
    type = PyCThermalExpansionEigenstrain
    block = OPyC
    eigenstrain_name = OPyC_thermal_strain
    temperature = temperature
  []

  [OPyC_conc]
    type = ArrheniusDiffusionCoef
    block = OPyC
    d1 = 6.3e-8 # m^2/s
    q1 = 222.0e+3 # J/mol
    d2 = 0.0
    q2 = 0.0
    temperature = temperature
  []
[]

[Dampers]
  [temp]
    type = MaxIncrement
    variable = temperature
    max_increment = 50
  []
  [disp_x]
    type = MaxIncrement
    variable = disp_x
    max_increment = 1e-6
  []
[]

[Debug]
  show_var_residual_norms = true
  show_var_residual = 'disp_x temperature conc'
[]

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

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'

  line_search = 'none'

  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-7
  nl_max_its = 15

  l_tol = 1e-4
  l_max_its = 50

  start_time = 0.0
  end_time = 84.641e6 #85.3682e6
  num_steps = 1000

  dtmax = 2e6
  dtmin = 1

  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 20
    growth_factor = 1.5
    optimal_iterations = 8 #6
    linear_iteration_ratio = 100
    time_t = '0    76e6  76.001e6 84.641e6 84.6482e6'
    time_dt = '20  20     20      20       20'
  []

  [Quadrature]
    order = THIRD
  []
[]

[Postprocessors]
  [_dt]
    type = TimestepSize
    execute_on = timestep_end
  []
  [cs_release]
    type = SideIntegralMassFlux
    variable = conc
    boundary = exterior
  []
  [int_cs_release]
    type = TimeIntegratedPostprocessor
    value = cs_release
  []
  [cs_release_fuel]
    type = SideIntegralMassFlux
    variable = conc
    boundary = fuel_outer_boundary
  []
  [int_cs_release_fuel]
    type = TimeIntegratedPostprocessor
    value = cs_release_fuel
  []
  [cs_release_PyCGapBndry]
    type = SideIntegralMassFlux
    variable = conc
    boundary = IPyC_inner_boundary
  []
  [int_cs_release_PyCGapBndry]
    type = TimeIntegratedPostprocessor
    value = cs_release_PyCGapBndry
  []

  [ave_gas_temp]
    type = ElementAverageValue
    block = buffer
    variable = temperature
    execute_on = 'initial timestep_end'
  []

  [ave_gap_temp]
    type = SideAverageValue
    boundary = buffer_IPyC_boundary
    variable = temperature
    execute_on = 'initial timestep_end'
  []

  [fis_gas_produced]
    type = ElementIntegralMaterialProperty
    mat_prop = fis_gas_produced
    block = fuel
    execute_on = 'initial timestep_end'
  []

  [fis_gas_released]
    type = ElementIntegralMaterialProperty
    mat_prop = fis_gas_released
    block = fuel
    execute_on = 'initial timestep_end'
  []

  [gap_volume]
    type = InternalVolume
    boundary = buffer_IPyC_boundary
    execute_on = 'initial linear'
    use_displaced_mesh = true
  []

  [buffer_void_volume]
    type = VoidVolume
    block = buffer
    theoretical_density = 2250
    execute_on = 'initial timestep_end'
    use_displaced_mesh = true
  []

  [kernel_void_volume]
    type = VoidVolume
    block = fuel
    theoretical_density = 14330
    execute_on = 'initial timestep_end'
    use_displaced_mesh = true
  []

  [volumeTotal]
    type = InternalVolume
    boundary = exterior
    execute_on = 'initial timestep_end'
    scale_factor = -1
  []
  [volumeFuel]
    type = InternalVolume
    boundary = fuel_outer_boundary
    execute_on = 'initial timestep_end'
    scale_factor = -1
  []
  [volumeGas]
    type = InternalVolume
    boundary = buffer_outer_boundary
    execute_on = 'initial timestep_end'
    scale_factor = -1
    addition = 4.67e-11
  []
  [volumeBufferShell]
    type = InternalVolume
    boundary = buffer_outer_boundary
    execute_on = 'initial timestep_end'
  []
  [ave_temp_interior]
    type = SideAverageValue
    boundary = buffer_outer_boundary
    variable = temperature
    execute_on = 'initial timestep_end'
  []

  [gap_HTC]
    type = ElementExtremeValue
    variable = gap_HTC
    block = buffer
    value_type = 'max'
    execute_on = 'initial timestep_end'
  []

  ### Postprocessors for CO production
  [total_fission_rate]
    type = ElementIntegralPower
    variable = temperature
    fission_rate = fission_rate
    block = fuel
    energy_per_fission = 1.0
    outputs = exodus
    execute_on = 'initial timestep_end'
  []
  [total_fissions]
    type = TimeIntegratedPostprocessor
    value = total_fission_rate
    outputs = exodus
    execute_on = 'initial timestep_end'
  []
  [avg_surface_temp]
    type = SideAverageValue
    variable = temperature
    boundary = exterior
    outputs = exodus
    execute_on = 'initial timestep_end'
  []
  [time_int_surf_temp]
    type = TimeIntegratedPostprocessor
    value = avg_surface_temp
    outputs = exodus
    execute_on = 'initial timestep_end'
  []

  ##### irradiation conditions

  [particle_power]
    type = ElementIntegralPower
    variable = temperature
    use_material_fission_rate = true
    fission_rate_material = fission_rate
    block = fuel
    execute_on = 'initial timestep_end'
  []

  [max_fluence]
    type = ElementExtremeValue
    variable = fast_neutron_fluence
    block = 'fuel buffer IPyC SiC OPyC'
    value_type = 'max'
    execute_on = 'initial timestep_end'
  []

  [max_burnup]
    type = ElementExtremeValue
    variable = burnup
    block = fuel
    value_type = 'max'
    execute_on = 'initial timestep_end'
  []

  #### II strain

  [OPyC_radial_IIDC_strain]
    type = ElementExtremeValue
    variable = radial_IIDC_strain
    block = OPyC
    value_type = 'max'
    execute_on = 'initial timestep_end'
  []

  [OPyC_tangential_IIDC_strain]
    type = ElementExtremeValue
    variable = tangential_IIDC_strain
    block = OPyC
    value_type = 'max'
    execute_on = 'initial timestep_end'
  []

  [IPyC_radial_IIDC_strain]
    type = ElementExtremeValue
    variable = radial_IIDC_strain
    block = IPyC
    value_type = 'max'
    execute_on = 'initial timestep_end'
  []

  [IPyC_tangential_IIDC_strain]
    type = ElementExtremeValue
    variable = tangential_IIDC_strain
    block = IPyC
    value_type = 'max'
    execute_on = 'initial timestep_end'
  []

  #### temperatures

  [max_T_kernel]
    type = NodalExtremeValue
    variable = temperature
    block = fuel
    value_type = 'max'
    execute_on = 'initial timestep_end'
  []

  [max_T_buffer]
    type = NodalExtremeValue
    variable = temperature
    block = buffer
    value_type = 'max'
    execute_on = 'initial timestep_end'
  []

  [min_T_buffer]
    type = NodalExtremeValue
    variable = temperature
    block = buffer
    value_type = 'min'
    execute_on = 'initial timestep_end'
  []

  [max_T_IPyC]
    type = NodalExtremeValue
    variable = temperature
    block = IPyC
    value_type = 'max'
    execute_on = 'initial timestep_end'
  []

  [max_T_SiC]
    type = NodalExtremeValue
    variable = temperature
    block = SiC
    value_type = 'max'
    execute_on = 'initial timestep_end'
  []

  #### displacement BCs

  [max_disp_kernel]
    type = NodalExtremeValue
    variable = disp_x
    block = fuel
    value_type = 'max'
    execute_on = 'initial timestep_end'
  []

  [min_disp_buffer]
    type = NodalExtremeValue
    variable = disp_x
    block = buffer
    value_type = 'min'
    execute_on = 'initial timestep_end'
  []

  [max_disp_IPyC]
    type = NodalExtremeValue
    variable = disp_x
    block = IPyC
    value_type = 'max'
    execute_on = 'initial timestep_end'
  []

