BufferThermal

Computes thermal conductivity (W/m-K) and specific heat capacity (J/kg-K) for Buffer.

Description

Thermal Conductivity

PARFUME model

The thermal conductivity of the buffer is given by $var element = document.getElementById("moose-equation-5c8eb297-ba1f-4f8e-879b-a08e0a532e05");katex.render(" k = \\frac{k_{init} k_{theo} (\\rho_{theo} - \\rho_{init})}{k_{theo} (\\rho_{theo} - \\rho) + k_{init} (\\rho - \\rho_{init})},", element, {displayMode:true,throwOnError:false});$

where $var element = document.getElementById("moose-equation-f415de64-6d69-4fba-afcf-684ab62519aa");katex.render("k", element, {displayMode:false,throwOnError:false});$ (W/m-K) is the thermal conductivity of the buffer and $var element = document.getElementById("moose-equation-8ea56126-6a94-47f3-8cf3-02863bb265e2");katex.render("\\rho", element, {displayMode:false,throwOnError:false});$ (kg/m $var element = document.getElementById("moose-equation-7e0183c4-d8b3-4643-b82d-3b97cab027a4");katex.render("^{3}", element, {displayMode:false,throwOnError:false});$ ) is the density of the buffer. The values at initial ( $var element = document.getElementById("moose-equation-bb20838c-fe96-465b-bfa0-a9676645d890");katex.render("\\rho_{init}", element, {displayMode:false,throwOnError:false});$ ) and theoretical ( $var element = document.getElementById("moose-equation-a846e769-45e6-4baf-a404-3ffd1454a910");katex.render("\\rho_{theo}", element, {displayMode:false,throwOnError:false});$ = 2.25 g/cm $var element = document.getElementById("moose-equation-148cd2bf-7417-40dc-8960-7268193d5499");katex.render("^{3}", element, {displayMode:false,throwOnError:false});$ ) densities are from Ho (1993).

The functional relationship is calculated with density value of 2.25 g/cm $var element = document.getElementById("moose-equation-20e450d6-0507-453c-b8af-c57176e5a982");katex.render("^{3}", element, {displayMode:false,throwOnError:false});$ for densities exceeding the theoretical density, but results should be considered invalid.

The initial thermal conductivity ( $var element = document.getElementById("moose-equation-fb0c7136-bd4b-48d4-9d0b-3eb813759ada");katex.render("k_{init}", element, {displayMode:false,throwOnError:false});$ ) of the buffer is set to 0.5 W/m-K. It is intended for an initial density of the buffer of 1000 kg/m $var element = document.getElementById("moose-equation-afe79fba-5e63-4efc-a91f-d08fa2bc6f63");katex.render("^{3}", element, {displayMode:false,throwOnError:false});$ , but it is also used for slightly different densities ( $var element = document.getElementById("moose-equation-8e02e637-7b98-40b3-b66d-e56757910977");katex.render("\\pm", element, {displayMode:false,throwOnError:false});$ 10%). The thermal conductivity of the buffer at its theoretical density ( $var element = document.getElementById("moose-equation-63e8e113-76d3-4df7-8b84-df8214ee82c7");katex.render("k_{theo}", element, {displayMode:false,throwOnError:false});$ ) is set to 4.0 W/m-K.

The source code of PARFUME (Miller et al., 2018) produces the same buffer thermal conductivity values for varying buffer density when using the same inputs.

UK model

The thermal conductivity of the buffer is given by Petti et al. (2004) $var element = document.getElementById("moose-equation-c24f2fb3-1fd7-4328-a7f1-1341c459039d");katex.render(" k = 10.98222\\frac{1-p}{1+2p} + 0.00444", element, {displayMode:true,throwOnError:false});$

where $var element = document.getElementById("moose-equation-c0f281b6-7dc5-484f-aa74-5b7796a13dc7");katex.render("k", element, {displayMode:false,throwOnError:false});$ (W/m-K) is the thermal conductivity of the buffer and $var element = document.getElementById("moose-equation-db7f5a39-f05d-40f6-8bdf-29b102b00f33");katex.render("p", element, {displayMode:false,throwOnError:false});$ (-) is the porosity of the buffer. The value of theoretical density ( $var element = document.getElementById("moose-equation-37c92043-ee8b-4716-85e5-7a819d71da2f");katex.render("\\rho_{theo}", element, {displayMode:false,throwOnError:false});$ = 2.25 g/cm $var element = document.getElementById("moose-equation-eeae0ba7-0209-40de-a200-6e5564d6ada3");katex.render("^{3}", element, {displayMode:false,throwOnError:false});$ ), used to compute porosity from density, is from Ho (1993).

The functional relationship is calculated with density value of 2.25 g/cm $var element = document.getElementById("moose-equation-aeb5f485-9367-4f6e-9999-e92b030a7695");katex.render("^{3}", element, {displayMode:false,throwOnError:false});$ for densities exceeding the theoretical density, but results should be considered invalid.

Specific Heat Capacity

The specific heat capacity of the buffer is given by Barabash et al. (2002). The specific heat capacity of the buffer is set to a constant value of 720 J/kg-K.

Example Input Syntax

[Materials<<<{"href": "../../syntax/Materials/index.html"}>>>]
  [Buffer_thermal_conductivity]
    type = BufferThermal<<<{"description": "Computes thermal conductivity (W/m-K) and specific heat capacity (J/kg-K) for Buffer.", "href": "BufferThermal.html"}>>>
    thermal_conductivity_scale_factor<<<{"description": "Multiplier for Buffer thermal conductivity"}>>> = 1.0
    specific_heat_scale_factor<<<{"description": "Scale factor for Buffer specific heat capacity"}>>> = 1.0
    initial_density<<<{"description": "Initial density for Buffer."}>>> = 1000
  []
[]

Input Parameters

initial_densityInitial density for Buffer.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Initial density for Buffer.

Required Parameters

blockThe list of blocks (ids or names) that this object will be applied
C++ Type:std::vector<SubdomainName>
Controllable:No
Description:The list of blocks (ids or names) that this object will be applied
boundaryThe list of boundaries (ids or names) from the mesh where this object applies
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:The list of boundaries (ids or names) from the mesh where this object applies
computeTrueWhen false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
Default:True
C++ Type:bool
Controllable:No
Description:When false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
constant_onNONEWhen ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
Default:NONE
C++ Type:MooseEnum
Options:NONE, ELEMENT, SUBDOMAIN
Controllable:No
Description:When ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
declare_suffixAn optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:An optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.
thermal_conductivity_modelPARFUMEThe model to use for thermal conductivity: PARFUME UK
Default:PARFUME
C++ Type:MooseEnum
Options:PARFUME, UK
Controllable:No
Description:The model to use for thermal conductivity: PARFUME UK

Optional Parameters

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

Advanced Parameters

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

Outputs Parameters

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

Material Property Retrieval Parameters

specific_heat_scale_factor1Scale factor for Buffer specific heat capacity
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Scale factor for Buffer specific heat capacity
thermal_conductivity_scale_factor1Multiplier for Buffer thermal conductivity
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Multiplier for Buffer thermal conductivity

Advanced: Scaling Factors Parameters

Input Files

(examples/TRISO/failure_probability_direct_integration/asphericity.i)
(examples/TRISO/failure_probability_direct_integration/ipyc_cracking.i)
(test/tests/triso_failure/triso_failure_diffusivity.i)
(test/tests/triso_failure/triso_1d_kernel_migration.i)
(examples/TRISO/pebble/triso_1d.i)
(examples/TRISO/failure_probability_monte_carlo/triso_1d_constant.i)
(test/tests/triso_pebble/triso_1d.i)
(examples/TRISO/pebble/triso_1d_failed.i)
(test/tests/triso/buffer_thermal_material/buffer_thermal_specific_heat.i)
(examples/TRISO/correlation_function/h_asphericity/triso_1d.i)
(examples/TRISO/correlation_function/h_ipyc_cracking/triso_cracking.i)
(examples/TRISO/correlation_function/h_ipyc_sic_debonding/triso_debonding.i)
(assessment/TRISO/validation/AGR-2/AGR-2_base.i)
(test/tests/triso/buffer_creep/ad_buffer_creep.i)
(examples/TRISO/failure_probability_monte_carlo/triso_1d_function.i)
(test/tests/triso_failure/higher_order_correlation.i)
(assessment/TRISO/validation/AGR-34/Compacts/AGR-34_base.i)
(examples/TRISO/parfume/parfume.i)
(test/tests/triso/buffer_thermal_material/buffer_thermal_conductivity.i)
(assessment/TRISO/validation/AGR-1/AGR-1_base.i)
(test/tests/triso/kernel_migration/kernel_migration_distance.i)
(test/tests/triso/mesh/ipyc_crack.i)
(assessment/TRISO/validation/AGR-34/SharedFiles/capsule_driver.i)
(test/tests/triso_failure/triso_1d_ipyc_weibull_probability.i)
(examples/TRISO/correlation_function/h_asphericity/triso_asphericity_mortar.i)
(test/tests/triso_failure/ad_triso_1d_ipyc_weibull_probability.i)
(examples/TRISO/correlation_function/h_asphericity/triso_asphericity.i)
(examples/TRISO/parfume/parfume_un.i)
(examples/TRISO/failure_probability_direct_integration/triso_1d.i)
(test/tests/triso/buffer_thermal_material/buffer_k_UK.i)
(test/tests/triso/buffer_creep/buffer_creep.i)

References

V. Barabash, I. Mazul, R. Latypov, A. Pokrovsky, and C.H. Wu. The effect of low temperature neutron irradiation and annealing on the thermal conductivity of advanced carbon-based materials. Journal of Nuclear Materials, 307-311:1300–1304, 2002. doi:10.1016/S0022-3115(02)00961-3.

@article{BARABASH20021300,
    author = "Barabash, V. and Mazul, I. and Latypov, R. and Pokrovsky, A. and Wu, C.H.",
    title = "The effect of low temperature neutron irradiation and annealing on the thermal conductivity of advanced carbon-based materials",
    journal = "Journal of Nuclear Materials",
    volume = "307-311",
    pages = "1300-1304",
    year = "2002",
    issn = "0022-3115",
    doi = "10.1016/S0022-3115(02)00961-3"
}

F. Ho. NP-MHTGR: Material Models of Pyrocarbon and Pyrolytic Silicon Carbide. Report CEGA-002820 Rev. 1, CEGA Corporation, July 1993.

@techreport{CEGA1993,
    author = "Ho, F.",
    title = "{NP-MHTGR: Material Models of Pyrocarbon and Pyrolytic Silicon Carbide}",
    institution = "CEGA Corporation",
    year = "1993",
    month = "July",
    number = "CEGA-002820 Rev. 1",
    type = "Report"
}

G.K. Miller, D.A. Petti, J.T. Maki, D.L. Knudson, and W.F. Skerjanc. PARFUME Theory and Model Basis Report. Report INL/EXT-08-14497 (Rev.1), Idaho National Laboratory, September 2018.

@techreport{Miller2018,
    author = "Miller, G.K. and Petti, D.A. and Maki, J.T. and Knudson, D.L. and Skerjanc, W.F.",
    title = "{PARFUME Theory and Model Basis Report}",
    institution = "Idaho National Laboratory",
    year = "2018",
    month = "September",
    number = "INL/EXT-08-14497 (Rev.1)",
    type = "Report"
}

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/triso/buffer_thermal_material/buffer_thermal_specific_heat.i)

#Specific Heat Capacity of the Buffer
# The geometry is a cube (edge length = 5 cm) made of buffer material (initial density = 1.0 g/cm$^{3}$) subject to internal heat generation.
# The cube is under uniform temperature (initially 673.15 K) and has no heat sink.
# The thermal power is ramped linearly from 0 to 0.08 Watts over 10$^{4}$ seconds and then remains constant.
# Since the specific heat capacity of the buffer is constant ($C_{P}$ = 720 J/kg-K), the temperature increase $\Delta\T_{K}$ (K) in the cube during a timestep $\Delta\t$ (s) can be calculated by:
# \Delta\T_{K} = \frac{P \cdot \Delta\t}{V \cdot \rho \cdot C_{P}}
# Where $P$ (W) is the thermal power during the timestep, $V$ (1.25x10$^{-4}$ m$^{3}$) is the volume of the cube, and $\rho$ (1000 kg/m$^{3}$) is the density of the buffer.
# A sample of the BISON and analytical calculated temperatures is shown in below.
#
# |BISON $T$ (K)   | Analytical $T$ (K)|
# |----------------|-------------------|
# | 677.82         | 677.82            |
# | 846.71         | 846.71            |
# | 1024.48        | 1024.48           |
# | 1202.26        | 1202.26           |
# | 1380.04        | 1380.04           |
# | 1468.93        | 1468.93           |
# | 1557.82        | 1557.82           |
# | 1735.59        | 1735.59           |
# | 1913.37        | 1913.37           |

[GlobalParams]
  order = FIRST
  family = LAGRANGE
  energy_per_fission = 3.2e-11 # J/fission
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 3
    xmin = 0.0
    xmax = 0.05
    ymin = 0.0
    ymax = 0.05
    zmin = 0.0
    zmax = 0.05
  []
[]

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

[Variables]
  [temp]
    initial_condition = 673.15
  []
[]

[AuxVariables]
  [fission_rate]
  []

  [specific_heat]
    order = CONSTANT
    family = MONOMIAL
  []

[]

[Functions]
  [power_history]
    type = PiecewiseLinear
    x = '0  1e4  1e8'
    y = '0 2e13 2e13'
  []

  [temp_func]
    type = PiecewiseLinear
    x = '  0 5.3e6 6.3e6 1e8'
    y = '673   673   673 673'
  []

  [HTC_func]
    type = PiecewiseLinear
    x = '0 5.3e6 6.3e6 6.4e6 1e8'
    y = '0     0     0     0   0'
  []
[]

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

  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temp
  []

  [heat_source]
    type = NeutronHeatSource
    variable = temp
    fission_rate = fission_rate
  []
[]

[AuxKernels]
  [fissionrate]
    type = FissionRateGeneral
    fission_rate_formulation = GENERIC
    variable = fission_rate
    fission_rate_function = power_history
    value = 1.0
  []

  [specific_heat]
    type = MaterialRealAux
    variable = specific_heat
    property = specific_heat
    execute_on = timestep_end
  []
[]

[BCs]
  [heat_removal]
    type = ConvectiveFluxFunction
    boundary = 'back front top bottom left right'
    variable = temp
    T_infinity = temp_func
    coefficient = HTC_func
  []
[]

[Materials]
  [Buffer_thermal_conductivity]
    type = BufferThermal
    thermal_conductivity_scale_factor = 1.0
    specific_heat_scale_factor = 1.0
    initial_density = 1000
  []

  [Buffer_density]
    type = ParsedMaterial
    block = '0'
    property_name = density
    expression = 1000
  []
[]

[Dampers]
  [limitT]
    type = MaxIncrement
    max_increment = 100.0
    variable = temp
  []
[]

[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_max_its = 50
  l_tol = 1e-2

  nl_max_its = 150
  nl_rel_tol = 1e-4
  nl_abs_tol = 1e-6

  start_time = 0.0
  end_time = 1.4e6
  num_steps = 100

  dtmax = 2e6
  dtmin = 1e-6

  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 5e2
    time_t = '1e4 1e5'
    time_dt = '5e2 1e5'
  []
[]

[Postprocessors]
  [temp]
    type = ElementAverageValue
    variable = temp
    execute_on = 'initial timestep_end'
  []

  [specific_heat]
    type = ElementAverageValue
    variable = specific_heat
    execute_on = 'initial timestep_end'
  []

  [total_power]
    type = ElementIntegralPower
    variable = temp
    fission_rate = fission_rate
    execute_on = timestep_end
  []

  [volume]
    type = VolumePostprocessor
    use_displaced_mesh = true
  []
[]

[Outputs]
  csv = true
  exodus = false
  [console]
    type = Console
  []
[]

(examples/TRISO/failure_probability_direct_integration/asphericity.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
aspect_ratio = 1.04

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

initial_fuel_density = 10966

[GlobalParams]
  order = FIRST
  family = LAGRANGE
  displacements = 'disp_x disp_y'
  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 = RZ
  [gen]
    type = TRISO2DMeshGenerator
    elem_type = quad4
    coordinates = '0 ${coordinates1} ${coordinates2} ${coordinates2} ${coordinates3} ${coordinates4} '
                  '${coordinates5}'
    mesh_density = '20 8 0 4 4 4'
    block_names = 'fuel buffer IPyC SiC OPyC'
    num_sectors = 60
    aspect_ratio = ${aspect_ratio}
  []
[]

