CarbonMonoxideProduction

Computes CO production in oxide fuel based on the Proksch or GA correlation.

This Postprocessor computes carbon monoxide production in an oxide fuel block. The following two models are implemented: Proksch and GA. The GA and Proksch models only apply to a UO $var element = document.getElementById("moose-equation-5d346164-d9e2-4737-afb1-efc48a92a0e4");katex.render("_2", element, {displayMode:false,throwOnError:false});$ fuel kernel.

warning

The GA model expects the surface temperature of the fuel kernel while the Proksch model expects the TRISO particle surface temperature.

GA model

The CO yield (atoms/fission) is given by (Kovacs et al., 1985):

$var element = document.getElementById("moose-equation-b2aafc91-40b8-4c3f-901f-6c5178392677");katex.render("CO_{prod} = min(0.625,1.64\\times\\exp\\frac{-3311}{T})", element, {displayMode:true,throwOnError:false});$

It has a 0.625 limit (taken from PARFUME) while the original reference has a 0.61 limit. It is used primarily for comparison to historic evaluations. It applies only to UO $var element = document.getElementById("moose-equation-ab7255e4-066d-4ec8-8bec-c40763961315");katex.render("_2", element, {displayMode:false,throwOnError:false});$ .

Proksch model

The Proksch model uses the empirical correlation from Proksch (Proksch et al., 1982). It only applies to UO $var element = document.getElementById("moose-equation-0b0207a8-e919-4e54-abd3-b0a4db619cd3");katex.render("_2", element, {displayMode:false,throwOnError:false});$ . Equation 1 in this paper is:

$var element = document.getElementById("moose-equation-04bdba71-3966-43bf-966d-2798e75f12e9");katex.render(" \\log{\\frac{(O/F)}{t^2}} = -0.21 - \\frac{8500}{T}", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-b936a6a9-048e-404a-a4f1-1d501c3d0db1");katex.render("O/F", element, {displayMode:false,throwOnError:false});$ is the oxygen release at the end of irradiation (atoms/fission), $var element = document.getElementById("moose-equation-249f72f8-1a07-419f-92cc-f45172eea3d3");katex.render("t", element, {displayMode:false,throwOnError:false});$ is the irradiation time (days), and $var element = document.getElementById("moose-equation-b6643f39-68d0-45b3-9320-6d9149bd6cae");katex.render("T", element, {displayMode:false,throwOnError:false});$ is the time averaged particle surface temperature (K).

Converting time to seconds and solving for $var element = document.getElementById("moose-equation-5650fb2e-b07c-42b8-8643-f639390e4743");katex.render("(O/F)", element, {displayMode:false,throwOnError:false});$ : $var element = document.getElementById("moose-equation-122df9a6-6bf9-44cd-8bef-c0d7d865a26e");katex.render("O/F = \\frac{t^2}{(1.211\\times 10^{10}) 10^{8500/(\\textrm{timeIntSurfTemp}/t)}}", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-73a1f2a3-4721-48ce-8030-0e86bcfb0985");katex.render("t", element, {displayMode:false,throwOnError:false});$ is the irradiation time and $var element = document.getElementById("moose-equation-b084e4b4-9328-4208-85cb-87aae1c2476c");katex.render("\\textrm{timeIntSurfTemp}", element, {displayMode:false,throwOnError:false});$ is the time integrated surface temperature of the TRISO particle (from coupled post processor). (Note that to get the time averaged surface temperature, the time integrated surface temperature is divided by total time.)

The Proksch paper further explains that the $var element = document.getElementById("moose-equation-556ec081-479c-4ac2-b206-14c33c16e97a");katex.render("(O/F)", element, {displayMode:false,throwOnError:false});$ ratio is diffusion limited at an equilibrium maximum value given by Equation 2: $var element = document.getElementById("moose-equation-8701129c-a680-40fc-8a20-28a19fe25964");katex.render(" O/F = 0.4 f_u + 0.85 f_{pu}", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-e8d84cce-9594-442c-bbbf-9f417b155a9f");katex.render("f_u", element, {displayMode:false,throwOnError:false});$ is the fission fraction of U $var element = document.getElementById("moose-equation-61263a8a-baf7-4493-bb0e-6d22eff734f6");katex.render("_{235}", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-e7a1532a-83db-4084-a0d1-74d0b259ef45");katex.render("f_{pu}", element, {displayMode:false,throwOnError:false});$ is the fission fraction of Pu $var element = document.getElementById("moose-equation-f82be5ed-20ad-4173-b24e-67325628a8de");katex.render("_{239}", element, {displayMode:false,throwOnError:false});$ plus Pu $var element = document.getElementById("moose-equation-0c2c6891-e79d-4d56-b2fc-85185627e3a6");katex.render("_{241}", element, {displayMode:false,throwOnError:false});$ .

Only U $var element = document.getElementById("moose-equation-e6288466-1f12-4b77-9cdb-c47c944be0bb");katex.render("_{235}", element, {displayMode:false,throwOnError:false});$ fissions are included here ( $var element = document.getElementById("moose-equation-34e3396b-c6ee-4d78-8d68-d90923bd485a");katex.render("f_u", element, {displayMode:false,throwOnError:false});$ = 1, $var element = document.getElementById("moose-equation-0a103d3d-98ae-47aa-bcad-610a6ea13fe8");katex.render("f_{pu}", element, {displayMode:false,throwOnError:false});$ = 0) such that $var element = document.getElementById("moose-equation-3ffd64ed-efb2-4adf-a140-4d1344d04d93");katex.render("(O/F)", element, {displayMode:false,throwOnError:false});$ is limited to 0.4.

Assuming all the oxygen forms carbon monoxide, CO yield $var element = document.getElementById("moose-equation-50878acb-abaf-430c-be37-3c6fab10c9d3");katex.render("CO_{prod} = O/F", element, {displayMode:false,throwOnError:false});$ .

CO Production

Assuming each oxygen atom combines with a carbon atom, and expressing the CO produced in moles: $var element = document.getElementById("moose-equation-36bd505e-855c-43f3-b9b2-854ea90763ee");katex.render(" CO_{moles} = CO_{prod} * \\text{totalFissions} / \\text{AvogadrosNumber}", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-53613566-d083-488e-b5f9-e1e5260ef705");katex.render("\\textrm{totalFissions}", element, {displayMode:false,throwOnError:false});$ is the time and volume integration of the fission density rate (from a coupled post processor).

Example Input Syntax

[Postprocessors<<<{"href": "../../syntax/Postprocessors/index.html"}>>>]
  [co_production]
    type = CarbonMonoxideProduction<<<{"description": "Computes CO production in oxide fuel based on the Proksch or GA correlation.", "href": "CarbonMonoxideProduction.html"}>>>
    total_fissions<<<{"description": "The name of the postprocessor containing the total fissions."}>>> = total_fissions
    initial_enrichment<<<{"description": "initial enrichment fraction of U235 (wt%)"}>>> = 0.14029
    execute_on<<<{"description": "The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html."}>>> = 'initial timestep_end'
  []
[]

Input Files

(test/tests/triso_failure/triso_1d_failure_error.i)
(assessment/TRISO/benchmark/IAEA_CRP-6/fuel_performance/case_9/case_9_1D.i)
(assessment/TRISO/benchmark/IAEA_CRP-6/fuel_performance/case_13/case_13_1D.i)
(test/tests/triso_failure/triso_ipyc_characteristic_strength.i)
(examples/TRISO/accident_simulation/triso2D_accident.i)
(test/tests/triso/base_irradiation/triso1D_accident.i)
(test/tests/triso_failure/ad_ipyc_characteristic_strength.i)
(test/tests/triso_failure/triso_1d_ipyc_failure.i)
(test/tests/triso_failure/triso_1d_layer_stress_strength.i)
(examples/TRISO/full_particle/1D/full_particle_1D.i)
(test/tests/carbon_monoxide_production/carbon_monoxide_production_test.i)
(examples/TRISO/accident_simulation/triso2D_accident_mortar.i)
(test/tests/triso_failure/triso_1d_pd_penetration.i)
(test/tests/triso_failure/ad_triso_1d_weibull_probability.i)
(test/tests/triso_failure/sub.i)
(examples/TRISO/full_particle/2D/full_particle.i)
(test/tests/triso_failure/triso_1d_asphericity_failure.i)
(test/tests/triso_failure/ad_triso_1d_failure.i)
(test/tests/triso_failure/triso_1d_weibull_probability.i)
(assessment/TRISO/benchmark/IAEA_CRP-6/fuel_performance/case_11/case_11_1D.i)
(test/tests/triso_failure/triso_1d_failure.i)
(examples/TRISO/accident_simulation/triso1D_accident.i)
(test/tests/triso/base_irradiation/triso1D_accident_action.i)
(examples/NuclearMaterialActions/TRISO/full_particle_action.i)
(examples/TRISO/accident_simulation/triso2D_accident_ad.i)
(assessment/TRISO/benchmark/IAEA_CRP-6/fuel_performance/case_10/case_10_1D.i)

References

William J. Kovacs, Karl Bongartz, and Dan T. Goodin. High-temperature gas-cooled reactor fuel pressure vessel performance models. Nuclear Technology, 68(3):344–354, 1985. doi:10.13182/NT85-A33580.

@article{Kovacs:1985,
    author = "Kovacs, William J. and Bongartz, Karl and Goodin, Dan T.",
    title = "High-Temperature Gas-Cooled Reactor Fuel Pressure Vessel Performance Models",
    journal = "Nuclear Technology",
    volume = "68",
    number = "3",
    pages = "344-354",
    year = "1985",
    publisher = "Taylor \& Francis",
    doi = "10.13182/NT85-A33580"
}

E. Proksch, A. Strigl, and H Nabielek. Production of carbon monoxide during burn-up of $\mathrm UO_2$ kerneled HTR fuel particles. Journal of Nuclear Material, 107:280–285, 1982.

@ARTICLE{proksch:1982,
    author = "Proksch, E. and Strigl, A. and Nabielek, H",
    title = "Production of Carbon Monoxide During Burn-up of $\mathrm{UO}\_2$ Kerneled {HTR} Fuel Particles",
    journal = "Journal of Nuclear Material",
    year = "1982",
    volume = "107",
    pages = "280-285"
}

(test/tests/carbon_monoxide_production/carbon_monoxide_production_test.i)

# Tests the carbon monoxide production postprocessor

# A constant volumetric fission rate of 1e19 fissions/m^3-s is applied to a 1 cm cube.
# All sides of the cube are held at 1000K to force a constant average surface temperature.
# The problem is solved over ten time steps of 1e7 s.
#
# The total number of fissions is computed using:
#   1) the ElementIntegralPower post processor and specifying energy_per_fission = 1 to
#      get the total fission rate
#   2) the TimeIntegratedPostprocessor post processor to time integrate the total fission rate
#
# The time integrated particle surface temperature is computed using:
#   1) the SideAverageValue post processor to give the time dependent average temperature
#      over the particle surface
#   2) the TimeIntegratedPostprocessor post processor to give the time integrated average temperature
#      over the particle surface
#
#    At t=1e8 (after ten time steps)
#       _total_fissions = 1e19(fissions/m^3-s)*(0.01m)**3*1e8
#                       = 1e21 fissions
#       _time_avg_surf_temp = _time_int_surf_temp/total_time
#                           = 1e11/1e8
#                           = 1000K
#
# 1. For the Proksch model, the moles of oxygen (and thus carbon monoxide) are given by:
#
#   moles CO = [_total_fissions*_t^2/((1.211e10)*10^(8500/(_time_avg_surf_temp))] / Avogadros_number
#
#       moles co = (1e21*1e8^2/((1.211e10)*10^(8500/1000))) / 6.02214076e23
#                = 4.336156561E-06 moles
#
#       which is what the post processor gets
#
# 2. For the GA model, the moles of oxygen are given by:
#
# moles co = (1.64*exp(-3311/1000)) * 1e21 / 6.02214076e23 = 9.934452008E-05
#

[Mesh]
  [mesh]
    type = FileMeshGenerator
    file = cube_1cm.e
  []
[]

[Variables]
  [T]
    order = FIRST
    family = LAGRANGE
    initial_condition = 1000
  []
[]

[AuxVariables]

  [fission_rate]
    order = FIRST
    family = LAGRANGE
  []
[]

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

  [ie]
    type = HeatConductionTimeDerivative
    variable = T
  []

  [heat_source]
    type = NeutronHeatSource
    variable = T
    energy_per_fission = 3.2e-11
    fission_rate = fission_rate
  []
[]

[AuxKernels]

  [fissionrate]
    type = FissionRateGeneral
    fission_rate_formulation = GENERIC
    variable = fission_rate
    value = 1.0e19
    execute_on = 'initial timestep_begin'
  []
[]

[BCs]

  [bottom_T]
    type = DirichletBC
    variable = T
    boundary = '1 2 3 4 5 6'
    value = 1000.0
  []
[]

[Materials]

  [fuel]
    type = HeatConductionMaterial
    block = 1
    thermal_conductivity = 10
    specific_heat = 100
  []
  [density]
    type = ParsedMaterial
    block = 1
    property_name = density
    expression = 10000
  []
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'

  nl_abs_tol = 1e-10
  nl_rel_tol = 1e-8
  start_time = 0.0
  num_steps = 10
  dt = 1.0e7
[]

[Postprocessors]
  [total_fission_rate]
    type = ElementIntegralPower
    variable = T
    fission_rate = fission_rate
    block = 1
    energy_per_fission = 1.0
    execute_on = 'initial timestep_end'
  []

  [total_fissions]
    type = TimeIntegratedPostprocessor
    value = total_fission_rate
  []

  [avg_surface_temp]
    type = SideAverageValue
    variable = T
    boundary = '1 2 3 4 5 6'
    execute_on = 'initial timestep_end'
  []

  [time_int_surf_temp]
    type = TimeIntegratedPostprocessor
    value = avg_surface_temp
    execute_on = 'initial timestep_end'
  []

  [co_production]
    type = CarbonMonoxideProduction
    total_fissions = total_fissions
    initial_enrichment = 0.14029
    execute_on = 'initial timestep_end'
  []
[]

[Outputs]
  csv = true
[]

(test/tests/triso_failure/triso_1d_failure_error.i)

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

[Mesh]
  coord_type = RSPHERICAL
  [gen]
    type = TRISO1DMeshGenerator
    elem_type = EDGE3
    coordinates = '0 2.485e-4 3.425e-4 3.425e-4 3.835e-4 4.195e-4 4.595e-4'
    mesh_density = '6 6 0 6 8 6'
    block_names = 'fuel buffer IPyC SiC OPyC'
  []
[]

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

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

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

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

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

[AuxKernels]
  [stress_yy]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_yy
    index_i = 1
    index_j = 1
    execute_on = timestep_end
  []
  [fast_neutron_flux]
    type = FastNeutronFluxAux
    variable = fast_neutron_flux
    factor = 1.708707e18 # n/m^2-sec
  []
  [fast_neutron_fluence]
    type = FastNeutronFluenceAux
    variable = fast_neutron_fluence
    fast_neutron_flux = fast_neutron_flux
  []
  [fission_rate]
    type = FunctionAux
    variable = fission_rate
    block = fuel
    function = fission_rate
  []
  [burnup]
    type = BurnupAux
    variable = burnup
    block = fuel
    fission_rate = fission_rate
    molecular_weight = 0.270
  []
[]

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

[ThermalContact]
  [thermal_contact]
    type = GasGapHeatTransfer
    variable = temperature
    primary = IPyC_inner_boundary
    secondary = buffer_outer_boundary
    # coupling to a postprocessor
    initial_moles = initial_moles
    gas_released = 'fis_gas_released co_production'
    released_gas_types = 'Kr Xe;
                          CO'
    released_fractions = '0.153 0.847;
                          1'
    tangential_tolerance = 1e-6
    #    contact_pressure_input = 10e6
    #    quadrature = true
  []
[]

[BCs]
  [no_disp_x]
    type = DirichletBC
    variable = disp_x
    boundary = xzero
    value = 0.0
  []
  [freesurf_temperature]
    type = DirichletBC
    variable = temperature
    boundary = exterior
    value = 1346.0
  []
  [exterior_pressure_x]
    type = Pressure
    use_displaced_mesh = false
    variable = disp_x
    boundary = exterior
    factor = 0.1e6
  []
  [PlenumPressure]
    #  apply gas pressure on buffer and IPyC boundaries
    [plenumPressure]
      use_displaced_mesh = false
      boundary = buffer_IPyC_boundary
      initial_pressure = 0
      startup_time = 1.0e4
      # coupling to post processor
      output_initial_moles = initial_moles
      temperature = ave_temperature_interior
      volume = volumeGas
      material_input = 'fis_gas_released co_production'
      output = plenum_pressure
    []
  []

[]

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

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

[Debug]
  show_var_residual_norms = true
[]

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

[Postprocessors]
  [dt]
    type = TimestepSize
  []
  [burnup]
    type = ElementExtremeValue
    block = fuel
    variable = burnup
  []
  [fis_gas_produced]
    type = ElementIntegralFisGasGeneratedSifgrs
    block = fuel
  []
  [fis_gas_released]
    type = ElementIntegralFisGasReleasedSifgrs
    block = fuel
  []
  [volumeTotal]
    type = InternalVolume
    boundary = exterior
  []
  [volumeFuel]
    type = InternalVolume
    boundary = fuel_outer_boundary
  []
  [volumeGas]
    type = InternalVolume
    boundary = 'fuel_outer_boundary IPyC_inner_boundary'
    addition = -5.53e-11
    execute_on = 'initial timestep_end'
  []
  [volumeBufferShell]
    type = InternalVolume
    boundary = buffer_IPyC_boundary
  []
  [ave_temperature_interior]
    type = SideAverageValue
    boundary = buffer_IPyC_boundary
    variable = temperature
    execute_on = 'initial timestep_end'
  []
  [total_fission_rate]
    type = ElementIntegralPower
    variable = temperature
    fission_rate = fission_rate
    block = fuel
    energy_per_fission = 1.0
  []
  [total_fissions]
    type = TimeIntegratedPostprocessor
    value = total_fission_rate
  []
  [avg_surface_temperature]
    type = SideAverageValue
    variable = temperature
    boundary = exterior
  []
  [time_int_surf_temperature]
    type = TimeIntegratedPostprocessor
    value = avg_surface_temperature
  []
  [co_production]
    type = CarbonMonoxideProduction
    total_fissions = total_fissions
    time_integrated_triso_temperature = time_int_surf_temperature
    initial_enrichment = 0.14029
  []
  [tang_SiC]
    type = ElementalVariableValue
    variable = stress_yy
    elementid = 18
  []
  [strength_SiC]
    type = WeibullEffectiveMeanStrength
    block = SiC
    weibull_modulus = 6
    characteristic_strength = characteristic_strength_SiC
  []
  [failure_indicator_SiC]
    type = WeibullFailureOutputUsingCorrelation
    block = SiC
    weibull_modulus = 6
  []
  [strength_IPyC]
    type = WeibullEffectiveMeanStrength
    block = IPyC
    weibull_modulus = 6
    characteristic_strength = characteristic_strength_IPyC
  []
  [failure_indicator_IPyC]
    type = WeibullFailureOutputUsingCorrelation
    block = IPyC
    weibull_modulus = 6
    stress_type = scalar_quantity
    scalar_type = MaxPrincipal
    effective_mean_strength = strength_IPyC
  []
  [strength_OPyC]
    type = WeibullEffectiveMeanStrength
    block = OPyC
    weibull_modulus = 6
    characteristic_strength = characteristic_strength_OPyC
  []
  [failure_indicator_OPyC]
    type = WeibullFailureOutputUsingCorrelation
    block = OPyC
    weibull_modulus = 6
    stress_type = scalar_quantity
    scalar_type = MaxPrincipal
    effective_mean_strength = strength_OPyC
  []
  [failure_indicator_SiC_crackedIPyC]
    type = WeibullFailureOutputUsingCorrelation
    block = SiC
    weibull_modulus = 6
    stress_type = scalar_quantity
    scalar_type = MaxPrincipal
    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_type = scalar_quantity
    scalar_type = MaxPrincipal
    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
  []
[]

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

(assessment/TRISO/benchmark/IAEA_CRP-6/fuel_performance/case_9/case_9_1D.i)

#
# This case is taken from Advances in high temperature gas cooled reactor fuel
# technology. Technical Report IAEA-TECDOC-1674, International Atomic Energy
# Agency, 2012.
#
# The correctness of the results computed by this case must be checked against
# results from the IAEA benchmark.
#


initial_fuel_density = 10840.0

[GlobalParams]
  density = ${initial_fuel_density} # kg/m^3
  flux_conversion_factor = 1.0
  order = SECOND
  family = LAGRANGE
  displacements = 'disp_x'
[]

[Mesh]
  coord_type = RSPHERICAL
  [gen]
    type = TRISO1DFiveLayerMeshGenerator
    elem_type = EDGE3
    kernel_radius = 272e-6
    buffer_thickness = 97e-6
    IPyC_thickness = 33e-6
    SiC_thickness = 34e-6
    OPyC_thickness = 39e-6
    kernel_mesh_density = 6
    buffer_mesh_density = 6
    IPyC_mesh_density = 6
    SiC_mesh_density = 8
    OPyC_mesh_density = 6
    block_names = 'fuel buffer IPyC SiC OPyC'
  []
[]

[Variables]
  [disp_x]
  []
  [temperature]
    initial_condition = 1576.0
  []
[]

[Functions]
  [radial_eigenstrain]
    type = ParsedFunction
    expression = 't*(4.52013e-4/6.0*t*t*t*t*t - 8.36313e-3/5.0*t*t*t*t + 5.67549e-2/4.0*t*t*t - 1.74247e-1/3.0*t*t + 2.62692e-1/2.0*t - 1.43234e-1)'
  []
  [tangential_eigenstrain]
    type = ParsedFunction
    expression = 't*(1.30457e-4/4.0*t*t*t - 2.10029e-3/3.0*t*t + 9.07826e-3/2.0*t - 3.24737e-2)'
  []
  [fission_rate]
    type = ParsedFunction
    expression = 1.5060805e20 # units of fissions/m**3/s
  []
  [k_function]
    type = ParsedFunction
    expression = '4.93e-29'
  []
[]

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

[Physics/SolidMechanics/QuasiStatic]
  [IPyC_OPyC]
    block = 'IPyC OPyC'
    strain = finite
    eigenstrain_names = 'thermal_strain pyc_eigenstrain'
  []
  [rest]
    block = 'fuel buffer SiC'
    strain = finite
    eigenstrain_names = thermal_strain
  []
[]

[Kernels]
  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temperature
  []
  [heat]
    type = HeatConduction
    variable = temperature
  []
  [heat_source]
    type = NeutronHeatSource
    variable = temperature
    block = fuel
    energy_per_fission = 3.2e-11 # units of J/fission
    fission_rate = fission_rate
  []
[]

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

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

[ThermalContact]
  [thermal_contact]
    type = GasGapHeatTransfer
    variable = temperature
    primary = IPyC_inner_boundary
    secondary = buffer_outer_boundary
    initial_moles = initial_moles # coupling to a postprocessor which supplies the initial plenum/gap gas mass
    gas_released = 'fis_gas_released co_production' # coupling to postprocessors which supply the fission gas addition, co addition
    released_gas_types = 'Kr Xe;
                          CO'
    released_fractions = '0.153 0.847;
                          1'
    tangential_tolerance = 1e-6
    #    contact_pressure_input = 10e6
    #    quadrature = true
  []
[]

[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_temperature]
    type = DirichletBC
    variable = temperature
    boundary = exterior
    value = 1576.0
  []

  # 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 = 0
      startup_time = 1.0e4
      R = 8.3143
      output_initial_moles = initial_moles # coupling to post processor to get initial fill gas mass
      temperature = ave_temp_interior # coupling to post processor to get gas temperature approximation
      volume = volumeGas # coupling to post processor to get gas volume
      material_input = 'fis_gas_released co_production' # coupling to post processor to get fission gas added, co added
      output = plenum_pressure # coupling to post processor to output plenum/gap pressure
    []
  []

[]

[Materials]

  [flux]
    type = FastNeutronFlux
    calculate_fluence = true
    factor = 2.730961e18 # n/m^2-sec
  []

  [fission_gas_release] # Sifgr fission gas release mode
    type = UO2Sifgrs
    block = fuel
    temperature = temperature
    fission_rate = fission_rate # coupling to fission_rate aux variable
    grain_radius_const = 5.0e-6
  []

  [stress]
    type = ComputeFiniteStrainElasticStress
    block = 'fuel buffer SiC'
  []
  [PyC_stress]
    type = PyCCreep
    block = 'IPyC OPyC'
    k = k_function
    poissons_ratio = 0.4
    temperature = temperature
  []
  [normal_vectors_triso]
    type = NormalVectorsTRISO
    block = 'IPyC OPyC'
  []
  [PyC_eigenstrain]
    type = PyCIrradiationEigenstrain
    block = 'IPyC OPyC'
    radial_eigenstrain_function = radial_eigenstrain
    tangential_eigenstrain_function = tangential_eigenstrain
    eigenstrain_name = pyc_eigenstrain
  []

  [fuel_thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    block = fuel
    thermal_expansion_coeff = 10e-6
    stress_free_temperature = 1576.0
    eigenstrain_name = thermal_strain
    temperature = temperature
  []
  [PyC_thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    block = 'buffer IPyC OPyC'
    thermal_expansion_coeff = 5.5e-6
    stress_free_temperature = 1576.0
    eigenstrain_name = thermal_strain
    temperature = temperature
  []
  [SiC_thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    block = SiC
    thermal_expansion_coeff = 4.9e-6
    stress_free_temperature = 1576.0
    eigenstrain_name = thermal_strain
    temperature = temperature
  []

  [fuel_thermal]
    type = UO2Thermal
    thermal_conductivity_model = FINK_LUCUTA
    block = fuel
    temperature = temperature
    burnup = burnup
  []

  [fuel_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = fuel
    youngs_modulus = 2e8
    poissons_ratio = 0.345
  []

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

  [buffer_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = buffer
    youngs_modulus = 2e8
    poissons_ratio = 0.345
  []

  [buffer_temperature]
    type = HeatConductionMaterial
    block = buffer
    thermal_conductivity = 0.5 # J/m-s-K
    specific_heat = 720.0 # J/kg-K
  []

  [buffer_den]
    type = StrainAdjustedDensity
    strain_free_density = 1100 #kg/m^3
    block = buffer
  []

  [PyC_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = 'IPyC OPyC'
    youngs_modulus = 3.96e10
    poissons_ratio = 0.33
  []

  [PyC_temperature]
    type = HeatConductionMaterial
    block = 'IPyC OPyC'
    thermal_conductivity = 4.0 # J/m-s-K
    specific_heat = 720.0 # J/kg-K
  []

  [PyC_den]
    type = StrainAdjustedDensity
    strain_free_density = 1850.0 # kg/m^3
    block = 'IPyC OPyC'
  []

  [SiC_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = SiC
    youngs_modulus = 3.7e11
    poissons_ratio = 0.13
  []

  [SiC_temperature]
    type = HeatConductionMaterial
    block = SiC
    thermal_conductivity = 13.9 # J/m-s-K
    specific_heat = 620.0 # J/kg-K
  []

  [SiC_den]
    type = StrainAdjustedDensity
    strain_free_density = 3200.0 # kg/m^3
    block = SiC
  []
[]

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

[Debug]
  show_var_residual_norms = true
[]

[Executioner]
  type = Transient

  petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
  petsc_options_value = '201                hypre    boomeramg      4'

  line_search = 'none'

  solve_type = 'PJFNK'

  nl_rel_tol = 1e-7
  nl_abs_tol = 1e-10
  nl_max_its = 15

  l_tol = 1e-3
  l_max_its = 50

  start_time = 0.0
  end_time = 7689600

  dtmax = 2e5
  dtmin = 1
  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 20
    optimal_iterations = 6
    iteration_window = 2
    linear_iteration_ratio = 100
  []
[]