  #### hoop stresses

  [hoop_opyc_max]
    type = ElementExtremeValue
    variable = stress_yy
    block = OPyC
    execute_on = 'initial timestep_end'
  []

  [hoop_sic_max]
    type = ElementExtremeValue
    variable = stress_yy
    block = SiC
    execute_on = 'initial timestep_end'
  []

  [hoop_ipyc_max]
    type = ElementExtremeValue
    variable = stress_yy
    block = IPyC
    execute_on = 'initial timestep_end'
  []

  [hoop_buffer_max]
    type = ElementExtremeValue
    variable = stress_yy
    block = buffer
    execute_on = 'initial timestep_end'
  []

  [hoop_opyc_min]
    type = ElementExtremeValue
    variable = stress_yy
    block = OPyC
    value_type = min
    execute_on = 'initial timestep_end'
  []

  [hoop_sic_min]
    type = ElementExtremeValue
    variable = stress_yy
    block = SiC
    value_type = min
    execute_on = 'initial timestep_end'
  []

  [hoop_ipyc_min]
    type = ElementExtremeValue
    variable = stress_yy
    block = IPyC
    value_type = min
    execute_on = 'initial timestep_end'
  []

  [hoop_buffer_min]
    type = ElementExtremeValue
    variable = stress_yy
    block = buffer
    value_type = min
    execute_on = 'initial timestep_end'
  []

  ### Check warning for Density

  [oPyC_density]
    type = ElementExtremeValue
    variable = density
    block = OPyC
    execute_on = 'initial timestep_end'
  []

  [sic_density]
    type = ElementExtremeValue
    variable = density
    block = SiC
    execute_on = 'initial timestep_end'
  []

  [IPyC_density]
    type = ElementExtremeValue
    variable = density
    block = IPyC
    execute_on = 'initial timestep_end'
  []

  [buffer_density]
    type = ElementExtremeValue
    variable = density
    block = buffer
    execute_on = 'initial timestep_end'
  []

  [kernel_density]
    type = ElementExtremeValue
    variable = density
    block = fuel
    execute_on = 'initial timestep_end'
  []

  [pd_penetration]
    type = PdPenetration
    boundary = SiC_inner_boundary
    variable = temperature
    execute_on = 'initial timestep_end'
  []
[]

[Outputs]
  print_linear_residuals = true
  time_step_interval =  1
  exodus = true
  csv = true
  perf_graph = true
[]

(test/tests/triso_failure/triso_1d_kernel_migration.i)

kernel_radius = 213.35e-6
buffer_thickness = 98.9e-6
IPyC_thickness = 40.4e-6
SiC_thickness = 35.2e-6
OPyC_thickness = 43.4e-6

coordinates1 = '${fparse kernel_radius}'
coordinates2 = '${fparse coordinates1+buffer_thickness}'
coordinates3 = '${fparse coordinates2+IPyC_thickness}'
coordinates4 = '${fparse coordinates3+SiC_thickness}'
coordinates5 = '${fparse coordinates4+OPyC_thickness}'

[GlobalParams]
  order = FIRST
  family = LAGRANGE
  displacements = 'disp_x'
  initial_enrichment = 0.14029 # [wt-]
  flux_conversion_factor = 1.0 # convert E>0.10 to E>0.18 MeV
  stress_free_temperature = 1573 # used for thermal expansion
  energy_per_fission = 3.204e-11 # [J/fission]
  O_U = 1.428 # Initial Oxygen to Uranium atom ratio
  C_U = 0.392 # Initial Carbon to Uranium atom ratio
[]

[Mesh]
  coord_type = RSPHERICAL
  [mesh]
    type = TRISO1DMeshGenerator
    elem_type = EDGE2
    coordinates = '0 ${coordinates1} ${coordinates2} ${coordinates2} ${coordinates3} ${coordinates4} '
                  '${coordinates5}'
    mesh_density = '20 8 0 4 4 4'
    block_names = 'fuel buffer IPyC SiC OPyC'
  []
[]

[Problem]
  type = ReferenceResidualProblem
  reference_vector = 'ref'
  extra_tag_vectors = 'ref'
[]

[UserObjects]
  [particle_geometry]
    type = TRISOGeometry
    outer_OPyC = OPyC_outer_boundary
    outer_SiC = SiC_outer_boundary
    outer_IPyC = IPyC_outer_boundary
    inner_IPyC = IPyC_inner_boundary
    outer_buffer = buffer_outer_boundary
    outer_kernel = fuel_outer_boundary
    include_particle = true
    include_pebble = false
    execute_on = 'INITIAL TIMESTEP_END'
  []
[]

[Variables]
  [temperature]
    initial_condition = 1573
  []
[]

[AuxVariables]
  [fission_rate]
    order = CONSTANT
    family = MONOMIAL
  []
  [burnup]
    order = CONSTANT
    family = MONOMIAL
  []
  [fast_neutron_flux]
    order = CONSTANT
    family = MONOMIAL
  []
  [fast_neutron_fluence]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [fission_rate]
    type = ConstantFunction
    value = 5.75e19
  []
  [high_fidelity_strength_crackedIPyC]
    type = PiecewiseLinear
    x = '0 1.0e11'
    y = '1000000 1000000'
  []
  [high_fidelity_strength_crackedOPyC]
    type = PiecewiseLinear
    x = '0 1.0e11'
    y = '1000000 1000000'
  []
  [stress_correlation_crackedOPyC]
    type = PiecewiseLinear
    x = '0 1.0e11'
    y = '1 1'
  []
  [stress_correlation_crackedIPyC]
    type = PiecewiseLinear
    x = '0 1.0e11'
    y = '100 100'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  generate_output = 'stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz '
                    'max_principal_stress'
  add_variables = true
  strain = FINITE
  incremental = true
  [fuel]
    block = fuel
    eigenstrain_names = 'UCO_swelling_eigenstrain UCO_TE_strain'
    extra_vector_tags = 'ref'
  []
  [buffer]
    block = buffer
    eigenstrain_names = 'Buffer_IIDC_strain Buffer_TE_strain'
    extra_vector_tags = 'ref'
  []
  [IPyC]
    block = IPyC
    eigenstrain_names = 'IPyC_IIDC_strain IPyC_TE_strain'
    extra_vector_tags = 'ref'
  []
  [SiC]
    block = SiC
    eigenstrain_names = 'SiC_thermal_eigenstrain'
    extra_vector_tags = 'ref'
  []
  [OPyC]
    block = OPyC
    eigenstrain_names = 'OPyC_IIDC_strain OPyC_TE_strain'
    extra_vector_tags = 'ref'
  []
[]

[Kernels]
  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temperature
    extra_vector_tags = 'ref'
  []
  [heat]
    type = HeatConduction
    variable = temperature
    extra_vector_tags = 'ref'
  []
  [heat_source]
    type = NeutronHeatSource
    variable = temperature
    block = fuel
    fission_rate = fission_rate
    extra_vector_tags = 'ref'
  []
[]

[AuxKernels]
  [fissionrate]
    type = MaterialRealAux
    variable = fission_rate
    property = fission_rate
    block = fuel
    execute_on = timestep_begin
  []
  [burnup]
    type = MaterialRealAux
    variable = burnup
    property = burnup
    block = fuel
    execute_on = timestep_begin
  []
  [fast_neutron_flux]
    type = MaterialRealAux
    variable = fast_neutron_flux
    property = fast_neutron_flux
    execute_on = timestep_begin
  []
  [fast_neutron_fluence]
    type = MaterialRealAux
    variable = fast_neutron_fluence
    property = fast_neutron_fluence
    execute_on = timestep_begin
  []
[]

[ThermalContact]
  [thermal_contact]
    type = GasGapHeatTransfer
    variable = temperature
    primary = IPyC_inner_boundary
    secondary = buffer_outer_boundary
    initial_moles = initial_moles
    gas_released = 'fis_gas_released'
    released_gas_types = 'Kr Xe'
    released_fractions = '0.185 0.815'
    tangential_tolerance = 1e-6
    quadrature = false
    min_gap = 1e-7
    max_gap = 50e-6
    gap_geometry_type = sphere
  []
[]