[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
    mesh_generator = 'gen'
  []
[]

[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
  []
[]

[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
    sphere_origin = '0 0 0'
  []
[]

[BCs]
  [no_disp_x]
    type = DirichletBC
    variable = disp_x
    boundary = xzero
    value = 0.0
  []
  [no_disp_y]
    type = DirichletBC
    variable = disp_y
    boundary = bottom
    value = 0.0
  []
  [freesurf_temp]
    type = FunctionDirichletBC
    variable = temperature
    function = temp_bc
    boundary = exterior
  []
  [Pressure]
    [exterior]
      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]
  [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 = ${initial_fuel_density}
    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 = ${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
  []
  [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'
    triso_geometry = particle_geometry
  []
  [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-8
  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

  # For testing, we only run 20 time steps
  num_steps = 20

  dtmin = 1e-4
  dt = 6e5
[]

[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 = max
    mat_prop = max_principal_stress
  []
  [strength_SiC]
    type = WeibullEffectiveMeanStrength
    block = SiC
    weibull_modulus = 6
  []
  [weibull_failure_probability_SiC]
    type = WeibullFailureProbability
    block = SiC
    weibull_modulus = 6
    characteristic_strength = characteristic_strength
  []
  [weibull_failure_probability_IPyC]
    type = WeibullFailureProbability
    block = IPyC
    weibull_modulus = 9.5
    characteristic_strength = characteristic_strength
  []
[]

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

(examples/TRISO/failure_probability_direct_integration/ipyc_cracking.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
aspect_ratio = 1.04

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

initial_fuel_density = 10966

[GlobalParams]
  order = FIRST
  family = LAGRANGE
  displacements = 'disp_x disp_y'
  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 = RZ
  [gen]
    type = TRISO2DMeshGenerator
    elem_type = quad4
    coordinates = '0 ${coordinates1} ${coordinates2} ${coordinates2} ${coordinates3} ${coordinates4} '
                  '${coordinates5}'
    mesh_density = '20 8 0 4 4 4'
    block_names = 'fuel buffer IPyC SiC OPyC'
    num_sectors = 60
    aspect_ratio = ${aspect_ratio}
    all_bottom_left = true
  []
[]

[XFEM]
  qrule = volfrac
  output_cut_plane = true
[]

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

[UserObjects]
  [ipyc_crack]
    type = LineSegmentCutUserObject
    cut_data = '0.0000 0.0 0.001 0.0'
    #cut_data = '0 0 0.00174 -0.00257'
    time_start_cut = 0.0
    time_end_cut = 0.0
    block = IPyC
  []
  [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
    mesh_generator = 'gen'
  []
[]

[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
  []
[]

[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 = 5e-6
    quadrature = false
    min_gap = 1e-7
    max_gap = 50e-6
    gap_geometry_type = sphere
    sphere_origin = '0 0 0'
  []
[]

[BCs]
  [no_disp_x]
    type = DirichletBC
    variable = disp_x
    boundary = xzero
    value = 0.0
  []
  [no_disp_y]
    type = DirichletBC
    variable = disp_y
    boundary = '2001 2002 2004 2005'
    value = 0.0
  []
  [freesurf_temp]
    type = FunctionDirichletBC
    variable = temperature
    function = temp_bc
    boundary = exterior
  []
  [Pressure]
    [exterior]
      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]
  [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 = ${initial_fuel_density}
    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 = ${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
  []
  [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'
    triso_geometry = particle_geometry
  []
  [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 = 1e-11
  nl_abs_tol = 1e-11
  nl_max_its = 20

  l_tol = 1e-4
  l_max_its = 50

  start_time = 0.0
  end_time = 4.831315e7

  # For testing, we only run 20 time steps
  num_steps = 20

  dtmin = 1e-4
  dt = 6e5
[]

[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 = max
    mat_prop = max_principal_stress
  []
  [strength_SiC]
    type = WeibullEffectiveMeanStrength
    block = SiC
    weibull_modulus = 6
  []
  [weibull_failure_probability_SiC_crackedIPyC]
    type = WeibullFailureProbability
    block = SiC
    weibull_modulus = 6
    characteristic_strength = characteristic_strength
  []
[]

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

(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
[]

(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
[]

(examples/TRISO/pebble/triso_1d.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 = SECOND
  family = LAGRANGE
  initial_enrichment = 0.14029 # [wt-]
  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 = EDGE3
    coordinates = '0 ${coordinates1} ${coordinates2} ${coordinates3} ${coordinates4} ${coordinates5}'
    mesh_density = '18 14 12 16 16'
    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
  []
[]

[Variables]
  [temperature]
    initial_condition = 773.15
  []
  [conc_Cs]
    initial_condition = 0.0
    scaling = 1e18
  []
[]

[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
  []
  [fis_gas_produced]
    order = CONSTANT
    family = MONOMIAL
  []
  [fis_gas_released]
    order = CONSTANT
    family = MONOMIAL
  []
  [Cs_diff_coef]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [power_history]
    type = PiecewiseLinear
    x = '0 1e3 4.51008e7' #change time (s) for desired EFPD
    y = '0 1 1'
  []
  [fission_rate]
    type = LinearCombinationFunction
    functions = power_history
    w = 2.927e18
  []
  [temp_bc_func]
    type = ParsedFunction
    value = temp_bc
    symbol_names = temp_bc
    symbol_values = temp_bc
  []
[]

[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_Cs_dt]
    type = TimeDerivative
    variable = conc_Cs
  []
  [mass_Cs]
    type = ArrheniusDiffusion
    variable = conc_Cs
    arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
    extra_vector_tags = 'ref'
  []
  [mass_source_Cs]
    type = SpeciesSourceRate
    variable = conc_Cs
    property_name = Cs_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
  []
  [Cs_diff_coef]
    type = MaterialRealAux
    variable = Cs_diff_coef
    property = arrhenius_diffusion_coef_Cs
    execute_on = timestep_end
  []
[]

[BCs]
  [freesurf_temp]
    type = FunctionDirichletBC
    variable = temperature
    function = temp_bc_func
    boundary = exterior
  []
  [freesurf_conc_Cs]
    type = DirichletBC
    variable = conc_Cs
    boundary = exterior
    value = 0.0
  []
[]

[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 = 1.109e18
  []
  [UCO_burnup]
    type = TRISOBurnup
    initial_density = 10966.0
  []

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

  [UCO_density]
    type = StrainAdjustedDensity
    block = fuel
    strain_free_density = 10966.0
  []

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

  # Arrhenius diffusion coefficients for kernel, PyC, and SiC
  #   come from IAEA TECDOC-978, French parameters.
  [fuel_conc_Cs]
    type = ArrheniusDiffusionCoef
    block = fuel
    d1 = 5.6e-8 # m^2/s
    q1 = 209e3 # J/mol
    temperature = temperature
    arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
  []

  [mass_source_Cs_property]
    type = SpeciesSourceMaterial
    property_name = Cs_generation
    kind = Cs
    block = fuel
  []

  ### Buffer Properties

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

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

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

  ### IPyC  properties

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

  [IPyC_density]
    type = StrainAdjustedDensity
    block = IPyC
    strain_free_density = 1907.0
  []

  [IPyC_conc_Cs]
    type = ArrheniusDiffusionCoef
    block = IPyC
    d1 = 6.3e-8 # m^2/s
    q1 = 222e3 # J/mol
    temperature = temperature
    arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
  []

  ### SiC properties

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

  [SiC_density]
    type = StrainAdjustedDensity
    block = SiC
    strain_free_density = 3200.0
  []

  [SiC_conc_Cs]
    type = ArrheniusDiffusionCoef
    block = SiC
    d1 = 5.5e-14 # m^2/s
    q1 = 125e3 # J/mol
    temperature = temperature
    arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
  []

  ###  OPyC properties

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

  [OPyC_density]
    type = StrainAdjustedDensity
    block = OPyC
    strain_free_density = 1907.0
  []

  [OPyC_conc_Cs]
    type = ArrheniusDiffusionCoef
    block = OPyC
    d1 = 6.3e-8 # m^2/s
    q1 = 222e3 # J/mol
    temperature = temperature
    arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
  []
[]

[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-8
  nl_abs_tol = 1e-6
  nl_max_its = 20

  l_tol = 1e-4
  l_max_its = 50

  dt = 500000
  num_steps = 10
[]

[Postprocessors]
  [temp_bc]
    type = Receiver
  []
  [release_heat_inc]
    type = SideIntegralMassFlux
    variable = temperature
    boundary = exterior
    arrhenius_prpty_name = thermal_conductivity
    execute_on = 'initial timestep_end'
  []

  [release_Cs_inc]
    type = SideIntegralMassFlux
    variable = conc_Cs
    boundary = exterior
    arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
    execute_on = 'initial timestep_end'
  []
  [released_Cs]
    type = TimeIntegratedPostprocessor
    value = release_Cs_inc
    execute_on = 'initial timestep_end'
  []
  [total_Cs]
    type = ElementIntegralMaterialProperty
    mat_prop = Cs_generation_total
    block = fuel
    execute_on = 'initial timestep_end'
  []
  [x_Cs_released]
    type = FractionalRelease
    released = released_Cs
    total = total_Cs
  []
  [retained_Cs]
    type = ElementIntegralVariablePostprocessor
    variable = conc_Cs
  []

  [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'
  []

  ### 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'
  []

  [aver_temp_exterior]
    type = SideAverageValue
    variable = temperature
    boundary = exterior
    execute_on = 'initial timestep_end'
  []
[]

[Outputs]
  perf_graph = true
  print_linear_residuals = true
  print_linear_converged_reason = false
  print_nonlinear_converged_reason = false
[]

(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
[]

(test/tests/triso_pebble/triso_1d.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 = SECOND
  family = LAGRANGE
  initial_enrichment = 0.14029 # [wt-]
  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 = EDGE3
    coordinates = '0 ${coordinates1} ${coordinates2} ${coordinates3} ${coordinates4} ${coordinates5}'
    mesh_density = '18 14 12 16 16'
    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
  []
[]

[Variables]
  [temperature]
    initial_condition = 773.15
  []
  [conc_Ag]
    initial_condition = 0.0
    scaling = 1e14
  []
  [conc_Cs]
    initial_condition = 0.0
    scaling = 1e14
  []
  [conc_Sr]
    initial_condition = 0.0
    scaling = 1e14
  []
[]

[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
  []
  [fis_gas_produced]
    order = CONSTANT
    family = MONOMIAL
  []
  [fis_gas_released]
    order = CONSTANT
    family = MONOMIAL
  []
  [Ag_diff_coef]
    order = CONSTANT
    family = MONOMIAL
  []
  [Cs_diff_coef]
    order = CONSTANT
    family = MONOMIAL
  []
  [Sr_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 = 5.75e19
  []
  [d1_function]
    type = ParsedFunction
    expression = 'exp(t/4.5e25)'
  []
  [temp_bc_func]
    type = ParsedFunction
    expression = temp_bc
    symbol_names = temp_bc
    symbol_values = temp_bc
  []
[]

[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'
  []

  [mass_Cs_dt]
    type = TimeDerivative
    variable = conc_Cs
  []
  [mass_Cs]
    type = ArrheniusDiffusion
    variable = conc_Cs
    arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
    extra_vector_tags = 'ref'
  []
  [mass_source_Cs]
    type = SpeciesSourceRate
    variable = conc_Cs
    property_name = Cs_generation
    block = fuel
    extra_vector_tags = 'ref'
  []

  [mass_Sr_dt]
    type = MassLumpedTimeDerivative
    variable = conc_Sr
  []
  [mass_Sr]
    type = ArrheniusDiffusion
    variable = conc_Sr
    arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
    extra_vector_tags = 'ref'
  []
  [mass_source_Sr]
    type = SpeciesSourceRate
    variable = conc_Sr
    property_name = Sr_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
  []
  [Cs_diff_coef]
    type = MaterialRealAux
    variable = Cs_diff_coef
    property = arrhenius_diffusion_coef_Cs
    execute_on = timestep_end
  []
  [Sr_diff_coef]
    type = MaterialRealAux
    variable = Sr_diff_coef
    property = arrhenius_diffusion_coef_Sr
    execute_on = timestep_end
  []
[]

[BCs]
  [freesurf_temp]
    type = FunctionDirichletBC
    variable = temperature
    function = temp_bc_func
    boundary = exterior
  []
  [freesurf_conc_Ag]
    type = DirichletBC
    variable = conc_Ag
    boundary = exterior
    value = 0.0
  []
  [freesurf_conc_Cs]
    type = DirichletBC
    variable = conc_Cs
    boundary = exterior
    value = 0.0
  []
  [freesurf_conc_Sr]
    type = DirichletBC
    variable = conc_Sr
    boundary = exterior
    value = 0.0
  []
[]

[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 = 6.28e17
  []
  [UCO_burnup]
    type = TRISOBurnup
    initial_density = 10966.0
  []

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

  [UCO_density]
    type = ParsedMaterial
    block = fuel
    property_name = density
    expression = 10966.0
  []

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

  # 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
  []
  [fuel_conc_Cs]
    type = ArrheniusDiffusionCoef
    block = fuel
    d1 = 5.6e-8 # m^2/s
    q1 = 209e3 # J/mol
    temperature = temperature
    arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
  []
  [fuel_conc_Sr]
    type = ArrheniusDiffusionCoef
    block = fuel
    d1 = 2.2e-3 # m^2/s
    q1 = 488e3 # J/mol
    temperature = temperature
    arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
  []
  [mass_source_Ag_property]
    type = SpeciesSourceMaterial
    property_name = Ag_generation
    kind = Ag
    block = fuel
  []
  [mass_source_Cs_property]
    type = SpeciesSourceMaterial
    property_name = Cs_generation
    kind = Cs
    block = fuel
  []
  [mass_source_Sr_property]
    type = SpeciesSourceMaterial
    property_name = Sr_generation
    kind = Sr
    block = fuel
  []

  ### Buffer Properties

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

  [Buffer_density]
    type = ParsedMaterial
    block = buffer
    property_name = density
    expression = 1050.0
  []

  [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
  []
  [buffer_conc_Cs]
    type = ArrheniusDiffusionCoef
    block = buffer
    d1 = 1e-8 # m^2/s
    q1 = 0.0
    temperature = temperature
    arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
  []
  [buffer_conc_Sr]
    type = ArrheniusDiffusionCoef
    block = buffer
    d1 = 1e-8 # m^2/s
    q1 = 0.0
    temperature = temperature
    arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
  []

  ### IPyC  properties

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

  [IPyC_density]
    type = ParsedMaterial
    block = IPyC
    property_name = density
    expression = 1907.0
  []

  [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
  []
  [IPyC_conc_Cs]
    type = ArrheniusDiffusionCoef
    block = IPyC
    d1 = 6.3e-8 # m^2/s
    q1 = 222e3 # J/mol
    temperature = temperature
    arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
  []
  [IPyC_conc_Sr]
    type = ArrheniusDiffusionCoef
    block = IPyC
    d1 = 2.3e-6 # m^2/s
    q1 = 197e3 # J/mol
    temperature = temperature
    arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
  []

  ### SiC properties

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

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

  [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
  []
  [SiC_conc_Cs]
    type = ArrheniusDiffusionCoef
    block = SiC
    d1 = 5.5e-14 # m^2/s
    q1 = 125e3 # J/mol
    temperature = temperature
    arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
  []
  [SiC_conc_Sr]
    type = ArrheniusDiffusionCoef
    block = SiC
    d1 = 1.2e-9 # m^2/s
    q1 = 205e3 # J/mol
    temperature = temperature
    arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
  []

  ###  OPyC properties

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

  [OPyC_density]
    type = ParsedMaterial
    block = OPyC
    property_name = density
    expression = 1907.0
  []


  [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
  []
  [OPyC_conc_Cs]
    type = ArrheniusDiffusionCoef
    block = OPyC
    d1 = 6.3e-8 # m^2/s
    q1 = 222e3 # J/mol
    temperature = temperature
    arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
  []
  [OPyC_conc_Sr]
    type = ArrheniusDiffusionCoef
    block = OPyC
    d1 = 2.3e-6 # m^2/s
    q1 = 197e3 # J/mol
    temperature = temperature
    arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
  []
[]

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

[Debug]
  show_var_residual_norms = true
  show_var_residual = 'temperature conc_Ag conc_Cs conc_Sr'
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'

  line_search = 'none'

  automatic_scaling = true

  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-12
  nl_max_its = 20

  nl_forced_its = 2

  l_tol = 1e-4
  l_max_its = 50

  start_time = 0.0
  dt = 20000
  num_steps = 2
[]