[Postprocessors]
  [burnup]
    type = ElementExtremeValue
    block = fuel
    variable = burnup
  []
  [fis_gas_produced] # fission gas produced (moles)
    type = ElementIntegralFisGasGeneratedSifgrs
    block = fuel
  []

  [fis_gas_released] # fission gas released to plenum (moles)
    type = ElementIntegralFisGasReleasedSifgrs
    block = fuel
  []
  [volumeTotal]
    type = InternalVolume
    boundary = exterior
  []
  [volumeFuel]
    type = InternalVolume
    boundary = fuel_outer_boundary
  []
  [volumeGas]
    type = InternalVolume
    boundary = 'fuel_outer_boundary IPyC_inner_boundary'
    # ro = 369e-6
    # ri = 272e-6
    # vb = 4/3*pi*(ro^3-ri^3) = 1.26e-10
    # buffer density = 1100
    # PyC density    = 1850
    # fill ratio = 1100/1850
    # vb*1100/1850 = 7.50e-11
    # Must remove 7.50e-11 m^3 from the volume
    addition = -7.50e-11
    execute_on = 'initial timestep_end'
  []
  [volumeBufferShell]
    type = InternalVolume
    boundary = buffer_IPyC_boundary
  []
  [ave_temp_interior]
    type = SideAverageValue
    boundary = buffer_IPyC_boundary
    variable = temperature
    execute_on = 'initial timestep_end'
  []

  # Postprocessors for CO production

  [total_fission_rate]
    type = ElementIntegralPower
    variable = temperature
    fission_rate = fission_rate
    block = fuel
    energy_per_fission = 1.0
  []

  [total_fissions]
    type = TimeIntegratedPostprocessor
    value = total_fission_rate
  []

  [avg_surface_temp]
    type = SideAverageValue
    variable = temperature
    boundary = exterior
  []

  [time_int_surf_temp]
    type = TimeIntegratedPostprocessor
    value = avg_surface_temp
  []

  [co_production]
    type = CarbonMonoxideProduction
    total_fissions = total_fissions
    time_integrated_triso_temperature = time_int_surf_temp
    initial_enrichment = 0.14029
  []

  [tang_SiC]
    type = ElementalVariableValue
    variable = stress_yy
    elementid = 18
  []
[]

[PerformanceMetricOutputs]
[]

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

(assessment/TRISO/benchmark/IAEA_CRP-6/fuel_performance/case_13/case_13_1D.i)

#
# This case is taken from Advances in high temperature gas cooled reactor fuel
# technology. Technical Report IAEA-TECDOC-1674, International Atomic Energy
# Agency, 2012.
#
# The correctness of the results computed by this case must be checked against
# results from the IAEA benchmark.
#


initial_fuel_density = 10810.0

[GlobalParams]
  density = ${initial_fuel_density} # kg/m^3
  flux_conversion_factor = 1.0
  order = SECOND
  family = LAGRANGE
  displacements = 'disp_x'
[]

[Mesh]
  coord_type = RSPHERICAL
  [gen]
    type = TRISO1DFiveLayerMeshGenerator
    elem_type = EDGE3
    kernel_radius = 251e-6
    buffer_thickness = 95e-6
    IPyC_thickness = 41e-6
    SiC_thickness = 35e-6
    OPyC_thickness = 40e-6
    kernel_mesh_density = 6
    buffer_mesh_density = 6
    IPyC_mesh_density = 6
    SiC_mesh_density = 8
    OPyC_mesh_density = 6
    block_names = 'fuel buffer IPyC SiC OPyC'
  []
[]

[Variables]
  [disp_x]
  []
  [temperature]
    initial_condition = 1298.0
  []
[]

[Functions]
  [radial_eigenstrain]
    type = ParsedFunction
    expression = 't*(4.52013e-4/6.0*t*t*t*t*t - 8.36313e-3/5.0*t*t*t*t + 5.67549e-2/4.0*t*t*t - 1.74247e-1/3.0*t*t + 2.62692e-1/2.0*t - 1.43234e-1)'
  []
  [tangential_eigenstrain]
    type = ParsedFunction
    expression = 't*(1.30457e-4/4.0*t*t*t - 2.10029e-3/3.0*t*t + 9.07826e-3/2.0*t - 3.24737e-2)'
  []
  [fission_rate]
    type = ParsedFunction
    expression = 9.30203234e19 # units of fissions/m**3/s
  []
  [k_function]
    type = ParsedFunction
    expression = '4.93e-29'
  []
[]

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

[Physics/SolidMechanics/QuasiStatic]
  [IPyC_OPyC]
    block = 'IPyC OPyC'
    strain = finite
    eigenstrain_names = 'thermal_strain pyc_eigenstrain'
  []
  [rest]
    block = 'fuel buffer SiC'
    strain = finite
    eigenstrain_names = thermal_strain
  []
[]

[Kernels]
  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temperature
  []
  [heat]
    type = HeatConduction
    variable = temperature
  []
  [heat_source]
    type = NeutronHeatSource
    variable = temperature
    block = fuel
    energy_per_fission = 3.2e-11 # units of J/fission
    fission_rate = fission_rate
  []
[]

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

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

[ThermalContact]
  [thermal_contact]
    type = GasGapHeatTransfer
    variable = temperature
    primary = IPyC_inner_boundary
    secondary = buffer_outer_boundary
    initial_moles = initial_moles # coupling to a postprocessor which supplies the initial plenum/gap gas mass
    gas_released = 'fis_gas_released co_production' # coupling to postprocessors which supply the fission gas addition, co addition
    released_gas_types = 'Kr Xe;
                          CO'
    released_fractions = '0.153 0.847;
                          1'
    tangential_tolerance = 1e-6
    #    contact_pressure_input = 10e6
    #    quadrature = true
  []
[]

[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_temperature]
    type = DirichletBC
    variable = temperature
    boundary = exterior
    value = 1298.0
  []

  # 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 = 0
      startup_time = 1.0e4
      R = 8.3143
      output_initial_moles = initial_moles # coupling to post processor to get initial fill gas mass
      temperature = ave_temp_interior # coupling to post processor to get gas temperature approximation
      volume = volumeGas # coupling to post processor to get gas volume
      material_input = 'fis_gas_released co_production' # coupling to post processor to get fission gas added, co added
      output = plenum_pressure # coupling to post processor to output plenum/gap pressure
    []
  []

[]

[Materials]

  [flux]
    type = FastNeutronFlux
    calculate_fluence = true
    factor = 1.041666666667e18 # n/m^2-sec
  []

  [fission_gas_release] # Sifgr fission gas release mode
    type = UO2Sifgrs
    block = fuel
    temperature = temperature
    fission_rate = fission_rate # coupling to fission_rate aux variable
    grain_radius_const = 5.0e-6
  []

  [stress]
    type = ComputeFiniteStrainElasticStress
    block = 'fuel buffer SiC'
  []
  [PyC_stress]
    type = PyCCreep
    block = 'IPyC OPyC'
    k = k_function
    poissons_ratio = 0.4
    temperature = temperature
  []
  [normal_vectors_triso]
    type = NormalVectorsTRISO
    block = 'IPyC OPyC'
  []
  [PyC_eigenstrain]
    type = PyCIrradiationEigenstrain
    block = 'IPyC OPyC'
    radial_eigenstrain_function = radial_eigenstrain
    tangential_eigenstrain_function = tangential_eigenstrain
    eigenstrain_name = pyc_eigenstrain
  []
  [fuel_thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    block = fuel
    thermal_expansion_coeff = 10e-6
    stress_free_temperature = 1298.0
    eigenstrain_name = thermal_strain
    temperature = temperature
  []
  [PyC_thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    block = 'buffer IPyC OPyC'
    thermal_expansion_coeff = 5.5e-6
    stress_free_temperature = 1298.0
    eigenstrain_name = thermal_strain
    temperature = temperature
  []
  [SiC_thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    block = SiC
    thermal_expansion_coeff = 4.9e-6
    stress_free_temperature = 1298.0
    eigenstrain_name = thermal_strain
    temperature = temperature
  []

  [fuel_thermal]
    type = UO2Thermal
    thermal_conductivity_model = FINK_LUCUTA
    block = fuel
    temperature = temperature
    burnup = burnup
  []

  [fuel_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = fuel
    youngs_modulus = 2e8
    poissons_ratio = 0.345
  []

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

  [buffer_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = buffer
    youngs_modulus = 2e8
    poissons_ratio = 0.345
  []

  [buffer_temperature]
    type = HeatConductionMaterial
    block = buffer
    thermal_conductivity = 0.5 # J/m-s-K
    specific_heat = 720.0 # J/kg-K
  []

  [buffer_den]
    type = StrainAdjustedDensity
    strain_free_density = 1010 #kg/m^3
    block = buffer
  []

  [PyC_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = 'IPyC OPyC'
    youngs_modulus = 3.96e10
    poissons_ratio = 0.33
  []

  [PyC_temperature]
    type = HeatConductionMaterial
    block = 'IPyC OPyC'
    thermal_conductivity = 4.0 # J/m-s-K
    specific_heat = 720.0 # J/kg-K
  []

  [PyC_den]
    type = StrainAdjustedDensity
    strain_free_density = 1870.0 # kg/m^3
    block = 'IPyC OPyC'
  []

  [SiC_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = SiC
    youngs_modulus = 3.7e11
    poissons_ratio = 0.13
  []

  [SiC_temperature]
    type = HeatConductionMaterial
    block = SiC
    thermal_conductivity = 13.9 # J/m-s-K
    specific_heat = 620.0 # J/kg-K
  []

  [SiC_den]
    type = StrainAdjustedDensity
    strain_free_density = 3200.0 # kg/m^3
    block = SiC
  []
[]

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

[Debug]
  show_var_residual_norms = true
[]

[Executioner]
  type = Transient

  petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
  petsc_options_value = '201                hypre    boomeramg      4'

  line_search = 'none'

  solve_type = 'PJFNK'

  nl_rel_tol = 1e-7
  nl_abs_tol = 1e-10
  nl_max_its = 15

  l_tol = 1e-3
  l_max_its = 50

  start_time = 0.0
  end_time = 51840000

  dtmax = 2e5
  dtmin = 1
  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 20
    optimal_iterations = 6
    iteration_window = 2
    linear_iteration_ratio = 100
  []
[]

[Postprocessors]
  [burnup]
    type = ElementExtremeValue
    block = fuel
    variable = burnup
  []
  [fis_gas_produced] # fission gas produced (moles)
    type = ElementIntegralFisGasGeneratedSifgrs
    block = fuel
  []

  [fis_gas_released] # fission gas released to plenum (moles)
    type = ElementIntegralFisGasReleasedSifgrs
    block = fuel
  []
  [volumeTotal]
    type = InternalVolume
    boundary = exterior
  []
  [volumeFuel]
    type = InternalVolume
    boundary = fuel_outer_boundary
  []
  [volumeGas]
    type = InternalVolume
    boundary = 'fuel_outer_boundary IPyC_inner_boundary'
    # ro = 346e-6
    # ri = 251e-6
    # vb = 4/3*pi*(ro^3-ri^3) = 1.07e-10
    # buffer density = 1010
    # PyC density    = 1870
    # fill ratio = 1010/1870
    # vb*1010/1870 = 5.79e-11
    # Must remove 5.79e-11 m^3 from the volume
    addition = -5.79e-11
    execute_on = 'initial timestep_end'
  []
  [volumeBufferShell]
    type = InternalVolume
    boundary = buffer_IPyC_boundary
  []
  [ave_temp_interior]
    type = SideAverageValue
    boundary = buffer_IPyC_boundary
    variable = temperature
    execute_on = 'initial timestep_end'
  []

  # Postprocessors for CO production

  [total_fission_rate]
    type = ElementIntegralPower
    variable = temperature
    fission_rate = fission_rate
    block = fuel
    energy_per_fission = 1.0
  []

  [total_fissions]
    type = TimeIntegratedPostprocessor
    value = total_fission_rate
  []

  [avg_surface_temp]
    type = SideAverageValue
    variable = temperature
    boundary = exterior
  []

  [time_int_surf_temp]
    type = TimeIntegratedPostprocessor
    value = avg_surface_temp
  []

  [co_production]
    type = CarbonMonoxideProduction
    total_fissions = total_fissions
    time_integrated_triso_temperature = time_int_surf_temp
    initial_enrichment = 0.14029
  []

  [tang_SiC]
    type = ElementalVariableValue
    variable = stress_yy
    elementid = 18
  []
[]

[PerformanceMetricOutputs]
[]

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

(test/tests/triso_failure/triso_ipyc_characteristic_strength.i)

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

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

[Variables]
  [disp_x]
  []
  [temp]
    initial_condition = 1346.0
  []
[]

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

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

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

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

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

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

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

[BCs]
  # pin particle along symmetry planes
  [no_disp_x]
    type = DirichletBC
    variable = disp_x
    boundary = xzero
    value = 0.0
  []
  # fix temperature on free surface
  [freesurf_temp]
    type = DirichletBC
    variable = temp
    boundary = exterior
    value = 1346.0
  []
  # exterior and internal pressures
  [exterior_pressure_x]
    type = Pressure
    use_displaced_mesh = false
    variable = disp_x
    boundary = exterior
    factor = 0.1e6
  []
  #  apply gas pressure on buffer and IPyC boundaries
  [PlenumPressure]
    [plenumPressure]
      use_displaced_mesh = false
      boundary = buffer_IPyC_boundary
      initial_pressure = 0
      startup_time = 1.0e4
      R = 8.3143
      # coupling to post processor
      output_initial_moles = initial_moles
      temperature = ave_temp_interior
      volume = volumeGas
      material_input = 'fis_gas_released co_production'
      output = plenum_pressure
    []
  []
[]

[Materials]
  [max_principal_stress]
    type = RankTwoInvariant
    property_name = max_principal_stress
    rank_two_tensor = stress
    invariant = MaxPrincipal
  []
  [flux]
    type = FastNeutronFlux
    calculate_fluence = true
    factor = 1.708707e18
  []
  [fission_gas_release]
    type = UO2Sifgrs
    block = fuel
    temperature = temp
    fission_rate = fission_rate
    grain_radius_const = 5.0e-6
  []
  [stress]
    type = ComputeLinearElasticStress
    block = 'fuel buffer SiC'
  []
  [PyC_stress]
    type = PyCCreep
    block = 'IPyC OPyC'
    k = k_function
    poissons_ratio = 0.4
    temperature = temp
  []
  [normal_vectors_triso]
    type = NormalVectorsTRISO
    block = 'IPyC OPyC'
  []
  [PyC_eigenstrain]
    type = PyCIrradiationEigenstrain
    block = 'IPyC OPyC'
    radial_eigenstrain_function = radial_eigenstrain
    tangential_eigenstrain_function = tangential_eigenstrain
    eigenstrain_name = pyc_eigenstrain
  []
  [fuel_thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    block = fuel
    thermal_expansion_coeff = 10e-6
    stress_free_temperature = 1346.0
    eigenstrain_name = thermal_strain
    temperature = temp
  []
  [PyC_thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    block = 'buffer IPyC OPyC'
    thermal_expansion_coeff = 5.5e-6
    stress_free_temperature = 1346.0
    eigenstrain_name = thermal_strain
    temperature = temp
  []
  [SiC_thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    block = SiC
    thermal_expansion_coeff = 4.9e-6
    stress_free_temperature = 1346.0
    eigenstrain_name = thermal_strain
    temperature = temp
  []
  [fuel_thermal]
    type = UO2Thermal
    thermal_conductivity_model = FINK_LUCUTA
    block = fuel
    temperature = temp
    burnup = burnup
  []
  [fuel_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = fuel
    youngs_modulus = 2e8
    poissons_ratio = 0.345
  []
  [fuel_den]
    type = StrainAdjustedDensity
    block = fuel
    strain_free_density = 10810.0
  []
  [buffer_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = buffer
    youngs_modulus = 2e8
    poissons_ratio = 0.345
  []
  [buffer_temp]
    type = HeatConductionMaterial
    block = buffer
    thermal_conductivity = 0.5
    specific_heat = 720.0
  []
  [buffer_den]
    type = StrainAdjustedDensity
    strain_free_density = 1000
    block = buffer
  []
  [PyC_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = 'IPyC OPyC'
    youngs_modulus = 3.96e10
    poissons_ratio = 0.33
  []
  [PyC_temp]
    type = HeatConductionMaterial
    block = 'IPyC OPyC'
    thermal_conductivity = 4.0
    specific_heat = 720.0
  []
  [PyC_den]
    type = StrainAdjustedDensity
    strain_free_density = 1880.0
    block = 'IPyC OPyC'
  []
  [SiC_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = SiC
    youngs_modulus = 3.7e11
    poissons_ratio = 0.13
  []
  [SiC_temp]
    type = HeatConductionMaterial
    block = SiC
    thermal_conductivity = 13.9
    specific_heat = 620.0
  []
  [SiC_den]
    type = StrainAdjustedDensity
    strain_free_density = 3200.0
    block = SiC
  []
  [characteristic_strength_SiC]
    type = GenericConstantMaterial
    prop_values = '9640000'
    block = SiC
    prop_names = 'characteristic_strength'
  []
  [characteristic_strength_PyC]
    type = PyCCharacteristicStrength
    temperature = temp
    X = 1.02
    flux_conversion_factor = 0.85
    block = 'IPyC OPyC'
  []
[]

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

[Debug]
  show_var_residual_norms = true
[]

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

[Postprocessors]
  [dt]
    type = TimestepSize
  []
  [burnup]
    type = ElementExtremeValue
    block = fuel
    variable = burnup
  []
  [fis_gas_produced]
    type = ElementIntegralFisGasGeneratedSifgrs
    block = fuel
  []
  [fis_gas_released]
    type = ElementIntegralFisGasReleasedSifgrs
    block = fuel
  []
  [volumeTotal]
    type = InternalVolume
    boundary = exterior
  []
  [volumeFuel]
    type = InternalVolume
    boundary = fuel_outer_boundary
  []
  [volumeGas]
    type = InternalVolume
    boundary = 'fuel_outer_boundary IPyC_inner_boundary'
    addition = -5.53e-11
    execute_on = 'initial timestep_end'
  []
  [volumeBufferShell]
    type = InternalVolume
    boundary = buffer_IPyC_boundary
  []
  [ave_temp_interior]
    type = SideAverageValue
    boundary = buffer_IPyC_boundary
    variable = temp
    execute_on = 'initial timestep_end'
  []
  # Postprocessors for CO production
  [total_fission_rate]
    type = ElementIntegralPower
    variable = temp
    fission_rate = fission_rate
    block = fuel
    energy_per_fission = 1.0
  []
  [total_fissions]
    type = TimeIntegratedPostprocessor
    value = total_fission_rate
  []
  [avg_surface_temp]
    type = SideAverageValue
    variable = temp
    boundary = exterior
  []
  [time_int_surf_temp]
    type = TimeIntegratedPostprocessor
    value = avg_surface_temp
  []
  [co_production]
    type = CarbonMonoxideProduction
    total_fissions = total_fissions
    time_integrated_triso_temperature = time_int_surf_temp
    initial_enrichment = 0.14029
  []
  [tang_SiC]
    type = ElementalVariableValue
    variable = stress_yy
    elementid = 18
  []
  [strength_SiC]
    type = WeibullEffectiveMeanStrength
    block = SiC
    weibull_modulus = 6
  []
  [failure_indicator_SiC]
    type = WeibullFailureOutputUsingCorrelation
    block = SiC
    weibull_modulus = 6
    stress_name = max_principal_stress
    effective_mean_strength = strength_SiC
  []
  [strength_IPyC]
    type = WeibullEffectiveMeanStrength
    block = IPyC
    weibull_modulus = 6
  []
  [failure_indicator_IPyC]
    type = WeibullFailureOutputUsingCorrelation
    block = IPyC
    weibull_modulus = 6
    stress_name = max_principal_stress
    effective_mean_strength = strength_IPyC
  []
  [strength_OPyC]
    type = WeibullEffectiveMeanStrength
    block = OPyC
    weibull_modulus = 6
  []
  [failure_indicator_OPyC]
    type = WeibullFailureOutputUsingCorrelation
    block = OPyC
    weibull_modulus = 6
    stress_name = max_principal_stress
    effective_mean_strength = strength_OPyC
  []
  [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
  []
  [characteristic_strength]
    type = ElementExtremeMaterialProperty
    mat_prop = characteristic_strength
    block = IPyC
    value_type = max
  []
  [flence]
    type = ElementExtremeMaterialProperty
    mat_prop = fast_neutron_fluence
    block = IPyC
    value_type = max
  []
[]

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

(examples/TRISO/accident_simulation/triso2D_accident.i)

# This example is 2D-RZ analysis of a TRISO fuel particle. Fully coupled
# heat transfer and solid mechanics, plus diffusion of the fission product
# species cesium (Cs) are simulated.  The mesh includes contact surfaces
# between the buffer and IPyC layers to facilitate a gap opening between
# these layers. These surfaces are initially in mechanical contact but
# are assumed to have no strength in tension. A coarse mesh is used to
# provide a short run time.

# The calculation simulates fuel-life in three steps. The first step is an
# irradiation period, where constant power and a fixed particle surface
# temperature (1500 K) are assumed over a lifetime of 76 Ms (2.4 yrs).
# For the second step, fuel removal and storage are simulated by setting
# the reactor power and Cs source terms to zero, reducing the particle
# surface temperature to ambient (300 K), and then holding it
# for 100 days. A third and final step simulates accident
# behavior by increasing the particle surface temperature from ambient
# to 2073 K over 2 hrs, and then holding it at this elevated temperature
# for an additional 200 hrs. At the particle outer boundary, the Cs
# concentration is held at zero and the pressure at ambient during the
# entire simulation. The particle is assumed to be stress-free at an
# initial temperature of 1500 K.
#
# Details about this simulation are given in Section 4 of the following
# article: J. D. Hales, R. L. Williamson, S. R. Novascone, D. M. Perez,
# B. W. Spencer and G. Pastore, "Multidimensional multiphysics simulation
# of TRISO particle fuel", Journal of Nuclear Materials, Vol. 443, p. 531,
# 2013.


initial_fuel_density = 11000.0

[GlobalParams]
  order = SECOND
  family = LAGRANGE
  displacements = 'disp_x disp_y'
  flux_conversion_factor = 0.85
[]

[Mesh]
  coord_type = RZ
  [mesh]
    type = FileMeshGenerator
    file = triso2Dmed.e
  []
[]

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

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [temp]
    initial_condition = 1500.0
  []
  [conc]
    initial_condition = 0.0
  []
[]

[AuxVariables]
  [fission_rate]
    block = fuel
    order = CONSTANT
    family = MONOMIAL
  []
  [fluence]
    order = CONSTANT
    family = MONOMIAL
  []
  [burnup]
    block = fuel
    order = CONSTANT
    family = MONOMIAL
  []
  [gap_condSlave]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_xx]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_yy]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_zz]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [power_history]
    type = PiecewiseLinear
    x = '0 76e6 76.001e6'
    y = '1 1     0'
  []
  [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'
  []
  [integral_flux_error]
    type = ParsedFunction
    symbol_names = 'buffer_integral_flux IPyC_integral_flux'
    symbol_values = 'buffer_integral_flux IPyC_integral_flux'
    expression = 'IPyC_integral_flux + buffer_integral_flux'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  generate_output = 'stress_xx stress_yy stress_zz stress_xy stress_yz stress_zx hydrostatic_stress'
  strain = FINITE
  incremental = true
  add_variables = false
  [default]
    block = 'fuel buffer IPyC OPyC'
    eigenstrain_names = 'thermal_strain swelling_strain'
    extra_vector_tags = 'ref'
  []
  [SiC]
    block = 'SiC'
    eigenstrain_names = 'thermal_strain'
    extra_vector_tags = 'ref'
  []
[]

[Kernels]
  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temp
    extra_vector_tags = 'ref'
  []
  [heat]
    type = HeatConduction
    variable = temp
    extra_vector_tags = 'ref'
  []
  [heat_source]
    type = NeutronHeatSource
    variable = temp
    block = fuel
    energy_per_fission = 3.2e-11 # units of J/fission
    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 moles/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]
  [fission_rate]
    type = FissionRateGeneral
    fission_rate_formulation = GENERIC
    variable = fission_rate
    block = fuel
    fission_rate_function = power_history
    value = 3.89e19
    execute_on = timestep_begin
  []
  [fluence]
    type = MaterialRealAux
    property = fast_neutron_fluence
    variable = fluence
  []
  [burnup]
    type = BurnupAux
    variable = burnup
    block = fuel
    fission_rate = fission_rate
    molecular_weight = 0.270 # units of kg/mole
    execute_on = timestep_begin
    density = ${initial_fuel_density}
  []
  [creep_xx]
    type = RankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_xx
    index_i = 0
    index_j = 0
    block = 'buffer IPyC SiC OPyC'
    execute_on = timestep_end
  []
  [creep_yy]
    type = RankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_yy
    index_i = 1
    index_j = 1
    block = 'buffer IPyC SiC OPyC'
    execute_on = timestep_end
  []
  [creep_zz]
    type = RankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_zz
    index_i = 2
    index_j = 2
    block = 'buffer IPyC SiC OPyC'
    execute_on = timestep_end
  []
  [conductanceSlave]
    type = MaterialRealAux
    property = gap_conductance
    variable = gap_condSlave
    boundary = BufferGapBndry
    execute_on = linear
  []
[]

[Contact]
  [pellet_clad_mechanical]
    primary = 15
    secondary = 17
    penalty = 1e5
    model = frictionless
    formulation = penalty
  []
[]

[ThermalContact]
  [thermal_contact]
    type = GasGapHeatTransfer
    variable = temp
    primary = 15
    secondary = 17
    initial_moles = initial_moles # coupling to a postprocessor which supplies the initial plenum/gap gas mass
    gas_released = 'fis_gas_released co_production' # coupling to postprocessors which supply the fission gas addition, co addition
    released_gas_types = 'Kr Xe;
                          CO'
    released_fractions = '0.153 0.847;
                          1'
    gap_geometry_type = CYLINDER
    tangential_tolerance = 1e-6
    roughness_coef = 0.0
    quadrature = true
  []
  [cesium_contact]
    type = GapHeatTransfer
    variable = conc
    primary = 15
    secondary = 17
    tangential_tolerance = 1e-6
    gap_conductivity_function = d_gap
    gap_conductivity_function_variable = temp
    appended_property_name = _conc
    emissivity_primary = 0
    emissivity_secondary = 0
    quadrature = true
  []
[]

[BCs]
  # pin particle along symmetry planes
  [no_disp_x]
    type = DirichletBC
    variable = disp_x
    boundary = xzero
    value = 0.0
    extra_vector_tags = 'ref'
  []
  [no_disp_y]
    type = DirichletBC
    variable = disp_y
    boundary = yzero
    value = 0.0
    extra_vector_tags = 'ref'
  []
  # fix temperature on free surface
  [freesurf_temp]
    type = FunctionDirichletBC
    variable = temp
    boundary = exterior
    function = temp_bc
    extra_vector_tags = 'ref'
  []
  # fix concentration on free surface
  [freesurf_conc]
    type = DirichletBC
    variable = conc
    boundary = exterior
    value = 0.0
    extra_vector_tags = 'ref'
  []
  [PlenumPressure] #  apply plenum pressure on clad inner walls and pellet surfaces
    [plenumPressure]
      boundary = BufferGapVol
      initial_pressure = 0
      startup_time = 1.0e4
      R = 8.3145
      output_initial_moles = initial_moles # coupling to post processor to get initial fill gas mass
      temperature = ave_temp_interior # coupling to post processor to get gas temperature approximation
      volume = volumeGas # coupling to post processor to get gas volume
      material_input = 'fis_gas_released co_production' # coupling to post processor to get fission gas added, co added
      output = plenum_pressure # coupling to post processor to output plenum/gap pressure
    []
  []
[]