[BCs]
  [no_disp_x]
    type = DirichletBC
    variable = disp_x
    boundary = xzero
    value = 0.0
  []
  [freesurf_temp]
    type = DirichletBC
    variable = temperature
    value = 1573
    boundary = exterior
  []
  [exterior_pressure_x]
    type = Pressure
    variable = disp_x
    boundary = exterior
    factor = 0.1e6
  []
  [PlenumPressure]
    [plenumPressure]
      boundary = buffer_IPyC_boundary
      startup_time = 1e4
      initial_pressure = 0
      output_initial_moles = initial_moles
      temperature = ave_gas_temp
      volume = 'gap_volume buffer_void_volume kernel_void_volume'
      material_input = 'fis_gas_released'
      output = gas_pressure
    []
  []
[]

[Materials]
  [fission_rate]
    type = GenericFunctionMaterial
    prop_names = fission_rate
    prop_values = fission_rate
    block = fuel
  []
  [fast_neutron_flux]
    type = FastNeutronFlux
    calculate_fluence = true
    factor = 6.2425e+17
  []
  [UCO_burnup]
    type = TRISOBurnup
    initial_density = 10966
    block = fuel
  []
  [UCO_thermal]
    type = UCOThermal
    block = fuel
    temperature = temperature
  []
  [UCO_elasticity_tensor]
    type = UCOElasticityTensor
    block = fuel
    temperature = temperature
  []
  [UCO_stress]
    type = ComputeFiniteStrainElasticStress
    block = fuel
  []
  [UCO_VolumetricSwellingEigenstrain]
    type = UCOVolumetricSwellingEigenstrain
    block = fuel
    eigenstrain_name = UCO_swelling_eigenstrain
  []
  [fuel_thermal_expansion]
    type = ComputeThermalExpansionEigenstrain
    block = fuel
    thermal_expansion_coeff = 10.0e-6
    temperature = temperature
    eigenstrain_name = UCO_TE_strain
  []
  [UCO_density]
    type = StrainAdjustedDensity
    block = fuel
    strain_free_density = 10966
  []
  [fission_gas_release]
    type = UCOFGR
    block = fuel
    average_grain_radius = 10e-6
    temperature = temperature
    triso_geometry = particle_geometry
    cutoff_neutron_flux = 0.0
  []
  [normal_vectors_triso]
    type = NormalVectorsTRISO
    block = 'buffer IPyC OPyC'
  []
  [BAF_IPyC]
    type = BaconAnisotropyFactor
    initial_BAF = 1.0465
    block = IPyC
  []
  [BAF_OPyC]
    type = BaconAnisotropyFactor
    initial_BAF = 1.0429
    block = OPyC
  []
  [buffer_elasticity_tensor]
    type = BufferElasticityTensor
    block = buffer
    temperature = temperature
  []
  [buffer_stress]
    type = BufferCEGACreep
    block = buffer
    temperature = temperature
  []
  [buffer_thermal]
    type = BufferThermal
    block = buffer
    initial_density = 1050.0
  []
  [buffer_density]
    type = StrainAdjustedDensity
    block = buffer
    strain_free_density = 1050.0
  []
  [buffer_TE]
    type = BufferThermalExpansionEigenstrain
    block = buffer
    eigenstrain_name = Buffer_TE_strain
    temperature = temperature
  []
  [buffer_IIDC]
    type = BufferCEGAIrradiationEigenstrain
    block = buffer
    eigenstrain_name = Buffer_IIDC_strain
    temperature = temperature
  []
  [IPyC_elasticity_tensor]
    type = PyCElasticityTensor
    block = IPyC
    temperature = temperature
  []
  [IPyC_stress]
    type = PyCCEGACreep
    block = IPyC
    creep_rate_scale_factor = 1
    temperature = temperature
  []

  [IPyC_thermal]
    type = HeatConductionMaterial
    block = IPyC
    thermal_conductivity = 4.0
    specific_heat = 720.0
  []
  [IPyC_density]
    type = GenericConstantMaterial
    block = IPyC
    prop_names = 'density'
    prop_values = 1890
  []
  [IPyC_IIDC]
    type = PyCCEGAIrradiationEigenstrain
    block = IPyC
    eigenstrain_name = IPyC_IIDC_strain
    temperature = temperature
    irradiation_eigenstrain_scale_factor = 1
  []
  [IPyC_TE]
    type = PyCThermalExpansionEigenstrain
    block = IPyC
    eigenstrain_name = IPyC_TE_strain
    temperature = temperature
  []
  [SiC_elasticity_tensor]
    type = MonolithicSiCElasticityTensor
    block = SiC
    temperature = temperature
    elastic_modulus_model = miller
  []
  [SiC_stress]
    type = ComputeFiniteStrainElasticStress
    block = SiC
  []
  [SiC_thermal]
    type = MonolithicSiCThermal
    block = SiC
    temperature = temperature
    thermal_conductivity_model = miller
  []
  [SiC_density]
    type = StrainAdjustedDensity
    block = SiC
    strain_free_density = 3200.0
  []
  [SiC_thermal_expansion]
    type = ComputeThermalExpansionEigenstrain
    block = SiC
    thermal_expansion_coeff = 4.9e-6
    temperature = temperature
    eigenstrain_name = SiC_thermal_eigenstrain
  []
  [OPyC_elasticity_tensor]
    type = PyCElasticityTensor
    block = OPyC
    temperature = temperature
    initial_BAF = 1.0
  []
  [OPyC_stress]
    type = PyCCEGACreep
    block = OPyC
    creep_rate_scale_factor = 1
    temperature = temperature
  []
  [OPyC_thermal_conductivity]
    type = HeatConductionMaterial
    block = OPyC
    thermal_conductivity = 4.0
    specific_heat = 720.0
  []
  [OPyC_density]
    type = GenericConstantMaterial
    block = OPyC
    prop_names = 'density'
    prop_values = 1900
  []
  [OPyC_IIDC]
    type = PyCCEGAIrradiationEigenstrain
    block = OPyC
    eigenstrain_name = OPyC_IIDC_strain
    temperature = temperature
    irradiation_eigenstrain_scale_factor = 1
  []
  [OPyC_TE]
    type = PyCThermalExpansionEigenstrain
    block = OPyC
    eigenstrain_name = OPyC_TE_strain
    temperature = temperature
  []
  [characteristic_strength_SiC]
    type = GenericConstantMaterial
    prop_values = '9640000'
    block = SiC
    prop_names = 'characteristic_strength'
  []
  [characteristic_strength_PyC]
    type = PyCCharacteristicStrength
    temperature = temperature
    X = 1.02
    block = 'IPyC OPyC'
  []
[]

[Dampers]
  [temp]
    type = MaxIncrement
    variable = temperature
    max_increment = 100
  []
[]

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

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'

  line_search = 'none'

  nl_rel_tol = 5e-6
  nl_abs_tol = 1e-8
  nl_max_its = 20

  l_tol = 1e-4
  l_max_its = 50

  start_time = 0.0
  num_steps = 10

  dtmin = 1e-4
  dt = 1e4
[]