[Postprocessors]
  [temp_bc]
    type = Receiver
  []
  [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
  []
  [release_Cs_inc]
    type = SideIntegralMassFlux
    variable = conc_Cs
    boundary = exterior
    arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
    execute_on = 'initial timestep_end'
  []
  [released_Cs]
    type = TimeIntegratedPostprocessor
    value = release_Cs_inc
    execute_on = 'initial timestep_end'
  []
  [total_Cs]
    type = ElementIntegralMaterialProperty
    mat_prop = Cs_generation_total
    block = fuel
    execute_on = 'initial timestep_end'
  []
  [x_Cs_released]
    type = FractionalRelease
    released = released_Cs
    total = total_Cs
  []
  [retained_Cs]
    type = ElementIntegralVariablePostprocessor
    variable = conc_Cs
  []
  [release_Sr_inc]
    type = SideIntegralMassFlux
    variable = conc_Sr
    boundary = exterior
    arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
    execute_on = 'initial timestep_end'
  []
  [released_Sr]
    type = TimeIntegratedPostprocessor
    value = release_Sr_inc
    execute_on = 'initial timestep_end'
  []
  [released_heat_inc]
    type = SideIntegralMassFlux
    variable = temperature
    boundary = exterior
    arrhenius_prpty_name = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [total_Sr]
    type = ElementIntegralMaterialProperty
    mat_prop = Sr_generation_total
    block = fuel
    execute_on = 'initial timestep_end'
  []
  [x_Sr_released]
    type = FractionalRelease
    released = released_Sr
    total = total_Sr
  []
  [retained_Sr]
    type = ElementIntegralVariablePostprocessor
    variable = conc_Sr
  []

  [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'
  []

  ### 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'
  []

  [aver_temp_exterior]
    type = SideAverageValue
    variable = temperature
    boundary = exterior
    execute_on = 'initial timestep_end'
  []

[]

[Outputs]
  print_linear_residuals = false
[]

(examples/TRISO/pebble/triso_1d_failed.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 = SECOND
  family = LAGRANGE
  initial_enrichment = 0.14029 # [wt-]
  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 = EDGE3
    coordinates = '0 ${coordinates1} ${coordinates2} ${coordinates3} ${coordinates4} ${coordinates5}'
    mesh_density = '18 14 12 16 16'
    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
  []
[]

[Variables]
  [temperature]
    initial_condition = 773.15
  []
  [conc_Cs]
    initial_condition = 0.0
    scaling = 1e18
  []
[]

[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
  []
  [fis_gas_produced]
    order = CONSTANT
    family = MONOMIAL
  []
  [fis_gas_released]
    order = CONSTANT
    family = MONOMIAL
  []
  [Cs_diff_coef]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [power_history]
    type = PiecewiseLinear
    x = '0 1e3 4.51008e7' #change time (s) for desired EFPD
    y = '0 1 1'
  []
  [fission_rate]
    type = LinearCombinationFunction
    functions = power_history
    w = 2.927e18
  []
  [temp_bc_func]
    type = ParsedFunction
    value = temp_bc
    symbol_names = temp_bc
    symbol_values = temp_bc
  []
[]

[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_Cs_dt]
    type = TimeDerivative
    variable = conc_Cs
  []
  [mass_Cs]
    type = ArrheniusDiffusion
    variable = conc_Cs
    arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
    extra_vector_tags = 'ref'
  []
  [mass_source_Cs]
    type = SpeciesSourceRate
    variable = conc_Cs
    property_name = Cs_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
  []
  [Cs_diff_coef]
    type = MaterialRealAux
    variable = Cs_diff_coef
    property = arrhenius_diffusion_coef_Cs
    execute_on = timestep_end
  []
[]

[BCs]
  [freesurf_temp]
    type = FunctionDirichletBC
    variable = temperature
    function = temp_bc_func
    boundary = exterior
  []
  [freesurf_conc_Cs]
    type = DirichletBC
    variable = conc_Cs
    boundary = exterior
    value = 0.0
  []
[]

[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 = 1.109e18
  []
  [UCO_burnup]
    type = TRISOBurnup
    initial_density = ${initial_fuel_density}
  []

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

  [UCO_density]
    type = StrainAdjustedDensity
    block = fuel
    strain_free_density = 10966.0
  []

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

  # Arrhenius diffusion coefficients for kernel, PyC, and SiC
  #   come from IAEA TECDOC-978, French parameters.
  [fuel_conc_Cs]
    type = ArrheniusDiffusionCoef
    block = fuel
    d1 = 5.6e-8 # m^2/s
    q1 = 209e3 # J/mol
    temperature = temperature
    arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
  []

  [mass_source_Cs_property]
    type = SpeciesSourceMaterial
    property_name = Cs_generation
    kind = Cs
    block = fuel
  []
  ### Buffer Properties

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

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

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

  ### IPyC  properties

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

  [IPyC_density]
    type = StrainAdjustedDensity
    block = IPyC
    strain_free_density = 1907.0
  []

  [IPyC_conc_Cs]
    type = ArrheniusDiffusionCoef
    block = IPyC
    d1 = 6.3e-8 # m^2/s
    q1 = 222e3 # J/mol
    temperature = temperature
    arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
  []

  ### SiC properties

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

  [SiC_density]
    type = StrainAdjustedDensity
    block = SiC
    strain_free_density = 3200.0
  []

  [SiC_conc_Cs]
    type = ArrheniusDiffusionCoef
    block = SiC
    d1 = 1e-6 # m^2/s
    q1 = 0 # J/mol
    temperature = temperature
    arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
  []

  ###  OPyC properties

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

  [OPyC_density]
    type = StrainAdjustedDensity
    block = OPyC
    strain_free_density = 1907.0
  []

  [OPyC_conc_Cs]
    type = ArrheniusDiffusionCoef
    block = OPyC
    d1 = 6.3e-8 # m^2/s
    q1 = 222e3 # J/mol
    temperature = temperature
    arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
  []
[]

[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-8
  nl_abs_tol = 1e-6
  nl_max_its = 20

  l_tol = 1e-4
  l_max_its = 50

  end_time = 4.831315e7

  dt = 500000
  num_steps = 10
[]

[Postprocessors]
  [temp_bc]
    type = Receiver
  []
  [release_heat_inc]
    type = SideIntegralMassFlux
    variable = temperature
    boundary = exterior
    arrhenius_prpty_name = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [release_Cs_inc]
    type = SideIntegralMassFlux
    variable = conc_Cs
    boundary = exterior
    arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
    execute_on = 'initial timestep_end'
  []
  [released_Cs]
    type = TimeIntegratedPostprocessor
    value = release_Cs_inc
    execute_on = 'initial timestep_end'
  []
  [total_Cs]
    type = ElementIntegralMaterialProperty
    mat_prop = Cs_generation_total
    block = fuel
    execute_on = 'initial timestep_end'
  []
  [x_Cs_released]
    type = FractionalRelease
    released = released_Cs
    total = total_Cs
  []
  [retained_Cs]
    type = ElementIntegralVariablePostprocessor
    variable = conc_Cs
  []

  [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'
  []

  ### 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'
  []

  [aver_temp_exterior]
    type = SideAverageValue
    variable = temperature
    boundary = exterior
    execute_on = 'initial timestep_end'
  []
[]

[Outputs]
  perf_graph = true
  print_linear_residuals = false
  print_linear_converged_reason = false
  print_nonlinear_converged_reason = false
[]

(test/tests/triso/buffer_thermal_material/buffer_thermal_specific_heat.i)

#Specific Heat Capacity of the Buffer
# The geometry is a cube (edge length = 5 cm) made of buffer material (initial density = 1.0 g/cm$^{3}$) subject to internal heat generation.
# The cube is under uniform temperature (initially 673.15 K) and has no heat sink.
# The thermal power is ramped linearly from 0 to 0.08 Watts over 10$^{4}$ seconds and then remains constant.
# Since the specific heat capacity of the buffer is constant ($C_{P}$ = 720 J/kg-K), the temperature increase $\Delta\T_{K}$ (K) in the cube during a timestep $\Delta\t$ (s) can be calculated by:
# \Delta\T_{K} = \frac{P \cdot \Delta\t}{V \cdot \rho \cdot C_{P}}
# Where $P$ (W) is the thermal power during the timestep, $V$ (1.25x10$^{-4}$ m$^{3}$) is the volume of the cube, and $\rho$ (1000 kg/m$^{3}$) is the density of the buffer.
# A sample of the BISON and analytical calculated temperatures is shown in below.
#
# |BISON $T$ (K)   | Analytical $T$ (K)|
# |----------------|-------------------|
# | 677.82         | 677.82            |
# | 846.71         | 846.71            |
# | 1024.48        | 1024.48           |
# | 1202.26        | 1202.26           |
# | 1380.04        | 1380.04           |
# | 1468.93        | 1468.93           |
# | 1557.82        | 1557.82           |
# | 1735.59        | 1735.59           |
# | 1913.37        | 1913.37           |

[GlobalParams]
  order = FIRST
  family = LAGRANGE
  energy_per_fission = 3.2e-11 # J/fission
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 3
    xmin = 0.0
    xmax = 0.05
    ymin = 0.0
    ymax = 0.05
    zmin = 0.0
    zmax = 0.05
  []
[]

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

[Variables]
  [temp]
    initial_condition = 673.15
  []
[]

[AuxVariables]
  [fission_rate]
  []

  [specific_heat]
    order = CONSTANT
    family = MONOMIAL
  []

[]

[Functions]
  [power_history]
    type = PiecewiseLinear
    x = '0  1e4  1e8'
    y = '0 2e13 2e13'
  []

  [temp_func]
    type = PiecewiseLinear
    x = '  0 5.3e6 6.3e6 1e8'
    y = '673   673   673 673'
  []

  [HTC_func]
    type = PiecewiseLinear
    x = '0 5.3e6 6.3e6 6.4e6 1e8'
    y = '0     0     0     0   0'
  []
[]

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

  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temp
  []

  [heat_source]
    type = NeutronHeatSource
    variable = temp
    fission_rate = fission_rate
  []
[]

[AuxKernels]
  [fissionrate]
    type = FissionRateGeneral
    fission_rate_formulation = GENERIC
    variable = fission_rate
    fission_rate_function = power_history
    value = 1.0
  []

  [specific_heat]
    type = MaterialRealAux
    variable = specific_heat
    property = specific_heat
    execute_on = timestep_end
  []
[]

[BCs]
  [heat_removal]
    type = ConvectiveFluxFunction
    boundary = 'back front top bottom left right'
    variable = temp
    T_infinity = temp_func
    coefficient = HTC_func
  []
[]

[Materials]
  [Buffer_thermal_conductivity]
    type = BufferThermal
    thermal_conductivity_scale_factor = 1.0
    specific_heat_scale_factor = 1.0
    initial_density = 1000
  []

  [Buffer_density]
    type = ParsedMaterial
    block = '0'
    property_name = density
    expression = 1000
  []
[]

[Dampers]
  [limitT]
    type = MaxIncrement
    max_increment = 100.0
    variable = temp
  []
[]

[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_max_its = 50
  l_tol = 1e-2

  nl_max_its = 150
  nl_rel_tol = 1e-4
  nl_abs_tol = 1e-6

  start_time = 0.0
  end_time = 1.4e6
  num_steps = 100

  dtmax = 2e6
  dtmin = 1e-6

  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 5e2
    time_t = '1e4 1e5'
    time_dt = '5e2 1e5'
  []
[]

[Postprocessors]
  [temp]
    type = ElementAverageValue
    variable = temp
    execute_on = 'initial timestep_end'
  []

  [specific_heat]
    type = ElementAverageValue
    variable = specific_heat
    execute_on = 'initial timestep_end'
  []

  [total_power]
    type = ElementIntegralPower
    variable = temp
    fission_rate = fission_rate
    execute_on = timestep_end
  []

  [volume]
    type = VolumePostprocessor
    use_displaced_mesh = true
  []
[]

[Outputs]
  csv = true
  exodus = false
  [console]
    type = Console
  []
[]

(examples/TRISO/correlation_function/h_asphericity/triso_1d.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}'

initial_fuel_density = 10966

[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 = '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
  []
[]

[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
  []
[]

[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]
  [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 = ${initial_fuel_density}
    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 = ${initial_fuel_density}
  []
  [fission_gas_release]
    type = UCOFGR
    block = fuel
    average_grain_radius = 10e-6
    temperature = temperature
    triso_geometry = particle_geometry
  []
  [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 = 1e-8
  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 = 6e5
[]

[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
  []
[]

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

(examples/TRISO/correlation_function/h_ipyc_cracking/triso_cracking.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}'

initial_fuel_density = 10966

[GlobalParams]
  order = FIRST
  family = LAGRANGE
  displacements = 'disp_x disp_y'
  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 = RZ
  [mesh]
    type = TRISO2DMeshGenerator
    elem_type = quad4
    coordinates = '0 ${coordinates1} ${coordinates2} ${coordinates2} ${coordinates3} ${coordinates4} ${coordinates5}'
    mesh_density = '20 8 0 4 4 4'
    block_names = 'fuel buffer IPyC SiC OPyC'
    num_sectors = 60
    all_bottom_left = True
  []
[]

[XFEM]
  qrule = volfrac
  output_cut_plane = true
[]

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

[UserObjects]
  [ipyc_crack]
    type = LineSegmentCutUserObject
    cut_data = '0.0000 0 0.001 0'
    time_start_cut = 0.0
    time_end_cut = 0.0
    block = IPyC
  []
  [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
    mesh_generator = mesh
  []
[]

[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
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  generate_output = 'stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz max_principal_stress min_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 = 5e-6
    quadrature = false
    min_gap = 1e-7
    max_gap = 50e-6
    gap_geometry_type = sphere
    sphere_origin = '0 0 0'
  []
[]

[BCs]
  [no_disp_x]
    type = DirichletBC
    variable = disp_x
    boundary = xzero
    value = 0.0
  []
  [no_disp_y]
    type = DirichletBC
    variable = disp_y
    boundary = '2001 2002 2004 2005'
    value = 0.0
  []
  [freesurf_temp]
    type = FunctionDirichletBC
    variable = temperature
    function = temp_bc
    boundary = exterior
  []
  [Pressure]
    [exterior]
      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]
  [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 = ${initial_fuel_density}
    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 = ${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
  []
  [normal_vectors_triso]
    type = NormalVectorsTRISO
    block = 'buffer IPyC OPyC'
    triso_geometry = particle_geometry
  []
  [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 = StrainAdjustedDensity
    block = IPyC
    strain_free_density = 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 = StrainAdjustedDensity
    block = OPyC
    strain_free_density = 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 = NEWTON

  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 = 6e5

  automatic_scaling = true
[]

[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 = max
    mat_prop = max_principal_stress
  []
  [strength_SiC]
     type = WeibullEffectiveMeanStrength
     block = SiC
     weibull_modulus = 6
  []
  [weibull_failure_probability_SiC]
    type = WeibullFailureProbability
    block = SiC
    weibull_modulus = 6
    characteristic_strength = characteristic_strength
  []
[]

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

(examples/TRISO/correlation_function/h_ipyc_sic_debonding/triso_debonding.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
aspect_ratio = 1.0

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

initial_fuel_density = 10966

[GlobalParams]
  order = FIRST
  family = LAGRANGE
  displacements = 'disp_x disp_y'
  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
  anisotropy = false
[]

[Mesh]
  coord_type = RZ
  [gen]
    type = TRISO2DMeshGenerator
    elem_type = quad4
    coordinates = '0 ${coordinates1} ${coordinates2} ${coordinates2} ${coordinates3} ${coordinates4} '
                  '${coordinates5}'
    mesh_density = '20 8 0 8 8 8'
    block_names = 'fuel buffer IPyC SiC OPyC'
    num_sectors = 60
    aspect_ratio = ${aspect_ratio}
    all_bottom_left = true
  []
  [breakmesh]
    input = gen
    type = BreakMeshByBlockGenerator
    block_pairs = '3 4'
    add_interface_on_two_sides = true
    split_interface = true
  []
  [opyc_node]
    type = ExtraNodesetGenerator
    input = breakmesh
    new_boundary = 'opyc_node'
    nodes = '4133'
  []
[]

[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
  []
[]

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

[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
  []
[]

[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
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  generate_output = 'stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz'
  add_variables = true
  temperature = temperature
  strain = FINITE
  incremental = true
  decomposition_method = TaylorExpansion
  volumetric_locking_correction = 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'
  []
[]