[Materials]
  [flux]
    type = FastNeutronFlux
    calculate_fluence = true
    factor = 5e17
  []

  [fission_gas_release] # Sifgrs fission gas release mode
    type = UO2Sifgrs
    block = fuel
    temperature = temp
    fission_rate = fission_rate # coupling to fission_rate aux variable
    grain_radius_const = 5.0e-6
  []

  [fuel_thermal]
    type = UO2Thermal
    thermal_conductivity_model = FINK_LUCUTA
    block = fuel
    temperature = temp
    burnup = burnup
    initial_porosity = 0.0
  []
  [fuel_swelling]
    type = UO2VolumetricSwellingEigenstrain
    gas_swelling_model_type = MATPRO
    block = fuel
    temperature = temp
    burnup = burnup
    eigenstrain_name = 'swelling_strain'
    initial_fuel_density = ${initial_fuel_density}
  []
  [fuel_stress]
    type = ComputeFiniteStrainElasticStress
    block = 'fuel'
  []
  [fuel_elasticity]
    type = ComputeIsotropicElasticityTensor
    block = fuel
    youngs_modulus = 2.2e11
    poissons_ratio = .345
  []
  [fuel_thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    block = fuel
    thermal_expansion_coeff = 10e-6
    stress_free_temperature = 1500.0
    eigenstrain_name = thermal_strain
    temperature = temp
  []
  [fuel_den]
    type = StrainAdjustedDensity
    block = fuel
    strain_free_density = ${initial_fuel_density} # kg/m^3
  []
  [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
    gas_constant = 8.3143 # J/K-mol
    temperature = temp
  []

  [buffer_eigenstrain]
    type = PyCIrradiationEigenstrain
    block = buffer
    pyc_type = buffer
    eigenstrain_name = 'swelling_strain'
  []
  [buffer_thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    block = buffer
    thermal_expansion_coeff = 5.65e-6
    stress_free_temperature = 1500.0
    eigenstrain_name = thermal_strain
    temperature = temp
  []
  [buffer_elasticity]
    type = ComputeIsotropicElasticityTensor
    block = buffer
    youngs_modulus = 2e10
    poissons_ratio = .23
  []
  [buffer_stress]
    type = PyCCreep
    block = buffer
    temperature = temp
  []
  [buffer_temp]
    type = HeatConductionMaterial
    block = buffer
    thermal_conductivity = 0.5 # J/m-s-K
    specific_heat = 720.0 # J/kg-K
  []
  [buffer_den]
    type = StrainAdjustedDensity
    strain_free_density = 1000.0 #kg/m^3
    block = buffer
  []
  [buffer_conc]
    type = ArrheniusDiffusionCoef
    block = buffer
    d1 = 1.0e-12 # m^2/s
    q1 = 0.0
    d2 = 0.0
    q2 = 0.0
    gas_constant = 8.3143 # J/K-mol
    temperature = temp
  []
  [normal_vectors_triso]
    type = NormalVectorsTRISO
    block = 'IPyC OPyC buffer'
  []
  [IPyC_eigenstrain]
    type = PyCIrradiationEigenstrain
    block = IPyC
    pyc_type = dense
    eigenstrain_name = 'swelling_strain'
  []
  [IPyC_thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    block = IPyC
    thermal_expansion_coeff = 5.65e-6
    stress_free_temperature = 1500.0
    eigenstrain_name = thermal_strain
    temperature = temp
  []
  [IPyC_elasticity]
    type = ComputeIsotropicElasticityTensor
    block = IPyC
    youngs_modulus = 4.74e10
    poissons_ratio = .23
  []
  [IPyC_disp]
    type = PyCCreep
    block = 'IPyC OPyC'
    temperature = temp
  []
  [IPyC_temp]
    type = HeatConductionMaterial
    block = 'IPyC OPyC'
    thermal_conductivity = 4.0
    specific_heat = 720.0
  []
  [IPyC_den]
    type = StrainAdjustedDensity
    block = 'IPyC OPyC'
    strain_free_density = 1900.0
  []
  [IPyC_conc]
    type = ArrheniusDiffusionCoef
    block = IPyC
    d1 = 6.3e-8
    q1 = 222.0e+3
    d2 = 0.0
    q2 = 0.0
    gas_constant = 8.3143 # J/K-mol
    temperature = temp
  []
  [SiC_thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    block = SiC
    thermal_expansion_coeff = 4.9e-6
    stress_free_temperature = 1500.0
    eigenstrain_name = thermal_strain
    temperature = temp
  []
  [SiC_elasticity]
    type = ComputeIsotropicElasticityTensor
    block = SiC
    youngs_modulus = 3.4e11
    poissons_ratio = .13
  []
  [SiC_creep]
    type = MonolithicSiCCreepUpdate
    block = SiC
    temperature = temp
    k_function = k_function
  []
  [SiC_stress]
    type = ComputeMultipleInelasticStress
    block = SiC
    tangent_operator = elastic
    inelastic_models = 'SiC_creep'
  []
  [SiC_temp]
    type = HeatConductionMaterial
    block = SiC
    thermal_conductivity = 13.9 # J/m-s-K
    specific_heat = 620.0 # J/kg-K
  []
  [SiC_den]
    type = StrainAdjustedDensity
    strain_free_density = 3180.0 # kg/m^3
    block = SiC
  []
  [SiC_conc]
    type = ArrheniusDiffusionCoef
    block = SiC
    d1 = 5.5e-14 # m^2/s
    d1_function = d1_function
    d1_function_variable = fluence
    q1 = 125.0e+3 # J/mol
    d2 = 1.6e-2 # m^2/s
    q2 = 514.0e+3 # J/mol
    gas_constant = 8.3143 # J/K-mol
    temperature = temp
  []

  [OPyC_eigenstrain]
    type = PyCIrradiationEigenstrain
    block = OPyC
    pyc_type = dense
    eigenstrain_name = 'swelling_strain'
  []
  [OPyC_thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    block = OPyC
    thermal_expansion_coeff = 5.65e-6
    stress_free_temperature = 1500.0
    eigenstrain_name = thermal_strain
    temperature = temp
  []
  [OPyC_elasticity]
    type = ComputeIsotropicElasticityTensor
    block = OPyC
    youngs_modulus = 4.74e10
    poissons_ratio = .23
  []
  [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
    gas_constant = 8.3143 # J/K-mol
    temperature = temp
  []
[]

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

[Debug]
  show_var_residual_norms = 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-4
  nl_abs_tol = 1e-9
  nl_max_its = 15

  l_tol = 1e-3
  l_max_its = 50

  start_time = 0.0
  end_time = 85.3682e6
  dt = 100

  dtmax = 2e6
  dtmin = 1

  automatic_scaling = true
  compute_scaling_once = false
  scaling_group_variables = 'conc; disp_x disp_y; temp'

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

  [Predictor]
    type = SimplePredictor
    scale = 1
    skip_times_old = '0    76e6  76.001e6 84.641e6 84.6482e6'
  []

  [Quadrature]
    order = THIRD
    side_order = FIFTH
  []
[]

[Outputs]
  perf_graph = true
  exodus = true
  [console]
    type = Console
    max_rows = 25
  []
  [csv]
    type = CSV
    sync_times = '100 6308007 75696087'
    sync_only = true
  []
[]

[Postprocessors]
  [Cs_release]
    type = SideIntegralMassFlux
    variable = conc
    boundary = exterior
    execute_on = timestep_end
  []
  [dt]
    type = TimestepSize
    execute_on = timestep_end
  []
  [fis_gas_produced] # fission gas produced (moles)
    type = ElementIntegralFisGasGeneratedSifgrs
    block = fuel
    execute_on = 'initial linear nonlinear timestep_begin timestep_end'
  []
  [fis_gas_released] # fission gas released to plenum (moles)
    type = ElementIntegralFisGasReleasedSifgrs
    block = fuel
    execute_on = 'initial linear nonlinear timestep_begin timestep_end'
  []
  [volumeTotal]
    type = InternalVolume
    boundary = exterior
    execute_on = 'initial timestep_end'
  []
  [volumeFuel]
    type = InternalVolume
    boundary = fuel
    execute_on = 'initial timestep_end'
  []
  [volumeGas]
    type = InternalVolume
    boundary = BufferGapVol
    # ro = 3.125e-4
    # ri = 2.125e-4
    # vb = 4/3*pi*(ro^3-ri^3) = 8.76e-11
    # buffer density = 1000
    # PyC density    = 1900
    # fill ratio = 10/19
    # vb*10/19 = 4.6e-11
    # Must remove 4.6e-11 m^3 from the volume
    addition = -4.6e-11
    execute_on = 'initial linear nonlinear timestep_begin timestep_end'
  []
  [volumeBufferShell]
    type = InternalVolume
    boundary = BufferGapVol
    execute_on = 'initial timestep_end'
  []
  [ave_temp_interior]
    type = SideAverageValue
    boundary = BufferGapVol
    variable = temp
    execute_on = 'initial linear nonlinear timestep_begin timestep_end'
  []

  # Postprocessors for CO production

  [total_fission_rate]
    type = ElementIntegralPower
    variable = temp
    fission_rate = fission_rate
    block = fuel
    energy_per_fission = 1.0
    execute_on = 'initial linear nonlinear timestep_begin timestep_end'
  []
  [total_fissions]
    type = TimeIntegratedPostprocessor
    value = total_fission_rate
    execute_on = 'initial linear nonlinear timestep_begin timestep_end'
  []
  [avg_surface_temp]
    type = SideAverageValue
    variable = temp
    boundary = exterior
    execute_on = 'initial linear nonlinear timestep_begin timestep_end'
  []
  [time_int_surf_temp]
    type = TimeIntegratedPostprocessor
    value = avg_surface_temp
    execute_on = 'initial linear nonlinear timestep_begin timestep_end'
  []
  [co_production]
    type = CarbonMonoxideProduction
    total_fissions = total_fissions
    time_integrated_triso_temperature = time_int_surf_temp
    initial_enrichment = 0.14029
    execute_on = 'initial linear nonlinear timestep_begin timestep_end'
  []
  [num_lin_it]
    type = NumLinearIterations
  []
  [num_nonlin_it]
    type = NumNonlinearIterations
  []
  [tot_lin_it]
    type = CumulativeValuePostprocessor
    postprocessor = num_lin_it
  []
  [tot_nonlin_it]
    type = CumulativeValuePostprocessor
    postprocessor = num_nonlin_it
  []
  [alive_time]
    type = PerfGraphData
    section_name = Root
    data_type = TOTAL
  []

  [buffer_avg_conc]
    type = SideAverageValue
    variable = conc
    boundary = 17
  []
  [IPyC_avg_conc]
    type = SideAverageValue
    variable = conc
    boundary = 15
  []
  [buffer_integral_flux]
    type = SideIntegralMassFlux
    variable = conc
    boundary = 17
  []
  [IPyC_integral_flux]
    type = SideIntegralMassFlux
    variable = conc
    boundary = 15
  []
  [integral_flux_error]
    type = FunctionValuePostprocessor
    function = integral_flux_error
  []
  [integral_Cs_release]
    type = TimeIntegratedPostprocessor
    value = Cs_release
  []
  [Cs_production]
    type = FunctionValuePostprocessor
    function = power_history
    scale_factor = 1.22e-5 # units of moles/m**3-s
  []
  [time_integral_Cs_production]
    type = TimeIntegratedPostprocessor
    value = Cs_production
  []
  [volumeFuel_initial]
    type = InternalVolume
    boundary = fuel
    execute_on = initial
  []
  [integral_Cs_production]
    type = ParsedPostprocessor
    pp_names = 'time_integral_Cs_production volumeFuel_initial'
    expression = 'time_integral_Cs_production * volumeFuel_initial'
  []
  [Cs_release_fraction]
    type = ParsedPostprocessor
    pp_names = 'integral_Cs_release integral_Cs_production'
    expression = 'integral_Cs_release / integral_Cs_production'
  []
[]

[VectorPostprocessors]
  [temperaturevpp]
    type = SideValueSampler
    boundary = 11
    variable = temp
    sort_by = x
    outputs = 'csv'
    use_displaced_mesh = true
  []
[]

(test/tests/triso/base_irradiation/triso1D_accident.i)

initial_fuel_density = 11000.0

[GlobalParams]
  density = ${initial_fuel_density} # kg/m^3
  order = SECOND
  displacements = 'disp_x'
[]

[Mesh]
  coord_type = RSPHERICAL
  [mesh]
    type = FileMeshGenerator
    file = triso1DFineTruss3.e
  []
[]

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

[Variables]
  [disp_x]
  []
  [temperature]
    initial_condition = 1500.0
  []
  [conc_Cs]
    initial_condition = 0.0
    scaling = 1e18
  []
[]

[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
  []
  [gap_condSlave]
    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 = false
    strain = FINITE
    eigenstrain_names = 'fuel_thermal_strain fuel_swelling'
    generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz'
    extra_vector_tags = 'ref'
  []
  [buffer]
    block = buffer
    add_variables = false
    strain = FINITE
    eigenstrain_names = 'buffer_thermal_strain buffer_eigenstrain'
    generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz creep_strain_xx creep_strain_yy creep_strain_zz'
    extra_vector_tags = 'ref'
  []
  [IPyC]
    block = IPyC
    add_variables = false
    strain = FINITE
    eigenstrain_names = 'IPyC_eigenstrain IPyC_thermal_strain'
    generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz creep_strain_xx creep_strain_yy creep_strain_zz'
    extra_vector_tags = 'ref'
  []
  [SiC]
    block = SiC
    add_variables = false
    strain = FINITE
    eigenstrain_names = 'SiC_thermal_strain'
    generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz creep_strain_xx creep_strain_yy creep_strain_zz'
    extra_vector_tags = 'ref'
  []
  [OPyC]
    block = OPyC
    add_variables = false
    strain = FINITE
    eigenstrain_names = 'OPyC_eigenstrain OPyC_thermal_strain'
    generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz creep_strain_xx creep_strain_yy creep_strain_zz'
    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
    energy_per_fission = 3.2e-11 # units of J/fission
    fission_rate = fission_rate
    extra_vector_tags = 'ref'
  []
  [mass_ie]
    type = TimeDerivative
    variable = conc_Cs
    extra_vector_tags = 'ref'
  []
  [mass]
    type = ArrheniusDiffusion
    variable = conc_Cs
    extra_vector_tags = 'ref'
  []
  [mass_source]
    type = BodyForce
    variable = conc_Cs
    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_Cs
    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 = BurnupAux
    variable = burnup
    fission_rate = fission_rate
    molecular_weight = 0.270 # units of kg/mol
    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 = BufferGapBndry
    execute_on = 'initial timestep_end'
  []
[]

[Contact]
  [pellet_clad_mechanical]
    primary = 15
    secondary = 17
    penalty = 1e5
    model = frictionless
    formulation = kinematic
  []
[]

[ThermalContact]
  [thermal_contact]
    type = GasGapHeatTransfer
    variable = temperature
    primary = 15
    secondary = 17
    initial_moles = initial_moles # coupling to a postprocessor which supplies the initial plenum/gap gas mass
    gas_released = 'fis_gas_released co_production' # coupling to postprocessors which supply the fission gas addition, co addition
    released_gas_types = 'Kr Xe;
                          CO'
    released_fractions = '0.153 0.847;
                          1'
    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_Cs
    primary = 15
    secondary = 17
    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
    boundary = exterior
    function = temp_bc
  []

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

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

  # apply plenum pressure on clad inner walls and pellet surfaces
  [PlenumPressure]
    [plenumPressure]
      boundary = BufferGapVol
      initial_pressure = 100
      startup_time = 0
      R = 8.3145
      output_initial_moles = initial_moles
      temperature = ave_temp_interior
      volume = volumeGas
      material_input = 'fis_gas_released co_production'
      output = plenum_pressure
    []
  []
[]

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

  [fuel_thermal]
    type = UO2Thermal
    block = fuel
    thermal_conductivity_model = FINK_LUCUTA
    initial_porosity = 0.0
    temperature = temperature
    burnup = burnup
  []
  [fuel_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = fuel
    youngs_modulus = 2.2e11
    poissons_ratio = 0.345
  []
  [fuel_elastic_stress]
    type = ComputeFiniteStrainElasticStress
    block = fuel
  []
  [fuel_swelling]
    type = UO2VolumetricSwellingEigenstrain
    gas_swelling_model_type = MATPRO
    block = fuel
    temperature = temperature
    burnup = burnup
    eigenstrain_name = fuel_swelling
    initial_fuel_density = ${initial_fuel_density}
  []
  [fuel_thermal_expansion]
    type = ComputeThermalExpansionEigenstrain
    block = fuel
    thermal_expansion_coeff = 10.0e-6
    temperature = temperature
    stress_free_temperature = 1500.0
    eigenstrain_name = fuel_thermal_strain
  []
  [fuel_den]
    type = StrainAdjustedDensity
    block = fuel
    strain_free_density = ${initial_fuel_density}
  []
  [fission_gas_release]
    type = UO2Sifgrs
    block = fuel
    temperature = temperature
    fission_rate = fission_rate
  []
  [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
    gas_constant = 8.3143 # J/K-mol
    temperature = temperature
  []

  [buffer_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = buffer
    youngs_modulus = 2.0e10
    poissons_ratio = 0.23
  []
  [buffer_stress]
    type = PyCCreep
    block = buffer
    flux_conversion_factor = 1.0
    temperature = temperature
  []
  [buffer_temp]
    type = HeatConductionMaterial
    block = buffer
    thermal_conductivity = 0.5 # J/m-s-K
    specific_heat = 720.0 # J/kg-K
  []
  [buffer_den]
    type = StrainAdjustedDensity
    strain_free_density = 1000.0 #kg/m^3
    block = buffer
  []
  [buffer_thermal_expansion]
    type = ComputeThermalExpansionEigenstrain
    block = buffer
    thermal_expansion_coeff = 5.65e-6
    temperature = temperature
    stress_free_temperature = 1500.0
    eigenstrain_name = buffer_thermal_strain
  []
  [buffer_irraditation]
    type = PyCIrradiationEigenstrain
    block = buffer
    pyc_type = buffer
    eigenstrain_name = buffer_eigenstrain
  []
  [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_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = IPyC
    youngs_modulus = 4.74e10
    poissons_ratio = 0.23
  []
  [IPyC_stress]
    type = PyCCreep
    block = IPyC
    flux_conversion_factor = 1.0
    temperature = temperature
  []
  [IPyC_temp]
    type = HeatConductionMaterial
    block = IPyC
    thermal_conductivity = 4.0 # J/m-s-K
    specific_heat = 720.0 # J/kg-K
  []
  [IPyC_den]
    type = StrainAdjustedDensity
    strain_free_density = 1900.0 # kg/m^3
    block = IPyC
  []
  [IPyC_densification]
    type = PyCIrradiationEigenstrain
    block = IPyC
    pyc_type = dense
    eigenstrain_name = IPyC_eigenstrain
  []
  [IPyC_thermal_expansion]
    type = ComputeThermalExpansionEigenstrain
    block = IPyC
    thermal_expansion_coeff = 5.65e-6
    temperature = temperature
    stress_free_temperature = 1500.0
    eigenstrain_name = IPyC_thermal_strain
  []
  [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_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = SiC
    youngs_modulus = 3.4e11
    poissons_ratio = 0.13
  []
  [monolithic_SiC_creep]
    type = MonolithicSiCCreepUpdate
    block = SiC
    fast_neutron_flux = fast_neutron_flux
    temperature = temperature
    k_function = k_function
  []
  [stress]
    type = ComputeMultipleInelasticStress
    inelastic_models = monolithic_SiC_creep
    block = SiC
  []
  [SiC_temp]
    type = HeatConductionMaterial
    block = SiC
    thermal_conductivity = 13.9 # J/m-s-K
    specific_heat = 620.0 # J/kg-K
  []
  [SiC_den]
    type = StrainAdjustedDensity
    strain_free_density = 3180.0 # kg/m^3
    block = SiC
  []
  [SiC_thermal_expansion]
    type = ComputeThermalExpansionEigenstrain
    block = SiC
    thermal_expansion_coeff = 4.9e-6
    temperature = temperature
    stress_free_temperature = 1500.0
    eigenstrain_name = SiC_thermal_strain
  []
  [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_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = OPyC
    youngs_modulus = 4.74e10
    poissons_ratio = 0.23
  []
  [OPyC_stress]
    type = PyCCreep
    block = OPyC
    flux_conversion_factor = 1.0
    temperature = temperature
  []
  [OPyC_temp]
    type = HeatConductionMaterial
    block = OPyC
    thermal_conductivity = 4.0 # J/m-s-K
    specific_heat = 720.0 # J/kg-K
  []
  [OPyC_den]
    type = StrainAdjustedDensity
    strain_free_density = 1900.0 # kg/m^3
    block = OPyC
  []
  [OPyC_densification]
    type = PyCIrradiationEigenstrain
    block = OPyC
    pyc_type = dense
    eigenstrain_name = OPyC_eigenstrain
  []
  [OPyC_thermal_expansion]
    type = ComputeThermalExpansionEigenstrain
    block = OPyC
    thermal_expansion_coeff = 5.65e-6
    temperature = temperature
    stress_free_temperature = 1500.0
    eigenstrain_name = OPyC_thermal_strain
  []
  [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
  []
[]

[Debug]
  show_var_residual_norms = 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-7
  nl_max_its = 15

  l_tol = 1e-8
  l_max_its = 50

  start_time = 0.0
  #end_time = 85.3682e6
  end_time = 1e3
  num_steps = 1000

  dtmax = 2e6
  dtmin = 1

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

  [Quadrature]
    order = THIRD
  []
[]

[Postprocessors]
  [release_Cs_inc]
    type = SideIntegralMassFlux
    variable = conc_Cs
    boundary = exterior
  []
  [Int_Cs_release]
    type = TimeIntegratedPostprocessor
    value = release_Cs_inc
  []
  [release_fuel_Cs]
    type = SideIntegralMassFlux
    variable = conc_Cs
    boundary = fuel
  []
  [Int_Cs_release_fuel]
    type = TimeIntegratedPostprocessor
    value = release_fuel_Cs
  []
  [release_PyCGapBndry_Cs]
    type = SideIntegralMassFlux
    variable = conc_Cs
    boundary = PyCGapBndry
  []
  [Int_Cs_release_PyCGapBndry]
    type = TimeIntegratedPostprocessor
    value = release_PyCGapBndry_Cs
  []
  [fis_gas_produced]
    type = ElementIntegralFisGasGeneratedSifgrs
    block = fuel
    execute_on = linear
  []
  [fis_gas_released]
    type = ElementIntegralFisGasReleasedSifgrs
    block = fuel
    execute_on = linear
  []
  [volumeTotal]
    type = InternalVolume
    boundary = exterior
    execute_on = 'initial timestep_end'
  []
  [volumeFuel]
    type = InternalVolume
    boundary = fuel
    execute_on = 'initial timestep_end'
  []
  [volumeGas]
    type = InternalVolume
    boundary = BufferGapVol
    addition = -4.6e-11
    execute_on = 'initial linear'
  []
  [volumeBufferShell]
    type = InternalVolume
    boundary = BufferGapVol
    execute_on = 'initial timestep_end'
  []
  [ave_temp_interior]
    type = SideAverageValue
    boundary = BufferGapVol
    variable = temperature
    execute_on = 'initial timestep_end'
  []

  # Postprocessors for CO production
  [total_fission_rate]
    type = ElementIntegralPower
    variable = temperature
    fission_rate = fission_rate
    block = fuel
    energy_per_fission = 1.0
    outputs = exodus
    execute_on = 'initial linear'
  []
  [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'
  []
  [co_production]
    type = CarbonMonoxideProduction
    total_fissions = total_fissions
    time_integrated_triso_temperature = time_int_surf_temp
    initial_enrichment = 0.14029
    execute_on = 'initial nonlinear'
  []
[]

[Outputs]
  print_linear_residuals = false
  [console]
    type = Console
    max_rows = 5
    outlier_variable_norms = false
  []
  [exodus]
    type = Exodus
    file_base = triso1D_accident_out
  []
[]

(test/tests/triso_failure/ad_ipyc_characteristic_strength.i)

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

[Mesh]
  coord_type = RSPHERICAL

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

[Variables]
  [disp_x]
  []
  [temp]
    initial_condition = 1346.0
  []
[]

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

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


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

[Kernels]
  [heat_ie]
    type = ADHeatConductionTimeDerivative
    variable = temp
  []
  [heat]
    type = ADHeatConduction
    variable = temp
  []
  [heat_source]
    type = ADNeutronHeatSource
    variable = temp
    block = fuel
    energy_per_fission = 3.2e-11
    fission_rate = fission_rate
  []
[]

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

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

[ThermalContact]
  [thermal_contact]
    type = GasGapHeatTransfer
    variable = temp
    primary = IPyC_inner_boundary
    secondary = buffer_outer_boundary
    # coupling to a postprocessor
    initial_moles = initial_moles
    gas_released = 'fis_gas_released co_production'
    released_gas_types = 'Kr Xe;
                          CO'
    released_fractions = '0.153 0.847;
                          1'
    tangential_tolerance = 1e-6
    use_automatic_differentiation = true
  []
[]

[BCs]
  # pin particle along symmetry planes
  [no_disp_x]
    type = ADDirichletBC
    variable = disp_x
    boundary = xzero
    value = 0.0
  []
  # fix temperature on free surface
  [freesurf_temp]
    type = ADDirichletBC
    variable = temp
    boundary = exterior
    value = 1346.0
  []
  # exterior and internal pressures
  [exterior_pressure_x]
    type = ADPressure
    use_displaced_mesh = false
    variable = disp_x
    boundary = exterior
    factor = 0.1e6
  []
  #  apply gas pressure on buffer and IPyC boundaries
  [PlenumPressure]
    [plenumPressure]
      use_displaced_mesh = false
      boundary = buffer_IPyC_boundary
      initial_pressure = 0
      startup_time = 1.0e4
      R = 8.3143
      # coupling to post processor
      output_initial_moles = initial_moles
      temperature = ave_temp_interior
      volume = volumeGas
      material_input = 'fis_gas_released co_production'
      output = plenum_pressure
      use_automatic_differentiation = true
    []
  []
[]