[Postprocessors]
  [ave_gas_temp]
    type = ElementAverageValue
    block = buffer
    variable = temperature
    execute_on = 'initial timestep_end'
  []
  [fis_gas_released]
    type = ElementIntegralMaterialProperty
    mat_prop = fis_gas_released
    block = fuel
    use_displaced_mesh = false
    execute_on = 'initial timestep_end'
  []
  [gap_volume]
    type = InternalVolume
    boundary = buffer_IPyC_boundary
    execute_on = 'initial linear'
    use_displaced_mesh = true
  []
  [buffer_void_volume]
    type = VoidVolume
    block = buffer
    theoretical_density = 2250
    execute_on = 'initial timestep_end'
    use_displaced_mesh = true
  []
  [kernel_th_density]
    type = UCOTheoreticalDensity
    execute_on = initial
  []
  [kernel_void_volume]
    type = VoidVolume
    block = fuel
    theoretical_density = kernel_th_density
    execute_on = 'initial timestep_end'
    use_displaced_mesh = true
  []
  [particle_power]
    type = ElementIntegralPower
    variable = temperature
    use_material_fission_rate = true
    fission_rate_material = fission_rate
    block = fuel
    execute_on = 'initial timestep_end'
  []
  [max_fluence]
    type = ElementExtremeValue
    variable = fast_neutron_fluence
    value_type = 'max'
    execute_on = 'initial timestep_end'
  []
  [max_burnup]
    type = ElementExtremeValue
    variable = burnup
    block = fuel
    value_type = 'max'
    execute_on = 'initial timestep_end'
  []
  [SiC_stress_max]
    type = ElementExtremeMaterialProperty
    block = SiC
    value_type = max
    mat_prop = stress_yy
  []
  [SiC_stress_min]
    type = ElementExtremeMaterialProperty
    block = SiC
    value_type = min
    mat_prop = stress_yy
  []
  [strength_SiC]
    type = WeibullEffectiveMeanStrength
    block = SiC
    weibull_modulus = 6
  []
  [kernel_migration_distance]
    type = KernelMigrationDistance
    block = 'fuel buffer IPyC SiC OPyC'
    variable = temperature
    temperature_gradient = 15000
    kernel_type = UO2
  []
  [failure_indicator_kernel_migration]
    type = KernelMigrationFailureIndicator
    kernel_migration_distance = kernel_migration_distance
    triso_geometry = particle_geometry
  []
  [failure_indicator_SiC]
    type = WeibullFailureOutputUsingCorrelation
    block = SiC
    weibull_modulus = 6
    stress_name = max_principal_stress
    effective_mean_strength = strength_SiC
  []
  [strength_IPyC]
    type = WeibullEffectiveMeanStrength
    block = IPyC
    weibull_modulus = 6
  []
  [failure_indicator_IPyC]
    type = WeibullFailureOutputUsingCorrelation
    block = IPyC
    weibull_modulus = 6
    stress_name = max_principal_stress
    effective_mean_strength = strength_IPyC
  []
  [strength_OPyC]
    type = WeibullEffectiveMeanStrength
    block = OPyC
    weibull_modulus = 6
  []
  [failure_indicator_OPyC]
    type = WeibullFailureOutputUsingCorrelation
    block = OPyC
    weibull_modulus = 6
    stress_name = max_principal_stress
    effective_mean_strength = strength_OPyC
  []
  [pd_penetration]
    type = PdPenetration
    boundary = SiC_inner_boundary
    variable = temperature
    execute_on = 'initial timestep_end'
  []
  [failure_indicator_pd_penetration]
    type = PdPenetrationFailureIndicator
    triso_geometry = particle_geometry
    pd_penetration = pd_penetration
  []
  [failure_indicator_SiC_crackedIPyC]
    type = WeibullFailureOutputUsingCorrelation
    block = SiC
    weibull_modulus = 6
    stress_name = max_principal_stress
    high_fidelity_analysis_strength = 'high_fidelity_strength_crackedIPyC'
    stress_correlation_function = 'stress_correlation_crackedIPyC'
  []
  [failure_indicator_SiC_crackedOPyC]
    type = WeibullFailureOutputUsingCorrelation
    block = SiC
    weibull_modulus = 6
    stress_name = max_principal_stress
    high_fidelity_analysis_strength = 'high_fidelity_strength_crackedIPyC'
    stress_correlation_function = 'stress_correlation_crackedOPyC'
  []
  [triso_failure]
    type = TRISOFailureEvaluation
    IPyC_failure = failure_indicator_IPyC
    OPyC_failure = failure_indicator_OPyC
    SiC_failure = failure_indicator_SiC
    SiC_failure_crackedIPyC = failure_indicator_SiC_crackedIPyC
    SiC_failure_crackedOPyC = failure_indicator_SiC_crackedOPyC
    SiC_failure_pd_penetration = failure_indicator_pd_penetration
    SiC_failure_kernel_migration = failure_indicator_kernel_migration
  []
[]

[Outputs]
  show = 'kernel_migration_distance failure_indicator_kernel_migration triso_failure '
  print_linear_residuals = false
  time_step_interval =  1
  csv = true
  perf_graph = true
[]

(test/tests/triso_failure/triso_1d_pd_penetration.i)

[GlobalParams]
  density = 10810.0
  flux_conversion_factor = 1.0
  order = SECOND
  family = LAGRANGE
  displacements = 'disp_x'
[]

[Mesh]
  coord_type = RSPHERICAL
  [gen]
    type = TRISO1DFiveLayerMeshGenerator
    elem_type = EDGE3
    kernel_radius = 2.485e-4
    buffer_thickness = 9.4e-5
    IPyC_thickness = 4.1e-5
    SiC_thickness = 3.6e-5
    OPyC_thickness = 4.0e-5
    kernel_mesh_density = 6
    buffer_mesh_density = 6
    IPyC_mesh_density = 6
    SiC_mesh_density = 8
    OPyC_mesh_density = 6
  []
[]

[Variables]
  [disp_x]
  []
  [temperature]
    initial_condition = 1346.0
  []
[]

[UserObjects]
  [particle_geometry]
    type = TRISOGeometry
    outer_OPyC = OPyC_outer_boundary
    outer_SiC = SiC_outer_boundary
    outer_IPyC = IPyC_outer_boundary
    inner_IPyC = IPyC_inner_boundary
    outer_buffer = buffer_outer_boundary
    outer_kernel = fuel_outer_boundary
  []
[]

[Functions]
  [radial_eigenstrain]
    type = ParsedFunction
    expression = 't*(4.52013e-4/6.0*t*t*t*t*t - 8.36313e-3/5.0*t*t*t*t + 5.67549e-2/4.0*t*t*t - 1.74247e-1/3.0*t*t + 2.62692e-1/2.0*t - 1.43234e-1)'
  []
  [tangential_eigenstrain]
    type = ParsedFunction
    expression = 't*(1.30457e-4/4.0*t*t*t - 2.10029e-3/3.0*t*t + 9.07826e-3/2.0*t - 3.24737e-2)'
  []
  [fission_rate]
    type = ParsedFunction
    expression = 7.75e19 # units of fissions/m**3
  []
  [k_function]
    type = ParsedFunction
    expression = '4.93e-29'
  []
  [high_fidelity_strength_crackedIPyC]
    type = PiecewiseLinear
    x = '0 1.0e11'
    y = '1000000 1000000'
  []
  [high_fidelity_strength_crackedOPyC]
    type = PiecewiseLinear
    x = '0 1.0e11'
    y = '1000000 1000000'
  []
  [stress_correlation_crackedOPyC]
    type = PiecewiseLinear
    x = '0 1.0e11'
    y = '1 1'
  []
  [stress_correlation_crackedIPyC]
    type = PiecewiseLinear
    x = '0 1.0e11'
    y = '100 100'
  []
[]

[AuxVariables]
  [stress_yy]
    order = CONSTANT
    family = MONOMIAL
  []
  [burnup]
    block = fuel
    initial_condition = 0.0
  []
  [fission_rate]
    block = fuel
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  strain = small
  [fuel_buffer_sic]
    block = 'fuel buffer SiC'
    eigenstrain_names = thermal_strain
  []
  [ipyc_opyc]
    block = 'IPyC OPyC'
    incremental = true
    eigenstrain_names = 'thermal_strain pyc_eigenstrain'
  []
[]

[Kernels]
  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temperature
  []
  [heat]
    type = HeatConduction
    variable = temperature
  []
  [heat_source]
    type = NeutronHeatSource
    variable = temperature
    block = fuel
    energy_per_fission = 3.2e-11
    fission_rate = fission_rate
  []
[]

[AuxKernels]
  [stress_yy]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_yy
    index_i = 1
    index_j = 1
    execute_on = timestep_end
  []
  [fission_rate]
    type = FunctionAux
    variable = fission_rate
    block = fuel
    function = fission_rate
  []
  [burnup]
    type = BurnupAux
    variable = burnup
    block = fuel
    fission_rate = fission_rate
    molecular_weight = 0.270 # units of kg/mole
  []
[]

[Contact]
  [pellet_clad_mechanical]
    primary = IPyC_inner_boundary
    secondary = buffer_outer_boundary
    penalty = 1e5
    model = frictionless
    formulation = kinematic
  []
[]