[Physics/SolidMechanics/CohesiveZone]
  [czm]
    boundary = 'IPyC_SiC'
    displacements = 'disp_x disp_y'
    strain = FINITE
  []
[]

[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 = true
    min_gap = 1e-7
    max_gap = 50e-6
    gap_geometry_type = sphere
    sphere_origin = '0 0 0'
  []

  [thermal_contact_ipyc_sic]
    type = GapHeatTransfer
    variable = temperature
    primary = IPyC_SiC
    secondary = SiC_IPyC
    quadrature = true
    tangential_tolerance = 1e-6
    min_gap = 1e-7
    max_gap = 50e-6
    gap_conductivity = 100
    gap_geometry_type = sphere
    sphere_origin = '0 0 0'
  []
[]

[BCs]
  [no_disp_x]
    type = DirichletBC
    variable = disp_x
    boundary = xzero
    value = 0.0
  []
  [no_disp_y]
    type = DirichletBC
    variable = disp_y
    boundary = '2001 2002 opyc_node'
    value = 0.0
  []

  [freesurf_temp]
    type = FunctionDirichletBC
    variable = temperature
    function = temp_bc
    boundary = exterior
  []
  [Pressure]
    [exterior]
      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]
  [tangential_stress]
    type = RankTwoCylindricalComponent
    rank_two_tensor = stress
    cylindrical_axis_point1 = '0 0 0'
    cylindrical_axis_point2 = '0 0 1'
    cylindrical_component = HoopStress
    property_name = tangential_stress
    outputs = all
  []
  [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
  []
  [normal_vectors_triso]
    type = NormalVectorsTRISO
    block = 'buffer IPyC OPyC'
    triso_geometry = particle_geometry
  []
  [normal_strength]
    type = GenericFunctionMaterial
    prop_names = 'N'
    prop_values = 'if(y>345e-6,0.5,1.0)*3e7'
    outputs = all
  []
  [czm]
    type = BiLinearMixedModeTraction
    boundary = 'IPyC_SiC'
    penalty_stiffness = 4e14
    lag_mode_mixity = true
    GI_c = 8
    GII_c = 4
    normal_strength = N
    shear_strength = 1e7
    displacements = 'disp_x disp_y'
    eta = 2
    viscosity = 1
    alpha = 1e-10
    mixed_mode_criterion = POWER_LAW
    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 = ${initial_fuel_density}
    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 = ${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
  []
  [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'
  []
[]

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

[Bounds]
  [temperature_lower_bound]
    type = ConstantBounds
    variable = bounds_dummy
    bounded_variable = temperature
    bound_type = lower
    bound_value = 1
  []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_factor_shift_type -pc_factor_shift_amount -snes_type'
  petsc_options_value = 'lu nonzero 1e-10 vinewtonrsls'

  line_search = 'none'

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

  l_tol = 1e-4
  l_max_its = 50

  start_time = 0.0
  end_time = 4.831315e7

  dt =  86400
  dtmin = 1
[]

[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'
  []
  [strength_SiC]
    type = WeibullEffectiveMeanStrength
    block = SiC
    weibull_modulus = 6
  []
  [weibull_failure_probability_SiC]
    type = WeibullFailureProbability
    block = SiC
    weibull_modulus = 6
    characteristic_strength = characteristic_strength
  []
  [weibull_failure_probability_IPyC]
    type = WeibullFailureProbability
    block = IPyC
    weibull_modulus = 9.5
    characteristic_strength = characteristic_strength
  []
  [max_radial_sic]
    type = ElementExtremeValue
    variable = radial_stress
    block = SiC
    value_type = 'max'
    execute_on = 'initial timestep_end'
  []
  [SiC_stress]
    type = ElementExtremeValue
    variable = tangential_stress
    block = SiC
    value_type = 'max'
    execute_on = 'initial timestep_end'
  []
[]

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

(assessment/TRISO/validation/AGR-2/AGR-2_base.i)

#COMPACT = <compact_id>
#DATA_FILE = <data_file_name>

[GlobalParams]
  order = SECOND
  family = LAGRANGE
  energy_per_fission = 3.204e-11 # [J/fission]
  time_average_mass_rate = false
[]

[Mesh]
  coord_type = RSPHERICAL
  [gen]
    type = TRISO1DFiveLayerMeshGenerator
    elem_type = EDGE3
    kernel_mesh_density = 20
    buffer_mesh_density = 15
    IPyC_mesh_density = 12
    SiC_mesh_density = 8
    OPyC_mesh_density = 6
    block_names = 'fuel buffer IPyC SiC OPyC'
    include_gap = false
    kernel_bias = 0.8
    buffer_bias = 1.25
    buffer_dual_bias = 0.8
    IPyC_bias = 1.25
    IPyC_dual_bias = 0.8
    SiC_bias = 1.25
    SiC_dual_bias = 0.8
    OPyC_bias = 1.25
    OPyC_dual_bias = 0.8
  []
[]

[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
  []
[]

[Variables]
  [temperature]
    initial_condition = 923.15
  []
[]

[AuxVariables]
  [fission_rate]
    block = fuel
    order = CONSTANT
    family = MONOMIAL
  []
  [burnup]
    block = fuel
    order = CONSTANT
    family = MONOMIAL
  []
  [fast_neutron_fluence]
    order = CONSTANT
    family = MONOMIAL
  []
  [density]
    order = CONSTANT
    family = MONOMIAL
  []
  [thermal_conductivity]
    order = CONSTANT
    family = MONOMIAL
  []
  [specific_heat]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [temp_bc_file]
    type = PiecewiseLinear
    #data_file = DATA_FILE
    x_index_in_file = 0
    y_index_in_file = 1
    xy_in_file_only = false
    format = columns
  []
  [temp_bc_safety]
    type = ParsedFunction
    symbol_names = 'test_temperature'
    symbol_values = '1873.15'
    expression = 'start := 50284800+1800;
             ramp1 := 120.0/3600.0;
             ramp2 := 120.0/3600.0;
             ramp3 := 50.0/3600.0;
             ramp4 := -600.0/3600.0;
             room := 303.15;
             plateau1 := 673.15;
             plateau2 := 1523.15;
             hold1 := 7200;
             hold2 := 43200;
             hold3 := 1080000;
             ramp_time1 := (plateau1-room)/ramp1;
             ramp_time2 := (plateau2-plateau1)/ramp2;
             ramp_time3 := (test_temperature-plateau2)/ramp3;
             ramp_time4 := (room-test_temperature)/ramp4;
             t1 := start+ramp_time1;
             t2 := t1+hold1;
             t3 := t2+ramp_time2;
             t4 := t3+hold2;
             t5 := t4+ramp_time3;
             t6 := t5+hold3;
             t7 := t6+ramp_time4;
             if(t<start,room,
             if(t<t1,room+(t-start)*ramp1,
             if(t<t2,plateau1,
             if(t<t3,plateau1+(t-t2)*ramp2,
             if(t<t4,plateau2,
             if(t<t5,plateau2+(t-t4)*ramp3,
             if(t<t6,test_temperature,
             if(t<t7,test_temperature+(t-t6)*ramp4,
             room))))))))'
  []
  [temp_bc]
    type = ParsedFunction
    symbol_names = 'tbcf tbcs'
    symbol_values = 'temp_bc_file temp_bc_safety'
    expression = 'if(t<=50284800,tbcf,tbcs)'
  []
  [power_history] # W/m^3
    type = PiecewiseLinear
    #data_file = DATA_FILE
    x_index_in_file = 0
    y_index_in_file = 2
    xy_in_file_only = false
    format = columns
  []
  [fission_rate_from_power]
    type = LinearCombinationFunction
    functions = power_history
    # W/m^3 / (1.602e-13 J/MeV) / (200 MeV/fission)
    w = 3.1211e10
  []
  [fission_rate]
    type = ParsedFunction
    symbol_names = 'fr'
    symbol_values = 'fission_rate_from_power'
    expression = 'if(t<=50284800,fr,0)'
  []
  [fast_neutron_fluence]
    type = PiecewiseLinear
    #data_file = DATA_FILE
    x_index_in_file = 0
    y_index_in_file = 3
    xy_in_file_only = false
    format = columns
  []
  [d1_function]
    type = ParsedFunction
    expression = 'exp(t/4.5e25)'
  []
[]

[Kernels]
  [heat_dt]
    type = HeatConductionTimeDerivative
    variable = temperature
  []
  [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_fluence]
    type = MaterialRealAux
    variable = fast_neutron_fluence
    property = fast_neutron_fluence
    block = 'fuel buffer IPyC SiC OPyC'
    execute_on = timestep_begin
  []

  [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
  []
[]

[BCs]

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

[Materials]

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

  [fast_neutron_fluence]
    type = GenericFunctionMaterial
    prop_names = fast_neutron_fluence
    prop_values = fast_neutron_fluence
  []

  ### Fuel properties

  [burnup]
    type = TRISOBurnup
    time_average_fission_rate = false
  []

  [fuel_thermal]
    block = fuel
    temperature = temperature
  []

  [fuel_density]
    type = ParsedMaterial
    block = fuel
    property_name = density
    expression = ${initial_fuel_density}
  []

  ### Buffer Properties

  [buffer_thermal]
    type = BufferThermal
    block = buffer
  []

  [Buffer_density]
    type = ParsedMaterial
    block = buffer
    property_name = density
    expression = ${initial_buffer_density}
  []

  ### IPyC  properties

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

  [IPyC_density]
    type = ParsedMaterial
    block = IPyC
    property_name = density
    expression = ${initial_ipyc_density}
  []

  ### SiC properties

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

  [SiC_density]
    type = ParsedMaterial
    block = SiC
    property_name = density
    expression = ${initial_sic_density}
  []

  ###  OPyC properties

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

  [OPyC_density]
    type = ParsedMaterial
    block = OPyC
    property_name = density
    expression = ${initial_opyc_density}
  []

[]

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

[Debug]
  show_var_residual_norms = true
[]

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

[Executioner]
  type = Transient
  solve_type = NEWTON

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

  line_search = 'none'

  nl_rel_tol = 1e-6
  nl_abs_tol = 5e-12
  nl_max_its = 50

  l_tol = 1e-4
  l_max_its = 50

  start_time = 0.0
  end_time = 50284800
  num_steps = 1500

  dt = 86400
  dtmax = 86400
  dtmin = 100
  [TimeStepper]
    type = FunctionDT
    function = 'if(t<50284799,86400,1800)'
  []
  automatic_scaling = true
  compute_scaling_once = false
[]

[Postprocessors]
  [_dt]
    type = TimestepSize
    execute_on = timestep_end
  []

  ### Temperature
  [temp_min]
    type = NodalExtremeValue
    variable = temperature
    value_type = 'min'
    execute_on = 'initial timestep_end'
  []
  [temp_max]
    type = NodalExtremeValue
    variable = temperature
    value_type = 'max'
    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'
  []
[]

[Outputs]
  perf_graph = true
  print_linear_residuals = false
  [console]
    type = Console
    time_step_interval =  1
  []
  [exodus]
    type = Exodus
    file_base = COMPACT
  []
  [release]
    type = CSV
    file_base = release_COMPACT
    sort_columns = true
  []
  [final_release]
    type = CSV
    file_base = final_release_COMPACT
    sort_columns = true
    execute_on = 'final'
  []
[]

(test/tests/triso/buffer_creep/ad_buffer_creep.i)

#Irradiation-induced Creep Properties of the Buffer
#The geometry is a cube (edge length = 5 cm) made of buffer material (initial density = 1.0 g/cm^3) subject to creep.
#A pressure boundary condition of 50 MPa is applied to one side to induce a constant stress in the x-axis.
#The Poisson's ratio in creep is equal to 0.5.
#The temperature is constant and equal to 1273.15 K.
#The fast neutron flux (E>0.10 MeV) is ramped linearly from 0 to 7.5e18 n/m^2-s over 1e4 seconds and then remains constant.
#Since the stress is constant, the creep rate can be approximated as K * sigma * flux * flux_conversion_factor. With K = 8.5265e-35, sigma = -5e7 N/m^2,
# flux = 7.5e18 n/m2-s and flux_conversion_factor = 0.85, creep rate calculated as 2.7178e-08 1/s.
#At time = 7.5e6 seconds, the analytical creep strain is -0.2038.

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  volumetric_locking_correction = true
  order = FIRST
  family = LAGRANGE
  flux_conversion_factor = 0.85
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 3
    xmin = 0.0
    xmax = 0.05
    ymin = 0.0
    ymax = 0.05
    zmin = 0.0
    zmax = 0.05
  []
[]

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

[Variables]
  [temp]
    initial_condition = 1273.15
  []
[]

[AuxVariables]
  [fast_neutron_fluence]
    order = CONSTANT
    family = MONOMIAL
  []
  [density]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [flux_history]
    type = PiecewiseLinear
    x = '0    1e4    1e8'
    y = '0 7.5e18 7.5e18'
  []
  [pressure_ramp]
    type = PiecewiseLinear
    x = '0 1e3'
    y = '0 1'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [perm_Buffer]
    strain = FINITE
    add_variables = true
    eigenstrain_names = ' '
    generate_output = 'vonmises_stress stress_xx stress_yy stress_zz creep_strain_xx'
    extra_vector_tags = 'ref'
    use_automatic_differentiation = true
  []
[]

[Kernels]
  [heat]
    type = ADHeatConduction
    variable = temp
  []
  [heat_ie]
    type = ADHeatConductionTimeDerivative
    variable = temp
  []
[]

[AuxKernels]
  [fast_neutron_fluence]
    type = ADMaterialRealAux
    variable = fast_neutron_fluence
    property = fast_neutron_fluence
    block = '0'
    execute_on = timestep_begin
  []
  [density]
    type = ADMaterialRealAux
    variable = density
    property = density
    block = '0'
    execute_on = 'initial timestep_end'
  []
[]

[BCs]
  [no_z_all]
    type = ADDirichletBC
    variable = disp_z
    boundary = 'back'
    value = 0
  []
  [no_y_all]
    type = ADDirichletBC
    variable = disp_y
    boundary = 'bottom'
    value = 0
  []
  [no_x_all]
    type = ADDirichletBC
    variable = disp_x
    boundary = 'right'
    value = 0
  []
  [Pressure]
    [appliedPressure]
      boundary = 'left'
      factor = 50e6
      function = pressure_ramp
      use_automatic_differentiation = true
    []
  []
  [heat_removal]
    type = ADDirichletBC
    variable = temp
    boundary = 'back bottom right'
    value = 1273.15
  []
[]

[Materials]
  [flux]
    type = ADFastNeutronFlux
    calculate_fluence = true
    flux_function = flux_history
  []
  [normal_vectors_triso]
    type = NormalVectorsTRISO
    normal_x = 1
    normal_y = 0
    normal_z = 0
  []
  [Buffer_stress]
    type = ADBufferCEGACreep
    temperature = temp
  []

  [Buffer_elasticity_tensor]
    type = ADBufferElasticityTensor
    temperature = temp
  []

  [buffer_thermal]
    type = ADBufferThermal
    initial_density = 1000
  []

  [Buffer_density]
    type = ADStrainAdjustedDensity
    strain_free_density = 1000.0
  []
[]

[Dampers]
  [limitT]
    type = MaxIncrement
    max_increment = 200.0
    variable = temp
  []

  [limitX]
    type = MaxIncrement
    max_increment = 1e-4
    variable = disp_x
  []

  [limitY]
    type = MaxIncrement
    max_increment = 1e-4
    variable = disp_y
  []

  [limitZ]
    type = MaxIncrement
    max_increment = 1e-4
    variable = disp_z
  []
[]

[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'

  l_max_its = 50
  l_tol = 1e-2

  nl_max_its = 150
  nl_rel_tol = 1e-08
  nl_abs_tol = 1e-7

  start_time = 0.0
  end_time = 7.5e6
  num_steps = 140


  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 1e6
    time_t = '1e4 1e5'
    time_dt = '1e6 1e6'
  []
[]

[Postprocessors]
  [temp]
    type = ElementAverageValue
    variable = temp
    execute_on = 'initial timestep_end'
  []

  [fluence]
    type = ElementAverageValue
    variable = fast_neutron_fluence
    execute_on = 'initial timestep_end'
  []

  [disp_x_max]
    type = NodalExtremeValue
    variable = disp_x
    execute_on = 'initial timestep_end'
  []

  [sigma_x_max]
    type = ElementAverageValue
    variable = stress_xx
    execute_on = 'initial timestep_end'
  []

  [creep_strain_xx]
    type = ElementAverageValue
    variable = creep_strain_xx
    execute_on = 'initial timestep_end'
  []