[Materials]
  [max_principal_stress]
    type = ADRankTwoInvariant
    property_name = max_principal_stress
    rank_two_tensor = stress
    invariant = MaxPrincipal
  []
  [flux]
    type = ADFastNeutronFlux
    calculate_fluence = true
    factor = 1.708707e18
  []
  [fission_gas_release]
    type = ADUO2Sifgrs
    block = fuel
    temperature = temp
    fission_rate = fission_rate
    grain_radius_const = 5.0e-6
  []
  [stress]
    type = ADComputeLinearElasticStress
    block = 'fuel buffer SiC'
  []
  [PyC_stress]
    type = ADPyCCreep
    block = 'IPyC OPyC'
    k = k_function
    poissons_ratio = 0.4
    temperature = temp
  []
  [normal_vectors_triso]
    type = NormalVectorsTRISO
    block = 'IPyC OPyC'
  []
  [PyC_eigenstrain]
    type = ADPyCIrradiationEigenstrain
    block = 'IPyC OPyC'
    radial_eigenstrain_function = radial_eigenstrain
    tangential_eigenstrain_function = tangential_eigenstrain
    eigenstrain_name = pyc_eigenstrain
  []
  [fuel_thermal_strain]
    type = ADComputeThermalExpansionEigenstrain
    block = fuel
    thermal_expansion_coeff = 10e-6
    stress_free_temperature = 1346.0
    eigenstrain_name = thermal_strain
    temperature = temp
  []
  [PyC_thermal_strain]
    type = ADComputeThermalExpansionEigenstrain
    block = 'buffer IPyC OPyC'
    thermal_expansion_coeff = 5.5e-6
    stress_free_temperature = 1346.0
    eigenstrain_name = thermal_strain
    temperature = temp
  []
  [SiC_thermal_strain]
    type = ADComputeThermalExpansionEigenstrain
    block = SiC
    thermal_expansion_coeff = 4.9e-6
    stress_free_temperature = 1346.0
    eigenstrain_name = thermal_strain
    temperature = temp
  []
  [fuel_thermal]
    type = ADUO2Thermal
    thermal_conductivity_model = FINK_LUCUTA
    block = fuel
    temperature = temp
    burnup = burnup
  []
  [fuel_elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    block = fuel
    youngs_modulus = 2e8
    poissons_ratio = 0.345
  []
  [fuel_den]
    type = ADStrainAdjustedDensity
    block = fuel
    strain_free_density = 10810.0
  []
  [buffer_elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    block = buffer
    youngs_modulus = 2e8
    poissons_ratio = 0.345
  []
  [buffer_temp]
    type = ADHeatConductionMaterial
    block = buffer
    thermal_conductivity = 0.5
    specific_heat = 720.0
  []
  [buffer_den]
    type = ADStrainAdjustedDensity
    strain_free_density = 1000
    block = buffer
  []
  [PyC_elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    block = 'IPyC OPyC'
    youngs_modulus = 3.96e10
    poissons_ratio = 0.33
  []
  [PyC_temp]
    type = ADHeatConductionMaterial
    block = 'IPyC OPyC'
    thermal_conductivity = 4.0
    specific_heat = 720.0
  []
  [PyC_den]
    type = ADStrainAdjustedDensity
    strain_free_density = 1880.0
    block = 'IPyC OPyC'
  []
  [SiC_elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    block = SiC
    youngs_modulus = 3.7e11
    poissons_ratio = 0.13
  []
  [SiC_temp]
    type = ADHeatConductionMaterial
    block = SiC
    thermal_conductivity = 13.9
    specific_heat = 620.0
  []
  [SiC_den]
    type = ADStrainAdjustedDensity
    strain_free_density = 3200.0
    block = SiC
  []
  [characteristic_strength_SiC]
    type = ADGenericConstantMaterial
    prop_values = '9640000'
    block = SiC
    prop_names = 'characteristic_strength'
  []
  [characteristic_strength_PyC]
    type = ADPyCCharacteristicStrength
    temperature = temp
    X = 1.02
    flux_conversion_factor = 0.85
    block = 'IPyC OPyC'
  []
[]

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

[Debug]
  show_var_residual_norms = true
[]

[Executioner]
  type = Transient
  petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
  petsc_options_value = '201                hypre    boomeramg      4'
  line_search = 'none'
  solve_type = 'PJFNK'
  nl_rel_tol = 5e-8
  nl_abs_tol = 1e-10
  nl_max_its = 15
  l_tol = 1e-3
  l_max_its = 50
  start_time = 0.0
  num_steps = 10
  dtmax = 2e5
  dtmin = 1
  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 20
    optimal_iterations = 6
    iteration_window = 2
    linear_iteration_ratio = 100
  []
[]

[Postprocessors]
  [dt]
    type = TimestepSize
  []
  [burnup]
    type = ElementExtremeValue
    block = fuel
    variable = burnup
  []
  [fis_gas_produced]
    type = ADElementIntegralFisGasGeneratedSifgrs
    block = fuel
  []
  [fis_gas_released]
    type = ADElementIntegralFisGasReleasedSifgrs
    block = fuel
  []
  [volumeTotal]
    type = InternalVolume
    boundary = exterior
  []
  [volumeFuel]
    type = InternalVolume
    boundary = fuel_outer_boundary
  []
  [volumeGas]
    type = InternalVolume
    boundary = 'fuel_outer_boundary IPyC_inner_boundary'
    addition = -5.53e-11
    execute_on = 'initial timestep_end'
  []
  [volumeBufferShell]
    type = InternalVolume
    boundary = buffer_IPyC_boundary
  []
  [ave_temp_interior]
    type = SideAverageValue
    boundary = buffer_IPyC_boundary
    variable = temp
    execute_on = 'initial timestep_end'
  []
  # Postprocessors for CO production
  [total_fission_rate]
    type = ElementIntegralPower
    variable = temp
    fission_rate = fission_rate
    block = fuel
    energy_per_fission = 1.0
  []
  [total_fissions]
    type = TimeIntegratedPostprocessor
    value = total_fission_rate
  []
  [avg_surface_temp]
    type = SideAverageValue
    variable = temp
    boundary = exterior
  []
  [time_int_surf_temp]
    type = TimeIntegratedPostprocessor
    value = avg_surface_temp
  []
  [co_production]
    type = CarbonMonoxideProduction
    total_fissions = total_fissions
    time_integrated_triso_temperature = time_int_surf_temp
    initial_enrichment = 0.14029
  []
  [tang_SiC]
    type = ElementalVariableValue
    variable = stress_yy
    elementid = 18
  []
  [strength_SiC]
    type = ADWeibullEffectiveMeanStrength
    block = SiC
    weibull_modulus = 6
  []
  [failure_indicator_SiC]
    type = ADWeibullFailureOutputUsingCorrelation
    block = SiC
    weibull_modulus = 6
    stress_name = max_principal_stress
    effective_mean_strength = strength_SiC
  []
  [strength_IPyC]
    type = ADWeibullEffectiveMeanStrength
    block = IPyC
    weibull_modulus = 6
  []
  [failure_indicator_IPyC]
    type = ADWeibullFailureOutputUsingCorrelation
    block = IPyC
    weibull_modulus = 6
    stress_name = max_principal_stress
    effective_mean_strength = strength_IPyC
  []
  [strength_OPyC]
    type = ADWeibullEffectiveMeanStrength
    block = OPyC
    weibull_modulus = 6
  []
  [failure_indicator_OPyC]
    type = ADWeibullFailureOutputUsingCorrelation
    block = OPyC
    weibull_modulus = 6
    stress_name = max_principal_stress
    effective_mean_strength = strength_OPyC
  []
  [failure_indicator_SiC_crackedIPyC]
    type = ADWeibullFailureOutputUsingCorrelation
    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 = ADWeibullFailureOutputUsingCorrelation
    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
  []
  [characteristic_strength]
    type = ADElementExtremeMaterialProperty
    mat_prop = characteristic_strength
    block = IPyC
    value_type = max
  []
  [flence]
    type = ADElementExtremeMaterialProperty
    mat_prop = fast_neutron_fluence
    block = IPyC
    value_type = max
  []
[]

[Outputs]
  file_base = triso_ipyc_characteristic_strength_out
  print_linear_residuals = true
  time_step_interval =  1
  csv = true
[]

(test/tests/triso_failure/triso_1d_ipyc_failure.i)

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

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

[Variables]
  [disp_x]
  []
  [temp]
    initial_condition = 1346.0
  []
[]

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

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

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

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

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

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

[ThermalContact]
  [thermal_contact]
    type = GasGapHeatTransfer
    variable = temp
    primary = IPyC_inner_boundary
    secondary = buffer_outer_boundary
    # coupling to a postprocessor
    initial_moles = initial_moles
    gas_released = 'fis_gas_released co_production'
    released_gas_types = 'Kr Xe;
                          CO'
    released_fractions = '0.153 0.847;
                          1'
    tangential_tolerance = 1e-6
    #    contact_pressure_input = 10e6
    #    quadrature = true
  []
[]

[BCs]
  # pin particle along symmetry planes
  [no_disp_x]
    type = DirichletBC
    variable = disp_x
    boundary = xzero
    value = 0.0
  []
  # fix temperature on free surface
  [freesurf_temp]
    type = DirichletBC
    variable = temp
    boundary = exterior
    value = 1346.0
  []
  # exterior and internal pressures
  [exterior_pressure_x]
    type = Pressure
    use_displaced_mesh = false
    variable = disp_x
    boundary = exterior
    factor = 0.1e6
  []
  #  apply gas pressure on buffer and IPyC boundaries
  [PlenumPressure]
    [plenumPressure]
      use_displaced_mesh = false
      boundary = buffer_IPyC_boundary
      initial_pressure = 0
      startup_time = 1.0e4
      R = 8.3143
      # coupling to post processor
      output_initial_moles = initial_moles
      temperature = ave_temp_interior
      volume = volumeGas
      material_input = 'fis_gas_released co_production'
      output = plenum_pressure
    []
  []
[]

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

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

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

[Debug]
  show_var_residual_norms = true
[]

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

[Postprocessors]
  [dt]
    type = TimestepSize
  []
  [burnup]
    type = ElementExtremeValue
    block = fuel
    variable = burnup
  []
  [fis_gas_produced]
    type = ElementIntegralFisGasGeneratedSifgrs
    block = fuel
  []
  [fis_gas_released]
    type = ElementIntegralFisGasReleasedSifgrs
    block = fuel
  []
  [volumeTotal]
    type = InternalVolume
    boundary = exterior
  []
  [volumeFuel]
    type = InternalVolume
    boundary = fuel_outer_boundary
  []
  [volumeGas]
    type = InternalVolume
    boundary = 'fuel_outer_boundary IPyC_inner_boundary'
    addition = -5.53e-11
    execute_on = 'initial timestep_end'
  []
  [volumeBufferShell]
    type = InternalVolume
    boundary = buffer_IPyC_boundary
  []
  [ave_temp_interior]
    type = SideAverageValue
    boundary = buffer_IPyC_boundary
    variable = temp
    execute_on = 'initial timestep_end'
  []
  # Postprocessors for CO production
  [total_fission_rate]
    type = ElementIntegralPower
    variable = temp
    fission_rate = fission_rate
    block = fuel
    energy_per_fission = 1.0
  []
  [total_fissions]
    type = TimeIntegratedPostprocessor
    value = total_fission_rate
  []
  [avg_surface_temp]
    type = SideAverageValue
    variable = temp
    boundary = exterior
  []
  [time_int_surf_temp]
    type = TimeIntegratedPostprocessor
    value = avg_surface_temp
  []
  [co_production]
    type = CarbonMonoxideProduction
    total_fissions = total_fissions
    time_integrated_triso_temperature = time_int_surf_temp
    initial_enrichment = 0.14029
  []
  [tang_SiC]
    type = ElementalVariableValue
    variable = stress_yy
    elementid = 18
  []
  [strength_SiC]
    type = WeibullEffectiveMeanStrength
    block = SiC
    weibull_modulus = 6
  []
  [failure_indicator_SiC]
    type = WeibullFailureOutputUsingCorrelation
    block = SiC
    weibull_modulus = 6
    stress_name = max_principal_stress
    effective_mean_strength = strength_SiC
  []
  [strength_IPyC]
    type = WeibullEffectiveMeanStrength
    block = IPyC
    weibull_modulus = 6
  []
  [failure_indicator_IPyC]
    type = WeibullFailureOutputUsingCorrelation
    block = IPyC
    weibull_modulus = 6
    stress_name = max_principal_stress
    effective_mean_strength = strength_IPyC
  []
  [strength_OPyC]
    type = WeibullEffectiveMeanStrength
    block = OPyC
    weibull_modulus = 6
  []
  [failure_indicator_OPyC]
    type = WeibullFailureOutputUsingCorrelation
    block = OPyC
    weibull_modulus = 6
    stress_name = max_principal_stress
    effective_mean_strength = strength_OPyC
  []
  [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
  []
[]

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

(test/tests/triso_failure/triso_1d_layer_stress_strength.i)

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

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

[Variables]
  [disp_x]
  []
  [temp]
    initial_condition = 1346.0
  []
[]

[Functions]
  [radial_eigenstrain]
    type = ParsedFunction
    expression = 't*(4.52013e-4/6.0*t*t*t*t*t - 8.36313e-3/5.0*t*t*t*t + 5.67549e-2/4.0*t*t*t - 1.74247e-1/3.0*t*t + 2.62692e-1/2.0*t - 1.43234e-1)'
  []
  [tangential_eigenstrain]
    type = ParsedFunction
    expression = 't*(1.30457e-4/4.0*t*t*t - 2.10029e-3/3.0*t*t + 9.07826e-3/2.0*t - 3.24737e-2)'
  []
  [fission_rate]
    type = ParsedFunction
    expression = 7.75e19 # units of fissions/m**3
  []
  [k_function]
    type = ParsedFunction
    expression = '4.93e-29'
  []
  [high_fidelity_strength_crackedIPyC]
    type = PiecewiseLinear
    x = '0 1.0e11'
    y = '1000000 1000000'
  []
  [high_fidelity_strength_crackedOPyC]
    type = PiecewiseLinear
    x = '0 1.0e11'
    y = '1000000 1000000'
  []
  [stress_correlation_crackedOPyC]
    type = PiecewiseLinear
    x = '0 1.0e11'
    y = '1 1'
  []
  [stress_correlation_crackedIPyC]
    type = PiecewiseLinear
    x = '0 1.0e11'
    y = '100 100'
  []
  [ipyc_stress_strength]
    type = ParsedFunction
    expression = 'a-b'
    symbol_names = 'a b'
    symbol_values = 'stress_IPyC actual_strength_IPyC'
  []
  [opyc_stress_strength]
    type = ParsedFunction
    expression = 'a-b'
    symbol_names = 'a b'
    symbol_values = 'stress_OPyC actual_strength_OPyC'
  []
  [sic_crackedipyc_stress_strength]
    type = ParsedFunction
    expression = 'a-b'
    symbol_names = 'a b'
    symbol_values = 'stress_SiC_crackedIPyC actual_strength_SiC_crackedIPyC'
  []
  [sic_crackedopyc_stress_strength]
    type = ParsedFunction
    expression = 'a-b'
    symbol_names = 'a b'
    symbol_values = 'stress_SiC_crackedOPyC actual_strength_SiC_crackedOPyC'
  []
[]

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

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

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

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

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

[ThermalContact]
  [thermal_contact]
    type = GasGapHeatTransfer
    variable = temp
    primary = IPyC_inner_boundary
    secondary = buffer_outer_boundary
    # coupling to a postprocessor
    initial_moles = initial_moles
    gas_released = 'fis_gas_released co_production'
    released_gas_types = 'Kr Xe;
                            CO'
    released_fractions = '0.153 0.847;
                            1'
    tangential_tolerance = 1e-6
    #    contact_pressure_input = 10e6
    #    quadrature = true
  []
[]

[BCs]
  # pin particle along symmetry planes
  [no_disp_x]
    type = DirichletBC
    variable = disp_x
    boundary = xzero
    value = 0.0
  []
  # fix temperature on free surface
  [freesurf_temp]
    type = DirichletBC
    variable = temp
    boundary = exterior
    value = 1346.0
  []
  # exterior and internal pressures
  [exterior_pressure_x]
    type = Pressure
    use_displaced_mesh = false
    variable = disp_x
    boundary = exterior
    factor = 0.1e6
  []
  #  apply gas pressure on buffer and IPyC boundaries
  [PlenumPressure]
    [plenumPressure]
      use_displaced_mesh = false
      boundary = buffer_IPyC_boundary
      initial_pressure = 0
      startup_time = 1.0e4
      R = 8.3143
      # coupling to post processor
      output_initial_moles = initial_moles
      temperature = ave_temp_interior
      volume = volumeGas
      material_input = 'fis_gas_released co_production'
      output = plenum_pressure
    []
  []
[]

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

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

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

[Debug]
  show_var_residual_norms = true
[]

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

[Postprocessors]
  [dt]
    type = TimestepSize
  []
  [burnup]
    type = ElementExtremeValue
    block = fuel
    variable = burnup
  []
  [fis_gas_produced]
    type = ElementIntegralFisGasGeneratedSifgrs
    block = fuel
  []
  [fis_gas_released]
    type = ElementIntegralFisGasReleasedSifgrs
    block = fuel
  []
  [volumeTotal]
    type = InternalVolume
    boundary = exterior
  []
  [volumeFuel]
    type = InternalVolume
    boundary = fuel_outer_boundary
  []
  [volumeGas]
    type = InternalVolume
    boundary = 'fuel_outer_boundary IPyC_inner_boundary'
    addition = -5.53e-11
    execute_on = 'initial timestep_end'
  []
  [volumeBufferShell]
    type = InternalVolume
    boundary = buffer_IPyC_boundary
  []
  [ave_temp_interior]
    type = SideAverageValue
    boundary = buffer_IPyC_boundary
    variable = temp
    execute_on = 'initial timestep_end'
  []
  # Postprocessors for CO production
  [total_fission_rate]
    type = ElementIntegralPower
    variable = temp
    fission_rate = fission_rate
    block = fuel
    energy_per_fission = 1.0
  []
  [total_fissions]
    type = TimeIntegratedPostprocessor
    value = total_fission_rate
  []
  [avg_surface_temp]
    type = SideAverageValue
    variable = temp
    boundary = exterior
  []
  [time_int_surf_temp]
    type = TimeIntegratedPostprocessor
    value = avg_surface_temp
  []
  [co_production]
    type = CarbonMonoxideProduction
    total_fissions = total_fissions
    time_integrated_triso_temperature = time_int_surf_temp
    initial_enrichment = 0.14029
  []
  [tang_SiC]
    type = ElementalVariableValue
    variable = stress_yy
    elementid = 18
  []
  [strength_SiC]
    type = WeibullEffectiveMeanStrength
    block = SiC
    weibull_modulus = 6
  []
  [stress_SiC]
    type = WeibullFailureOutputUsingCorrelation
    block = SiC
    weibull_modulus = 6
    stress_name = max_principal_stress
    effective_mean_strength = strength_SiC
    output_type = 'stress'
  []
  [actual_strength_SiC]
    type = WeibullFailureOutputUsingCorrelation
    block = SiC
    weibull_modulus = 6
    stress_name = max_principal_stress
    effective_mean_strength = strength_SiC
    output_type = 'strength'
  []
  [strength_IPyC]
    type = WeibullEffectiveMeanStrength
    block = IPyC
    weibull_modulus = 6
  []
  [stress_IPyC]
    type = WeibullFailureOutputUsingCorrelation
    block = IPyC
    weibull_modulus = 6
    stress_name = max_principal_stress
    effective_mean_strength = strength_IPyC
    output_type = 'stress'
  []
  [actual_strength_IPyC]
    type = WeibullFailureOutputUsingCorrelation
    block = IPyC
    weibull_modulus = 6
    stress_name = max_principal_stress
    effective_mean_strength = strength_IPyC
    output_type = 'strength'
  []
  [IPyC_stressminusstrength]
    type = FunctionValuePostprocessor
    function = 'ipyc_stress_strength'
  []
  [strength_OPyC]
    type = WeibullEffectiveMeanStrength
    block = OPyC
    weibull_modulus = 6
  []
  [stress_OPyC]
    type = WeibullFailureOutputUsingCorrelation
    block = OPyC
    weibull_modulus = 6
    stress_name = max_principal_stress
    effective_mean_strength = strength_OPyC
    output_type = 'stress'
  []
  [actual_strength_OPyC]
    type = WeibullFailureOutputUsingCorrelation
    block = OPyC
    weibull_modulus = 6
    stress_name = max_principal_stress
    effective_mean_strength = strength_OPyC
    output_type = 'strength'
  []
  [OPyC_stressminusstrength]
    type = FunctionValuePostprocessor
    function = 'opyc_stress_strength'
  []
  [stress_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'
    output_type = 'stress'
  []
  [actual_strength_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'
    output_type = 'strength'
  []
  [SiC_crackedIPyC_stressminusstrength]
    type = FunctionValuePostprocessor
    function = 'sic_crackedipyc_stress_strength'
  []
  [stress_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'
    output_type = 'stress'
  []
  [actual_strength_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'
    output_type = 'strength'
  []
  [SiC_crackedOPyC_stressminusstrength]
    type = FunctionValuePostprocessor
    function = 'sic_crackedopyc_stress_strength'
  []
[]

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

(examples/TRISO/full_particle/1D/full_particle_1D.i)


initial_fuel_density = 10810.0

[GlobalParams]
  density = ${initial_fuel_density}
  flux_conversion_factor = 1.0
  order = SECOND
  family = LAGRANGE
  displacements = 'disp_x'
[]

[Mesh]
  coord_type = RSPHERICAL
  [gen]
    type = TRISO1DMeshGenerator
    elem_type = EDGE3
    coordinates = '0 2.485e-4 3.425e-4 3.425e-4 3.835e-4 4.195e-4 4.595e-4'
    mesh_density = '6 6 0 6 8 6'
    block_names = 'fuel buffer IPyC SiC OPyC'
  []
[]

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

[AuxVariables]
  [fission_rate]
    block = fuel
  []
  [burnup]
    block = fuel
  []
  [grain_radius]
    initial_condition = 5.0e-6
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [fuel]
    block = fuel
    add_variables = true
    strain = FINITE
    eigenstrain_names = 'fuel_thermal_strain'
    generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz stress_xy stress_yz stress_xz strain_xy strain_yz strain_xz'
  []
  [buffer]
    block = buffer
    add_variables = true
    strain = FINITE
    eigenstrain_names = 'buffer_thermal_strain buffer_eigenstrain'
    generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz stress_xy stress_yz stress_xz strain_xy strain_yz strain_xz'
  []
  [IPyC]
    block = IPyC
    add_variables = true
    strain = FINITE
    eigenstrain_names = 'IPyC_eigenstrain IPyC_thermal_strain'
    generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz stress_xy stress_yz stress_xz strain_xy strain_yz strain_xz'
  []
  [SiC]
    block = SiC
    add_variables = true
    strain = FINITE
    eigenstrain_names = 'SiC_thermal_strain'
    generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz stress_xy stress_yz stress_xz strain_xy strain_yz strain_xz'
  []
  [OPyC]
    block = OPyC
    add_variables = true
    strain = FINITE
    eigenstrain_names = 'OPyC_eigenstrain OPyC_thermal_strain'
    generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz stress_xy stress_yz stress_xz strain_xy strain_yz strain_xz'
  []
[]

[Functions]
  [fission_rate]
    type = ParsedFunction
    expression = 7.75e19
  []
[]

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

[AuxKernels]
  [fission_rate]
    type = FunctionAux
    variable = fission_rate
    block = fuel
    function = fission_rate
  []
  [burnup]
    type = BurnupAux
    variable = burnup
    block = fuel
    fission_rate = fission_rate
    molecular_weight = 0.270
  []
  [grain_radius]
    type = GrainRadiusAux
    block = fuel
    variable = grain_radius
    temperature = temperature
    execute_on = linear
  []
[]

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

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

[BCs]
  [no_disp_x]
    type = DirichletBC
    variable = disp_x
    boundary = xzero
    value = 0.0
  []
  [freesurf_temperature]
    type = DirichletBC
    variable = temperature
    boundary = exterior
    value = 1346.0
  []
  [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 = 0
      startup_time = 1.0e4
      R = 8.3143
      # couplings to post processor
      output_initial_moles = initial_moles
      temperature = ave_temperature_interior
      volume = volumeGas
      material_input = 'fis_gas_released co_production'
      output = plenum_pressure
    []
  []
[]

[Materials]
  [flux]
    type = FastNeutronFlux
    calculate_fluence = true
    factor = 1.708707e18 # n/m^2-sec
  []
  [fuel_thermal]
    type = UO2Thermal
    block = fuel
    temperature = temperature
    thermal_conductivity_model = FINK_LUCUTA
    initial_porosity = 0.0
    burnup = burnup
  []
  [fuel_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = fuel
    youngs_modulus = 2.0e8
    poissons_ratio = 0.345
  []
  [fuel_elastic_stress]
    type = ComputeFiniteStrainElasticStress
    block = fuel
  []
  [fuel_density]
    type = StrainAdjustedDensity
    block = fuel
    strain_free_density = ${initial_fuel_density}
  []
  [fuel_thermal_expansion]
    type = ComputeThermalExpansionEigenstrain
    block = fuel
    thermal_expansion_coeff = 10.0e-6
    temperature = temperature
    stress_free_temperature = 1346.0
    eigenstrain_name = fuel_thermal_strain
  []
  [fission_gas_release]
    type = UO2Sifgrs
    block = fuel
    temperature = temperature
    fission_rate = fission_rate
    grain_radius = grain_radius
  []
  [buffer_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = buffer
    youngs_modulus = 2.0e8
    poissons_ratio = 0.345
  []
  [buffer_elastic_stress]
    type = ComputeFiniteStrainElasticStress
    block = buffer
  []
  [buffer_temperature]
    type = HeatConductionMaterial
    block = buffer
    thermal_conductivity = 0.5
    specific_heat = 720.0
  []
  [buffer_density]
    type = StrainAdjustedDensity
    strain_free_density = 1000.0
    block = buffer
  []
  [buffer_thermal_expansion]
    type = ComputeThermalExpansionEigenstrain
    block = buffer
    thermal_expansion_coeff = 5.5e-6
    temperature = temperature
    stress_free_temperature = 1346.0
    eigenstrain_name = buffer_thermal_strain
  []
  [normal_vectors_triso]
    type = NormalVectorsTRISO
    block = 'IPyC OPyC buffer'
  []
  [buffer_irraditation]
    type = PyCIrradiationEigenstrain
    block = buffer
    pyc_type = buffer
    eigenstrain_name = buffer_eigenstrain
  []
  [IPyC_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = IPyC
    youngs_modulus = 3.96e10
    poissons_ratio = 0.33
  []
  [IOPyC_stress]
    type = PyCCreep
    block = 'IPyC OPyC'
    temperature = temperature
  []
  [IOPyC_thermal]
    type = HeatConductionMaterial
    block = 'IPyC OPyC'
    thermal_conductivity = 4.0
    specific_heat = 720.0
  []
  [IOPyC_density]
    type = StrainAdjustedDensity
    strain_free_density = 1880.0
    block = 'IPyC OPyC'
  []
  [IPyC_densification]
    type = PyCIrradiationEigenstrain
    block = IPyC
    pyc_type = dense
    eigenstrain_name = IPyC_eigenstrain
  []
  [IPyC_thermal_expansion]
    type = ComputeThermalExpansionEigenstrain
    block = IPyC
    thermal_expansion_coeff = 5.5e-6
    temperature = temperature
    stress_free_temperature = 1346.0
    eigenstrain_name = IPyC_thermal_strain
  []
  [SiC_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = SiC
    youngs_modulus = 3.7e11
    poissons_ratio = 0.13
  []
  [SiC_elastic_stress]
    type = ComputeFiniteStrainElasticStress
    block = SiC
  []
  [SiC_temperature]
    type = HeatConductionMaterial
    block = SiC
    thermal_conductivity = 13.9
    specific_heat = 620.0
  []
  [SiC_density]
    type = StrainAdjustedDensity
    strain_free_density = 3200.0
    block = SiC
  []
  [SiC_thermal_expansion]
    type = ComputeThermalExpansionEigenstrain
    block = SiC
    thermal_expansion_coeff = 4.9e-6
    temperature = temperature
    stress_free_temperature = 1346.0
    eigenstrain_name = SiC_thermal_strain
  []
  [OPyC_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = OPyC
    youngs_modulus = 3.96e10
    poissons_ratio = 0.33
  []
  [OPyC_densification]
    type = PyCIrradiationEigenstrain
    block = OPyC
    pyc_type = dense
    eigenstrain_name = OPyC_eigenstrain
  []
  [OPyC_thermal_expansion]
    type = ComputeThermalExpansionEigenstrain
    block = OPyC
    thermal_expansion_coeff = 5.5e-6
    temperature = temperature
    stress_free_temperature = 1346.0
    eigenstrain_name = OPyC_thermal_strain
  []
[]