[ThermalContact]
  [thermal_contact]
    type = GasGapHeatTransfer
    variable = temperature
    primary = IPyC_inner_boundary
    secondary = buffer_outer_boundary
    initial_moles = initial_moles
    gas_released = 'fis_gas_released co_production'
    released_gas_types = 'Kr Xe;
                          CO'
    released_fractions = '0.153 0.847;
                          1'
    tangential_tolerance = 1e-6
  []
[]

[BCs]
  # pin particle along symmetry planes
  [no_disp_x]
    type = DirichletBC
    variable = disp_x
    boundary = xzero
    value = 0.0
  []
  # fix temperature on free surface
  [freesurf_temp]
    type = DirichletBC
    variable = temperature
    boundary = exterior
    value = 1346.0
  []
  # exterior and internal pressures
  [exterior_pressure_x]
    type = Pressure
    use_displaced_mesh = false
    variable = disp_x
    boundary = exterior
    factor = 0.1e6
  []
  #  apply gas pressure on buffer and IPyC boundaries
  [PlenumPressure]
    [plenumPressure]
      use_displaced_mesh = false
      boundary = buffer_IPyC_boundary
      initial_pressure = 0
      startup_time = 1.0e4
      # coupling to post processor
      output_initial_moles = initial_moles
      temperature = ave_temp_interior
      volume = volumeGas
      material_input = 'fis_gas_released co_production'
      output = plenum_pressure
    []
  []
[]

[Materials]
  [max_principal_stress]
    type = RankTwoInvariant
    property_name = max_principal_stress
    rank_two_tensor = stress
    invariant = MaxPrincipal
  []
  [flux]
    type = FastNeutronFlux
    calculate_fluence = true
    factor = 1.708707e18
  []
  [fission_gas_release]
    type = UO2Sifgrs
    block = fuel
    temperature = temperature
    fission_rate = fission_rate
    grain_radius_const = 5.0e-6
  []
  [stress]
    type = ComputeLinearElasticStress
    block = 'fuel buffer SiC'
  []
  [PyC_stress]
    type = PyCCreep
    block = 'IPyC OPyC'
    k = k_function
    poissons_ratio = 0.4
    temperature = temperature
  []
  [normal_vectors_triso]
    type = NormalVectorsTRISO
    block = 'IPyC OPyC'
  []
  [PyC_eigenstrain]
    type = PyCIrradiationEigenstrain
    block = 'IPyC OPyC'
    radial_eigenstrain_function = radial_eigenstrain
    tangential_eigenstrain_function = tangential_eigenstrain
    eigenstrain_name = pyc_eigenstrain
  []
  [fuel_thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    block = fuel
    thermal_expansion_coeff = 10e-6
    stress_free_temperature = 1346.0
    eigenstrain_name = thermal_strain
    temperature = temperature
  []
  [PyC_thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    block = 'buffer IPyC OPyC'
    thermal_expansion_coeff = 5.5e-6
    stress_free_temperature = 1346.0
    eigenstrain_name = thermal_strain
    temperature = temperature
  []
  [SiC_thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    block = SiC
    thermal_expansion_coeff = 4.9e-6
    stress_free_temperature = 1346.0
    eigenstrain_name = thermal_strain
    temperature = temperature
  []
  [fuel_thermal]
    type = UO2Thermal
    thermal_conductivity_model = FINK_LUCUTA
    block = fuel
    temperature = temperature
    burnup = burnup
  []
  [fuel_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = fuel
    youngs_modulus = 2e8
    poissons_ratio = 0.345
  []
  [fuel_den]
    type = StrainAdjustedDensity
    block = fuel
    strain_free_density = 10810.0
  []
  [buffer_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = buffer
    youngs_modulus = 2e8
    poissons_ratio = 0.345
  []
  [buffer_temp]
    type = HeatConductionMaterial
    block = buffer
    thermal_conductivity = 0.5
    specific_heat = 720.0
  []
  [buffer_den]
    type = StrainAdjustedDensity
    strain_free_density = 1000
    block = buffer
  []
  [PyC_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = 'IPyC OPyC'
    youngs_modulus = 3.96e10
    poissons_ratio = 0.33
  []
  [PyC_temp]
    type = HeatConductionMaterial
    block = 'IPyC OPyC'
    thermal_conductivity = 4.0
    specific_heat = 720.0
  []
  [PyC_den]
    type = StrainAdjustedDensity
    strain_free_density = 1880.0
    block = 'IPyC OPyC'
  []
  [SiC_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = SiC
    youngs_modulus = 3.7e11
    poissons_ratio = 0.13
  []
  [SiC_temp]
    type = HeatConductionMaterial
    block = SiC
    thermal_conductivity = 13.9
    specific_heat = 620.0
  []
  [SiC_den]
    type = StrainAdjustedDensity
    strain_free_density = 3200.0
    block = SiC
  []
  [characteristic_strength_SiC]
    type = GenericConstantMaterial
    prop_values = '9640000'
    prop_names = 'characteristic_strength'
    block = SiC
  []

  [characteristic_strength_PyC]
    type = GenericConstantMaterial
    prop_values = '964000'
    prop_names = 'characteristic_strength'
    block = 'IPyC OPyC'
  []
[]

[Dampers]
  [temperature]
    type = MaxIncrement
    variable = temperature
    max_increment = 50
  []
[]

[Debug]
  show_var_residual_norms = true
[]

[Executioner]
  type = Transient
  petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
  petsc_options_value = '201                hypre    boomeramg      4'
  line_search = 'none'
  solve_type = 'PJFNK'
  nl_rel_tol = 5e-6
  nl_abs_tol = 1e-10
  nl_max_its = 15
  l_tol = 1e-3
  l_max_its = 50
  start_time = 0.0
  num_steps = 2
  dtmax = 2e5
  dtmin = 1
  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 20
    optimal_iterations = 6
    iteration_window = 2
    linear_iteration_ratio = 100
  []
[]

[Postprocessors]
  [dt]
    type = TimestepSize
  []
  [burnup]
    type = ElementExtremeValue
    block = fuel
    variable = burnup
  []
  [fis_gas_produced]
    type = ElementIntegralFisGasGeneratedSifgrs
    block = fuel
  []
  [fis_gas_released]
    type = ElementIntegralFisGasReleasedSifgrs
    block = fuel
  []
  [volumeTotal]
    type = InternalVolume
    boundary = exterior
  []
  [volumeFuel]
    type = InternalVolume
    boundary = fuel_outer_boundary
  []
  [volumeGas]
    type = InternalVolume
    boundary = 'fuel_outer_boundary IPyC_inner_boundary'
    addition = -5.53e-11
    execute_on = 'initial timestep_end'
  []
  [volumeBufferShell]
    type = InternalVolume
    boundary = buffer_IPyC_boundary
  []
  [ave_temp_interior]
    type = SideAverageValue
    boundary = buffer_IPyC_boundary
    variable = temperature
    execute_on = 'initial timestep_end'
  []
  # Postprocessors for CO production
  [total_fission_rate]
    type = ElementIntegralPower
    variable = temperature
    fission_rate = fission_rate
    block = fuel
    energy_per_fission = 1.0
  []
  [total_fissions]
    type = TimeIntegratedPostprocessor
    value = total_fission_rate
  []
  [avg_surface_temp]
    type = SideAverageValue
    variable = temperature
    boundary = exterior
  []
  [time_int_surf_temp]
    type = TimeIntegratedPostprocessor
    value = avg_surface_temp
  []
  [co_production]
    type = CarbonMonoxideProduction
    total_fissions = total_fissions
    time_integrated_triso_temperature = time_int_surf_temp
    initial_enrichment = 0.14029
  []
  [tang_SiC]
    type = ElementalVariableValue
    variable = stress_yy
    elementid = 18
  []
  [strength_SiC]
    type = WeibullEffectiveMeanStrength
    block = SiC
    weibull_modulus = 6
  []
  [failure_indicator_SiC]
    type = WeibullFailureOutputUsingCorrelation
    block = SiC
    weibull_modulus = 6
    stress_name = max_principal_stress
    effective_mean_strength = strength_SiC
  []
  [strength_IPyC]
    type = WeibullEffectiveMeanStrength
    block = IPyC
    weibull_modulus = 6
  []
  [failure_indicator_IPyC]
    type = WeibullFailureOutputUsingCorrelation
    block = IPyC
    weibull_modulus = 6
    stress_name = max_principal_stress
    effective_mean_strength = strength_IPyC
  []
  [strength_OPyC]
    type = WeibullEffectiveMeanStrength
    block = OPyC
    weibull_modulus = 6
  []
  [failure_indicator_OPyC]
    type = WeibullFailureOutputUsingCorrelation
    block = OPyC
    weibull_modulus = 6
    stress_name = max_principal_stress
    effective_mean_strength = strength_OPyC
  []
  [pd_penetration]
    type = PdPenetration
    boundary = SiC_inner_boundary
    variable = temperature
    execute_on = 'initial timestep_end'
  []
  [failure_indicator_pd_penetration]
    type = PdPenetrationFailureIndicator
    triso_geometry = particle_geometry
    pd_penetration = pd_penetration
  []
  [failure_indicator_SiC_crackedIPyC]
    type = WeibullFailureOutputUsingCorrelation
    block = SiC
    weibull_modulus = 6
    stress_name = max_principal_stress
    high_fidelity_analysis_strength = 'high_fidelity_strength_crackedIPyC'
    stress_correlation_function = 'stress_correlation_crackedIPyC'
  []
  [failure_indicator_SiC_crackedOPyC]
    type = WeibullFailureOutputUsingCorrelation
    block = SiC
    weibull_modulus = 6
    stress_name = max_principal_stress
    high_fidelity_analysis_strength = 'high_fidelity_strength_crackedIPyC'
    stress_correlation_function = 'stress_correlation_crackedOPyC'
  []
  [triso_failure]
    type = TRISOFailureEvaluation
    IPyC_failure = failure_indicator_IPyC
    OPyC_failure = failure_indicator_OPyC
    SiC_failure = failure_indicator_SiC
    SiC_failure_crackedIPyC = failure_indicator_SiC_crackedIPyC
    SiC_failure_crackedOPyC = failure_indicator_SiC_crackedOPyC
    SiC_failure_pd_penetration = failure_indicator_pd_penetration
  []
[]