  [density]
    type = ElementAverageValue
    variable = density
    execute_on = 'initial timestep_end'
  []
[]

[Outputs]
  csv = true
  exodus = false
  [console]
    type = Console
  []
[]

(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
[]

(test/tests/triso_failure/higher_order_correlation.i)

[GlobalParams]
  order = FIRST
  family = LAGRANGE
  displacements = 'disp_x'
  initial_enrichment = 0.155 # [wt-]
  flux_conversion_factor = 1.0 # convert E>0.10 to E>0.18 MeV
  stress_free_temperature = 973.15 # 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 = TRISO1DFiveLayerMeshGenerator
    elem_type = EDGE3
    kernel_radius = 212.5e-6
    buffer_thickness = 100e-6
    IPyC_thickness = 41e-6
    SiC_thickness = 34e-6
    OPyC_thickness = 44e-6
    kernel_mesh_density = 5
    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 = 40e-6
    SiC_thickness_mean = 35e-6
    OPyC_thickness_mean = 40e-6
  []
  [triso_failure_terminator]
    type = Terminator
    expression = 'triso_failure > 0'
  []
[]

[Variables]
  [temperature]
    initial_condition = 973.15
  []
[]

[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]
  [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 = PiecewiseLinear
    x = '0 1.0e10'
    y = '1.198892e9 1.198892e9'
  []
  [stress_correlation_crackedIPyC]
    type = TRISOStressCorrelationFunction
    triso_geometry = particle_geometry
    polynomial_coefficients_IPyC = '1 6922 -2.359e8'
    polynomial_coefficients_SiC = '1 -1.257e4 1.82e8'
    polynomial_coefficients_OPyC = '1 -1.257e4 1.82e8'
    correlation_factor = -1.1932
  []
  [high_fidelity_strength_asphericity]
    type = PiecewiseLinear
    x = '0 1.0e10'
    y = '0.993212e9 0.993212e9'
  []
  [stress_correlation_asphericity]
    type = TRISOStressCorrelationFunction
    triso_geometry = particle_geometry
    polynomial_coefficients_IPyC = '1 -1.716e4 2.123e8'
    polynomial_coefficients_SiC = '1 2.688e4 -1.414e7'
    polynomial_coefficients_OPyC = '1 -1.716e4 2.123e8'
    correlation_factor = 0.2923
  []
  [stress_change_correlation_asphericity]
    type = TRISOStressCorrelationFunction
    triso_geometry = particle_geometry
    polynomial_coefficients_IPyC = '1 -1.664e4 1.929e8'
    polynomial_coefficients_SiC = '1 2.625e4 -1.112e7'
    polynomial_coefficients_OPyC = '1 -1.664e4 1.929e8'
    correlation_factor = 0.5241
  []
[]

[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
  []
[]

[BCs]
  [no_disp_x]
    type = DirichletBC
    variable = disp_x
    boundary = xzero
    value = 0.0
  []
  [freesurf_temp]
    type = FunctionDirichletBC
    variable = temperature
    function = 973.15
    boundary = exterior
  []
  [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]
  [tangential_stress]
    type = RankTwoCylindricalComponent
    rank_two_tensor = stress
    cylindrical_axis_point1 = '0 0 0'
    cylindrical_axis_point2 = '0 0 1'
    cylindrical_component = HoopStress
    property_name = tangential_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
    flux_function = power_history
    factor = 1.16e18
  []
  [UCO_burnup]
    type = TRISOBurnup
    initial_density = 11000
    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 = 11000.0
  []
  [fission_gas_release]
    type = UCOFGR
    block = fuel
    average_grain_radius = 10e-6
    temperature = temperature
    triso_geometry = particle_geometry
    cutoff_neutron_flux = 0.0
  []
  [BAF]
    type = BaconAnisotropyFactor
    initial_BAF = 1.05
    block = 'buffer IPyC 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 = 1900
  []
  [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 = 1e+06

  dtmax = 2e5
  dtmin = 1e-4

  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 1
    optimal_iterations = 10
    linear_iteration_ratio = 100
  []
[]

[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 = max
    mat_prop = tangential_stress
  []
  [strength_SiC]
    type = WeibullEffectiveMeanStrength
    block = SiC
    weibull_modulus = 6
    use_displaced_mesh = true
  []
  [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
    use_displaced_mesh = true
  []
  [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'
  []
  [triso_failure]
    type = TRISOFailureEvaluation
    IPyC_failure = failure_indicator_IPyC
    SiC_failure_crackedIPyC = failure_indicator_SiC_crackedIPyC
    SiC_failure = failure_indicator_SiC
  []
[]

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

(assessment/TRISO/validation/AGR-34/Compacts/AGR-34_base.i)

initial_fuel_density = 11100.0

[GlobalParams]
  order = SECOND
  family = LAGRANGE
  initial_enrichment = 0.19717 # [wt-]
  energy_per_fission = 3.204e-11 # [J/fission]
  O_U = 1.430 # Initial Oxygen to Uranium atom ratio
  C_U = 0.361 # Initial Carbon to Uranium atom ratio
[]

[Mesh]
  coord_type = RSPHERICAL
  [gen]
    type = TRISO1DFiveLayerMeshGenerator
    elem_type = EDGE3
    kernel_radius = 178.65e-6
    buffer_thickness = 109.7e-6
    IPyC_thickness = 40.4e-6
    SiC_thickness = 33.5e-6
    OPyC_thickness = 41.3e-6
    kernel_mesh_density = 18
    buffer_mesh_density = 14
    IPyC_mesh_density = 12
    SiC_mesh_density = 16
    OPyC_mesh_density = 16
    block_names = 'fuel buffer IPyC SiC OPyC'
    include_gap = false
    kernel_bias = 0.8
    buffer_bias = 1.25
  []
[]

[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
  []
[]

[Variables]
  [temperature]
    initial_condition = 888.5
  []
[]

[AuxVariables]
  [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
  []
[]

[Functions]
  [temp_bc]
    type = PiecewiseLinear
    x_index_in_file = 0
    y_index_in_file = 1
    xy_in_file_only = false
    format = columns
  []
  [power_history]
    type = PiecewiseLinear
    x = '0 76e6'
    y = '1 1'
  []
  [fission_rate]
    type = LinearCombinationFunction
    functions = power_history
    w = 4.2602e+19
  []
  [d1_function]
    type = ParsedFunction
    expression = 'exp(t/4.5e25)'
  []
[]

[Kernels]
  [heat_dt]
    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
    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
  []

[]

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

[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 = 4.4440e+17
  []

### UCO fuel properties

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

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

  [UCO_density]
    type = ParsedMaterial
    block = fuel
    property_name = density
    expression = ${initial_fuel_density}
  []

### Buffer Properties

  [buffer_thermal]
    type = BufferThermal
    block = buffer
    initial_density = 1100.0
  []

  [Buffer_density]
    type = ParsedMaterial
    block = buffer
    property_name = density
    expression = 1100.0
  []


### IPyC  properties

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

  [IPyC_density]
    type = ParsedMaterial
    block = IPyC
    property_name = density
    expression = 1904.0
  []

### SiC properties

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

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

###  OPyC properties

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

  [OPyC_density]
    type = ParsedMaterial
    block = OPyC
    property_name = density
    expression = 1901.0
  []

[]

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

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

[Debug]
  show_var_residual_norms = true
  #show_var_residual = 'temperature conc_Ag conc_Cs conc_Sr'
  show_var_residual = 'temperature'
[]


[Executioner]
  type = Transient
  solve_type = 'PJFNK'
#  solve_type = 'NEWTON'

#  petsc_options_iname = '-pc_type  -snes_type'
#  petsc_options_value = 'lu vinewtonrsls'
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'

  line_search = 'none'

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

  l_tol = 1e-4
  l_max_its = 50

  start_time = 0.0
  end_time = 3.189024e7
  dt = 10000
[]

[Postprocessors]
  [_dt]
    type = TimestepSize
    execute_on = timestep_end
  []

### Temperature
  [temp_min]
    type = NodalExtremeValue
    variable = temperature
    value_type = 'min'
    execute_on = 'initial timestep_end'
  []
  [temp_max]
    type = NodalExtremeValue
    variable = temperature
    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'
  []

##### 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'
  []
[]

[Outputs]
  perf_graph = true
  print_linear_residuals = false
  [console]
    type = Console
    time_step_interval =  1
    #hide = 'release_Ag_inc release_Cs_inc release_Sr_inc'
  []
  [exodus]
    type = Exodus
    file_base = COMPACT
  []
  [release]
    type = CSV
    file_base = release_COMPACT
    sort_columns = true
    #show = 'release_Ag_inc released_Ag release_Cs_inc released_Cs release_Sr_inc released_Sr total_Ag total_Cs total_Sr x_Ag_released x_Cs_released x_Sr_released'
  []
  [final_release]
    type = CSV
    file_base = final_release_COMPACT
    sort_columns = true
    #show = 'retained_Ag retained_Cs retained_Sr released_Ag released_Cs released_Sr total_Ag total_Cs total_Sr x_Ag_released x_Cs_released x_Sr_released'
    execute_on = 'final'
  []
[]

(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/triso/buffer_thermal_material/buffer_thermal_conductivity.i)

#Thermal Conductivity of the Buffer
# The geometry is a cube (edge length = 5 cm) made of buffer material (initial density = 1.0 g/cm$^{3}$) subject to internal heat generation.
# The thermal power density is ramped linearly from 0 to 4x10$^{5}$ W/m$^{3}$ over 10$^{4}$ seconds and then held constant.
# Heat flows from the left surface (heat flux = 0) through the right surface (Dirichlet boundary condition).
# The temperature of the right surface is ramped from 673.15 to 1673.15 K.
# The specific heat capacity of the buffer was multiplied by 10$^{-6}$ to allow analytical solving of the steady-state heat equation.
# The density is varied from 1000 to 2240 kg/m$^{3}$ using a FunctionAux auxkernel.
# The maximum temperature $T_{max}$ (K) at the left surface is obtained by solving the 1D heat equation:
# T_{max} = \frac{q \cdot l^{2}}{2 \cdot k} + T_{BC}
# Where $q$ (W/m$^{3}$) is the thermal power density, $l$ (0.05 m) is the edge length of the cube, and $T_{BC}$ (K) is the boundary condition temperature of the right surface.
#
# A sample of the analytical and BISON values for thermal conductivities and calculated temperatures is shown below.
#
# |Density (kg/m$^{3}$) | Analytical k (W/m-K) | BISON k (W/m-K) | Analytical max T (K) | BISON max T (K) |
# |---------------------|----------------------|-----------------|----------------------|-----------------|
# | 1000.117            | 0.50004              | 0.50000         | 723.24               | 723.24          |
# | 1002.106            | 0.50080              | 0.50075         | 1573.42              | 1573.50         |
# | 1701.887            | 1.01713              | 1.01705         | 1730.77              | 1730.81         |
# | 2076.226            | 2.09794              | 2.09783         | 1779.40              | 1779.42         |
# | 2240.000            | 3.80376              | 3.80374         | 1804.60              | 1804.60         |

[GlobalParams]
  order = FIRST
  family = LAGRANGE
  energy_per_fission = 3.2e-11 # J/fission
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 3
    xmin = 0.0
    xmax = 0.05
    ymin = 0.0
    ymax = 0.05
    zmin = 0.0
    zmax = 0.05
  []
[]

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

[Variables]
  [temp]
    initial_condition = 673.15
  []
[]

[AuxVariables]
  [fission_rate]
    block = '0'
  []

  [density]
    order = CONSTANT
    family = MONOMIAL
  []

  [thermal_conductivity]
    order = CONSTANT
    family = MONOMIAL
  []

[]

[Functions]
  [power_history]
    type = PiecewiseLinear
    x = '0     1e4     1e8'
    y = '0 1.25e16 1.25e16'
  []

  [density_multiplier]
    type = PiecewiseLinear
    x = '0 5.3e6'
    y = '1000 2240'
  []

  [temp_func]
    type = PiecewiseLinear
    x = '     0   5.3e6'
    y = '673.15 1673.15'
  []

[]

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

  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temp
  []

  [heat_source]
    type = NeutronHeatSource
    variable = temp
    block = '0'
    fission_rate = fission_rate
  []

[]

[AuxKernels]
  [fissionrate]
    type = FissionRateGeneral
    fission_rate_formulation = GENERIC
    variable = fission_rate
    fission_rate_function = power_history
    block = '0'
    value = 1.0
  []

  [density]
    type = MaterialRealAux
    variable = density
    property = density
    block = '0'
    execute_on = 'initial linear'
  []

  [thermal_conductivity]
    type = MaterialRealAux
    variable = thermal_conductivity
    property = thermal_conductivity
    execute_on = timestep_end
  []

[]

[BCs]
  [temp_BC]
    type = FunctionDirichletBC
    variable = temp
    boundary = 'right'
    function = temp_func
  []

[]

[Materials]
  [Buffer_thermal_conductivity]
    type = BufferThermal
    thermal_conductivity_scale_factor = 1.0
    specific_heat_scale_factor = 1.0e-6
    initial_density = 1000
  []

  [Buffer_density]
    type = GenericFunctionMaterial
    prop_names = 'density'
    prop_values = density_multiplier
  []

[]

[Dampers]
  [limitT]
    type = MaxIncrement
    max_increment = 100.0
    variable = temp
  []

[]

[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_max_its = 50
  l_tol = 1e-2

  nl_max_its = 150
  nl_rel_tol = 1e-4
  nl_abs_tol = 1e-6

  start_time = 0.0
  end_time = 6e6
  num_steps = 100

  dtmax = 2e6
  dtmin = 1e-6

  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 5e2
    time_t = '1e4 1e5'
    time_dt = '5e2 1e5'
  []
[]

[Postprocessors]
  # Define postprocessors (some are required as specified above; others are optional; many others are available)

  [temp]
    type = ElementAverageValue
    variable = temp
    execute_on = 'initial timestep_end'
  []

  [thermal_conductivity]
    type = ElementAverageValue
    variable = thermal_conductivity
    execute_on = 'initial timestep_end'
  []

  [density]
    type = ElementAverageValue
    variable = density
    execute_on = 'initial timestep_end'
  []

  [total_power]
    type = ElementIntegralPower
    variable = temp
    fission_rate = fission_rate
    execute_on = timestep_end
  []

[]

[Outputs]
  csv = true
  exodus = false
  [console]
    type = Console
  []
[]

(assessment/TRISO/validation/AGR-1/AGR-1_base.i)

#COMPACT = <compact_id>
#DATA_FILE = <data_file_name>

# Definition of the mass source due to impurities in the OPyC layer.
#value = impurities * vol_kernel / vol_opyc
#value = 1.59e-6 * 4.07e-11 / 9.16e-11 # for UCO => 7.06e-7
#value = 1.57e-6 * 6.85e-11 / 1.18e-10 # for UO2 => 9.11e-7
mass_source_property_OPyC = 7.06e-7 # Default = UCO fuel kernel


initial_fuel_density = 10400

[GlobalParams]
  order = SECOND
  family = LAGRANGE
  initial_enrichment = 0.19736 # [wt-]
  energy_per_fission = 3.204e-11 # [J/fission]
  O_U = 1.3613 # Initial Oxygen to Uranium atom ratio
  C_U = 0.3253 # Initial Carbon to Uranium atom ratio
[]

[Mesh]
  coord_type = RSPHERICAL
  [gen]
    type = TRISO1DFiveLayerMeshGenerator
    elem_type = EDGE3
    kernel_radius = 175e-6
    buffer_thickness = 100e-6
    IPyC_thickness = 40e-6
    SiC_thickness = 35e-6
    OPyC_thickness = 40e-6
    kernel_mesh_density = 18
    buffer_mesh_density = 14
    IPyC_mesh_density = 6
    SiC_mesh_density = 8
    OPyC_mesh_density = 6
    block_names = 'fuel buffer IPyC SiC OPyC'
    include_gap = false
    kernel_bias = 0.8
    buffer_bias = 1.25
  []
[]

[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
  []
[]

[Variables]
  [temperature]
    initial_condition = 923.15
  []
[]