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

[Executioner]
  type = Transient
  petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
  petsc_options_value = '201                hypre    boomeramg      4'
  line_search = 'none'
  solve_type = 'PJFNK'
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-10
  nl_max_its = 15
  l_tol = 1e-3
  l_max_its = 50
  start_time = 0.0
  end_time = 3.10176e7
  dtmax = 2e5
  dtmin = 1
  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 20
    optimal_iterations = 6
    iteration_window = 2
    linear_iteration_ratio = 100
  []
[]

[Postprocessors]
  [dt]
    type = TimestepSize
  []
  [burnup]
    type = ElementExtremeValue
    block = fuel
    variable = burnup
  []
  [fis_gas_produced]
    type = ElementIntegralFisGasGeneratedSifgrs
    block = fuel
  []
  [fis_gas_released]
    type = ElementIntegralFisGasReleasedSifgrs
    block = fuel
  []
  [volumeTotal]
    type = InternalVolume
    boundary = exterior
  []
  [volumeFuel]
    type = InternalVolume
    boundary = fuel_outer_boundary
  []
  [volumeGas]
    type = InternalVolume
    boundary = 'fuel_outer_boundary IPyC_inner_boundary'
    addition = -5.53e-11
    execute_on = 'initial timestep_end'
  []
  [volumeBufferShell]
    type = InternalVolume
    boundary = buffer_IPyC_boundary
  []
  [ave_temperature_interior]
    type = SideAverageValue
    boundary = buffer_IPyC_boundary
    variable = temperature
    execute_on = 'initial timestep_end'
  []
  [total_fission_rate]
    type = ElementIntegralPower
    variable = temperature
    fission_rate = fission_rate
    block = fuel
    energy_per_fission = 1.0
  []
  [total_fissions]
    type = TimeIntegratedPostprocessor
    value = total_fission_rate
  []
  [avg_surface_temperature]
    type = SideAverageValue
    variable = temperature
    boundary = exterior
  []
  [time_int_surf_temperature]
    type = TimeIntegratedPostprocessor
    value = avg_surface_temperature
  []
  [co_production]
    type = CarbonMonoxideProduction
    total_fissions = total_fissions
    time_integrated_triso_temperature = time_int_surf_temperature
    initial_enrichment = 0.14029
  []
  [tang_SiC]
    type = ElementalVariableValue
    variable = stress_yy
    elementid = 18
  []
  [max_xx_IPyC]
    type = ElementExtremeValue
    variable = stress_xx
    block = IPyC
  []
  [max_yy_IPyC]
    type = ElementExtremeValue
    variable = stress_yy
    block = IPyC
  []
  [min_zz_IPyC]
    type = ElementExtremeValue
    variable = stress_zz
    block = IPyC
    value_type = min
  []
  [max_xx_SiC]
    type = ElementExtremeValue
    variable = stress_xx
    block = SiC
  []
  [max_yy_SiC]
    type = ElementExtremeValue
    variable = stress_yy
    block = SiC
  []
  [min_zz_SiC]
    type = ElementExtremeValue
    variable = stress_zz
    block = SiC
    value_type = min
  []
  [max_xx_OPyC]
    type = ElementExtremeValue
    variable = stress_xx
    block = OPyC
  []
  [max_yy_OPyC]
    type = ElementExtremeValue
    variable = stress_yy
    block = OPyC
  []
  [min_zz_OPyC]
    type = ElementExtremeValue
    variable = stress_zz
    block = OPyC
    value_type = min
  []
[]

[Outputs]
  print_linear_residuals = true
  time_step_interval =  1
  exodus = false
  csv = true
  perf_graph = true
  [chkfile]
    type = CSV
    execute_on = Final
    show = 'max_xx_IPyC max_yy_IPyC min_zz_IPyC max_xx_SiC max_yy_SiC min_zz_SiC'
  []
[]

(test/tests/carbon_monoxide_production/carbon_monoxide_production_test.i)

# Tests the carbon monoxide production postprocessor

# A constant volumetric fission rate of 1e19 fissions/m^3-s is applied to a 1 cm cube.
# All sides of the cube are held at 1000K to force a constant average surface temperature.
# The problem is solved over ten time steps of 1e7 s.
#
# The total number of fissions is computed using:
#   1) the ElementIntegralPower post processor and specifying energy_per_fission = 1 to
#      get the total fission rate
#   2) the TimeIntegratedPostprocessor post processor to time integrate the total fission rate
#
# The time integrated particle surface temperature is computed using:
#   1) the SideAverageValue post processor to give the time dependent average temperature
#      over the particle surface
#   2) the TimeIntegratedPostprocessor post processor to give the time integrated average temperature
#      over the particle surface
#
#    At t=1e8 (after ten time steps)
#       _total_fissions = 1e19(fissions/m^3-s)*(0.01m)**3*1e8
#                       = 1e21 fissions
#       _time_avg_surf_temp = _time_int_surf_temp/total_time
#                           = 1e11/1e8
#                           = 1000K
#
# 1. For the Proksch model, the moles of oxygen (and thus carbon monoxide) are given by:
#
#   moles CO = [_total_fissions*_t^2/((1.211e10)*10^(8500/(_time_avg_surf_temp))] / Avogadros_number
#
#       moles co = (1e21*1e8^2/((1.211e10)*10^(8500/1000))) / 6.02214076e23
#                = 4.336156561E-06 moles
#
#       which is what the post processor gets
#
# 2. For the GA model, the moles of oxygen are given by:
#
# moles co = (1.64*exp(-3311/1000)) * 1e21 / 6.02214076e23 = 9.934452008E-05
#

[Mesh]
  [mesh]
    type = FileMeshGenerator
    file = cube_1cm.e
  []
[]

[Variables]
  [T]
    order = FIRST
    family = LAGRANGE
    initial_condition = 1000
  []
[]

[AuxVariables]

  [fission_rate]
    order = FIRST
    family = LAGRANGE
  []
[]

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

  [ie]
    type = HeatConductionTimeDerivative
    variable = T
  []

  [heat_source]
    type = NeutronHeatSource
    variable = T
    energy_per_fission = 3.2e-11
    fission_rate = fission_rate
  []
[]

[AuxKernels]

  [fissionrate]
    type = FissionRateGeneral
    fission_rate_formulation = GENERIC
    variable = fission_rate
    value = 1.0e19
    execute_on = 'initial timestep_begin'
  []
[]

[BCs]

  [bottom_T]
    type = DirichletBC
    variable = T
    boundary = '1 2 3 4 5 6'
    value = 1000.0
  []
[]

[Materials]

  [fuel]
    type = HeatConductionMaterial
    block = 1
    thermal_conductivity = 10
    specific_heat = 100
  []
  [density]
    type = ParsedMaterial
    block = 1
    property_name = density
    expression = 10000
  []
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'

  nl_abs_tol = 1e-10
  nl_rel_tol = 1e-8
  start_time = 0.0
  num_steps = 10
  dt = 1.0e7
[]

[Postprocessors]
  [total_fission_rate]
    type = ElementIntegralPower
    variable = T
    fission_rate = fission_rate
    block = 1
    energy_per_fission = 1.0
    execute_on = 'initial timestep_end'
  []

  [total_fissions]
    type = TimeIntegratedPostprocessor
    value = total_fission_rate
  []

  [avg_surface_temp]
    type = SideAverageValue
    variable = T
    boundary = '1 2 3 4 5 6'
    execute_on = 'initial timestep_end'
  []

  [time_int_surf_temp]
    type = TimeIntegratedPostprocessor
    value = avg_surface_temp
    execute_on = 'initial timestep_end'
  []

  [co_production]
    type = CarbonMonoxideProduction
    total_fissions = total_fissions
    initial_enrichment = 0.14029
    execute_on = 'initial timestep_end'
  []
[]

[Outputs]
  csv = true
[]

(examples/TRISO/accident_simulation/triso2D_accident_mortar.i)

# This example is 2D-RZ analysis of a TRISO fuel particle. Fully coupled
# heat transfer and solid mechanics, plus diffusion of the fission product
# species cesium (Cs) are simulated.  The mesh includes contact surfaces
# between the buffer and IPyC layers to facilitate a gap opening between
# these layers. These surfaces are initially in mechanical contact but
# are assumed to have no strength in tension. A coarse mesh is used to
# provide a short run time.

# The calculation simulates fuel-life in three steps. The first step is an
# irradiation period, where constant power and a fixed particle surface
# temperature (1500 K) are assumed over a lifetime of 76 Ms (2.4 yrs).
# For the second step, fuel removal and storage are simulated by setting
# the reactor power and Cs source terms to zero, reducing the particle
# surface temperature to ambient (300 K), and then holding it
# for 100 days. A third and final step simulates accident
# behavior by increasing the particle surface temperature from ambient
# to 2073 K over 2 hrs, and then holding it at this elevated temperature
# for an additional 200 hrs. At the particle outer boundary, the Cs
# concentration is held at zero and the pressure at ambient during the
# entire simulation. The particle is assumed to be stress-free at an
# initial temperature of 1500 K.
#
# Details about this simulation are given in Section 4 of the following
# article: J. D. Hales, R. L. Williamson, S. R. Novascone, D. M. Perez,
# B. W. Spencer and G. Pastore, "Multidimensional multiphysics simulation
# of TRISO particle fuel", Journal of Nuclear Materials, Vol. 443, p. 531,
# 2013.

# This is a version using a thermomechanical mortar approach.


initial_fuel_density = 11000.0

[GlobalParams]
  order = SECOND
  family = LAGRANGE
  displacements = 'disp_x disp_y'
  flux_conversion_factor = 0.85
[]

[Mesh]
  coord_type = RZ
  [file]
    type = FileMeshGenerator
    file = triso2Dmed.e
  []
[]

[Problem]
  type = ReferenceResidualProblem
  reference_vector = 'ref'
  extra_tag_vectors = 'ref'
  converge_on = 'disp_x disp_y temp conc'
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [temp]
    initial_condition = 1500.0
  []
  [conc]
    initial_condition = 0.0
  []
[]

[AuxVariables]
  [fission_rate]
    block = fuel
    order = CONSTANT
    family = MONOMIAL
  []
  [fluence]
    order = CONSTANT
    family = MONOMIAL
  []
  [burnup]
    block = fuel
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_xx]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_yy]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_zz]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [power_history]
    type = PiecewiseLinear
    x = '0 76e6 76.001e6'
    y = '1 1     0'
  []
  [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'
  []
  [integral_flux_error]
    type = ParsedFunction
    symbol_names = 'buffer_integral_flux IPyC_integral_flux'
    symbol_values = 'buffer_integral_flux IPyC_integral_flux'
    expression = 'IPyC_integral_flux + buffer_integral_flux'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  generate_output = 'stress_xx stress_yy stress_zz stress_xy stress_yz stress_zx hydrostatic_stress'
  strain = FINITE
  incremental = true
  add_variables = false
  [default]
    block = 'fuel buffer IPyC OPyC'
    eigenstrain_names = 'thermal_strain swelling_strain'
    extra_vector_tags = 'ref'
  []
  [SiC]
    block = 'SiC'
    eigenstrain_names = 'thermal_strain'
    extra_vector_tags = 'ref'
  []
[]

[Kernels]
  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temp
    extra_vector_tags = 'ref'
    block = 'fuel buffer IPyC SiC OPyC'
  []
  [heat]
    type = HeatConduction
    variable = temp
    extra_vector_tags = 'ref'
    block = 'fuel buffer IPyC SiC OPyC'
  []
  [heat_source]
    type = NeutronHeatSource
    variable = temp
    block = fuel
    energy_per_fission = 3.2e-11 # units of J/fission
    fission_rate = fission_rate
    extra_vector_tags = 'ref'
  []
  [mass_ie]
    type = TimeDerivative
    variable = conc
    extra_vector_tags = 'ref'
    block = 'fuel buffer IPyC SiC OPyC'
  []
  [mass]
    type = ArrheniusDiffusion
    variable = conc
    extra_vector_tags = 'ref'
    block = 'fuel buffer IPyC SiC OPyC'
  []
  [mass_source]
    type = BodyForce
    variable = conc
    function = power_history
    value = 1.22e-5 # units of moles/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
    block = 'fuel buffer IPyC SiC OPyC'
    extra_vector_tags = 'ref'
  []
[]

[AuxKernels]
  [fission_rate]
    type = FissionRateGeneral
    fission_rate_formulation = GENERIC
    variable = fission_rate
    block = fuel
    fission_rate_function = power_history
    value = 3.89e19
    execute_on = timestep_begin
  []
  [fluence]
    type = MaterialRealAux
    property = fast_neutron_fluence
    variable = fluence
  []
  [burnup]
    type = BurnupAux
    variable = burnup
    block = fuel
    fission_rate = fission_rate
    molecular_weight = 0.270 # units of kg/mole
    execute_on = timestep_begin
    density = ${initial_fuel_density}
  []
  [creep_xx]
    type = RankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_xx
    index_i = 0
    index_j = 0
    block = 'buffer IPyC SiC OPyC'
    execute_on = timestep_end
  []
  [creep_yy]
    type = RankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_yy
    index_i = 1
    index_j = 1
    block = 'buffer IPyC SiC OPyC'
    execute_on = timestep_end
  []
  [creep_zz]
    type = RankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_zz
    index_i = 2
    index_j = 2
    block = 'buffer IPyC SiC OPyC'
    execute_on = timestep_end
  []
[]

[ThermalContactMortar]
  [thermal]
    secondary_variable = temp
    primary_boundary = 15
    secondary_boundary = 17

    initial_moles = initial_moles # coupling to a postprocessor which supplies the initial plenum/gap gas mass
    gas_released = 'fis_gas_released co_production' # coupling to postprocessors which supply the fission gas addition, co addition
    released_gas_types = 'Kr Xe;
                          CO'
    released_fractions = '0.153 0.847;
                          1'
    gap_geometry_type = CYLINDER
    min_gap = 1e-7
    max_gap = 50e-6
    roughness_coef = 0.0
    correct_edge_dropping = true
  []
[]

[Contact]
  [pellet_clad_mechanical]
    primary = 15
    secondary = 17
    model = frictionless
    formulation = mortar
    c_normal = 1.0e8
    correct_edge_dropping = true
  []
[]

[ThermalContact]
  [cesium_contact]
    type = GapHeatTransfer
    variable = conc
    primary = 15
    secondary = 17
    tangential_tolerance = 1e-6
    gap_conductivity_function = d_gap
    gap_conductivity_function_variable = temp
    appended_property_name = _conc
    emissivity_primary = 0
    emissivity_secondary = 0
    quadrature = true
  []
[]

[BCs]
  # pin particle along symmetry planes
  [no_disp_x]
    type = DirichletBC
    variable = disp_x
    boundary = xzero
    value = 0.0
    extra_vector_tags = 'ref'
  []
  [no_disp_y]
    type = DirichletBC
    variable = disp_y
    boundary = yzero
    value = 0.0
    extra_vector_tags = 'ref'
  []
  # fix temperature on free surface
  [freesurf_temp]
    type = FunctionDirichletBC
    variable = temp
    boundary = exterior
    function = temp_bc
    extra_vector_tags = 'ref'
  []
  # fix concentration on free surface
  [freesurf_conc]
    type = DirichletBC
    variable = conc
    boundary = exterior
    value = 0.0
    extra_vector_tags = 'ref'
  []
  [PlenumPressure] #  apply plenum pressure on clad inner walls and pellet surfaces
    [plenumPressure]
      boundary = BufferGapVol
      initial_pressure = 0
      startup_time = 1.0e4
      R = 8.3145
      output_initial_moles = initial_moles # coupling to post processor to get initial fill gas mass
      temperature = ave_temp_interior # coupling to post processor to get gas temperature approximation
      volume = volumeGas # coupling to post processor to get gas volume
      material_input = 'fis_gas_released co_production' # coupling to post processor to get fission gas added, co added
      output = plenum_pressure # coupling to post processor to output plenum/gap pressure
    []
  []
[]

[Materials]
  [flux]
    type = FastNeutronFlux
    calculate_fluence = true
    factor = 5e17
  []

  [fission_gas_release] # Sifgrs fission gas release mode
    type = UO2Sifgrs
    block = fuel
    temperature = temp
    fission_rate = fission_rate # coupling to fission_rate aux variable
    grain_radius_const = 5.0e-6
  []

  [fuel_thermal]
    type = UO2Thermal
    thermal_conductivity_model = FINK_LUCUTA
    block = fuel
    temperature = temp
    burnup = burnup
    initial_porosity = 0.0
  []
  [fuel_swelling]
    type = UO2VolumetricSwellingEigenstrain
    gas_swelling_model_type = MATPRO
    block = fuel
    temperature = temp
    burnup = burnup
    eigenstrain_name = 'swelling_strain'
    initial_fuel_density = ${initial_fuel_density}
  []
  [fuel_stress]
    type = ComputeFiniteStrainElasticStress
    block = 'fuel'
  []
  [fuel_elasticity]
    type = ComputeIsotropicElasticityTensor
    block = fuel
    youngs_modulus = 2.2e11
    poissons_ratio = .345
  []
  [fuel_thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    block = fuel
    thermal_expansion_coeff = 10e-6
    stress_free_temperature = 1500.0
    eigenstrain_name = thermal_strain
    temperature = temp
  []
  [fuel_den]
    type = StrainAdjustedDensity
    block = fuel
    strain_free_density = ${initial_fuel_density} # kg/m^3
  []
  [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
    gas_constant = 8.3143 # J/K-mol
    temperature = temp
  []

  [buffer_eigenstrain]
    type = PyCIrradiationEigenstrain
    block = buffer
    pyc_type = buffer
    eigenstrain_name = 'swelling_strain'
  []
  [buffer_thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    block = buffer
    thermal_expansion_coeff = 5.65e-6
    stress_free_temperature = 1500.0
    eigenstrain_name = thermal_strain
    temperature = temp
  []
  [buffer_elasticity]
    type = ComputeIsotropicElasticityTensor
    block = buffer
    youngs_modulus = 2e10
    poissons_ratio = .23
  []
  [buffer_stress]
    type = PyCCreep
    block = buffer
    temperature = temp
  []
  [buffer_temp]
    type = HeatConductionMaterial
    block = buffer
    thermal_conductivity = 0.5 # J/m-s-K
    specific_heat = 720.0 # J/kg-K
  []
  [buffer_den]
    type = StrainAdjustedDensity
    strain_free_density = 1000.0 #kg/m^3
    block = buffer
  []
  [buffer_conc]
    type = ArrheniusDiffusionCoef
    block = buffer
    d1 = 1.0e-12 # m^2/s
    q1 = 0.0
    d2 = 0.0
    q2 = 0.0
    gas_constant = 8.3143 # J/K-mol
    temperature = temp
  []
  [normal_vectors_triso]
    type = NormalVectorsTRISO
    block = 'IPyC OPyC buffer'
  []
  [IPyC_eigenstrain]
    type = PyCIrradiationEigenstrain
    block = IPyC
    pyc_type = dense
    eigenstrain_name = 'swelling_strain'
  []
  [IPyC_thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    block = IPyC
    thermal_expansion_coeff = 5.65e-6
    stress_free_temperature = 1500.0
    eigenstrain_name = thermal_strain
    temperature = temp
  []
  [IPyC_elasticity]
    type = ComputeIsotropicElasticityTensor
    block = IPyC
    youngs_modulus = 4.74e10
    poissons_ratio = .23
  []
  [IPyC_disp]
    type = PyCCreep
    block = 'IPyC OPyC'
    temperature = temp
  []
  [IPyC_temp]
    type = HeatConductionMaterial
    block = 'IPyC OPyC'
    thermal_conductivity = 4.0
    specific_heat = 720.0
  []
  [IPyC_den]
    type = StrainAdjustedDensity
    block = 'IPyC OPyC'
    strain_free_density = 1900.0
  []
  [IPyC_conc]
    type = ArrheniusDiffusionCoef
    block = IPyC
    d1 = 6.3e-8
    q1 = 222.0e+3
    d2 = 0.0
    q2 = 0.0
    gas_constant = 8.3143 # J/K-mol
    temperature = temp
  []
  [SiC_thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    block = SiC
    thermal_expansion_coeff = 4.9e-6
    stress_free_temperature = 1500.0
    eigenstrain_name = thermal_strain
    temperature = temp
  []
  [SiC_elasticity]
    type = ComputeIsotropicElasticityTensor
    block = SiC
    youngs_modulus = 3.4e11
    poissons_ratio = .13
  []
  [SiC_creep]
    type = MonolithicSiCCreepUpdate
    block = SiC
    temperature = temp
    k_function = k_function
  []
  [SiC_stress]
    type = ComputeMultipleInelasticStress
    block = SiC
    tangent_operator = elastic
    inelastic_models = 'SiC_creep'
  []
  [SiC_temp]
    type = HeatConductionMaterial
    block = SiC
    thermal_conductivity = 13.9 # J/m-s-K
    specific_heat = 620.0 # J/kg-K
  []
  [SiC_den]
    type = StrainAdjustedDensity
    strain_free_density = 3180.0 # kg/m^3
    block = SiC
  []
  [SiC_conc]
    type = ArrheniusDiffusionCoef
    block = SiC
    d1 = 5.5e-14 # m^2/s
    d1_function = d1_function
    d1_function_variable = fluence
    q1 = 125.0e+3 # J/mol
    d2 = 1.6e-2 # m^2/s
    q2 = 514.0e+3 # J/mol
    gas_constant = 8.3143 # J/K-mol
    temperature = temp
  []

  [OPyC_eigenstrain]
    type = PyCIrradiationEigenstrain
    block = OPyC
    pyc_type = dense
    eigenstrain_name = 'swelling_strain'
  []
  [OPyC_thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    block = OPyC
    thermal_expansion_coeff = 5.65e-6
    stress_free_temperature = 1500.0
    eigenstrain_name = thermal_strain
    temperature = temp
  []
  [OPyC_elasticity]
    type = ComputeIsotropicElasticityTensor
    block = OPyC
    youngs_modulus = 4.74e10
    poissons_ratio = .23
  []
  [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
    gas_constant = 8.3143 # J/K-mol
    temperature = temp
  []
[]

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

[Debug]
  show_var_residual_norms = true
[]

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

[Executioner]
  type = Transient
  solve_type = 'NEWTON'
  petsc_options = '-snes_converged_reason -ksp_converged_reason -snes_ksp_ew'
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -mat_mffd_err -pc_factor_shift_type -pc_factor_shift_amount'
  petsc_options_value = 'lu    superlu_dist   1e-5          NONZERO               1e-14'

  snesmf_reuse_base = false

  line_search = 'none'
  nl_rel_tol = 5e-4
  nl_abs_tol = 1e-10
  nl_max_its = 20
  l_max_its = 8

  start_time = 0.0
  end_time = 85.3682e6
  dt = 100

  dtmax = 2e6
  dtmin = 1

  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 100
    optimal_iterations = 10
    growth_factor = 1.5
    linear_iteration_ratio = 100
    time_t = '0    76e6  76.001e6 84.641e6 84.6482e6'
    time_dt = '20  20     20      20       20'
  []

  [Predictor]
    type = SimplePredictor
    scale = 0.5
    skip_times_old = '0    76e6  76.001e6 84.641e6 84.6482e6'
  []
[]

[Outputs]
  perf_graph = true
  exodus = true
  [console]
    type = Console
    max_rows = 25
  []
  [csv]
    type = CSV
    sync_times = '100 6308007 75696087'
    sync_only = true
  []
[]

[Postprocessors]
  [Cs_release]
    type = SideIntegralMassFlux
    variable = conc
    boundary = exterior
    execute_on = timestep_end
  []
  [dt]
    type = TimestepSize
    execute_on = timestep_end
  []
  [fis_gas_produced] # fission gas produced (moles)
    type = ElementIntegralFisGasGeneratedSifgrs
    block = fuel
    execute_on = 'initial linear nonlinear timestep_begin timestep_end'
  []
  [fis_gas_released] # fission gas released to plenum (moles)
    type = ElementIntegralFisGasReleasedSifgrs
    block = fuel
    execute_on = 'initial linear nonlinear timestep_begin timestep_end'
  []
  [volumeTotal]
    type = InternalVolume
    boundary = exterior
    execute_on = 'initial timestep_end'
  []
  [volumeFuel]
    type = InternalVolume
    boundary = fuel
    execute_on = 'initial timestep_end'
  []
  [volumeGas]
    type = InternalVolume
    boundary = BufferGapVol
    # ro = 3.125e-4
    # ri = 2.125e-4
    # vb = 4/3*pi*(ro^3-ri^3) = 8.76e-11
    # buffer density = 1000
    # PyC density    = 1900
    # fill ratio = 10/19
    # vb*10/19 = 4.6e-11
    # Must remove 4.6e-11 m^3 from the volume
    addition = -4.6e-11
    execute_on = 'initial linear nonlinear timestep_begin timestep_end'
  []
  [volumeBufferShell]
    type = InternalVolume
    boundary = BufferGapVol
    execute_on = 'initial timestep_end'
  []
  [ave_temp_interior]
    type = SideAverageValue
    boundary = BufferGapVol
    variable = temp
    execute_on = 'initial linear nonlinear timestep_begin timestep_end'
  []

  # Postprocessors for CO production

  [total_fission_rate]
    type = ElementIntegralPower
    variable = temp
    fission_rate = fission_rate
    block = fuel
    energy_per_fission = 1.0
    execute_on = 'initial linear nonlinear timestep_begin timestep_end'
  []
  [total_fissions]
    type = TimeIntegratedPostprocessor
    value = total_fission_rate
    execute_on = 'initial linear nonlinear timestep_begin timestep_end'
  []
  [avg_surface_temp]
    type = SideAverageValue
    variable = temp
    boundary = exterior
    execute_on = 'initial linear nonlinear timestep_begin timestep_end'
  []
  [time_int_surf_temp]
    type = TimeIntegratedPostprocessor
    value = avg_surface_temp
    execute_on = 'initial linear nonlinear timestep_begin timestep_end'
  []
  [co_production]
    type = CarbonMonoxideProduction
    total_fissions = total_fissions
    time_integrated_triso_temperature = time_int_surf_temp
    initial_enrichment = 0.14029
    execute_on = 'initial linear nonlinear timestep_begin timestep_end'
  []
  [num_lin_it]
    type = NumLinearIterations
  []
  [num_nonlin_it]
    type = NumNonlinearIterations
  []
  [tot_lin_it]
    type = CumulativeValuePostprocessor
    postprocessor = num_lin_it
  []
  [tot_nonlin_it]
    type = CumulativeValuePostprocessor
    postprocessor = num_nonlin_it
  []
  [alive_time]
    type = PerfGraphData
    section_name = Root
    data_type = TOTAL
  []

  [buffer_avg_conc]
    type = SideAverageValue
    variable = conc
    boundary = 17
  []
  [IPyC_avg_conc]
    type = SideAverageValue
    variable = conc
    boundary = 15
  []
  [buffer_integral_flux]
    type = SideIntegralMassFlux
    variable = conc
    boundary = 17
  []
  [IPyC_integral_flux]
    type = SideIntegralMassFlux
    variable = conc
    boundary = 15
  []
  [integral_flux_error]
    type = FunctionValuePostprocessor
    function = integral_flux_error
  []
  [integral_Cs_release]
    type = TimeIntegratedPostprocessor
    value = Cs_release
  []
  [Cs_production]
    type = FunctionValuePostprocessor
    function = power_history
    scale_factor = 1.22e-5 # units of moles/m**3-s
  []
  [time_integral_Cs_production]
    type = TimeIntegratedPostprocessor
    value = Cs_production
  []
  [volumeFuel_initial]
    type = InternalVolume
    boundary = fuel
    execute_on = initial
  []
  [integral_Cs_production]
    type = ParsedPostprocessor
    pp_names = 'time_integral_Cs_production volumeFuel_initial'
    expression = 'time_integral_Cs_production * volumeFuel_initial'
  []
  [Cs_release_fraction]
    type = ParsedPostprocessor
    pp_names = 'integral_Cs_release integral_Cs_production'
    expression = 'integral_Cs_release / integral_Cs_production'
  []
[]