[Outputs]
  print_linear_residuals = true
  time_step_interval =  1
  csv = true
  perf_graph = true
[]

(examples/TRISO/failure_probability_monte_carlo/triso_1d_constant.i)


initial_fuel_density = 5

[GlobalParams]
  order = FIRST
  family = LAGRANGE
  displacements = 'disp_x'
  initial_enrichment = 0.14029 # [wt-]
  flux_conversion_factor = 1.0 # convert E>0.10 to E>0.18 MeV
  stress_free_temperature = 481 # used for thermal expansion
  energy_per_fission = 3.204e-11 # [J/fission]
  O_U = 1.428 # Initial Oxygen to Uranium atom ratio
  C_U = 0.392 # Initial Carbon to Uranium atom ratio
[]

[Mesh]
  coord_type = RSPHERICAL
  [gen]
    type = TRISO1DFiveLayerMeshGenerator
    elem_type = EDGE3
    kernel_radius = 213.35e-6
    buffer_thickness = 98.9e-6
    IPyC_thickness = 40.4e-6
    SiC_thickness = 35.2e-6
    OPyC_thickness = 43.4e-6
    kernel_mesh_density = ${initial_fuel_density}
    buffer_mesh_density = 3
    IPyC_mesh_density = 5
    SiC_mesh_density = 3
    OPyC_mesh_density = 4
  []
[]

[Problem]
  type = ReferenceResidualProblem
  reference_vector = 'ref'
  extra_tag_vectors = 'ref'
[]

[UserObjects]
  [particle_geometry]
    type = TRISOGeometry
    outer_OPyC = OPyC_outer_boundary
    outer_SiC = SiC_outer_boundary
    outer_IPyC = IPyC_outer_boundary
    inner_IPyC = IPyC_inner_boundary
    outer_buffer = buffer_outer_boundary
    outer_kernel = fuel_outer_boundary
    include_particle = true
    include_pebble = false
    IPyC_thickness_mean = 40.4e-6
    SiC_thickness_mean = 35.2e-6
    OPyC_thickness_mean = 43.4e-6
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [sic_failure_terminator]
    type = Terminator
    expression = 'sic_failure_overall > 0'
  []
[]

[Variables]
  [temperature]
    initial_condition = 481
  []
[]

[AuxVariables]
  [fission_rate]
    order = CONSTANT
    family = MONOMIAL
  []
  [burnup]
    order = CONSTANT
    family = MONOMIAL
  []
  [fast_neutron_flux]
    order = CONSTANT
    family = MONOMIAL
  []
  [fast_neutron_fluence]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [temp_bc]
    type = PiecewiseLinear
    data_file = outer_temp.csv
    x_index_in_file = 0
    y_index_in_file = 1
    format = columns
  []
  [fission_rate]
    type = ConstantFunction
    value = 5.75e19
  []
  [high_fidelity_strength_crackedIPyC]
    type = ConstantFunction
    value = '1403604095.5707'
  []
  [stress_correlation_crackedIPyC]
    type = TRISOStressCorrelationFunction
    triso_geometry = particle_geometry
    polynomial_coefficients_IPyC = '1 0 0'
    polynomial_coefficients_SiC = '1 0 0'
    polynomial_coefficients_OPyC = '1 0 0'
    correlation_factor = -1.2447543103484047
  []
  [high_fidelity_strength_debonding]
    type = ConstantFunction
    value = '1705800293.3578'
  []
  [stress_correlation_debonding]
    type = TRISOStressCorrelationFunction
    triso_geometry = particle_geometry
    polynomial_coefficients_IPyC = '1 0 0'
    polynomial_coefficients_SiC = '1 0 0'
    polynomial_coefficients_OPyC = '1 0 0'
    correlation_factor = -0.14916368684964607
  []
  [high_fidelity_strength_asphericity]
    type = ConstantFunction
    value = '1371700766.8875'
  []
  [stress_correlation_asphericity]
    type = TRISOStressCorrelationFunction
    triso_geometry = particle_geometry
    polynomial_coefficients_IPyC = '1 0 0'
    polynomial_coefficients_SiC = '1 0 0'
    polynomial_coefficients_OPyC = '1 0 0'
    correlation_factor = 1.5191967987843993
  []
  [stress_change_correlation_asphericity]
    type = TRISOStressCorrelationFunction
    triso_geometry = particle_geometry
    polynomial_coefficients_IPyC = '1 0 0'
    polynomial_coefficients_SiC = '1 0 0'
    polynomial_coefficients_OPyC = '1 0 0'
    correlation_factor = 1.391516859626456
  []
  [sic_crackedipyc_stress_strength]
    type = ParsedFunction
    expression = 'a-b'
    symbol_names = 'a b'
    symbol_values = 'stress_SiC_crackedIPyC actual_strength_SiC_crackedIPyC'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  generate_output = 'stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz max_principal_stress'
  add_variables = true
  strain = FINITE
  incremental = true
  [fuel]
    block = fuel
    eigenstrain_names = 'UCO_swelling_eigenstrain UCO_TE_strain'
    extra_vector_tags = 'ref'
  []
  [buffer]
    block = buffer
    eigenstrain_names = 'Buffer_IIDC_strain Buffer_TE_strain'
    extra_vector_tags = 'ref'
  []
  [IPyC]
    block = IPyC
    eigenstrain_names = 'IPyC_IIDC_strain IPyC_TE_strain'
    extra_vector_tags = 'ref'
  []
  [SiC]
    block = SiC
    eigenstrain_names = 'SiC_thermal_eigenstrain'
    extra_vector_tags = 'ref'
  []
  [OPyC]
    block = OPyC
    eigenstrain_names = 'OPyC_IIDC_strain OPyC_TE_strain'
    extra_vector_tags = 'ref'
  []
[]

[Kernels]
  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temperature
    extra_vector_tags = 'ref'
  []
  [heat]
    type = HeatConduction
    variable = temperature
    extra_vector_tags = 'ref'
  []
  [heat_source]
    type = NeutronHeatSource
    variable = temperature
    block = fuel
    fission_rate = fission_rate
    extra_vector_tags = 'ref'
  []
[]