[AuxVariables]
  [fission_rate]
    block = fuel
    order = CONSTANT
    family = MONOMIAL
  []
  [burnup]
    block = fuel
    order = CONSTANT
    family = MONOMIAL
  []
  [fast_neutron_fluence]
    order = CONSTANT
    family = MONOMIAL
  []
  [density]
    order = CONSTANT
    family = MONOMIAL
  []
  [thermal_conductivity]
    order = CONSTANT
    family = MONOMIAL
  []
  [specific_heat]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [temp_bc_file]
    type = PiecewiseLinear
    #data_file = DATA_FILE
    x_index_in_file = 0
    y_index_in_file = 1
    xy_in_file_only = false
    format = columns
  []
  [temp_bc_safety]
    type = ParsedFunction
    symbol_names = 'test_temperature'
    symbol_values = '1873.15'
    expression = 'start := 55209600+1800;
             ramp1 := 120.0/3600.0;
             ramp2 := 120.0/3600.0;
             ramp3 := 50.0/3600.0;
             ramp4 := -600.0/3600.0;
             room := 303.15;
             plateau1 := 673.15;
             plateau2 := 1523.15;
             hold1 := 7200;
             hold2 := 43200;
             hold3 := 1080000;
             ramp_time1 := (plateau1-room)/ramp1;
             ramp_time2 := (plateau2-plateau1)/ramp2;
             ramp_time3 := (test_temperature-plateau2)/ramp3;
             ramp_time4 := (room-test_temperature)/ramp4;
             t1 := start+ramp_time1;
             t2 := t1+hold1;
             t3 := t2+ramp_time2;
             t4 := t3+hold2;
             t5 := t4+ramp_time3;
             t6 := t5+hold3;
             t7 := t6+ramp_time4;
             if(t<start,room,
             if(t<t1,room+(t-start)*ramp1,
             if(t<t2,plateau1,
             if(t<t3,plateau1+(t-t2)*ramp2,
             if(t<t4,plateau2,
             if(t<t5,plateau2+(t-t4)*ramp3,
             if(t<t6,test_temperature,
             if(t<t7,test_temperature+(t-t6)*ramp4,
             room))))))))'
  []
  [temp_bc]
    type = ParsedFunction
    symbol_names = 'tbcf tbcs'
    symbol_values = 'temp_bc_file temp_bc_safety'
    expression = 'if(t<=55209600,tbcf,tbcs)'
  []
  [power_history] # W/m^3
    type = PiecewiseLinear
    #data_file = DATA_FILE
    x_index_in_file = 0
    y_index_in_file = 2
    xy_in_file_only = false
    format = columns
  []
  [fast_neutron_fluence]
    type = PiecewiseLinear
    #data_file = DATA_FILE
    x_index_in_file = 0
    y_index_in_file = 3
    xy_in_file_only = false
    format = columns
  []
  [fission_rate_from_power]
    type = LinearCombinationFunction
    functions = power_history
    # W/m^3 / (1.602e-13 J/MeV) / (200 MeV/fission)
    w = 3.1211e10
  []
  [fission_rate]
    type = ParsedFunction
    symbol_names = 'fr'
    symbol_values = 'fission_rate_from_power'
    expression = 'if(t<=55209600,fr,0)'
  []
  [d1_function]
    type = ParsedFunction
    expression = 'exp(t/4.5e25)'
  []
[]

[Kernels]
  [heat_dt]
    type = HeatConductionTimeDerivative
    variable = temperature
  []
  [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_fluence]
    type = MaterialRealAux
    variable = fast_neutron_fluence
    property = fast_neutron_fluence
    block = 'fuel buffer IPyC SiC OPyC'
    execute_on = timestep_begin
  []

  [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
  []
[]

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

[Materials]

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

  [fast_neutron_fluence]
    type = GenericFunctionMaterial
    prop_names = fast_neutron_fluence
    prop_values = fast_neutron_fluence
  []

  ### UCO fuel properties

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

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

  [UCO_density]
    type = ParsedMaterial
    block = fuel
    property_name= density
    expression = ${initial_fuel_density}
  []

  ### Buffer Properties

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

  [Buffer_density]
    type = ParsedMaterial
    block = buffer
    property_name= density
    expression = 1050.0
  []

  ### IPyC  properties

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

  [IPyC_density]
    type = ParsedMaterial
    block = IPyC
    property_name= density
    expression = 1900.0
  []

  ### SiC properties

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

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

  ###  OPyC properties

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

  [OPyC_density]
    type = ParsedMaterial
    block = OPyC
    property_name= density
    expression = 1900.0
  []

[]

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

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

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

[Executioner]
  type = Transient
  solve_type = 'PJFNK' # Shall we switch to 'Newton'?
  # solve_type = 'Newton'

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

  line_search = 'none'

  nl_rel_tol = 1e-6
  nl_abs_tol = 1e-12
  nl_max_its = 50

  l_tol = 1e-4
  l_max_its = 50

  start_time = 0.0
  end_time = 55209600
  num_steps = 1500

  dt = 86400
  dtmax = 86400
  dtmin = 100

  [TimeStepper]
    type = FunctionDT
    function = 'if(t<55209600,86400,1800)'
  []
  automatic_scaling = true
  compute_scaling_once = false

[]

[Postprocessors]
  [_dt]
    type = TimestepSize
    execute_on = timestep_end
  []

  ### Temperature
  [temp_min]
    type = NodalExtremeValue
    variable = temperature
    value_type = 'min'
    execute_on = 'initial timestep_end'
  []
  [temp_max]
    type = NodalExtremeValue
    variable = temperature
    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'
  []

  ##### 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'
  []
[]

[Outputs]
  perf_graph = true
  print_linear_residuals = false
  [console]
    type = Console
    time_step_interval =  1
  []
  [exodus]
    type = Exodus
    file_base = COMPACT
  []
  [release]
    type = CSV
    file_base = release_COMPACT
    sort_columns = true
  []
  [final_release]
    type = CSV
    file_base = final_release_COMPACT
    sort_columns = true
    execute_on = 'final'
  []
[]

(test/tests/triso/kernel_migration/kernel_migration_distance.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
  []
[]

[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
  []
[]

[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
      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
    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 = 1e-10
  nl_abs_tol = 1e-9
  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
  []
[]

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

(test/tests/triso/mesh/ipyc_crack.i)

[GlobalParams]
  order = FIRST
  family = LAGRANGE
  displacements = 'disp_x disp_y'
  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 = RZ
  [gen]
    type = TRISO2DMeshGenerator
    elem_type = quad4
    coordinates = '0 2.1335e-4 3.1225e-4 3.1225e-4 3.5265e-4 3.8785e-4 4.3415e-4'
    mesh_density = '3 3 0 3 4 3'
    block_names = 'fuel buffer IPyC SiC OPyC'
    num_sectors = 20
    aspect_ratio = 1.0
    all_bottom_left = true
  []
[]

[XFEM]
  qrule = volfrac
  output_cut_plane = true
[]

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

[UserObjects]
  [ipyc_crack]
    type = LineSegmentCutUserObject
    cut_data = '0.0000 0.0 0.001 0.0'
    time_start_cut = 0.0
    time_end_cut = 0.0
    block = IPyC
  []
  [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
    mesh_generator = 'gen'
  []
[]

[Variables]
  [temperature]
    initial_condition = 650
  []
[]

[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
  []
[]

[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
  temperature = temperature
  [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
    sphere_origin = '0 0 0'
  []
[]

[BCs]
  [no_disp_x]
    type = DirichletBC
    variable = disp_x
    boundary = xzero
    value = 0.0
  []
  [no_disp_y]
    type = DirichletBC
    variable = disp_y
    boundary = '2001 2002 2004 2005'
    value = 0.0
  []
  [freesurf_temp]
    type = DirichletBC
    variable = temperature
    value = 650
    boundary = exterior
  []
  [Pressure]
    [exterior]
      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]
  [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'
    triso_geometry = particle_geometry
  []
  [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 = 1e-10
  nl_abs_tol = 5e-11
  nl_max_its = 20

  l_tol = 1e-4
  l_max_its = 50

  start_time = 0.0
  num_steps = 2

  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]
    type = ElementExtremeMaterialProperty
    block = SiC
    value_type = max
    mat_prop = max_principal_stress
  []
  [strength_SiC]
     type = WeibullEffectiveMeanStrength
     block = SiC
     weibull_modulus = 6
  []
[]

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

(assessment/TRISO/validation/AGR-34/SharedFiles/capsule_driver.i)

kernel_radius = 178.65e-6
buffer_thickness = 109.7e-6
IPyC_thickness = 40.4e-6
SiC_thickness = 33.5e-6
OPyC_thickness = 41.3e-6
buffer_density = 1100
ipyc_density = 1904
opyc_density = 1901
sic_density = 3203

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 = SECOND
  family = LAGRANGE
  initial_enrichment = 0.19717 # [wt-]
  energy_per_fission = 3.204e-11 # [J/fission]
  O_U = 1.430 # Initial Oxygen to Uranium atom ratio
  C_U = 0.361 # Initial Carbon to Uranium atom ratio
[]

[Mesh]
  coord_type = RSPHERICAL
  [mesh]
    type = TRISO1DMeshGenerator
    elem_type = EDGE3
    coordinates = '0 ${coordinates1} ${coordinates2} ${coordinates3} ${coordinates4} ${coordinates5}'
    mesh_density = '18 14 12 16 16'
    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
  []
[]

[Variables]
  [temperature]
    initial_condition = 1200
  []
  [conc_Ag]
    initial_condition = 0.0
    scaling = 1e12 #1e18
  []
  [conc_Cs]
    initial_condition = 0.0
    scaling = 1e12 #1e18
  []
  [conc_Sr]
    initial_condition = 0.0
    scaling = 1e12 #1e18
  []
[]

[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
  []
  [fis_gas_produced]
    order = CONSTANT
    family = MONOMIAL
  []
  [fis_gas_released]
    order = CONSTANT
    family = MONOMIAL
  []
  [Ag_diff_coef]
    order = CONSTANT
    family = MONOMIAL
  []
  [Cs_diff_coef]
    order = CONSTANT
    family = MONOMIAL
  []
  [Sr_diff_coef]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [temp_bc]
    type = PiecewiseLinear
    x_index_in_file = 0
    y_index_in_file = 1
    xy_in_file_only = false
    format = columns
    data_file='AGR-34_capsule_daily_data/Cap1Temps.csv'
  []
  [power_history]
    type = PiecewiseLinear
    x = '0 76e6'
    y = '1 1'
  []
  [fission_rate]
    type = LinearCombinationFunction
    functions = power_history
    w = 4.8156e+19
  []
[]

[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
    extra_vector_tags = 'ref'
  []
  [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'
  []

  [mass_Cs_dt]
    type = TimeDerivative
    variable = conc_Cs
    extra_vector_tags = 'ref'
  []
  [mass_Cs]
    type = ArrheniusDiffusion
    variable = conc_Cs
    arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
    extra_vector_tags = 'ref'
  []
  [mass_source_Cs]
    type = SpeciesSourceRate
    variable = conc_Cs
    property_name = Cs_generation
    block = fuel
    extra_vector_tags = 'ref'
  []

  [mass_Sr_dt]
    type = TimeDerivative
    variable = conc_Sr
    extra_vector_tags = 'ref'
  []
  [mass_Sr]
    type = ArrheniusDiffusion
    variable = conc_Sr
    arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
    extra_vector_tags = 'ref'
  []
  [mass_source_Sr]
    type = SpeciesSourceRate
    variable = conc_Sr
    property_name = Sr_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
  []
  [Cs_diff_coef]
    type = MaterialRealAux
    variable = Cs_diff_coef
    property = arrhenius_diffusion_coef_Cs
    execute_on = timestep_end
  []
  [Sr_diff_coef]
    type = MaterialRealAux
    variable = Sr_diff_coef
    property = arrhenius_diffusion_coef_Sr
    execute_on = timestep_end
  []
[]

[BCs]
  [freesurf_temp]
    type = FunctionDirichletBC
    variable = temperature
    function = temp_bc
    boundary = exterior
    extra_vector_tags = 'ref'
  []
  [freesurf_conc_Ag]
    type = DirichletBC
    variable = conc_Ag
    boundary = exterior
    value = 0.0
  []
  [freesurf_conc_Cs]
    type = DirichletBC
    variable = conc_Cs
    boundary = exterior
    value = 0.0
  []
  [freesurf_conc_Sr]
    type = DirichletBC
    variable = conc_Sr
    boundary = exterior
    value = 0.0
  []
[]

[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 = 0.5519e+18
  []
  [UCO_burnup]
    type = TRISOBurnup
    initial_density = ${initial_fuel_density}
  []

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

  [UCO_density]
    type = StrainAdjustedDensity
    block = fuel
    strain_free_density = 11098.0
  []

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

  # 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
  []
  [fuel_conc_Cs]
    type = ArrheniusDiffusionCoef
    block = fuel
    d1 = 5.6e-8 # m^2/s
    q1 = 209e3 # J/mol
    temperature = temperature
    arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
  []
  [fuel_conc_Sr]
    type = ArrheniusDiffusionCoef
    block = fuel
    d1 = 2.2e-3 # m^2/s
    q1 = 488e3 # J/mol
    temperature = temperature
    arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
  []
  [mass_source_Ag_property]
    type = SpeciesSourceMaterial
    property_name = Ag_generation
    kind = Ag
    block = fuel
  []
  [mass_source_Cs_property]
    type = SpeciesSourceMaterial
    property_name = Cs_generation
    kind = Cs
    block = fuel
  []
  [mass_source_Sr_property]
    type = SpeciesSourceMaterial
    property_name = Sr_generation
    kind = Sr
    block = fuel
  []

  ### Buffer Properties
  [buffer_thermal]
    type = BufferThermal
    block = buffer
    initial_density = ${buffer_density}
  []

  [Buffer_density]
    type = StrainAdjustedDensity
    block = buffer
    strain_free_density = ${buffer_density}
  []

  [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
  []
  [buffer_conc_Cs]
    type = ArrheniusDiffusionCoef
    block = buffer
    d1 = 1e-8 # m^2/s
    q1 = 0.0
    temperature = temperature
    arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
  []
  [buffer_conc_Sr]
    type = ArrheniusDiffusionCoef
    block = buffer
    d1 = 1e-8 # m^2/s
    q1 = 0.0
    temperature = temperature
    arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
  []

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

  [IPyC_density]
    type = StrainAdjustedDensity
    block = IPyC
    strain_free_density = ${ipyc_density}
  []

  [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
  []
  [IPyC_conc_Cs]
    type = ArrheniusDiffusionCoef
    block = IPyC
    d1 = 6.3e-8 # m^2/s
    q1 = 222e3 # J/mol
    temperature = temperature
    arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
  []
  [IPyC_conc_Sr]
    type = ArrheniusDiffusionCoef
    block = IPyC
    d1 = 2.3e-6 # m^2/s
    q1 = 197e3 # J/mol
    temperature = temperature
    arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
  []

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

  [SiC_density]
    type = StrainAdjustedDensity
    block = SiC
    strain_free_density = ${sic_density}
  []

  [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
  []
  [SiC_conc_Cs]
    type = ArrheniusDiffusionCoef
    block = SiC
    d1 = 5.5e-14 # m^2/s
    q1 = 125e3 # J/mol
    temperature = temperature
    arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
  []
  [SiC_conc_Sr]
    type = ArrheniusDiffusionCoef
    block = SiC
    d1 = 1.2e-9 # m^2/s
    q1 = 205e3 # J/mol
    temperature = temperature
    arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
  []

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

  [OPyC_density]
    type = StrainAdjustedDensity
    block = OPyC
    strain_free_density = ${opyc_density}
  []

  [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
  []
  [OPyC_conc_Cs]
    type = ArrheniusDiffusionCoef
    block = OPyC
    d1 = 6.3e-8 # m^2/s
    q1 = 222e3 # J/mol
    temperature = temperature
    arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
  []
  [OPyC_conc_Sr]
    type = ArrheniusDiffusionCoef
    block = OPyC
    d1 = 2.3e-6 # m^2/s
    q1 = 197e3 # J/mol
    temperature = temperature
    arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
  []
[]

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

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

[Debug]
  show_var_residual_norms = true
  show_var_residual = 'temperature conc_Ag conc_Cs conc_Sr'
[]

[Executioner]
  type = Transient
  solve_type = 'NEWTON'

  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'

  line_search = 'none'

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

  l_tol = 1e-4
  l_max_its = 50

  start_time = 0.0
  dt = 86400
  end_time = 31890240
[]