[VectorPostprocessors]
  [temperaturevpp]
    type = SideValueSampler
    boundary = 11
    variable = temp
    sort_by = x
    outputs = 'csv'
    use_displaced_mesh = true
  []
[]

(test/tests/triso_failure/triso_1d_pd_penetration.i)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[Debug]
  show_var_residual_norms = true
[]

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

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

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

(test/tests/triso_failure/ad_triso_1d_weibull_probability.i)

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

[Mesh]
  coord_type = RSPHERICAL
  [gen]
    type = TRISO1DMeshGenerator
    elem_type = EDGE3
    coordinates = '0 2.485e-4 3.425e-4 3.425e-4 3.835e-4 4.195e-4 4.595e-4'
    mesh_density = '6 6 0 6 8 6'
    block_names = 'fuel buffer IPyC SiC OPyC'
  []
[]

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

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

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

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

[Kernels]
  [heat_ie]
    type = ADHeatConductionTimeDerivative
    variable = temperature
  []
  [heat]
    type = ADHeatConduction
    variable = temperature
  []
  [heat_source]
    type = ADNeutronHeatSource
    variable = temperature
    block = fuel
    energy_per_fission = 3.2e-11
    fission_rate = fission_rate
  []
[]

[AuxKernels]
  [stress_yy]
    type = ADRankTwoAux
    rank_two_tensor = stress
    variable = stress_yy
    index_i = 1
    index_j = 1
    execute_on = timestep_end
  []
  [fission_rate]
    type = FunctionAux
    variable = fission_rate
    block = fuel
    function = fission_rate
  []
  [burnup]
    type = ADBurnupAux
    variable = burnup
    block = fuel
    fission_rate = fission_rate
    molecular_weight = 0.270
  []
[]

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

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

[BCs]
  [no_disp_x]
    type = ADDirichletBC
    variable = disp_x
    boundary = xzero
    value = 0.0
  []
  [freesurf_temperature]
    type = ADDirichletBC
    variable = temperature
    boundary = exterior
    value = 1346.0
  []
  [exterior_pressure_x]
    type = ADPressure
    use_displaced_mesh = false
    variable = disp_x
    boundary = exterior
    factor = 0.1e6
  []
  [PlenumPressure]
    #  apply gas pressure on buffer and IPyC boundaries
    [plenumPressure]
      use_displaced_mesh = false
      boundary = buffer_IPyC_boundary
      initial_pressure = 0
      startup_time = 1.0e4
      R = 8.3143
      # coupling to post processor
      output_initial_moles = initial_moles
      temperature = ave_temp_interior
      volume = volumeGas
      material_input = 'fis_gas_released co_production'
      output = plenum_pressure
      use_automatic_differentiation = true
    []
  []
[]

[Materials]
  [flux]
    type = ADFastNeutronFlux
    calculate_fluence = true
    factor = 1.708707e18
  []
  [fission_gas_release]
    type = ADUO2Sifgrs
    block = fuel
    temperature = temperature
    fission_rate = fission_rate
    grain_radius_const = 5.0e-6
  []
  [stress]
    type = ADComputeLinearElasticStress
    block = 'fuel buffer SiC'
  []
  [PyC_stress]
    type = ADPyCCreep
    block = 'IPyC OPyC'
    k = k_function
    poissons_ratio = 0.4
    temperature = temperature
  []
  [normal_vectors_triso]
    type = NormalVectorsTRISO
    block = 'buffer IPyC OPyC'
  []
  [PyC_eigenstrain]
    type = ADPyCIrradiationEigenstrain
    block = 'IPyC OPyC'
    radial_eigenstrain_function = radial_eigenstrain
    tangential_eigenstrain_function = tangential_eigenstrain
    eigenstrain_name = pyc_eigenstrain
  []
  [fuel_thermal_strain]
    type = ADComputeThermalExpansionEigenstrain
    block = fuel
    thermal_expansion_coeff = 10e-6
    stress_free_temperature = 1346.0
    eigenstrain_name = thermal_strain
    temperature = temperature
  []
  [PyC_thermal_strain]
    type = ADComputeThermalExpansionEigenstrain
    block = 'buffer IPyC OPyC'
    thermal_expansion_coeff = 5.5e-6
    stress_free_temperature = 1346.0
    eigenstrain_name = thermal_strain
    temperature = temperature
  []
  [SiC_thermal_strain]
    type = ADComputeThermalExpansionEigenstrain
    block = SiC
    thermal_expansion_coeff = 4.9e-6
    stress_free_temperature = 1346.0
    eigenstrain_name = thermal_strain
    temperature = temperature
  []
  [fuel_thermal]
    type = ADUO2Thermal
    thermal_conductivity_model = FINK_LUCUTA
    block = fuel
    temperature = temperature
    burnup = burnup
  []
  [fuel_elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    block = fuel
    youngs_modulus = 2e8
    poissons_ratio = 0.345
  []
  [fuel_den]
    type = ADStrainAdjustedDensity
    block = fuel
    strain_free_density = 10810.0
  []
  [buffer_elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    block = buffer
    youngs_modulus = 2e8
    poissons_ratio = 0.345
  []
  [buffer_thermal]
    type = ADHeatConductionMaterial
    block = buffer
    thermal_conductivity = 0.5
    specific_heat = 720.0
  []
  [buffer_den]
    type = ADStrainAdjustedDensity
    strain_free_density = 1000
    block = buffer
  []
  [PyC_elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    block = 'IPyC OPyC'
    youngs_modulus = 3.96e10
    poissons_ratio = 0.33
  []
  [PyC_thermal]
    type = ADHeatConductionMaterial
    block = 'IPyC OPyC'
    thermal_conductivity = 4.0
    specific_heat = 720.0
  []
  [PyC_den]
    type = ADStrainAdjustedDensity
    strain_free_density = 1880.0
    block = 'IPyC OPyC'
  []
  [SiC_elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    block = SiC
    youngs_modulus = 3.7e11
    poissons_ratio = 0.13
  []
  [SiC_thermal]
    type = ADHeatConductionMaterial
    block = SiC
    thermal_conductivity = 13.9
    specific_heat = 620.0
  []
  [SiC_den]
    type = ADStrainAdjustedDensity
    strain_free_density = 3200.0
    block = SiC
  []
  [characteristic_strength]
    type = ADGenericConstantMaterial
    prop_values = '1000 1000 1000'
    prop_names = 'characteristic_strength_SiC characteristic_strength_IPyC characteristic_strength_OPyC'
  []
[]

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

[Debug]
  show_var_residual_norms = true
[]

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

[Postprocessors]
  [burnup]
    type = ElementExtremeValue
    block = fuel
    variable = burnup
  []
  [fis_gas_produced]
    type = ADElementIntegralFisGasGeneratedSifgrs
    block = fuel
  []
  [fis_gas_released]
    type = ADElementIntegralFisGasReleasedSifgrs
    block = fuel
  []
  [volumeTotal]
    type = InternalVolume
    boundary = exterior
  []
  [volumeFuel]
    type = InternalVolume
    boundary = fuel_outer_boundary
  []
  [volumeGas]
    type = InternalVolume
    boundary = 'fuel_outer_boundary IPyC_inner_boundary'
    addition = -5.53e-11
    execute_on = 'initial timestep_end'
  []
  [volumeBufferShell]
    type = InternalVolume
    boundary = buffer_IPyC_boundary
  []
  [ave_temp_interior]
    type = SideAverageValue
    boundary = buffer_IPyC_boundary
    variable = temperature
    execute_on = 'initial timestep_end'
  []
  # Postprocessors for CO production
  [total_fission_rate]
    type = ElementIntegralPower
    variable = temperature
    fission_rate = fission_rate
    block = fuel
    energy_per_fission = 1.0
  []
  [total_fissions]
    type = TimeIntegratedPostprocessor
    value = total_fission_rate
  []
  [avg_surface_temperature]
    type = SideAverageValue
    variable = temperature
    boundary = exterior
  []
  [time_int_surf_temperature]
    type = TimeIntegratedPostprocessor
    value = avg_surface_temperature
  []
  [co_production]
    type = CarbonMonoxideProduction
    total_fissions = total_fissions
    time_integrated_triso_temperature = time_int_surf_temperature
    initial_enrichment = 0.14029
  []
  [tang_SiC]
    type = ElementalVariableValue
    variable = stress_yy
    elementid = 18
  []
  [Weibull_failure_probability_OPyC]
    type = ADWeibullFailureProbability
    block = OPyC
    weibull_modulus = 6
    characteristic_strength = characteristic_strength_OPyC
  []
  [Weibull_failure_probability_IPyC]
    type = ADWeibullFailureProbability
    block = IPyC
    weibull_modulus = 6
    characteristic_strength = characteristic_strength_IPyC
  []
  [Weibull_failure_probability_SiC]
    type = ADWeibullFailureProbability
    block = SiC
    weibull_modulus = 6
    characteristic_strength = characteristic_strength_SiC
  []
[]

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

(test/tests/triso_failure/sub.i)

[GlobalParams]
  density = 10810.0 # kg/m^3
  flux_conversion_factor = 1.0
  order = SECOND
  family = LAGRANGE
  displacements = 'disp_x'
[]

[Mesh]
  coord_type = RSPHERICAL
  [gen]
    type = TRISO1DMeshGenerator
    elem_type = EDGE3
    coordinates = '0 2.485e-4 3.425e-4 3.425e-4 3.835e-4 4.195e-4 4.595e-4'
    mesh_density = '6 6 0 6 8 6'
    block_names = 'fuel buffer IPyC SiC OPyC'
  []
[]

[Variables]
  [disp_x]
  []
  [temp]
    initial_condition = 1346.0
  []
[]

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

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

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

[Kernels]
  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temp
  []
  [heat]
    type = HeatConduction
    variable = temp
  []
  [heat_source]
    type = NeutronHeatSource
    variable = temp
    block = fuel
    energy_per_fission = 3.2e-11 # units of J/fission
    fission_rate = fission_rate
  []
[]

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

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

[ThermalContact]
  [thermal_contact]
    type = GasGapHeatTransfer
    variable = temp
    primary = IPyC_inner_boundary
    secondary = buffer_outer_boundary
    initial_moles = initial_moles # coupling to a postprocessor which supplies the initial plenum/gap gas mass
    gas_released = 'fis_gas_released co_production' # coupling to postprocessors which supply the fission gas addition, co addition
    released_gas_types = 'Kr Xe;
                          CO'
    released_fractions = '0.153 0.847;
                          1'
    tangential_tolerance = 1e-6
    #    contact_pressure_input = 10e6
    #    quadrature = true
  []
[]

[BCs]

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

  # fix temperature on free surface
  [freesurf_temp]
    type = DirichletBC
    variable = temp
    boundary = exterior
    value = 1346.0
  []

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

  [PlenumPressure] #  apply gas pressure on buffer and IPyC boundaries
    [plenumPressure]
      use_displaced_mesh = false
      boundary = buffer_IPyC_boundary
      initial_pressure = 0
      startup_time = 1.0e4
      output_initial_moles = initial_moles # coupling to post processor to get initial fill gas mass
      temperature = ave_temp_interior # coupling to post processor to get gas temperature approximation
      volume = volumeGas # coupling to post processor to get gas volume
      material_input = 'fis_gas_released co_production' # coupling to post processor to get fission gas added, co added
      output = plenum_pressure # coupling to post processor to output plenum/gap pressure
    []
  []

[]

[Materials]
  [max_principal_stress]
    type = RankTwoInvariant
    property_name = max_principal_stress
    rank_two_tensor = stress
    invariant = MaxPrincipal
  []
  [flux]
    type = FastNeutronFlux
    calculate_fluence = true
    factor = 1.708707e18 # n/m^2-sec
  []

  [fission_gas_release] # Sifgr fission gas release mode
    type = UO2Sifgrs
    block = fuel
    temperature = temp
    fission_rate = fission_rate # coupling to fission_rate aux variable
    grain_radius_const = 5.0e-6
  []

  [stress]
    type = ComputeLinearElasticStress
    block = 'fuel buffer SiC'
  []
  [PyC_stress]
    type = PyCCreep
    block = 'IPyC OPyC'
    k = k_function
    poissons_ratio = 0.4
    temperature = temp
  []
  [normal_vectors_triso]
    type = NormalVectorsTRISO
    block = 'IPyC OPyC'
  []
  [PyC_eigenstrain]
    type = PyCIrradiationEigenstrain
    block = 'IPyC OPyC'
    radial_eigenstrain_function = radial_eigenstrain
    tangential_eigenstrain_function = tangential_eigenstrain
    eigenstrain_name = pyc_eigenstrain
  []

  [fuel_thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    block = fuel
    thermal_expansion_coeff = 10e-6
    stress_free_temperature = 1346.0
    eigenstrain_name = thermal_strain
    temperature = temp
  []
  [PyC_thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    block = 'buffer IPyC OPyC'
    thermal_expansion_coeff = 5.5e-6
    stress_free_temperature = 1346.0
    eigenstrain_name = thermal_strain
    temperature = temp
  []
  [SiC_thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    block = SiC
    thermal_expansion_coeff = 4.9e-6
    stress_free_temperature = 1346.0
    eigenstrain_name = thermal_strain
    temperature = temp
  []

  [fuel_thermal] # temperature and burnup dependent thermal properties of UO2 (bison kernel)
    type = UO2Thermal
    thermal_conductivity_model = FINK_LUCUTA
    block = fuel
    temperature = temp
    burnup = burnup
  []

  [fuel_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = fuel
    youngs_modulus = 2e8
    poissons_ratio = 0.345
  []

  [fuel_den]
    type = StrainAdjustedDensity
    block = fuel
    strain_free_density = 10810.0
  []

  [buffer_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = buffer
    youngs_modulus = 2e8
    poissons_ratio = 0.345
  []

  [buffer_temp]
    type = HeatConductionMaterial
    block = buffer
    thermal_conductivity = 0.5 # J/m-s-K
    specific_heat = 720.0 # J/kg-K
  []

  [buffer_den]
    type = StrainAdjustedDensity
    strain_free_density = 1000 #kg/m^3
    block = buffer
  []

  [PyC_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = 'IPyC OPyC'
    youngs_modulus = 3.96e10 #47787559927.148 #3.96e10
    poissons_ratio = 0.33
  []

  [PyC_temp]
    type = HeatConductionMaterial
    block = 'IPyC OPyC'
    thermal_conductivity = 4.0 # J/m-s-K
    specific_heat = 720.0 # J/kg-K
  []

  [PyC_den]
    type = StrainAdjustedDensity
    strain_free_density = 1880.0 # kg/m^3
    block = 'IPyC OPyC'
  []

  [SiC_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = SiC
    youngs_modulus = 3.7e11
    poissons_ratio = 0.13
  []

  [SiC_temp]
    type = HeatConductionMaterial
    block = SiC
    thermal_conductivity = 13.9 # J/m-s-K
    specific_heat = 620.0 # J/kg-K
  []

  [SiC_den]
    type = StrainAdjustedDensity
    strain_free_density = 3200.0 # kg/m^3
    block = SiC
  []

  [characteristic_strength_SiC]
    type = GenericConstantMaterial
    prop_values = '9640000'
    prop_names = 'characteristic_strength'
    block = SiC
  []

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

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

[Debug]
  show_var_residual_norms = true
[]

[Executioner]
  type = Transient

  #  petsc_options = '-snes_mf_operator -snes_ksp_ew -ksp_monitor'
  #  petsc_options_iname = '-pc_type -pc_hypre_type'
  #  petsc_options_value = 'hypre boomeramg'

  petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
  petsc_options_value = '201                hypre    boomeramg      4'

  line_search = 'none'

  solve_type = 'PJFNK'

  nl_rel_tol = 5e-6
  nl_abs_tol = 1e-10
  nl_max_its = 15

  l_tol = 1e-3
  l_max_its = 50

  start_time = 0.0
  num_steps = 2

  dtmax = 2e5
  dtmin = 1
  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 20
    optimal_iterations = 6
    iteration_window = 2
    linear_iteration_ratio = 100
  []
[]

[Postprocessors]
  [dt]
    type = TimestepSize
  []
  [burnup]
    type = ElementExtremeValue
    block = fuel
    variable = burnup
  []
  [fis_gas_produced] # fission gas produced (moles)
    type = ElementIntegralFisGasGeneratedSifgrs
    block = fuel
  []

  [fis_gas_released] # fission gas released to plenum (moles)
    type = ElementIntegralFisGasReleasedSifgrs
    block = fuel
  []
  [volumeTotal]
    type = InternalVolume
    boundary = exterior
  []
  [volumeFuel]
    type = InternalVolume
    boundary = fuel_outer_boundary
  []
  [volumeGas]
    type = InternalVolume
    boundary = 'fuel_outer_boundary IPyC_inner_boundary'
    addition = -5.53e-11
    execute_on = 'initial timestep_end'
  []
  [volumeBufferShell]
    type = InternalVolume
    boundary = buffer_IPyC_boundary
  []
  [ave_temp_interior]
    type = SideAverageValue
    boundary = buffer_IPyC_boundary
    variable = temp
    execute_on = 'initial timestep_end'
  []

  # Postprocessors for CO production

  [total_fission_rate]
    type = ElementIntegralPower
    variable = temp
    fission_rate = fission_rate
    block = fuel
    energy_per_fission = 1.0
  []

  [total_fissions]
    type = TimeIntegratedPostprocessor
    value = total_fission_rate
  []

  [avg_surface_temp]
    type = SideAverageValue
    variable = temp
    boundary = exterior
  []

  [time_int_surf_temp]
    type = TimeIntegratedPostprocessor
    value = avg_surface_temp
  []

  [co_production]
    type = CarbonMonoxideProduction
    total_fissions = total_fissions
    time_integrated_triso_temperature = time_int_surf_temp
    initial_enrichment = 0.14029
  []

  [tang_SiC]
    type = ElementalVariableValue
    variable = stress_yy
    elementid = 18
  []

  [strength_SiC]
    type = WeibullEffectiveMeanStrength
    block = SiC
    weibull_modulus = 6
  []

  [failure_indicator_SiC]
    type = WeibullFailureOutputUsingCorrelation
    block = SiC
    weibull_modulus = 6
    stress_name = max_principal_stress
    effective_mean_strength = strength_SiC
  []

  [strength_IPyC]
    type = WeibullEffectiveMeanStrength
    block = IPyC
    weibull_modulus = 6
  []

  [failure_indicator_IPyC]
    type = WeibullFailureOutputUsingCorrelation
    block = IPyC
    weibull_modulus = 6
    stress_name = max_principal_stress
    effective_mean_strength = strength_IPyC
  []

  [strength_OPyC]
    type = WeibullEffectiveMeanStrength
    block = OPyC
    weibull_modulus = 6
  []

  [failure_indicator_OPyC]
    type = WeibullFailureOutputUsingCorrelation
    block = OPyC
    weibull_modulus = 6
    stress_name = max_principal_stress
    effective_mean_strength = strength_OPyC
  []

  [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
  []

  [ipyc_cracking]
    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
    failure_type = IPYC_CRACKING
  []

  [burnup_at_failure]
    type = TRISOFailureOccurrenceStatus
    failure_evaluation = ipyc_cracking
    failure_information = burnup
  []

  [left_bc]
    type = NodalExtremeValue
    boundary = xzero
    variable = disp_x
  []
[]

[UserObjects]
  [triso_failure_terminator]
    type = Terminator
    expression = 'triso_failure > 0'
  []
[]

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

[Controls]
  [stochastic]
    type = SamplerReceiver
  []
[]

(examples/TRISO/full_particle/2D/full_particle.i)


initial_fuel_density = 10810.0

[GlobalParams]
  density = ${initial_fuel_density}
  flux_conversion_factor = 1.0
  order = SECOND
  family = LAGRANGE
  displacements = 'disp_x disp_y'
  volumetric_locking_correction = false
[]

[Mesh]
  coord_type = RZ
  [mesh]
    type = FileMeshGenerator
    file = full_particle.e
  []
[]

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

[AuxVariables]
  [fission_rate]
    block = fuel
  []
  [burnup]
    block = fuel
  []
  [grain_radius]
    initial_condition = 5.0e-6
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [fuel]
    block = fuel
    add_variables = true
    strain = FINITE
    eigenstrain_names = 'fuel_thermal_strain'
    generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz stress_xy stress_yz stress_xz strain_xy strain_yz strain_xz'
  []
  [buffer]
    block = buffer
    add_variables = true
    strain = FINITE
    eigenstrain_names = 'buffer_thermal_strain buffer_eigenstrain'
    generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz stress_xy stress_yz stress_xz strain_xy strain_yz strain_xz'
  []
  [IPyC]
    block = IPyC
    add_variables = true
    strain = FINITE
    eigenstrain_names = 'IPyC_eigenstrain IPyC_thermal_strain'
    generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz stress_xy stress_yz stress_xz strain_xy strain_yz strain_xz'
  []
  [SiC]
    block = SiC
    add_variables = true
    strain = FINITE
    eigenstrain_names = 'SiC_thermal_strain'
    generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz stress_xy stress_yz stress_xz strain_xy strain_yz strain_xz'
  []
  [OPyC]
    block = OPyC
    add_variables = true
    strain = FINITE
    eigenstrain_names = 'OPyC_eigenstrain OPyC_thermal_strain'
    generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz strain_xx strain_yy strain_zz stress_xy stress_yz stress_xz strain_xy strain_yz strain_xz'
  []
[]

[Functions]
  [fast_neutron_flux]
    type = ParsedFunction
    expression = 1.708707e18
  []
  [fission_rate]
    type = ParsedFunction
    expression = 7.75e19
  []
[]

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

[AuxKernels]
  [fission_rate]
    type = FunctionAux
    variable = fission_rate
    block = fuel
    function = fission_rate
  []
  [burnup]
    type = BurnupAux
    variable = burnup
    block = fuel
    fission_rate = fission_rate
    molecular_weight = 0.270
  []
  [grain_radius]
    type = GrainRadiusAux
    block = fuel
    variable = grain_radius
    temperature = temperature
    execute_on = linear
  []
[]

[Contact]
  [pellet_clad_mechanical]
    primary = 15
    secondary = 17
    penalty = 1e5
    model = frictionless
    formulation = penalty
  []
[]

[ThermalContact]
  [thermal_contact]
    type = GasGapHeatTransfer
    variable = temperature
    primary = 15
    secondary = 17
    initial_moles = initial_moles
    gas_released = 'fis_gas_released co_production'
    released_gas_types = 'Kr Xe;
                          CO'
    released_fractions = '0.153 0.847;
                          1'
    tangential_tolerance = 1e-6
  []
[]

[BCs]
  [no_disp_x]
    type = DirichletBC
    variable = disp_x
    boundary = xzero
    value = 0.0
  []
  [no_disp_y]
    type = DirichletBC
    variable = disp_y
    boundary = yzero
    value = 0.0
  []
  [freesurf_temperature]
    type = DirichletBC
    variable = temperature
    boundary = exterior
    value = 1346
  []
  [exterior_pressure_x]
    type = Pressure
    variable = disp_x
    boundary = exterior
    factor = 0.1e6
  []
  [exterior_pressure_y]
    type = Pressure
    variable = disp_y
    boundary = exterior
    factor = 0.1e6
  []
  [PlenumPressure]
    [plenumPressure]
      boundary = 'PyCGapBndry BufferGapBndry'
      initial_pressure = 0
      startup_time = 1.0e4
      R = 8.3143
      output_initial_moles = initial_moles
      temperature = ave_temp_interior
      volume = volumeGas
      material_input = 'fis_gas_released co_production'
      output = plenum_pressure
    []
  []
[]

[Materials]
  [flux]
    type = FastNeutronFlux
    calculate_fluence = true
    factor = 1.708707e18 # n/m^2-sec
  []
  [fuel_thermal]
    type = UO2Thermal
    block = fuel
    temperature = temperature
    thermal_conductivity_model = FINK_LUCUTA
    initial_porosity = 0.0
    burnup = burnup
  []
  [fuel_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = fuel
    youngs_modulus = 2.0e8
    poissons_ratio = 0.345
  []
  [fuel_elastic_stress]
    type = ComputeFiniteStrainElasticStress
    block = fuel
  []
  [fuel_density]
    type = StrainAdjustedDensity
    block = fuel
    strain_free_density = ${initial_fuel_density}
  []
  [fuel_thermal_expansion]
    type = ComputeThermalExpansionEigenstrain
    block = fuel
    thermal_expansion_coeff = 10.0e-6
    temperature = temperature
    stress_free_temperature = 1346.0
    eigenstrain_name = fuel_thermal_strain
  []
  [fission_gas_release]
    type = UO2Sifgrs
    block = fuel
    temperature = temperature
    fission_rate = fission_rate
    grain_radius = grain_radius
  []
  [buffer_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = buffer
    youngs_modulus = 2.0e8
    poissons_ratio = 0.345
  []
  [buffer_elastic_stress]
    type = ComputeFiniteStrainElasticStress
    block = buffer
  []
  [buffer_temperature]
    type = HeatConductionMaterial
    block = buffer
    thermal_conductivity = 0.5
    specific_heat = 720.0
  []
  [buffer_density]
    type = StrainAdjustedDensity
    strain_free_density = 1000.0
    block = buffer
  []
  [buffer_thermal_expansion]
    type = ComputeThermalExpansionEigenstrain
    block = buffer
    thermal_expansion_coeff = 5.5e-6
    temperature = temperature
    stress_free_temperature = 1346.0
    eigenstrain_name = buffer_thermal_strain
  []
  [normal_vectors_triso]
    type = NormalVectorsTRISO
    block = 'IPyC OPyC buffer'
  []
  [buffer_irraditation]
    type = PyCIrradiationEigenstrain
    block = buffer
    pyc_type = buffer
    eigenstrain_name = buffer_eigenstrain
  []

  [IPyC_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = IPyC
    youngs_modulus = 3.96e10
    poissons_ratio = 0.33
  []
  [IOPyC_stress]
    type = PyCCreep
    block = 'IPyC OPyC'
    temperature = temperature
  []
  [IOPyC_temperature]
    type = HeatConductionMaterial
    block = 'IPyC OPyC'
    thermal_conductivity = 4.0
    specific_heat = 720.0
  []
  [IOPyC_density]
    type = StrainAdjustedDensity
    block = 'IPyC OPyC'
    strain_free_density = 1880.0
  []
  [IPyC_densification]
    type = PyCIrradiationEigenstrain
    block = IPyC
    pyc_type = dense
    eigenstrain_name = IPyC_eigenstrain
  []
  [IPyC_thermal_expansion]
    type = ComputeThermalExpansionEigenstrain
    block = IPyC
    thermal_expansion_coeff = 5.5e-6
    temperature = temperature
    stress_free_temperature = 1346.0
    eigenstrain_name = IPyC_thermal_strain
  []
  [SiC_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = SiC
    youngs_modulus = 3.7e11
    poissons_ratio = 0.13
  []
  [SiC_elastic_stress]
    type = ComputeFiniteStrainElasticStress
    block = SiC
  []
  [SiC_temperature]
    type = HeatConductionMaterial
    block = SiC
    thermal_conductivity = 13.9
    specific_heat = 620.0
  []
  [SiC_den]
    type = StrainAdjustedDensity
    strain_free_density = 3200.0
    block = SiC
  []
  [SiC_thermal_expansion]
    type = ComputeThermalExpansionEigenstrain
    block = SiC
    thermal_expansion_coeff = 4.9e-6
    temperature = temperature
    stress_free_temperature = 1346.0
    eigenstrain_name = SiC_thermal_strain
  []
  [OPyC_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = OPyC
    youngs_modulus = 3.96e10
    poissons_ratio = 0.33
  []
  [OPyC_densification]
    type = PyCIrradiationEigenstrain
    block = OPyC
    pyc_type = dense
    eigenstrain_name = OPyC_eigenstrain
  []
  [OPyC_thermal_expansion]
    type = ComputeThermalExpansionEigenstrain
    block = OPyC
    thermal_expansion_coeff = 5.5e-6
    temperature = temperature
    stress_free_temperature = 1346.0
    eigenstrain_name = OPyC_thermal_strain
  []
[]