[AuxKernels]
  [fissionrate]
    type = MaterialRealAux
    variable = fission_rate
    property = fission_rate
    block = fuel
    execute_on = timestep_begin
  []
  [burnup]
    type = MaterialRealAux
    variable = burnup
    property = burnup
    block = fuel
    execute_on = timestep_begin
  []
  [fast_neutron_flux]
    type = MaterialRealAux
    variable = fast_neutron_flux
    property = fast_neutron_flux
    execute_on = timestep_begin
  []
  [fast_neutron_fluence]
    type = MaterialRealAux
    variable = fast_neutron_fluence
    property = fast_neutron_fluence
    execute_on = timestep_begin
  []
[]

[ThermalContact]
  [thermal_contact]
    type = GasGapHeatTransfer
    variable = temperature
    primary = IPyC_inner_boundary
    secondary = buffer_outer_boundary
    initial_moles = initial_moles
    gas_released = 'fis_gas_released'
    released_gas_types = 'Kr Xe'
    released_fractions = '0.185 0.815'
    tangential_tolerance = 1e-6
    quadrature = false
    min_gap = 1e-7
    max_gap = 50e-6
    gap_geometry_type = sphere
  []
[]

[BCs]
  [no_disp_x]
    type = DirichletBC
    variable = disp_x
    boundary = xzero
    value = 0.0
  []
  [freesurf_temp]
    type = FunctionDirichletBC
    variable = temperature
    function = temp_bc
    boundary = exterior
  []
  [exterior_pressure_x]
    type = Pressure
    variable = disp_x
    boundary = exterior
    factor = 0.1e6
  []
  [PlenumPressure]
    [plenumPressure]
      boundary = buffer_IPyC_boundary
      startup_time = 1e4
      initial_pressure = 0
      R = 8.3145
      output_initial_moles = initial_moles
      temperature = ave_gas_temp
      volume = 'gap_volume buffer_void_volume kernel_void_volume'
      material_input = 'fis_gas_released'
      output = gas_pressure
    []
  []
[]

[Materials]
  [radial_stress]
    type = RankTwoCylindricalComponent
    rank_two_tensor = stress
    cylindrical_axis_point1 = '0 0 0'
    cylindrical_axis_point2 = '0 0 1'
    cylindrical_component = RadialStress
    property_name = radial_stress
    outputs = all
  []
  [fission_rate]
    type = GenericFunctionMaterial
    prop_names = fission_rate
    prop_values = fission_rate
    block = fuel
  []
  [fast_neutron_flux]
    type = FastNeutronFlux
    calculate_fluence = true
    factor = 6.2425e+17
  []
  [UCO_burnup]
    type = TRISOBurnup
    initial_density = 10966
    block = fuel
  []
  [UCO_thermal]
    type = UCOThermal
    block = fuel
    temperature = temperature
  []
  [UCO_elasticity_tensor]
    type = UCOElasticityTensor
    block = fuel
    temperature = temperature
  []
  [UCO_stress]
    type = ComputeFiniteStrainElasticStress
    block = fuel
  []
  [UCO_VolumetricSwellingEigenstrain]
    type = UCOVolumetricSwellingEigenstrain
    block = fuel
    eigenstrain_name = UCO_swelling_eigenstrain
  []
  [fuel_thermal_expansion]
    type = ComputeThermalExpansionEigenstrain
    block = fuel
    thermal_expansion_coeff = 10.0e-6
    temperature = temperature
    eigenstrain_name = UCO_TE_strain
  []
  [UCO_density]
    type = StrainAdjustedDensity
    block = fuel
    strain_free_density = 10966
  []
  [fission_gas_release]
    type = UCOFGR
    block = fuel
    average_grain_radius = 10e-6
    temperature = temperature
    triso_geometry = particle_geometry
    cutoff_neutron_flux = 0.0
  []
  [normal_vectors_triso]
    type = NormalVectorsTRISO
    block = 'buffer IPyC OPyC'
  []
  [BAF_IPyC]
    type = BaconAnisotropyFactor
    initial_BAF = 1.0465
    block = IPyC
  []
  [BAF_OPyC]
    type = BaconAnisotropyFactor
    initial_BAF = 1.0429
    block = OPyC
  []
  [buffer_elasticity_tensor]
    type = BufferElasticityTensor
    block = buffer
    temperature = temperature
  []
  [buffer_stress]
    type = BufferCEGACreep
    block = buffer
    temperature = temperature
  []
  [buffer_thermal]
    type = BufferThermal
    block = buffer
    initial_density = 1050.0
  []
  [buffer_density]
    type = StrainAdjustedDensity
    block = buffer
    strain_free_density = 1050.0
  []
  [buffer_TE]
    type = BufferThermalExpansionEigenstrain
    block = buffer
    eigenstrain_name = Buffer_TE_strain
    temperature = temperature
  []
  [buffer_IIDC]
    type = BufferCEGAIrradiationEigenstrain
    block = buffer
    eigenstrain_name = Buffer_IIDC_strain
    temperature = temperature
  []
  [IPyC_elasticity_tensor]
    type = PyCElasticityTensor
    block = IPyC
    temperature = temperature
  []
  [IPyC_stress]
    type = PyCCEGACreep
    block = IPyC
    creep_rate_scale_factor = 1
    temperature = temperature
  []

  [IPyC_thermal]
    type = HeatConductionMaterial
    block = IPyC
    thermal_conductivity = 4.0
    specific_heat = 720.0
  []
  [IPyC_density]
    type = GenericConstantMaterial
    block = IPyC
    prop_names = 'density'
    prop_values = 1890
  []
  [IPyC_IIDC]
    type = PyCCEGAIrradiationEigenstrain
    block = IPyC
    eigenstrain_name = IPyC_IIDC_strain
    temperature = temperature
    irradiation_eigenstrain_scale_factor = 1
  []
  [IPyC_TE]
    type = PyCThermalExpansionEigenstrain
    block = IPyC
    eigenstrain_name = IPyC_TE_strain
    temperature = temperature
  []
  [SiC_elasticity_tensor]
    type = MonolithicSiCElasticityTensor
    block = SiC
    temperature = temperature
    elastic_modulus_model = miller
  []
  [SiC_stress]
    type = ComputeFiniteStrainElasticStress
    block = SiC
  []
  [SiC_thermal]
    type = MonolithicSiCThermal
    block = SiC
    temperature = temperature
    thermal_conductivity_model = miller
  []
  [SiC_density]
    type = StrainAdjustedDensity
    block = SiC
    strain_free_density = 3200.0
  []
  [SiC_thermal_expansion]
    type = ComputeThermalExpansionEigenstrain
    block = SiC
    thermal_expansion_coeff = 4.9e-6
    temperature = temperature
    eigenstrain_name = SiC_thermal_eigenstrain
  []
  [OPyC_elasticity_tensor]
    type = PyCElasticityTensor
    block = OPyC
    temperature = temperature
    initial_BAF = 1.0
  []
  [OPyC_stress]
    type = PyCCEGACreep
    block = OPyC
    creep_rate_scale_factor = 1
    temperature = temperature
  []
  [OPyC_thermal_conductivity]
    type = HeatConductionMaterial
    block = OPyC
    thermal_conductivity = 4.0
    specific_heat = 720.0
  []
  [OPyC_density]
    type = GenericConstantMaterial
    block = OPyC
    prop_names = 'density'
    prop_values = 1900
  []
  [OPyC_IIDC]
    type = PyCCEGAIrradiationEigenstrain
    block = OPyC
    eigenstrain_name = OPyC_IIDC_strain
    temperature = temperature
    irradiation_eigenstrain_scale_factor = 1
  []
  [OPyC_TE]
    type = PyCThermalExpansionEigenstrain
    block = OPyC
    eigenstrain_name = OPyC_TE_strain
    temperature = temperature
  []
  [characteristic_strength_SiC]
    type = GenericConstantMaterial
    prop_values = '9640000'
    block = SiC
    prop_names = 'characteristic_strength'
  []
  [characteristic_strength_PyC]
    type = PyCCharacteristicStrength
    temperature = temperature
    X = 1.02
    block = 'IPyC OPyC'
  []
[]

[Dampers]
  [temp]
    type = MaxIncrement
    variable = temperature
    max_increment = 100
  []
[]