[Postprocessors]
  [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
  []
  [release_Cs_inc]
    type = SideIntegralMassFlux
    variable = conc_Cs
    boundary = exterior
    arrhenius_prpty_name = arrhenius_diffusion_coef_Cs
    execute_on = 'initial timestep_end'
  []
  [released_Cs]
    type = TimeIntegratedPostprocessor
    value = release_Cs_inc
    execute_on = 'initial timestep_end'
  []
  [total_Cs]
    type = ElementIntegralMaterialProperty
    mat_prop = Cs_generation_total
    block = fuel
    execute_on = 'initial timestep_end'
  []
  [x_Cs_released]
    type = FractionalRelease
    released = released_Cs
    total = total_Cs
  []
  [retained_Cs]
    type = ElementIntegralVariablePostprocessor
    variable = conc_Cs
  []
  [release_Sr_inc]
    type = SideIntegralMassFlux
    variable = conc_Sr
    boundary = exterior
    arrhenius_prpty_name = arrhenius_diffusion_coef_Sr
    execute_on = 'initial timestep_end'
  []
  [released_Sr]
    type = TimeIntegratedPostprocessor
    value = release_Sr_inc
    execute_on = 'initial timestep_end'
  []
  [total_Sr]
    type = ElementIntegralMaterialProperty
    mat_prop = Sr_generation_total
    block = fuel
    execute_on = 'initial timestep_end'
  []
  [x_Sr_released]
    type = FractionalRelease
    released = released_Sr
    total = total_Sr
  []
  [retained_Sr]
    type = ElementIntegralVariablePostprocessor
    variable = conc_Sr
  []

  [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'
  []

  ### 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'
  []
[]

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

(test/tests/triso_failure/triso_1d_ipyc_weibull_probability.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
  [gen]
    type = TRISO1DMeshGenerator
    elem_type = EDGE3
    coordinates = '0 ${coordinates1} ${coordinates2} ${coordinates2} ${coordinates3} ${coordinates4} ${coordinates5}'
    mesh_density = '5 3 0 5 3 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
    IPyC_thickness_mean = 40.4e-6
    SiC_thickness_mean = 35.2e-6
    OPyC_thickness_mean = 43.4e-6
  []
[]

[Variables]
  [temperature]
    initial_condition = 900
  []
[]

[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 = ConstantFunction
    value = '1363350801.3058'
  []
  [stress_correlation_crackedIPyC]
    type = TRISOStressCorrelationFunction
    triso_geometry = particle_geometry
    polynomial_coefficients_IPyC = '1 7017 -2.368e8'
    polynomial_coefficients_SiC = '1 1.492e4 -3.802e7'
    polynomial_coefficients_OPyC = '1 -1.273e4 1.849e8'
    correlation_factor = -1.1824630660785265
  []
  [high_fidelity_strength_asphericity]
    type = ConstantFunction
    value = '1086690814.283'
  []
  [stress_correlation_asphericity]
    type = TRISOStressCorrelationFunction
    triso_geometry = particle_geometry
    polynomial_coefficients_IPyC = '1 -2070 3.458e7'
    polynomial_coefficients_SiC = '1 -868.9 -1.368e7'
    polynomial_coefficients_OPyC = '1 1734 -1.988e7'
    correlation_factor = 1.0626986695756293
  []
  [stress_change_correlation_asphericity]
    type = TRISOStressCorrelationFunction
    triso_geometry = particle_geometry
    polynomial_coefficients_IPyC = '1 -856 1.593e7'
    polynomial_coefficients_SiC = '1 1774 -5.253e7'
    polynomial_coefficients_OPyC = '1 456.4 -1.459e7'
    correlation_factor = 1.0113764663823708
  []
[]

[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 = 900
    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
  []
  [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
  []
  [weibull_failure_probability_IPyC]
    type = WeibullFailureProbability
    block = IPyC
    weibull_modulus = 9.5
    characteristic_strength = characteristic_strength
  []
  [weibull_failure_probability_SiC_crackedIPyC]
    type = WeibullFailureProbabilityUsingCorrelation
    block = SiC
    weibull_modulus = 6
    stress_name = stress_yy
    high_fidelity_analysis_strength = 'high_fidelity_strength_crackedIPyC'
    stress_correlation_function = 'stress_correlation_crackedIPyC'
  []
  [weibull_failure_probability_SiC]
    type = WeibullFailureProbabilityUsingCorrelation
    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'
  []
[]

[Outputs]
  show = 'weibull_failure_probability_IPyC weibull_failure_probability_SiC weibull_failure_probability_SiC_crackedIPyC'
  print_linear_residuals = false
  time_step_interval =  1
  csv = true
  exodus = false
  perf_graph = false
  print_linear_converged_reason = false
  print_nonlinear_converged_reason = false
[]

(examples/TRISO/correlation_function/h_asphericity/triso_asphericity_mortar.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
aspect_ratio = 1.04

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

initial_fuel_density = 10966

[GlobalParams]
  order = FIRST
  family = LAGRANGE
  displacements = 'disp_x disp_y'
  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 = RZ
  [mesh]
    type = TRISO2DMeshGenerator
    elem_type = quad4
    coordinates = '0 ${coordinates1} ${coordinates2} ${coordinates2} ${coordinates3} ${coordinates4} ${coordinates5}'
    mesh_density = '20 8 0 4 4 4'
    block_names = 'fuel buffer IPyC SiC OPyC'
    num_sectors = 60
    aspect_ratio = ${aspect_ratio}
    all_bottom_left = True
  []
[]

[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
    mesh_generator = mesh
    block = 'fuel buffer IPyC SiC OPyC'
  []
[]

[Variables]
  [temperature]
    initial_condition = 481
    block = 'fuel buffer IPyC SiC OPyC'
  []
[]

[AuxVariables]
  [fission_rate]
    order = CONSTANT
    family = MONOMIAL
    block = 'fuel buffer IPyC SiC OPyC'
  []
  [burnup]
    order = CONSTANT
    family = MONOMIAL
    block = 'fuel buffer IPyC SiC OPyC'
  []
  [fast_neutron_flux]
    order = CONSTANT
    family = MONOMIAL
    block = 'fuel buffer IPyC SiC OPyC'
  []
  [fast_neutron_fluence]
    order = CONSTANT
    family = MONOMIAL
    block = 'fuel buffer IPyC SiC OPyC'
  []
[]

[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
  []
[]

[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'
    block = 'fuel buffer IPyC SiC OPyC'
  []
  [heat]
    type = HeatConduction
    variable = temperature
    extra_vector_tags = 'ref'
    block = 'fuel buffer IPyC SiC OPyC'
  []
  [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
    block = 'fuel buffer IPyC SiC OPyC'
  []
  [fast_neutron_fluence]
    type = MaterialRealAux
    variable = fast_neutron_fluence
    property = fast_neutron_fluence
    execute_on = timestep_begin
    block = 'fuel buffer IPyC SiC OPyC'
  []
[]

[ThermalContactMortar]
  [thermal_contact]
    secondary_variable = temperature
    primary_boundary = IPyC_inner_boundary
    secondary_boundary = buffer_outer_boundary


    initial_moles = initial_moles # coupling to a postprocessor which supplies the initial plenum/gap gas mass
    gas_released = 'fis_gas_released'
    released_gas_types = 'Kr Xe'
    released_fractions = '0.185 0.815'
    gap_geometry_type = sphere
    sphere_origin = '0 0 0'
    min_gap = 1e-7
    max_gap = 50e-6
  []
[]

[BCs]
  [no_disp_x]
    type = DirichletBC
    variable = disp_x
    boundary = xzero
    value = 0.0
  []
  [no_disp_y]
    type = DirichletBC
    variable = disp_y
    boundary = bottom
    value = 0.0
  []
  [freesurf_temp]
    type = FunctionDirichletBC
    variable = temperature
    function = temp_bc
    boundary = exterior
  []
  [Pressure]
    [exterior]
      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]
  [normal_vectors_triso]
    type = NormalVectorsTRISO
    block = 'buffer IPyC OPyC'
    triso_geometry = particle_geometry
  []
  [tangential_stress]
    type = RankTwoCylindricalComponent
    rank_two_tensor = stress
    cylindrical_axis_point1 = '0 0 0'
    cylindrical_axis_point2 = '0 0 1'
    cylindrical_component = HoopStress
    property_name = tangential_stress
    outputs = all
    block = 'fuel buffer IPyC SiC OPyC'
  []
  [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 = ${initial_fuel_density}
    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 = ${initial_fuel_density}
  []
  [fission_gas_release]
    type = UCOFGR
    block = fuel
    average_grain_radius = 10e-6
    temperature = temperature
    triso_geometry = particle_geometry
  []
  [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 = 6e5
[]

[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'
     block = 'fuel buffer IPyC SiC OPyC'
  []
  [max_burnup]
     type = ElementExtremeValue
     variable = burnup
     block = fuel
     value_type = 'max'
     execute_on = 'initial timestep_end'
  []
  [SiC_stress]
    type = ElementalVariableValue
    elementid = 6300
    variable = tangential_stress
  []
  [strength_SiC]
     type = WeibullEffectiveMeanStrength
     block = SiC
     weibull_modulus = 6
  []
[]

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

(test/tests/triso_failure/ad_triso_1d_ipyc_weibull_probability.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
  [gen]
    type = TRISO1DMeshGenerator
    elem_type = EDGE3
    coordinates = '0 ${coordinates1} ${coordinates2} ${coordinates2} ${coordinates3} ${coordinates4} ${coordinates5}'
    mesh_density = '5 3 0 5 3 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
    IPyC_thickness_mean = 40.4e-6
    SiC_thickness_mean = 35.2e-6
    OPyC_thickness_mean = 43.4e-6
  []
[]

[Variables]
  [temperature]
    initial_condition = 900
  []
[]

[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 = ConstantFunction
    value = '1363350801.3058'
  []
  [stress_correlation_crackedIPyC]
    type = TRISOStressCorrelationFunction
    triso_geometry = particle_geometry
    polynomial_coefficients_IPyC = '1 7017 -2.368e8'
    polynomial_coefficients_SiC = '1 1.492e4 -3.802e7'
    polynomial_coefficients_OPyC = '1 -1.273e4 1.849e8'
    correlation_factor = -1.1824630660785265
  []
  [high_fidelity_strength_asphericity]
    type = ConstantFunction
    value = '1086690814.283'
  []
  [stress_correlation_asphericity]
    type = TRISOStressCorrelationFunction
    triso_geometry = particle_geometry
    polynomial_coefficients_IPyC = '1 -2070 3.458e7'
    polynomial_coefficients_SiC = '1 -868.9 -1.368e7'
    polynomial_coefficients_OPyC = '1 1734 -1.988e7'
    correlation_factor = 1.0626986695756293
  []
  [stress_change_correlation_asphericity]
    type = TRISOStressCorrelationFunction
    triso_geometry = particle_geometry
    polynomial_coefficients_IPyC = '1 -856 1.593e7'
    polynomial_coefficients_SiC = '1 1774 -5.253e7'
    polynomial_coefficients_OPyC = '1 456.4 -1.459e7'
    correlation_factor = 1.0113764663823708
  []
[]

[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'
    use_automatic_differentiation = true
  []
  [buffer]
    block = buffer
    eigenstrain_names = 'Buffer_IIDC_strain Buffer_TE_strain'
    extra_vector_tags = 'ref'
    use_automatic_differentiation = true
  []
  [IPyC]
    block = IPyC
    eigenstrain_names = 'IPyC_IIDC_strain IPyC_TE_strain'
    extra_vector_tags = 'ref'
    use_automatic_differentiation = true
  []
  [SiC]
    block = SiC
    eigenstrain_names = 'SiC_thermal_eigenstrain'
    extra_vector_tags = 'ref'
    use_automatic_differentiation = true
  []
  [OPyC]
    block = OPyC
    eigenstrain_names = 'OPyC_IIDC_strain OPyC_TE_strain'
    extra_vector_tags = 'ref'
    use_automatic_differentiation = true
  []
[]

[Kernels]
  [heat_ie]
    type = ADHeatConductionTimeDerivative
    variable = temperature
    extra_vector_tags = 'ref'
  []
  [heat]
    type = ADHeatConduction
    variable = temperature
    extra_vector_tags = 'ref'
  []
  [heat_source]
    type = ADNeutronHeatSource
    variable = temperature
    block = fuel
    fission_rate = fission_rate
    extra_vector_tags = 'ref'
  []
[]

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

[BCs]
  [no_disp_x]
    type = ADDirichletBC
    variable = disp_x
    boundary = xzero
    value = 0.0
  []
  [freesurf_temp]
    type = ADDirichletBC
    variable = temperature
    value = 900
    boundary = exterior
  []
  [exterior_pressure_x]
    type = ADPressure
    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
      use_automatic_differentiation = true
    []
  []
[]

[Materials]
  [fission_rate]
    type = ADGenericFunctionMaterial
    prop_names = fission_rate
    prop_values = fission_rate
    block = fuel
  []
  [fast_neutron_flux]
    type = ADFastNeutronFlux
    calculate_fluence = true
    factor = 6.2425e+17
  []
  [UCO_burnup]
    type = ADTRISOBurnup
    initial_density = 10966
    block = fuel
  []
  [UCO_thermal]
    type = ADUCOThermal
    block = fuel
    temperature = temperature
  []
  [UCO_elasticity_tensor]
    type = ADUCOElasticityTensor
    block = fuel
    temperature = temperature
  []
  [UCO_stress]
    type = ADComputeFiniteStrainElasticStress
    block = fuel
  []
  [UCO_VolumetricSwellingEigenstrain]
    type = ADUCOVolumetricSwellingEigenstrain
    block = fuel
    eigenstrain_name = UCO_swelling_eigenstrain
  []
  [fuel_thermal_expansion]
    type = ADComputeThermalExpansionEigenstrain
    block = fuel
    thermal_expansion_coeff = 10.0e-6
    temperature = temperature
    eigenstrain_name = UCO_TE_strain
  []
  [UCO_density]
    type = ADStrainAdjustedDensity
    block = fuel
    strain_free_density = 10966
  []
  [fission_gas_release]
    type = ADUCOFGR
    block = fuel
    average_grain_radius = 10e-6
    temperature = temperature
    triso_geometry = particle_geometry
    cutoff_neutron_flux = 0.0
  []
  [BAF_IPyC]
    type = ADBaconAnisotropyFactor
    initial_BAF = 1.0465
    block = IPyC
  []
  [BAF_OPyC]
    type = ADBaconAnisotropyFactor
    initial_BAF = 1.0429
    block = OPyC
  []
  [buffer_elasticity_tensor]
    type = ADBufferElasticityTensor
    block = buffer
    temperature = temperature
  []
  [buffer_stress]
    type = ADBufferCEGACreep
    block = buffer
    temperature = temperature
  []
  [buffer_thermal]
    type = ADBufferThermal
    block = buffer
    initial_density = 1050.0
  []
  [buffer_density]
    type = ADStrainAdjustedDensity
    block = buffer
    strain_free_density = 1050.0
  []
  [buffer_TE]
    type = ADBufferThermalExpansionEigenstrain
    block = buffer
    eigenstrain_name = Buffer_TE_strain
    temperature = temperature
  []
  [buffer_IIDC]
    type = ADBufferCEGAIrradiationEigenstrain
    block = buffer
    eigenstrain_name = Buffer_IIDC_strain
    temperature = temperature
  []
  [IPyC_elasticity_tensor]
    type = ADPyCElasticityTensor
    block = IPyC
    temperature = temperature
  []
  [IPyC_stress]
    type = ADPyCCEGACreep
    block = IPyC
    creep_rate_scale_factor = 1
    temperature = temperature
  []