[Dampers]
  [temperature]
    type = MaxIncrement
    variable = temperature
    max_increment = 20
  []
[]

[Executioner]
  type = Transient
  petsc_options = '-snes_ksp_ew'
  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-10
  nl_max_its = 15
  l_tol = 1e-3
  l_max_its = 50
  start_time = 0.0
  end_time = 3.10176e7
  dtmax = 2e5
  dtmin = 1
  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 10
    optimal_iterations = 8
    iteration_window = 2
    linear_iteration_ratio = 100
  []
  [Quadrature]
    order = FIFTH
    side_order = SEVENTH
  []
[]

[Postprocessors]
  [max_xx_IPyC]
    type = ElementExtremeValue
    variable = stress_xx
    block = IPyC
  []
  [max_yy_IPyC]
    type = ElementExtremeValue
    variable = stress_yy
    block = IPyC
  []
  [min_zz_IPyC]
    type = ElementExtremeValue
    variable = stress_zz
    block = IPyC
    value_type = min
  []
  [max_xx_SiC]
    type = ElementExtremeValue
    variable = stress_xx
    block = SiC
  []
  [max_yy_SiC]
    type = ElementExtremeValue
    variable = stress_yy
    block = SiC
  []
  [min_zz_SiC]
    type = ElementExtremeValue
    variable = stress_zz
    block = SiC
    value_type = min
  []
  [max_xx_OPyC]
    type = ElementExtremeValue
    variable = stress_xx
    block = OPyC
  []
  [max_yy_OPyC]
    type = ElementExtremeValue
    variable = stress_yy
    block = OPyC
  []
  [min_zz_OPyC]
    type = ElementExtremeValue
    variable = stress_zz
    block = OPyC
    value_type = min
  []
  [fis_gas_produced]
    type = ElementIntegralFisGasGeneratedSifgrs
    block = fuel
    execute_on = 'initial linear'
  []
  [fis_gas_released]
    type = ElementIntegralFisGasReleasedSifgrs
    block = fuel
    execute_on = 'initial linear'
  []
  [volumeTotal]
    type = InternalVolume
    boundary = exterior
    execute_on = 'initial TIMESTEP_END'
  []
  [volumeFuel]
    type = InternalVolume
    boundary = fuel
    execute_on = 'initial TIMESTEP_END'
  []
  [volumeGas]
    type = InternalVolume
    boundary = BufferGapVol
    addition = -5.53e-11
    execute_on = 'initial TIMESTEP_END'
  []
  [volumeBufferShell]
    type = InternalVolume
    boundary = BufferGapVol
    execute_on = 'initial TIMESTEP_END'
  []
  [ave_temp_interior]
    type = SideAverageValue
    boundary = BufferGapVol
    variable = temperature
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [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'
  []
  [avg_surface_temperature]
    type = SideAverageValue
    variable = temperature
    boundary = exterior
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [time_int_surf_temperature]
    type = TimeIntegratedPostprocessor
    value = avg_surface_temperature
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [co_production]
    type = CarbonMonoxideProduction
    total_fissions = total_fissions
    time_integrated_triso_temperature = time_int_surf_temperature
    initial_enrichment = 0.14029
    execute_on = 'INITIAL TIMESTEP_END'
  []
[]

[PerformanceMetricOutputs]
[]

[Outputs]
  perf_graph = true
  exodus = true
  csv = true
  [chkfile]
    type = CSV
    execute_on = Final
    show = 'max_xx_IPyC max_yy_IPyC min_zz_IPyC max_xx_SiC max_yy_SiC min_zz_SiC co_production fis_gas_released avg_surface_temperature'
  []
[]

(test/tests/triso_failure/triso_1d_asphericity_failure.i)

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

[Mesh]
  coord_type = RSPHERICAL
  [gen]
    type = TRISO1DMeshGenerator
    elem_type = EDGE3
    coordinates = '0 2.485e-4 3.425e-4 3.425e-4 3.835e-4 4.195e-4 4.595e-4'
    mesh_density = '6 6 0 6 8 6'
    block_names = 'fuel buffer IPyC SiC OPyC'
  []
[]

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

[Functions]
  [radial_eigenstrain]
    type = ParsedFunction
    expression = 't*(4.52013e-4/6.0*t*t*t*t*t - 8.36313e-3/5.0*t*t*t*t + 5.67549e-2/4.0*t*t*t - 1.74247e-1/3.0*t*t + 2.62692e-1/2.0*t - 1.43234e-1)'
  []
  [tangential_eigenstrain]
    type = ParsedFunction
    expression = 't*(1.30457e-4/4.0*t*t*t - 2.10029e-3/3.0*t*t + 9.07826e-3/2.0*t - 3.24737e-2)'
  []
  [fission_rate]
    type = ParsedFunction
    expression = 7.75e19
  []
  [k_function]
    type = ParsedFunction
    expression = '4.93e-29'
  []
  [high_fidelity_strength_asphericity]
    type = PiecewiseLinear
    x = '0 1.0e11'
    y = '1000000 1000000'
  []
  [stress_correlation_asphericity]
    type = PiecewiseLinear
    x = '0 1.0e11'
    y = '1 1'
  []
  [stress_change_correlation_asphericity]
    type = PiecewiseLinear
    x = '0 1.0e11'
    y = '1 1'
  []
[]

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

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

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

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

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

[ThermalContact]
  [thermal_contact]
    type = GasGapHeatTransfer
    variable = temperature
    primary = IPyC_inner_boundary
    secondary = buffer_outer_boundary
    # coupling to a postprocessor
    initial_moles = initial_moles
    gas_released = 'fis_gas_released co_production'
    released_gas_types = 'Kr Xe;
                          CO'
    released_fractions = '0.153 0.847;
                          1'
    tangential_tolerance = 1e-6
    #    contact_pressure_input = 10e6
    #    quadrature = true
  []
[]

[BCs]
  [no_disp_x]
    type = DirichletBC
    variable = disp_x
    boundary = xzero
    value = 0.0
  []
  [freesurf_temperature]
    type = DirichletBC
    variable = temperature
    boundary = exterior
    value = 1346.0
  []
  [exterior_pressure_x]
    type = Pressure
    use_displaced_mesh = false
    variable = disp_x
    boundary = exterior
    factor = 0.1e6
  []
  [PlenumPressure]
    #  apply gas pressure on buffer and IPyC boundaries
    [plenumPressure]
      use_displaced_mesh = false
      boundary = buffer_IPyC_boundary
      initial_pressure = 0
      startup_time = 1.0e4
      R = 8.3143
      # coupling to post processor
      output_initial_moles = initial_moles
      temperature = ave_temp_interior
      volume = volumeGas
      material_input = 'fis_gas_released co_production'
      output = plenum_pressure
    []
  []

[]

[Materials]
  [stress_yy]
    type = RankTwoCartesianComponent
    rank_two_tensor = stress
    property_name = stress_yy
    index_i = 1
    index_j = 1
  []
  [flux]
    type = FastNeutronFlux
    calculate_fluence = true
    factor = 1.708707e18
  []
  [fission_gas_release]
    type = UO2Sifgrs
    block = fuel
    temperature = temperature
    fission_rate = fission_rate
    grain_radius_const = 5.0e-6
  []
  [stress]
    type = ComputeLinearElasticStress
    block = 'fuel buffer SiC'
  []
  [PyC_stress]
    type = PyCCreep
    block = 'IPyC OPyC'
    k = k_function
    poissons_ratio = 0.4
    temperature = temperature
  []
  [normal_vectors_triso]
    type = NormalVectorsTRISO
    block = 'IPyC OPyC'
  []
  [PyC_eigenstrain]
    type = PyCIrradiationEigenstrain
    block = 'IPyC OPyC'
    radial_eigenstrain_function = radial_eigenstrain
    tangential_eigenstrain_function = tangential_eigenstrain
    eigenstrain_name = pyc_eigenstrain
  []
  [fuel_thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    block = fuel
    thermal_expansion_coeff = 10e-6
    stress_free_temperature = 1346.0
    eigenstrain_name = thermal_strain
    temperature = temperature
  []
  [PyC_thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    block = 'buffer IPyC OPyC'
    thermal_expansion_coeff = 5.5e-6
    stress_free_temperature = 1346.0
    eigenstrain_name = thermal_strain
    temperature = temperature
  []
  [SiC_thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    block = SiC
    thermal_expansion_coeff = 4.9e-6
    stress_free_temperature = 1346.0
    eigenstrain_name = thermal_strain
    temperature = temperature
  []
  [fuel_thermal]
    type = UO2Thermal
    thermal_conductivity_model = FINK_LUCUTA
    block = fuel
    temperature = temperature
    burnup = burnup
  []
  [fuel_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = fuel
    youngs_modulus = 2e8
    poissons_ratio = 0.345
  []
  [fuel_den]
    type = StrainAdjustedDensity
    block = fuel
    strain_free_density = 10810.0
  []
  [buffer_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = buffer
    youngs_modulus = 2e8
    poissons_ratio = 0.345
  []
  [buffer_thermal]
    type = HeatConductionMaterial
    block = buffer
    thermal_conductivity = 0.5
    specific_heat = 720.0
  []
  [buffer_den]
    type = StrainAdjustedDensity
    strain_free_density = 1000
    block = buffer
  []
  [PyC_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = 'IPyC OPyC'
    youngs_modulus = 3.96e10
    poissons_ratio = 0.33
  []
  [PyC_thermal]
    type = HeatConductionMaterial
    block = 'IPyC OPyC'
    thermal_conductivity = 4.0
    specific_heat = 720.0
  []
  [PyC_den]
    type = StrainAdjustedDensity
    strain_free_density = 1880.0
    block = 'IPyC OPyC'
  []
  [SiC_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = SiC
    youngs_modulus = 3.7e11
    poissons_ratio = 0.13
  []
  [SiC_thermal]
    type = HeatConductionMaterial
    block = SiC
    thermal_conductivity = 13.9
    specific_heat = 620.0
  []
  [SiC_den]
    type = StrainAdjustedDensity
    strain_free_density = 3200.0
    block = SiC
  []

  [characteristic_strength]
    type = GenericConstantMaterial
    prop_values = '9640000'
    prop_names = 'characteristic_strength'
    block = SiC
  []
[]

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

[Debug]
  show_var_residual_norms = true
[]

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

[Postprocessors]
  [dt]
    type = TimestepSize
  []
  [burnup]
    type = ElementExtremeValue
    block = fuel
    variable = burnup
  []
  [fis_gas_produced]
    type = ElementIntegralFisGasGeneratedSifgrs
    block = fuel
  []
  [fis_gas_released]
    type = ElementIntegralFisGasReleasedSifgrs
    block = fuel
  []
  [volumeTotal]
    type = InternalVolume
    boundary = exterior
  []
  [volumeFuel]
    type = InternalVolume
    boundary = fuel_outer_boundary
  []
  [volumeGas]
    type = InternalVolume
    boundary = 'fuel_outer_boundary IPyC_inner_boundary'
    addition = -5.53e-11
    execute_on = 'initial timestep_end'
  []
  [volumeBufferShell]
    type = InternalVolume
    boundary = buffer_IPyC_boundary
  []
  [ave_temp_interior]
    type = SideAverageValue
    boundary = buffer_IPyC_boundary
    variable = temperature
    execute_on = 'initial timestep_end'
  []
  # Postprocessors for CO production
  [total_fission_rate]
    type = ElementIntegralPower
    variable = temperature
    fission_rate = fission_rate
    block = fuel
    energy_per_fission = 1.0
  []
  [total_fissions]
    type = TimeIntegratedPostprocessor
    value = total_fission_rate
  []
  [avg_surface_temperature]
    type = SideAverageValue
    variable = temperature
    boundary = exterior
  []
  [time_int_surf_temperature]
    type = TimeIntegratedPostprocessor
    value = avg_surface_temperature
  []
  [co_production]
    type = CarbonMonoxideProduction
    total_fissions = total_fissions
    time_integrated_triso_temperature = time_int_surf_temperature
    initial_enrichment = 0.14029
  []
  [tang_SiC]
    type = ElementalVariableValue
    variable = stress_yy
    elementid = 18
  []
  [strength_SiC]
    type = WeibullEffectiveMeanStrength
    block = SiC
    weibull_modulus = 6
  []
  [failure_indicator_SiC]
    type = WeibullFailureOutputUsingCorrelation
    block = SiC
    weibull_modulus = 6
    stress_name = stress_yy
    high_fidelity_analysis_strength = 'high_fidelity_strength_asphericity'
    stress_correlation_function = 'stress_correlation_asphericity'
    stress_change_correlation_function = 'stress_change_correlation_asphericity'
  []
  [triso_failure]
    type = TRISOFailureEvaluation
    SiC_failure = failure_indicator_SiC
  []
[]

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

(test/tests/triso_failure/ad_triso_1d_failure.i)

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

[Mesh]
  coord_type = RSPHERICAL
  [gen]
    type = TRISO1DMeshGenerator
    elem_type = EDGE3
    coordinates = '0 2.485e-4 3.425e-4 3.425e-4 3.835e-4 4.195e-4 4.595e-4'
    mesh_density = '6 6 0 6 8 6'
    block_names = 'fuel buffer IPyC SiC OPyC'
  []
[]

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

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

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

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

[Kernels]
  [heat_ie]
    type = ADHeatConductionTimeDerivative
    variable = temperature
  []
  [heat]
    type = ADHeatConduction
    variable = temperature
  []
  [heat_source]
    type = ADNeutronHeatSource
    variable = temperature
    block = fuel
    energy_per_fission = 3.2e-11
    fission_rate = fission_rate
  []
[]

[AuxKernels]
  [stress_yy]
    type = ADRankTwoAux
    rank_two_tensor = stress
    variable = stress_yy
    index_i = 1
    index_j = 1
    execute_on = timestep_end
  []
  [fission_rate]
    type = FunctionAux
    variable = fission_rate
    block = fuel
    function = fission_rate
  []
  [burnup]
    type = ADBurnupAux
    variable = burnup
    block = fuel
    fission_rate = fission_rate
    molecular_weight = 0.270
  []
[]

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

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

[BCs]
  [no_disp_x]
    type = ADDirichletBC
    variable = disp_x
    boundary = xzero
    value = 0.0
  []
  [freesurf_temperature]
    type = ADDirichletBC
    variable = temperature
    boundary = exterior
    value = 1346.0
  []
  [exterior_pressure_x]
    type = ADPressure
    use_displaced_mesh = false
    variable = disp_x
    boundary = exterior
    factor = 0.1e6
  []
  [PlenumPressure]
    #  apply gas pressure on buffer and IPyC boundaries
    [plenumPressure]
      use_displaced_mesh = false
      boundary = buffer_IPyC_boundary
      initial_pressure = 0
      startup_time = 1.0e4
      R = 8.3143
      # coupling to post processor
      output_initial_moles = initial_moles
      temperature = ave_temp_interior
      volume = volumeGas
      material_input = 'fis_gas_released co_production'
      output = plenum_pressure
      use_automatic_differentiation = true
    []
  []
[]

[Materials]
  [radial_stress]
    type = ADRankTwoCylindricalComponent
    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
  []
  [max_principal_stress]
    type = ADRankTwoInvariant
    property_name = max_principal_stress
    rank_two_tensor = stress
    invariant = MaxPrincipal
  []
  [flux]
    type = ADFastNeutronFlux
    calculate_fluence = true
    factor = 1.708707e18
  []
  [fission_gas_release]
    type = ADUO2Sifgrs
    block = fuel
    temperature = temperature
    fission_rate = fission_rate
    grain_radius_const = 5.0e-6
  []
  [stress]
    type = ADComputeLinearElasticStress
    block = 'fuel buffer SiC'
  []
  [PyC_stress]
    type = ADPyCCreep
    block = 'IPyC OPyC'
    k = k_function
    poissons_ratio = 0.4
    temperature = temperature
  []
  [normal_vectors_triso]
    type = NormalVectorsTRISO
    block = 'IPyC OPyC'
  []
  [PyC_eigenstrain]
    type = ADPyCIrradiationEigenstrain
    block = 'IPyC OPyC'
    radial_eigenstrain_function = radial_eigenstrain
    tangential_eigenstrain_function = tangential_eigenstrain
    eigenstrain_name = pyc_eigenstrain
  []
  [fuel_thermal_strain]
    type = ADComputeThermalExpansionEigenstrain
    block = fuel
    thermal_expansion_coeff = 10e-6
    stress_free_temperature = 1346.0
    eigenstrain_name = thermal_strain
    temperature = temperature
  []
  [PyC_thermal_strain]
    type = ADComputeThermalExpansionEigenstrain
    block = 'buffer IPyC OPyC'
    thermal_expansion_coeff = 5.5e-6
    stress_free_temperature = 1346.0
    eigenstrain_name = thermal_strain
    temperature = temperature
  []
  [SiC_thermal_strain]
    type = ADComputeThermalExpansionEigenstrain
    block = SiC
    thermal_expansion_coeff = 4.9e-6
    stress_free_temperature = 1346.0
    eigenstrain_name = thermal_strain
    temperature = temperature
  []
  [fuel_thermal]
    type = ADUO2Thermal
    thermal_conductivity_model = FINK_LUCUTA
    block = fuel
    temperature = temperature
    burnup = burnup
  []
  [fuel_elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    block = fuel
    youngs_modulus = 2e8
    poissons_ratio = 0.345
  []
  [fuel_den]
    type = ADStrainAdjustedDensity
    block = fuel
    strain_free_density = 10810.0
  []
  [buffer_elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    block = buffer
    youngs_modulus = 2e8
    poissons_ratio = 0.345
  []
  [buffer_thermal]
    type = ADHeatConductionMaterial
    block = buffer
    thermal_conductivity = 0.5
    specific_heat = 720.0
  []
  [buffer_den]
    type = ADStrainAdjustedDensity
    strain_free_density = 1000
    block = buffer
  []
  [PyC_elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    block = 'IPyC OPyC'
    youngs_modulus = 3.96e10
    poissons_ratio = 0.33
  []
  [PyC_thermal]
    type = ADHeatConductionMaterial
    block = 'IPyC OPyC'
    thermal_conductivity = 4.0
    specific_heat = 720.0
  []
  [PyC_den]
    type = ADStrainAdjustedDensity
    strain_free_density = 1880.0
    block = 'IPyC OPyC'
  []
  [SiC_elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    block = SiC
    youngs_modulus = 3.7e11
    poissons_ratio = 0.13
  []
  [SiC_thermal]
    type = ADHeatConductionMaterial
    block = SiC
    thermal_conductivity = 13.9
    specific_heat = 620.0
  []
  [SiC_den]
    type = ADStrainAdjustedDensity
    strain_free_density = 3200.0
    block = SiC
  []
  [characteristic_strength_SiC]
    type = ADGenericConstantMaterial
    prop_values = '9640000'
    prop_names = 'characteristic_strength'
    block = SiC
  []
  [characteristic_strength_PyC]
    type = ADGenericConstantMaterial
    prop_values = '964000'
    prop_names = 'characteristic_strength'
    block = 'IPyC OPyC'
  []
[]

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

[Debug]
  show_var_residual_norms = true
[]

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

[Postprocessors]
  [dt]
    type = TimestepSize
  []
  [burnup]
    type = ElementExtremeValue
    block = fuel
    variable = burnup
  []
  [fis_gas_produced]
    type = ADElementIntegralFisGasGeneratedSifgrs
    block = fuel
  []
  [fis_gas_released]
    type = ADElementIntegralFisGasReleasedSifgrs
    block = fuel
  []
  [volumeTotal]
    type = InternalVolume
    boundary = exterior
  []
  [volumeFuel]
    type = InternalVolume
    boundary = fuel_outer_boundary
  []
  [volumeGas]
    type = InternalVolume
    boundary = 'fuel_outer_boundary IPyC_inner_boundary'
    addition = -5.53e-11
    execute_on = 'initial timestep_end'
  []
  [volumeBufferShell]
    type = InternalVolume
    boundary = buffer_IPyC_boundary
  []
  [ave_temp_interior]
    type = SideAverageValue
    boundary = buffer_IPyC_boundary
    variable = temperature
    execute_on = 'initial timestep_end'
  []
  # Postprocessors for CO production
  [total_fission_rate]
    type = ADElementIntegralPower
    variable = temperature
    fission_rate = fission_rate
    block = fuel
    energy_per_fission = 1.0
  []
  [total_fissions]
    type = TimeIntegratedPostprocessor
    value = total_fission_rate
  []
  [avg_surface_temperature]
    type = SideAverageValue
    variable = temperature
    boundary = exterior
  []
  [time_int_surf_temperature]
    type = TimeIntegratedPostprocessor
    value = avg_surface_temperature
  []
  [co_production]
    type = CarbonMonoxideProduction
    total_fissions = total_fissions
    time_integrated_triso_temperature = time_int_surf_temperature
    initial_enrichment = 0.14029
  []
  [tang_SiC]
    type = ElementalVariableValue
    variable = stress_yy
    elementid = 18
  []
  [strength_SiC]
    type = ADWeibullEffectiveMeanStrength
    block = SiC
    weibull_modulus = 6
  []
  [failure_indicator_SiC]
    type = ADWeibullFailureOutputUsingCorrelation
    block = SiC
    weibull_modulus = 6
    stress_name = max_principal_stress
    effective_mean_strength = strength_SiC
  []
  [strength_IPyC]
    type = ADWeibullEffectiveMeanStrength
    block = IPyC
    weibull_modulus = 6
  []
  [failure_indicator_IPyC]
    type = ADWeibullFailureOutputUsingCorrelation
    block = IPyC
    weibull_modulus = 6
    stress_name = max_principal_stress
    effective_mean_strength = strength_IPyC
  []
  [failure_indicator_debonding]
    type = ADTRISODebondingFailureIndicator
    boundary = IPyC_outer_boundary
    bond_strength = 1e5
    stress_name = radial_stress
  []
  [strength_OPyC]
    type = ADWeibullEffectiveMeanStrength
    block = OPyC
    weibull_modulus = 6
  []
  [failure_indicator_OPyC]
    type = ADWeibullFailureOutputUsingCorrelation
    block = OPyC
    weibull_modulus = 6
    stress_name = max_principal_stress
    effective_mean_strength = strength_OPyC
  []
  [failure_indicator_SiC_crackedIPyC]
    type = ADWeibullFailureOutputUsingCorrelation
    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 = ADWeibullFailureOutputUsingCorrelation
    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_debonding = failure_indicator_debonding
  []
[]

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

(test/tests/triso_failure/triso_1d_weibull_probability.i)

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

[Mesh]
  coord_type = RSPHERICAL
  [gen]
    type = TRISO1DMeshGenerator
    elem_type = EDGE3
    coordinates = '0 2.485e-4 3.425e-4 3.425e-4 3.835e-4 4.195e-4 4.595e-4'
    mesh_density = '6 6 0 6 8 6'
    block_names = 'fuel buffer IPyC SiC OPyC'
  []
[]

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

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

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

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

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

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

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

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

[BCs]
  [no_disp_x]
    type = DirichletBC
    variable = disp_x
    boundary = xzero
    value = 0.0
  []
  [freesurf_temperature]
    type = DirichletBC
    variable = temperature
    boundary = exterior
    value = 1346.0
  []
  [exterior_pressure_x]
    type = Pressure
    use_displaced_mesh = false
    variable = disp_x
    boundary = exterior
    factor = 0.1e6
  []
  [PlenumPressure]
    #  apply gas pressure on buffer and IPyC boundaries
    [plenumPressure]
      use_displaced_mesh = false
      boundary = buffer_IPyC_boundary
      initial_pressure = 0
      startup_time = 1.0e4
      R = 8.3143
      # coupling to post processor
      output_initial_moles = initial_moles
      temperature = ave_temp_interior
      volume = volumeGas
      material_input = 'fis_gas_released co_production'
      output = plenum_pressure
    []
  []

[]

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

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

[Debug]
  show_var_residual_norms = true
[]

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

[Postprocessors]
  [burnup]
    type = ElementExtremeValue
    block = fuel
    variable = burnup
  []
  [fis_gas_produced]
    type = ElementIntegralFisGasGeneratedSifgrs
    block = fuel
  []
  [fis_gas_released]
    type = ElementIntegralFisGasReleasedSifgrs
    block = fuel
  []
  [volumeTotal]
    type = InternalVolume
    boundary = exterior
  []
  [volumeFuel]
    type = InternalVolume
    boundary = fuel_outer_boundary
  []
  [volumeGas]
    type = InternalVolume
    boundary = 'fuel_outer_boundary IPyC_inner_boundary'
    addition = -5.53e-11
    execute_on = 'initial timestep_end'
  []
  [volumeBufferShell]
    type = InternalVolume
    boundary = buffer_IPyC_boundary
  []
  [ave_temp_interior]
    type = SideAverageValue
    boundary = buffer_IPyC_boundary
    variable = temperature
    execute_on = 'initial timestep_end'
  []
  # Postprocessors for CO production
  [total_fission_rate]
    type = ElementIntegralPower
    variable = temperature
    fission_rate = fission_rate
    block = fuel
    energy_per_fission = 1.0
  []
  [total_fissions]
    type = TimeIntegratedPostprocessor
    value = total_fission_rate
  []
  [avg_surface_temperature]
    type = SideAverageValue
    variable = temperature
    boundary = exterior
  []
  [time_int_surf_temperature]
    type = TimeIntegratedPostprocessor
    value = avg_surface_temperature
  []
  [co_production]
    type = CarbonMonoxideProduction
    total_fissions = total_fissions
    time_integrated_triso_temperature = time_int_surf_temperature
    initial_enrichment = 0.14029
  []
  [tang_SiC]
    type = ElementalVariableValue
    variable = stress_yy
    elementid = 18
  []
  [Weibull_failure_probability_OPyC]
    type = WeibullFailureProbability
    block = OPyC
    weibull_modulus = 6
    characteristic_strength = characteristic_strength_OPyC
  []
  [Weibull_failure_probability_IPyC]
    type = WeibullFailureProbability
    block = IPyC
    weibull_modulus = 6
    characteristic_strength = characteristic_strength_IPyC
  []
  [Weibull_failure_probability_SiC]
    type = WeibullFailureProbability
    block = SiC
    weibull_modulus = 6
    characteristic_strength = characteristic_strength_SiC
  []
[]

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

(assessment/TRISO/benchmark/IAEA_CRP-6/fuel_performance/case_11/case_11_1D.i)

#
# This case is taken from Advances in high temperature gas cooled reactor fuel
# technology. Technical Report IAEA-TECDOC-1674, International Atomic Energy
# Agency, 2012.
#
# See also Hales, et al., Multidimensional multiphysics simulation of TRISO
# particle fuel, JNM, 443, 2013.  https://doi.org/10.1016/j.jnucmat.2013.07.070
#
# The correctness of the results computed by this case must be checked against
# results from the IAEA benchmark.  The best way to do this is to compare
# results with information in the JNM article.
#


initial_fuel_density = 10810.0

[GlobalParams]
  density = ${initial_fuel_density} # kg/m^3
  flux_conversion_factor = 1.0
  order = SECOND
  family = LAGRANGE
  displacements = 'disp_x'
[]