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

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'

  line_search = 'none'

  nl_rel_tol = 5e-6
  nl_abs_tol = 1e-8
  nl_max_its = 20

  l_tol = 1e-4
  l_max_its = 50

  start_time = 0.0
  end_time = 4.831315e7

  dtmin = 1e-4
  dt = 5e5
[]

[Postprocessors]
  [ave_gas_temp]
    type = ElementAverageValue
    block = buffer
    variable = temperature
    execute_on = 'initial timestep_end'
  []
  [fis_gas_released]
    type = ElementIntegralMaterialProperty
    mat_prop = fis_gas_released
    block = fuel
    use_displaced_mesh = false
    execute_on = 'initial timestep_end'
  []
  [gap_volume]
    type = InternalVolume
    boundary = buffer_IPyC_boundary
    execute_on = 'initial linear'
    use_displaced_mesh = true
  []
  [buffer_void_volume]
    type = VoidVolume
    block = buffer
    theoretical_density = 2250
    execute_on = 'initial timestep_end'
    use_displaced_mesh = true
  []
  [kernel_th_density]
    type = UCOTheoreticalDensity
    execute_on = initial
  []
  [kernel_void_volume]
    type = VoidVolume
    block = fuel
    theoretical_density = kernel_th_density
    execute_on = 'initial timestep_end'
    use_displaced_mesh = true
  []
  [particle_power]
    type = ElementIntegralPower
    variable = temperature
    use_material_fission_rate = true
    fission_rate_material = fission_rate
    block = fuel
    execute_on = 'initial timestep_end'
  []
  [max_fluence]
    type = ElementExtremeValue
    variable = fast_neutron_fluence
    value_type = 'max'
    execute_on = 'initial timestep_end'
  []
  [max_burnup]
    type = ElementExtremeValue
    variable = burnup
    block = fuel
    value_type = 'max'
    execute_on = 'initial timestep_end'
  []
  [SiC_stress]
    type = ElementExtremeMaterialProperty
    block = SiC
    value_type = min
    mat_prop = stress_yy
  []
  [strength_SiC]
    type = WeibullEffectiveMeanStrength
    block = SiC
    weibull_modulus = 6
  []
  [failure_indicator_SiC]
    type = WeibullFailureOutputUsingCorrelation
    block = SiC
    weibull_modulus = 6
    stress_name = stress_yy
    high_fidelity_analysis_strength = 'high_fidelity_strength_asphericity'
    stress_correlation_function = 'stress_correlation_asphericity'
    stress_change_correlation_function = 'stress_change_correlation_asphericity'
  []
  [strength_IPyC]
    type = WeibullEffectiveMeanStrength
    block = IPyC
    weibull_modulus = 9.5
  []
  [failure_indicator_IPyC]
    type = WeibullFailureOutputUsingCorrelation
    block = IPyC
    weibull_modulus = 9.5
    stress_name = max_principal_stress
    effective_mean_strength = strength_IPyC
  []
  [failure_indicator_SiC_crackedIPyC]
    type = WeibullFailureOutputUsingCorrelation
    block = SiC
    weibull_modulus = 6
    stress_name = stress_yy
    high_fidelity_analysis_strength = 'high_fidelity_strength_crackedIPyC'
    stress_correlation_function = 'stress_correlation_crackedIPyC'
  []
  [failure_indicator_debonding]
    type = TRISODebondingFailureIndicator
    boundary = IPyC_outer_boundary
    bond_strength = 10e6
    stress_name = radial_stress
  []
  [failure_indicator_SiC_debonding]
    type = WeibullFailureOutputUsingCorrelation
    block = SiC
    weibull_modulus = 6
    stress_name = stress_yy
    high_fidelity_analysis_strength = 'high_fidelity_strength_debonding'
    stress_correlation_function = 'stress_correlation_debonding'
  []
  [sic_failure_overall]
    type = TRISOFailureEvaluation
    IPyC_failure = failure_indicator_IPyC
    SiC_failure_crackedIPyC = failure_indicator_SiC_crackedIPyC
    SiC_failure = failure_indicator_SiC
    SiC_failure_pd_penetration = failure_indicator_pd_penetration
    SiC_failure_kernel_migration = failure_indicator_kernel_migration
    failure_type = SIC_FAILURE_OVERALL
  []
  [ipyc_cracking]
    type = TRISOFailureEvaluation
    IPyC_failure = failure_indicator_IPyC
    SiC_failure_crackedIPyC = failure_indicator_SiC_crackedIPyC
    SiC_failure = failure_indicator_SiC
    failure_type = IPYC_CRACKING
  []
  [sic_failure_due_to_pressure]
    type = TRISOFailureEvaluation
    IPyC_failure = failure_indicator_IPyC
    SiC_failure_crackedIPyC = failure_indicator_SiC_crackedIPyC
    SiC_failure = failure_indicator_SiC
    failure_type = SIC_FAILURE_DUE_TO_PRESSURE
  []
  [sic_failure_due_to_ipyc_cracking]
    type = TRISOFailureEvaluation
    IPyC_failure = failure_indicator_IPyC
    SiC_failure_crackedIPyC = failure_indicator_SiC_crackedIPyC
    SiC_failure = failure_indicator_SiC
    failure_type = SIC_FAILURE_DUE_TO_IPYC_CRACKING
  []
  [stress_SiC_crackedIPyC]
    type = WeibullFailureOutputUsingCorrelation
    block = SiC
    weibull_modulus = 6
    stress_name = stress_yy
    high_fidelity_analysis_strength = 'high_fidelity_strength_crackedIPyC'
    stress_correlation_function = 'stress_correlation_crackedIPyC'
    output_type = 'stress'
  []
  [actual_strength_SiC_crackedIPyC]
    type = WeibullFailureOutputUsingCorrelation
    block = SiC
    weibull_modulus = 6
    stress_name = stress_yy
    high_fidelity_analysis_strength = 'high_fidelity_strength_crackedIPyC'
    stress_correlation_function = 'stress_correlation_crackedIPyC'
    output_type = 'strength'
  []
  [SiC_crackedIPyC_stressminusstrength]
    type = FunctionValuePostprocessor
    function = 'sic_crackedipyc_stress_strength'
  []
  [debonding]
    type = TRISOFailureEvaluation
    IPyC_failure = failure_indicator_IPyC
    SiC_failure_crackedIPyC = failure_indicator_SiC_crackedIPyC
    SiC_failure = failure_indicator_SiC
    IPyC_SiC_debonding = failure_indicator_debonding
    SiC_failure_debonding = failure_indicator_SiC_debonding
    failure_type = IPYC_SIC_DEBONDING
  []
  [fluence_at_failure]
    type = TRISOFailureOccurrenceStatus
    failure_evaluation = ipyc_cracking
    failure_information = max_fluence
  []
  [weibull_failure_probability_IPyC]
    type = WeibullFailureProbability
    block = IPyC
    weibull_modulus = 9.5
    characteristic_strength = characteristic_strength
  []
  [weibull_failure_probability_SiC]
    type = WeibullFailureProbability
    block = SiC
    weibull_modulus = 6
    characteristic_strength = characteristic_strength
  []
  [pd_penetration]
    type = PdPenetration
    boundary = SiC_inner_boundary
    variable = temperature
    execute_on = 'initial timestep_end'
  []
  [failure_indicator_pd_penetration]
    type = PdPenetrationFailureIndicator
    triso_geometry = particle_geometry
    pd_penetration = pd_penetration
  []
  [kernel_migration_distance]
    type = KernelMigrationDistance
    block = 'fuel buffer IPyC SiC OPyC'
    variable = temperature
    temperature_gradient = 15000
    kernel_type = UCO
  []
  [failure_indicator_kernel_migration]
    type = KernelMigrationFailureIndicator
    kernel_migration_distance = kernel_migration_distance
    triso_geometry = particle_geometry
  []
[]

[Outputs]
  print_linear_residuals = false
  time_step_interval =  1
  csv = false
  exodus = false
  perf_graph = true
  print_linear_converged_reason = false
  print_nonlinear_converged_reason = false
[]

Description
Range of Applicability
Example Input Syntax
Input Parameters
Input Files
References