  [IPyC_thermal]
    type = ADHeatConductionMaterial
    block = IPyC
    thermal_conductivity = 4.0
    specific_heat = 720.0
  []
  [IPyC_density]
    type = ADGenericConstantMaterial
    block = IPyC
    prop_names = 'density'
    prop_values = 1890
  []
  [normal_vectors_triso]
    type = NormalVectorsTRISO
    block = 'buffer IPyC OPyC'
  []
  [IPyC_IIDC]
    type = ADPyCCEGAIrradiationEigenstrain
    block = IPyC
    eigenstrain_name = IPyC_IIDC_strain
    temperature = temperature
    irradiation_eigenstrain_scale_factor = 1
  []
  [IPyC_TE]
    type = ADPyCThermalExpansionEigenstrain
    block = IPyC
    eigenstrain_name = IPyC_TE_strain
    temperature = temperature
  []
  [SiC_elasticity_tensor]
    type = ADMonolithicSiCElasticityTensor
    block = SiC
    temperature = temperature
    elastic_modulus_model = miller
  []
  [SiC_stress]
    type = ADComputeFiniteStrainElasticStress
    block = SiC
  []
  [SiC_thermal]
    type = ADMonolithicSiCThermal
    block = SiC
    temperature = temperature
    thermal_conductivity_model = miller
  []
  [SiC_density]
    type = ADStrainAdjustedDensity
    block = SiC
    strain_free_density = 3200.0
  []
  [SiC_thermal_expansion]
    type = ADComputeThermalExpansionEigenstrain
    block = SiC
    thermal_expansion_coeff = 4.9e-6
    temperature = temperature
    eigenstrain_name = SiC_thermal_eigenstrain
  []
  [OPyC_elasticity_tensor]
    type = ADPyCElasticityTensor
    block = OPyC
    temperature = temperature
    initial_BAF = 1.0
  []
  [OPyC_stress]
    type = ADPyCCEGACreep
    block = OPyC
    creep_rate_scale_factor = 1
    temperature = temperature
  []
  [OPyC_thermal_conductivity]
    type = ADHeatConductionMaterial
    block = OPyC
    thermal_conductivity = 4.0
    specific_heat = 720.0
  []
  [OPyC_density]
    type = ADGenericConstantMaterial
    block = OPyC
    prop_names = 'density'
    prop_values = 1900
  []
  [OPyC_IIDC]
    type = ADPyCCEGAIrradiationEigenstrain
    block = OPyC
    eigenstrain_name = OPyC_IIDC_strain
    temperature = temperature
    irradiation_eigenstrain_scale_factor = 1
  []
  [OPyC_TE]
    type = ADPyCThermalExpansionEigenstrain
    block = OPyC
    eigenstrain_name = OPyC_TE_strain
    temperature = temperature
  []
  [characteristic_strength_SiC]
    type = ADGenericConstantMaterial
    prop_values = '9640000'
    block = SiC
    prop_names = 'characteristic_strength'
  []
  [characteristic_strength_PyC]
    type = ADPyCCharacteristicStrength
    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 = ADElementIntegralMaterialProperty
    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 = ADVoidVolume
    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 = ADVoidVolume
    block = fuel
    theoretical_density = kernel_th_density
    execute_on = 'initial timestep_end'
    use_displaced_mesh = true
  []
  [particle_power]
    type = ADElementIntegralPower
    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 = ADElementExtremeMaterialProperty
    block = SiC
    value_type = min
    mat_prop = stress_yy
  []
  [weibull_failure_probability_IPyC]
    type = ADWeibullFailureProbability
    block = IPyC
    weibull_modulus = 9.5
    characteristic_strength = characteristic_strength
  []
  [weibull_failure_probability_SiC_crackedIPyC]
    type = ADWeibullFailureProbabilityUsingCorrelation
    block = SiC
    weibull_modulus = 6
    stress_name = stress_yy
    high_fidelity_analysis_strength = 'high_fidelity_strength_crackedIPyC'
    stress_correlation_function = 'stress_correlation_crackedIPyC'
  []
  [weibull_failure_probability_SiC]
    type = ADWeibullFailureProbabilityUsingCorrelation
    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'
  []
[]

[Outputs]
  show = 'weibull_failure_probability_IPyC weibull_failure_probability_SiC weibull_failure_probability_SiC_crackedIPyC'
  print_linear_residuals = false
  time_step_interval =  1
  csv = true
  exodus = false
  perf_graph = false
  print_linear_converged_reason = false
  print_nonlinear_converged_reason = false
[]

(examples/TRISO/correlation_function/h_asphericity/triso_asphericity.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
aspect_ratio = 1.04

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

initial_fuel_density = 10966

[GlobalParams]
  order = FIRST
  family = LAGRANGE
  displacements = 'disp_x disp_y'
  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 = RZ
  [mesh]
    type = TRISO2DMeshGenerator
    elem_type = quad4
    coordinates = '0 ${coordinates1} ${coordinates2} ${coordinates2} ${coordinates3} ${coordinates4} ${coordinates5}'
    mesh_density = '20 8 0 4 4 4'
    block_names = 'fuel buffer IPyC SiC OPyC'
    num_sectors = 60
    aspect_ratio = ${aspect_ratio}
    all_bottom_left = True
  []
[]

[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
    mesh_generator = mesh
  []
[]

[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
  []
[]

[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
    sphere_origin = '0 0 0'
  []
[]

[BCs]
  [no_disp_x]
    type = DirichletBC
    variable = disp_x
    boundary = xzero
    value = 0.0
  []
  [no_disp_y]
    type = DirichletBC
    variable = disp_y
    boundary = bottom
    value = 0.0
  []
  [freesurf_temp]
    type = FunctionDirichletBC
    variable = temperature
    function = temp_bc
    boundary = exterior
  []
  [Pressure]
    [exterior]
      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]
  [tangential_stress]
    type = RankTwoCylindricalComponent
    rank_two_tensor = stress
    cylindrical_axis_point1 = '0 0 0'
    cylindrical_axis_point2 = '0 0 1'
    cylindrical_component = HoopStress
    property_name = tangential_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 = ${initial_fuel_density}
    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 = ${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
  []
  [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
  []
  [normal_vectors_triso]
    type = NormalVectorsTRISO
    block = 'buffer IPyC OPyC'
    triso_geometry = particle_geometry
  []
  [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 = 6e5
[]

[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 = ElementalVariableValue
    elementid = 6300
    variable = tangential_stress
  []
  [strength_SiC]
     type = WeibullEffectiveMeanStrength
     block = SiC
     weibull_modulus = 6
  []
[]

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

(examples/TRISO/failure_probability_direct_integration/triso_1d.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}'

initial_fuel_density = 10966

[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 = TRISO1DMeshGenerator
    elem_type = EDGE3
    coordinates = '0 ${coordinates1} ${coordinates2} ${coordinates2} ${coordinates3} ${coordinates4} ${coordinates5}'
    mesh_density = '5 3 0 5 3 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
    IPyC_thickness_mean = 40.4e-6
    SiC_thickness_mean = 35.2e-6
    OPyC_thickness_mean = 43.4e-6
  []
[]

[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 = '1363350801.3058'
  []
  [stress_correlation_crackedIPyC]
    type = TRISOStressCorrelationFunction
    triso_geometry = particle_geometry
    polynomial_coefficients_IPyC = '1 7017 -2.368e8'
    polynomial_coefficients_SiC = '1 1.492e4 -3.802e7'
    polynomial_coefficients_OPyC = '1 -1.273e4 1.849e8'
    correlation_factor = -1.1824630660785265
  []
  [high_fidelity_strength_asphericity]
    type = ConstantFunction
    value = '1086690814.283'
  []
  [stress_correlation_asphericity]
    type = TRISOStressCorrelationFunction
    triso_geometry = particle_geometry
    polynomial_coefficients_IPyC = '1 -2070 3.458e7'
    polynomial_coefficients_SiC = '1 -868.9 -1.368e7'
    polynomial_coefficients_OPyC = '1 1734 -1.988e7'
    correlation_factor = 1.0626986695756293
  []
  [stress_change_correlation_asphericity]
    type = TRISOStressCorrelationFunction
    triso_geometry = particle_geometry
    polynomial_coefficients_IPyC = '1 -856 1.593e7'
    polynomial_coefficients_SiC = '1 1774 -5.253e7'
    polynomial_coefficients_OPyC = '1 456.4 -1.459e7'
    correlation_factor = 1.0113764663823708
  []
[]

[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]
  [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 = ${initial_fuel_density}
    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 = ${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
  []
  [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

  #num_steps = 1

  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
  []
  [weibull_failure_probability_IPyC]
    type = WeibullFailureProbability
    block = IPyC
    weibull_modulus = 9.5
    characteristic_strength = characteristic_strength
  []
  [weibull_failure_probability_SiC_crackedIPyC]
    type = WeibullFailureProbabilityUsingCorrelation
    block = SiC
    weibull_modulus = 6
    stress_name = stress_yy
    high_fidelity_analysis_strength = 'high_fidelity_strength_crackedIPyC'
    stress_correlation_function = 'stress_correlation_crackedIPyC'
  []
  [weibull_failure_probability_SiC]
    type = WeibullFailureProbabilityUsingCorrelation
    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'
  []
[]

[Outputs]
  show = 'weibull_failure_probability_IPyC weibull_failure_probability_SiC weibull_failure_probability_SiC_crackedIPyC'
  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
[]

(test/tests/triso/buffer_thermal_material/buffer_k_UK.i)

# Thermal Conductivity of the Buffer
# The geometry is a cube (edge length = 5 cm) made of buffer material (initial density = 1.0 g/cm$^{3}$) subject to internal heat generation.
# The density is varied from 1000 to 2240 kg/m$^{3}$ using a FunctionAux auxkernel.
#
# The thermal conductivity computed by Bison and the exact value are reported and match.

[GlobalParams]
  order = FIRST
  family = LAGRANGE
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 3
    xmin = 0.0
    xmax = 0.05
    ymin = 0.0
    ymax = 0.05
    zmin = 0.0
    zmax = 0.05
  []
[]

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

[Variables]
  [temp]
    initial_condition = 673.15
  []
[]

[AuxVariables]
  [density]
    order = CONSTANT
    family = MONOMIAL
  []
  [thermal_conductivity]
    order = CONSTANT
    family = MONOMIAL
  []
  [k_exact]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [power_history]
    type = PiecewiseLinear
    x = '0     1e4     1e8'
    y = '0 1.25e16 1.25e16'
  []
  [density]
    type = PiecewiseLinear
    x = '   0 1000'
    y = '1000 2240'
  []
  [temp_func]
    type = PiecewiseLinear
    x = '  0    1000'
    y = '673.15 1673.15'
  []
[]

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

[AuxKernels]
  [density]
    type = MaterialRealAux
    variable = density
    property = density
    block = '0'
    execute_on = 'initial linear'
  []
  [thermal_conductivity]
    type = MaterialRealAux
    variable = thermal_conductivity
    property = thermal_conductivity
    execute_on = timestep_end
  []
  [k_exact]
    type = MaterialRealAux
    variable = k_exact
    property = k_exact
    execute_on = timestep_end
  []
[]

[BCs]
  [temp_BC]
    type = FunctionDirichletBC
    variable = temp
    boundary = 'right'
    function = temp_func
  []
[]

[Materials]
  [Buffer_thermal_conductivity]
    type = BufferThermal
    thermal_conductivity_scale_factor = 1.0
    specific_heat_scale_factor = 1.0e-6
    initial_density = 1000
    thermal_conductivity_model = UK
  []
  [k_exact]
    type = ParsedMaterial
    property_name = k_exact
    material_property_names = density
    expression = 'p := (2250-density)/2250;
                  10.98222 * (1 - p) / (1 + 2 * p) + 0.00444'
  []
  [Buffer_density]
    type = GenericFunctionMaterial
    prop_names = 'density'
    prop_values = 'density'
  []
[]

[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_max_its = 50
  l_tol = 1e-2

  nl_max_its = 150
  nl_rel_tol = 1e-4
  nl_abs_tol = 1e-6

  start_time = 0.0
  end_time = 1000
  dt = 100
  num_steps = 10

  dtmax = 2e6
  dtmin = 1e-6
[]

[Postprocessors]
  [thermal_conductivity]
    type = ElementAverageValue
    variable = thermal_conductivity
    execute_on = 'initial timestep_end'
  []
  [k_exact]
    type = ElementAverageValue
    variable = k_exact
    execute_on = 'initial timestep_end'
  []
  [density]
    type = ElementAverageValue
    variable = density
    execute_on = 'initial timestep_end'
  []
[]

[Outputs]
  csv = true
  exodus = false
  [console]
    type = Console
  []
[]

(test/tests/triso/buffer_creep/buffer_creep.i)

#Irradiation-induced Creep Properties of the Buffer
#The geometry is a cube (edge length = 5 cm) made of buffer material (initial density = 1.0 g/cm^3) subject to creep.
#A pressure boundary condition of 50 MPa is applied to one side to induce a constant stress in the x-axis.
#The Poisson's ratio in creep is equal to 0.5.
#The temperature is constant and equal to 1273.15 K.
#The fast neutron flux (E>0.10 MeV) is ramped linearly from 0 to 7.5e18 n/m^2-s over 1e4 seconds and then remains constant.
#Since the stress is constant, the creep rate can be approximated as K * sigma * flux * flux_conversion_factor. With K = 8.5265e-35, sigma = -5e7 N/m^2,
# flux = 7.5e18 n/m2-s and flux_conversion_factor = 0.85, creep rate calculated as 2.7178e-08 1/s.
#At time = 7.5e6 seconds, the analytical creep strain is -0.2038.

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
  volumetric_locking_correction = true
  order = FIRST
  family = LAGRANGE
  flux_conversion_factor = 0.85
[]

[Mesh]
  [gen]
    type = GeneratedMeshGenerator
    dim = 3
    xmin = 0.0
    xmax = 0.05
    ymin = 0.0
    ymax = 0.05
    zmin = 0.0
    zmax = 0.05
  []
[]

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

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [disp_z]
  []
  [temp]
    initial_condition = 1273.15
  []
[]

[AuxVariables]
  [fast_neutron_fluence]
    order = CONSTANT
    family = MONOMIAL
  []
  [density]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [flux_history]
    type = PiecewiseLinear
    x = '0    1e4    1e8'
    y = '0 7.5e18 7.5e18'
  []
  [pressure_ramp]
    type = PiecewiseLinear
    x = '0 1e3'
    y = '0 1'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [perm_Buffer]
    strain = FINITE
    eigenstrain_names = ' '
    generate_output = 'vonmises_stress stress_xx stress_yy stress_zz creep_strain_xx'
    extra_vector_tags = 'ref'
  []
[]

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

[AuxKernels]
  [fast_neutron_fluence]
    type = MaterialRealAux
    variable = fast_neutron_fluence
    property = fast_neutron_fluence
    block = '0'
    execute_on = timestep_begin
  []
  [density]
    type = MaterialRealAux
    variable = density
    property = density
    block = '0'
    execute_on = 'initial timestep_end'
  []
[]

[BCs]
  [no_z_all]
    type = DirichletBC
    variable = disp_z
    boundary = 'back'
    value = 0
  []
  [no_y_all]
    type = DirichletBC
    variable = disp_y
    boundary = 'bottom'
    value = 0
  []
  [no_x_all]
    type = DirichletBC
    variable = disp_x
    boundary = 'right'
    value = 0
  []
  [Pressure]
    [appliedPressure]
      boundary = 'left'
      factor = 50e6
      function = pressure_ramp
    []
  []
  [heat_removal]
    type = DirichletBC
    variable = temp
    boundary = 'back bottom right'
    value = 1273.15
  []
[]

[Materials]
  [flux]
    type = FastNeutronFlux
    calculate_fluence = true
    flux_function = flux_history
  []
  [normal_vectors_triso]
    type = NormalVectorsTRISO
    normal_x = 1
    normal_y = 0
    normal_z = 0
  []
  [Buffer_stress]
    type = BufferCEGACreep
    temperature = temp
  []

  [Buffer_elasticity_tensor]
    type = BufferElasticityTensor
    temperature = temp
  []

  [buffer_thermal]
    type = BufferThermal
    initial_density = 1000
  []

  [Buffer_density]
    type = StrainAdjustedDensity
    strain_free_density = 1000.0
  []
[]

[Dampers]
  [limitT]
    type = MaxIncrement
    max_increment = 200.0
    variable = temp
  []

  [limitX]
    type = MaxIncrement
    max_increment = 1e-4
    variable = disp_x
  []

  [limitY]
    type = MaxIncrement
    max_increment = 1e-4
    variable = disp_y
  []

  [limitZ]
    type = MaxIncrement
    max_increment = 1e-4
    variable = disp_z
  []
[]

[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'

  l_max_its = 50
  l_tol = 1e-2

  nl_max_its = 150
  nl_rel_tol = 1e-08
  nl_abs_tol = 1e-7

  start_time = 0.0
  end_time = 7.5e6
  num_steps = 140


  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 1e6
    time_t = '1e4 1e5'
    time_dt = '1e6 1e6'
  []
[]

[Postprocessors]
  [temp]
    type = ElementAverageValue
    variable = temp
    execute_on = 'initial timestep_end'
  []

  [fluence]
    type = ElementAverageValue
    variable = fast_neutron_fluence
    execute_on = 'initial timestep_end'
  []

  [disp_x_max]
    type = NodalExtremeValue
    variable = disp_x
    execute_on = 'initial timestep_end'
  []

  [sigma_x_max]
    type = ElementAverageValue
    variable = stress_xx
    execute_on = 'initial timestep_end'
  []

  [creep_strain_xx]
    type = ElementAverageValue
    variable = creep_strain_xx
    execute_on = 'initial timestep_end'
  []

  [density]
    type = ElementAverageValue
    variable = density
    execute_on = 'initial timestep_end'
  []
[]

[Outputs]
  csv = true
  exodus = false
  [console]
    type = Console
  []
[]

Description
Example Input Syntax
Input Parameters
Input Files
References