[Mesh]
  coord_type = RSPHERICAL
  [gen]
    type = TRISO1DMeshGenerator
    elem_type = EDGE3
    coordinates = '0 2.485e-4 3.425e-4 3.425e-4 3.835e-4 4.195e-4 4.595e-4'
    mesh_density = '6 6 0 6 8 6'
    block_names = 'fuel buffer IPyC SiC OPyC'
  []
[]

[Variables]
  [disp_x]
  []
  [temperature]
    initial_condition = 1608.0
  []
[]

[Functions]
  [radial_eigenstrain]
    type = ParsedFunction
    expression = 't*(4.52013e-4/6.0*t*t*t*t*t - 8.36313e-3/5.0*t*t*t*t + 5.67549e-2/4.0*t*t*t - 1.74247e-1/3.0*t*t + 2.62692e-1/2.0*t - 1.43234e-1)'
  []
  [tangential_eigenstrain]
    type = ParsedFunction
    expression = 't*(1.30457e-4/4.0*t*t*t - 2.10029e-3/3.0*t*t + 9.07826e-3/2.0*t - 3.24737e-2)'
  []
  [fission_rate]
    type = ParsedFunction
    expression = 1.1135e20 # units of fissions/m**3
  []
  [k_function]
    type = ParsedFunction
    expression = '4.93e-29'
  []
[]

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

[Physics/SolidMechanics/QuasiStatic]
  [IPyC_OPyC]
    block = 'IPyC OPyC'
    strain = finite
    eigenstrain_names = 'thermal_strain pyc_eigenstrain'
  []
  [rest]
    block = 'fuel buffer SiC'
    strain = finite
    eigenstrain_names = thermal_strain
  []
[]


[Kernels]
  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temperature
  []
  [heat]
    type = HeatConduction
    variable = temperature
  []
  [heat_source]
    type = NeutronHeatSource
    variable = temperature
    block = fuel
    energy_per_fission = 3.2e-11 # units of J/fission
    fission_rate = fission_rate
  []
[]

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

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

[ThermalContact]
  [thermal_contact]
    type = GasGapHeatTransfer
    variable = temperature
    primary = IPyC_inner_boundary
    secondary = buffer_outer_boundary
    initial_moles = initial_moles # coupling to a postprocessor which supplies the initial plenum/gap gas mass
    gas_released = 'fis_gas_released co_production' # coupling to postprocessors which supply the fission gas addition, co addition
    released_fractions = '0.153 0.847;
                          1'
    released_gas_types = 'Kr Xe;
                          CO'
    tangential_tolerance = 1e-6
    #    contact_pressure_input = 10e6
    #    quadrature = true
  []
[]

[BCs]

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

  # fix temperature on free surface
  [freesurf_temp]
    type = DirichletBC
    variable = temperature
    boundary = exterior
    value = 1608.0
  []

  # 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 = 0
      startup_time = 1.0e4
      R = 8.3143
      output_initial_moles = initial_moles # coupling to post processor to get initial fill gas mass
      temperature = ave_temp_interior # coupling to post processor to get gas temperature approximation
      volume = volumeGas # coupling to post processor to get gas volume
      material_input = 'fis_gas_released co_production' # coupling to post processor to get fission gas added, co added
      output = plenum_pressure # coupling to post processor to output plenum/gap pressure
    []
  []

[]

[Materials]

  [flux]
    type = FastNeutronFlux
    calculate_fluence = true
    factor = 2.37417e18 # n/m^2-sec
  []

  [fission_gas_release]
    type = UO2Sifgrs
    block = fuel
    temperature = temperature
    fission_rate = fission_rate
    grain_radius_const = 5.0e-6
  []

  [stress]
    type = ComputeFiniteStrainElasticStress
    block = 'fuel buffer SiC'
  []
  [PyC_stress]
    type = PyCCreep
    block = 'IPyC OPyC'
    k = k_function
    poissons_ratio = 0.4
    temperature = temperature
  []
  [normal_vectors_triso]
    type = NormalVectorsTRISO
    block = 'IPyC OPyC'
  []
  [PyC_eigenstrain]
    type = PyCIrradiationEigenstrain
    block = 'IPyC OPyC'
    radial_eigenstrain_function = radial_eigenstrain
    tangential_eigenstrain_function = tangential_eigenstrain
    eigenstrain_name = pyc_eigenstrain
  []

  [fuel_thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    block = fuel
    thermal_expansion_coeff = 10e-6
    stress_free_temperature = 1608.0
    eigenstrain_name = thermal_strain
    temperature = temperature
  []
  [PyC_thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    block = 'buffer IPyC OPyC'
    thermal_expansion_coeff = 5.5e-6
    stress_free_temperature = 1608.0
    eigenstrain_name = thermal_strain
    temperature = temperature
  []
  [SiC_thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    block = SiC
    thermal_expansion_coeff = 4.9e-6
    stress_free_temperature = 1608.0
    eigenstrain_name = thermal_strain
    temperature = temperature
  []

  [fuel_thermal]
    type = UO2Thermal
    thermal_conductivity_model = FINK_LUCUTA
    block = fuel
    temperature = temperature
    burnup = burnup
  []

  [fuel_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = fuel
    youngs_modulus = 2e8
    poissons_ratio = 0.345
  []

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

  [buffer_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = buffer
    youngs_modulus = 2e8
    poissons_ratio = 0.345
  []

  [buffer_temperature]
    type = HeatConductionMaterial
    block = buffer
    thermal_conductivity = 0.5 # J/m-s-K
    specific_heat = 720.0 # J/kg-K
  []

  [buffer_den]
    type = StrainAdjustedDensity
    strain_free_density = 1000 #kg/m^3
    block = buffer
  []

  [PyC_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = 'IPyC OPyC'
    youngs_modulus = 3.96e10
    poissons_ratio = 0.33
  []

  [PyC_temperature]
    type = HeatConductionMaterial
    block = 'IPyC OPyC'
    thermal_conductivity = 4.0 # J/m-s-K
    specific_heat = 720.0 # J/kg-K
  []

  [PyC_den]
    type = StrainAdjustedDensity
    strain_free_density = 1880.0 # kg/m^3
    block = 'IPyC OPyC'
  []

  [SiC_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = SiC
    youngs_modulus = 3.7e11
    poissons_ratio = 0.13
  []

  [SiC_temperature]
    type = HeatConductionMaterial
    block = SiC
    thermal_conductivity = 13.9 # J/m-s-K
    specific_heat = 620.0 # J/kg-K
  []

  [SiC_den]
    type = StrainAdjustedDensity
    strain_free_density = 3200.0 # kg/m^3
    block = SiC
  []
[]

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

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

[Debug]
  show_var_residual_norms = true
[]

[Executioner]
  type = Transient

  petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
  petsc_options_value = '201                hypre    boomeramg      4'

  line_search = 'none'

  solve_type = 'PJFNK'

  nl_rel_tol = 5e-6
  nl_abs_tol = 1e-10
  nl_max_its = 15

  l_tol = 1e-3
  l_max_its = 50

  start_time = 0.0
  end_time = 3.032e7

  dtmax = 2e5
  dtmin = 1
  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 20
    optimal_iterations = 6
    iteration_window = 2
    linear_iteration_ratio = 100
  []
[]

[Postprocessors]
  [burnup]
    type = ElementExtremeValue
    block = fuel
    variable = burnup
  []
  [fis_gas_produced]
    type = ElementIntegralFisGasGeneratedSifgrs
    block = fuel
  []

  [fis_gas_released]
    type = ElementIntegralFisGasReleasedSifgrs
    block = fuel
  []
  [volumeTotal]
    type = InternalVolume
    boundary = exterior
  []
  [volumeFuel]
    type = InternalVolume
    boundary = fuel_outer_boundary
  []
  [volumeGas]
    type = InternalVolume
    boundary = 'fuel_outer_boundary IPyC_inner_boundary'
    addition = -5.53e-11
    execute_on = 'initial timestep_end'
  []
  [volumeBufferShell]
    type = InternalVolume
    boundary = buffer_IPyC_boundary
  []
  [ave_temp_interior]
    type = SideAverageValue
    boundary = buffer_IPyC_boundary
    variable = temperature
    execute_on = 'initial timestep_end'
  []

  # Postprocessors for CO production

  [total_fission_rate]
    type = ElementIntegralPower
    variable = temperature
    fission_rate = fission_rate
    block = fuel
    energy_per_fission = 1.0
  []

  [total_fissions]
    type = TimeIntegratedPostprocessor
    value = total_fission_rate
  []

  [avg_surface_temp]
    type = SideAverageValue
    variable = temperature
    boundary = exterior
  []

  [time_int_surf_temp]
    type = TimeIntegratedPostprocessor
    value = avg_surface_temp
  []

  [co_production]
    type = CarbonMonoxideProduction
    total_fissions = total_fissions
    time_integrated_triso_temperature = time_int_surf_temp
    initial_enrichment = 0.14029
  []

  [tang_SiC]
    type = ElementalVariableValue
    variable = stress_yy
    elementid = 18
  []
[]

[PerformanceMetricOutputs]
[]

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

(test/tests/triso_failure/triso_1d_failure.i)

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

[Mesh]
  coord_type = RSPHERICAL
  [gen]
    type = TRISO1DMeshGenerator
    elem_type = EDGE3
    coordinates = '0 2.485e-4 3.425e-4 3.425e-4 3.835e-4 4.195e-4 4.595e-4'
    mesh_density = '6 6 0 6 8 6'
    block_names = 'fuel buffer IPyC SiC OPyC'
  []
[]

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

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

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

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

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

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

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

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

[BCs]
  [no_disp_x]
    type = DirichletBC
    variable = disp_x
    boundary = xzero
    value = 0.0
  []
  [freesurf_temperature]
    type = DirichletBC
    variable = temperature
    boundary = exterior
    value = 1346.0
  []
  [exterior_pressure_x]
    type = Pressure
    use_displaced_mesh = false
    variable = disp_x
    boundary = exterior
    factor = 0.1e6
  []
  [PlenumPressure]
    #  apply gas pressure on buffer and IPyC boundaries
    [plenumPressure]
      use_displaced_mesh = false
      boundary = buffer_IPyC_boundary
      initial_pressure = 0
      startup_time = 1.0e4
      R = 8.3143
      # coupling to post processor
      output_initial_moles = initial_moles
      temperature = ave_temp_interior
      volume = volumeGas
      material_input = 'fis_gas_released co_production'
      output = plenum_pressure
    []
  []

[]

[Materials]
  [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
  []
  [max_principal_stress]
    type = RankTwoInvariant
    property_name = max_principal_stress
    rank_two_tensor = stress
    invariant = MaxPrincipal
  []
  [flux]
    type = FastNeutronFlux
    calculate_fluence = true
    factor = 1.708707e18
  []
  [fission_gas_release]
    type = UO2Sifgrs
    block = fuel
    temperature = temperature
    fission_rate = fission_rate
    grain_radius_const = 5.0e-6
  []
  [stress]
    type = ComputeLinearElasticStress
    block = 'fuel buffer SiC'
  []
  [PyC_stress]
    type = PyCCreep
    block = 'IPyC OPyC'
    k = k_function
    poissons_ratio = 0.4
    temperature = temperature
  []
  [normal_vectors_triso]
    type = NormalVectorsTRISO
    block = 'IPyC OPyC'
  []
  [PyC_eigenstrain]
    type = PyCIrradiationEigenstrain
    block = 'IPyC OPyC'
    radial_eigenstrain_function = radial_eigenstrain
    tangential_eigenstrain_function = tangential_eigenstrain
    eigenstrain_name = pyc_eigenstrain
  []
  [fuel_thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    block = fuel
    thermal_expansion_coeff = 10e-6
    stress_free_temperature = 1346.0
    eigenstrain_name = thermal_strain
    temperature = temperature
  []
  [PyC_thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    block = 'buffer IPyC OPyC'
    thermal_expansion_coeff = 5.5e-6
    stress_free_temperature = 1346.0
    eigenstrain_name = thermal_strain
    temperature = temperature
  []
  [SiC_thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    block = SiC
    thermal_expansion_coeff = 4.9e-6
    stress_free_temperature = 1346.0
    eigenstrain_name = thermal_strain
    temperature = temperature
  []
  [fuel_thermal]
    type = UO2Thermal
    thermal_conductivity_model = FINK_LUCUTA
    block = fuel
    temperature = temperature
    burnup = burnup
  []
  [fuel_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = fuel
    youngs_modulus = 2e8
    poissons_ratio = 0.345
  []
  [fuel_den]
    type = StrainAdjustedDensity
    block = fuel
    strain_free_density = 10810.0
  []
  [buffer_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = buffer
    youngs_modulus = 2e8
    poissons_ratio = 0.345
  []
  [buffer_thermal]
    type = HeatConductionMaterial
    block = buffer
    thermal_conductivity = 0.5
    specific_heat = 720.0
  []
  [buffer_den]
    type = StrainAdjustedDensity
    strain_free_density = 1000
    block = buffer
  []
  [PyC_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = 'IPyC OPyC'
    youngs_modulus = 3.96e10
    poissons_ratio = 0.33
  []
  [PyC_thermal]
    type = HeatConductionMaterial
    block = 'IPyC OPyC'
    thermal_conductivity = 4.0
    specific_heat = 720.0
  []
  [PyC_den]
    type = StrainAdjustedDensity
    strain_free_density = 1880.0
    block = 'IPyC OPyC'
  []
  [SiC_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = SiC
    youngs_modulus = 3.7e11
    poissons_ratio = 0.13
  []
  [SiC_thermal]
    type = HeatConductionMaterial
    block = SiC
    thermal_conductivity = 13.9
    specific_heat = 620.0
  []
  [SiC_den]
    type = StrainAdjustedDensity
    strain_free_density = 3200.0
    block = SiC
  []
  [characteristic_strength_SiC]
    type = GenericConstantMaterial
    prop_values = '9640000'
    prop_names = 'characteristic_strength'
    block = SiC
  []
  [characteristic_strength_PyC]
    type = GenericConstantMaterial
    prop_values = '964000'
    prop_names = 'characteristic_strength'
    block = 'IPyC OPyC'
  []
[]

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

[Debug]
  show_var_residual_norms = true
[]

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

[Postprocessors]
  [dt]
    type = TimestepSize
  []
  [burnup]
    type = ElementExtremeValue
    block = fuel
    variable = burnup
  []
  [fis_gas_produced]
    type = ElementIntegralFisGasGeneratedSifgrs
    block = fuel
  []
  [fis_gas_released]
    type = ElementIntegralFisGasReleasedSifgrs
    block = fuel
  []
  [volumeTotal]
    type = InternalVolume
    boundary = exterior
  []
  [volumeFuel]
    type = InternalVolume
    boundary = fuel_outer_boundary
  []
  [volumeGas]
    type = InternalVolume
    boundary = 'fuel_outer_boundary IPyC_inner_boundary'
    addition = -5.53e-11
    execute_on = 'initial timestep_end'
  []
  [volumeBufferShell]
    type = InternalVolume
    boundary = buffer_IPyC_boundary
  []
  [ave_temp_interior]
    type = SideAverageValue
    boundary = buffer_IPyC_boundary
    variable = temperature
    execute_on = 'initial timestep_end'
  []
  # Postprocessors for CO production
  [total_fission_rate]
    type = ElementIntegralPower
    variable = temperature
    fission_rate = fission_rate
    block = fuel
    energy_per_fission = 1.0
  []
  [total_fissions]
    type = TimeIntegratedPostprocessor
    value = total_fission_rate
  []
  [avg_surface_temperature]
    type = SideAverageValue
    variable = temperature
    boundary = exterior
  []
  [time_int_surf_temperature]
    type = TimeIntegratedPostprocessor
    value = avg_surface_temperature
  []
  [co_production]
    type = CarbonMonoxideProduction
    total_fissions = total_fissions
    time_integrated_triso_temperature = time_int_surf_temperature
    initial_enrichment = 0.14029
  []
  [tang_SiC]
    type = ElementalVariableValue
    variable = stress_yy
    elementid = 18
  []
  [strength_SiC]
    type = WeibullEffectiveMeanStrength
    block = SiC
    weibull_modulus = 6
  []
  [failure_indicator_SiC]
    type = WeibullFailureOutputUsingCorrelation
    block = SiC
    weibull_modulus = 6
    stress_name = max_principal_stress
    effective_mean_strength = strength_SiC
  []
  [strength_IPyC]
    type = WeibullEffectiveMeanStrength
    block = IPyC
    weibull_modulus = 6
  []
  [failure_indicator_IPyC]
    type = WeibullFailureOutputUsingCorrelation
    block = IPyC
    weibull_modulus = 6
    stress_name = max_principal_stress
    effective_mean_strength = strength_IPyC
  []
  [failure_indicator_debonding]
    type = TRISODebondingFailureIndicator
    boundary = IPyC_outer_boundary
    bond_strength = 1e5
    stress_name = radial_stress
  []
  [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
  []
  [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_debonding = failure_indicator_debonding
  []
[]

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

(examples/TRISO/accident_simulation/triso1D_accident.i)

# This example is 1D spherical analysis of a TRISO fuel particle. Fully coupled
# heat transfer and solid mechanics, plus diffusion of the fission product
# species cesium (Cs) are simulated.  The mesh includes contact surfaces
# between the buffer and IPyC layers to facilitate a gap opening between
# these layers. These surfaces are initially in mechanical contact but
# are assumed to have no strength in tension. A coarse mesh is used to
# provide a short run time.

# The calculation simulates fuel-life in three steps. The first step is an
# irradiation period, where constant power and a fixed particle surface
# temperature (1500 K) are assumed over a lifetime of 76 Ms (2.4 yrs).
# For the second step, fuel removal and storage are simulated by setting
# the reactor power and Cs source terms to zero, reducing the particle
# surface temperature to ambient (300 K), and then holding it
# for 100 days. A third and final step simulates accident
# behavior by increasing the particle surface temperature from ambient
# to 2073 K over 2 hrs, and then holding it at this elevated temperature
# for an additional 200 hrs. At the particle outer boundary, the Cs
# concentration is held at zero and the pressure at ambient during the
# entire simulation. The particle is assumed to be stress-free at an
# initial temperature of 1500 K.
#
# Details about this simulation are given in Section 4 of the following
# article: J. D. Hales, R. L. Williamson, S. R. Novascone, D. M. Perez,
# B. W. Spencer and G. Pastore, "Multidimensional multiphysics simulation
# of TRISO particle fuel", Journal of Nuclear Materials, Vol. 443, p. 531,
# 2013.

# This is a version using an interface kernel to model gap mass transfer.
# Sorption constants are given in Table 1 of the following article: A.
# Londono-Hurtado, I. Szlufarska, R. Bratton and D. Morgan, "A review of
# fission product sorption in carbon structures", Journal of Nuclear
# Materials, Vol. 426, p. 254, 2012.

initial_fuel_density = 11000

[GlobalParams]
  order = SECOND
  family = LAGRANGE
  displacements = disp_x
  flux_conversion_factor = 0.85
[]

[Mesh]
  coord_type = RSPHERICAL
  [gen] # exclude gap to establish buffer-IPyC neighbor relationships for the sorption interface kernel
    type = TRISO1DMeshGenerator
    elem_type = EDGE3
    coordinates = '0 2.125e-4 3.125e-4 3.525e-4 3.875e-4 4.275e-4'
    mesh_density = '10 5 2 2 2'
    block_names = 'fuel buffer IPyC SiC OPyC'
  []
  [break] # create gap between buffer and IPyC to model mechanical and thermal contact
    type = BreakMeshByBlockGenerator
    input = gen
    block_pairs = 'buffer IPyC'
    split_interface = true
    add_interface_on_two_sides = true
  []
[]

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

[Variables]
  [disp_x]
  []
  [temp]
    initial_condition = 1500.0
  []
  [conc]
    initial_condition = 0.0
  []
[]

[AuxVariables]
  [fission_rate]
    block = fuel
    order = CONSTANT
    family = MONOMIAL
  []
  [fluence]
    order = CONSTANT
    family = MONOMIAL
  []
  [burnup]
    block = fuel
    order = CONSTANT
    family = MONOMIAL
  []
  [gap_cond]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_xx]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_yy]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_zz]
    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'
  []
  [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)'
  []
  [integral_flux_error]
    type = ParsedFunction
    symbol_names = 'buffer_integral_flux IPyC_integral_flux'
    symbol_values = 'buffer_integral_flux IPyC_integral_flux'
    expression = 'IPyC_integral_flux + buffer_integral_flux'
  []
  [partial_pressure_error]
    type = ParsedFunction
    symbol_names = 'buffer_partial_pressure IPyC_partial_pressure'
    symbol_values = 'buffer_partial_pressure IPyC_partial_pressure'
    expression = 'IPyC_partial_pressure - buffer_partial_pressure'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  generate_output = 'stress_xx stress_yy stress_zz stress_xy stress_yz stress_zx hydrostatic_stress'
  strain = FINITE
  incremental = true
  add_variables = false
  [default]
    block = 'fuel buffer IPyC OPyC'
    eigenstrain_names = 'thermal_strain swelling_strain'
    extra_vector_tags = 'ref'
  []
  [SiC]
    block = 'SiC'
    eigenstrain_names = 'thermal_strain'
    extra_vector_tags = 'ref'
  []
[]

[Kernels]
  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temp
    extra_vector_tags = 'ref'
  []
  [heat]
    type = HeatConduction
    variable = temp
    extra_vector_tags = 'ref'
  []
  [heat_source]
    type = NeutronHeatSource
    variable = temp
    block = fuel
    energy_per_fission = 3.2e-11 # units of J/fission
    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 moles/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]
  [fission_rate]
    type = FissionRateGeneral
    fission_rate_formulation = GENERIC
    variable = fission_rate
    block = fuel
    fission_rate_function = power_history
    value = 3.89e19
    execute_on = timestep_begin
  []
  [fluence]
    type = MaterialRealAux
    property = fast_neutron_fluence
    variable = fluence
  []
  [burnup]
    type = BurnupAux
    variable = burnup
    block = fuel
    fission_rate = fission_rate
    molecular_weight = 0.270 # units of kg/mole
    execute_on = timestep_begin
    density = ${initial_fuel_density}
  []
  [creep_xx]
    type = RankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_xx
    index_i = 0
    index_j = 0
    block = 'buffer IPyC SiC OPyC'
    execute_on = timestep_end
  []
  [creep_yy]
    type = RankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_yy
    index_i = 1
    index_j = 1
    block = 'buffer IPyC SiC OPyC'
    execute_on = timestep_end
  []
  [creep_zz]
    type = RankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_zz
    index_i = 2
    index_j = 2
    block = 'buffer IPyC SiC OPyC'
    execute_on = timestep_end
  []
  [conductance]
    type = MaterialRealAux
    property = gap_conductance
    variable = gap_cond
    boundary = buffer_IPyC
    execute_on = linear
  []
[]

[Contact]
  [pellet_clad_mechanical]
    primary = IPyC_buffer
    secondary = buffer_IPyC
    penalty = 1e5
    model = frictionless
    formulation = penalty
  []
[]

[ThermalContact]
  [thermal_contact]
    type = GasGapHeatTransfer
    variable = temp
    primary = IPyC_buffer
    secondary = buffer_IPyC
    initial_moles = initial_moles # coupling to a postprocessor which supplies the initial plenum/gap gas mass
    gas_released = 'fis_gas_released co_production' # coupling to postprocessors which supply the fission gas addition, co addition
    released_gas_types = 'Kr Xe;
                          CO'
    released_fractions = '0.153 0.847;
                          1'
    gap_geometry_type = SPHERE
    tangential_tolerance = 1e-6
    roughness_coef = 0.0
    quadrature = true
  []
[]

[InterfaceKernels]
  [cesium_gap]
    type = SorptionIsothermGapInterface
    variable = conc
    neighbor_var = conc
    partial_pressure_name = partial_pressure
    sorption_penalty = 1e5
    diffusivity = arrhenius_diffusion_coef
    use_flux_penalty = true
    flux_penalty = 1e3
    boundary = buffer_IPyC
    extra_vector_tags = 'ref'
  []
[]

[BCs]
  # pin particle along symmetry planes
  [no_disp_x]
    type = DirichletBC
    variable = disp_x
    boundary = xzero
    value = 0.0
    extra_vector_tags = 'ref'
  []
  # fix temperature on free surface
  [freesurf_temp]
    type = FunctionDirichletBC
    variable = temp
    boundary = exterior
    function = temp_bc
    extra_vector_tags = 'ref'
  []
  # fix concentration on free surface
  [freesurf_conc]
    type = DirichletBC
    variable = conc
    boundary = exterior
    value = 0.0
    extra_vector_tags = 'ref'
  []
  [PlenumPressure] #  apply plenum pressure on clad inner walls and pellet surfaces
    [plenumPressure]
      boundary = 'buffer_IPyC IPyC_buffer'
      initial_pressure = 0
      startup_time = 1.0e4
      R = 8.3145
      output_initial_moles = initial_moles # coupling to post processor to get initial fill gas mass
      temperature = ave_temp_interior # coupling to post processor to get gas temperature approximation
      volume = volumeGas # coupling to post processor to get gas volume
      material_input = 'fis_gas_released co_production' # coupling to post processor to get fission gas added, co added
      output = plenum_pressure # coupling to post processor to output plenum/gap pressure
    []
  []
[]

[Materials]
  [flux]
    type = FastNeutronFlux
    calculate_fluence = true
    factor = 5e17
  []

  [fission_gas_release] # Sifgrs fission gas release mode
    type = UO2Sifgrs
    block = fuel
    temperature = temp
    fission_rate = fission_rate # coupling to fission_rate aux variable
    grain_radius_const = 5.0e-6
  []

  [fuel_thermal]
    type = UO2Thermal
    thermal_conductivity_model = FINK_LUCUTA
    block = fuel
    temperature = temp
    burnup = burnup
    initial_porosity = 0.0
  []
  [fuel_swelling]
    type = UO2VolumetricSwellingEigenstrain
    gas_swelling_model_type = MATPRO
    block = fuel
    temperature = temp
    burnup = burnup
    eigenstrain_name = 'swelling_strain'
    initial_fuel_density = ${initial_fuel_density}
  []
  [fuel_stress]
    type = ComputeFiniteStrainElasticStress
    block = 'fuel'
  []
  [fuel_elasticity]
    type = ComputeIsotropicElasticityTensor
    block = fuel
    youngs_modulus = 2.2e11
    poissons_ratio = .345
  []
  [fuel_thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    block = fuel
    thermal_expansion_coeff = 10e-6
    stress_free_temperature = 1500.0
    eigenstrain_name = thermal_strain
    temperature = temp
  []
  [fuel_den]
    type = StrainAdjustedDensity
    block = fuel
    strain_free_density = ${initial_fuel_density} # kg/m^3
  []
  [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
    gas_constant = 8.3143 # J/K-mol
    temperature = temp
  []

  [buffer_eigenstrain]
    type = PyCIrradiationEigenstrain
    block = buffer
    pyc_type = buffer
    eigenstrain_name = 'swelling_strain'
  []
  [buffer_thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    block = buffer
    thermal_expansion_coeff = 5.65e-6
    stress_free_temperature = 1500.0
    eigenstrain_name = thermal_strain
    temperature = temp
  []
  [buffer_elasticity]
    type = ComputeIsotropicElasticityTensor
    block = buffer
    youngs_modulus = 2e10
    poissons_ratio = .23
  []
  [buffer_stress]
    type = PyCCreep
    block = buffer
    temperature = temp
  []
  [buffer_temp]
    type = HeatConductionMaterial
    block = buffer
    thermal_conductivity = 0.5 # J/m-s-K
    specific_heat = 720.0 # J/kg-K
  []
  [buffer_den]
    type = StrainAdjustedDensity
    strain_free_density = 1000.0 #kg/m^3
    block = buffer
  []
  [buffer_conc]
    type = ArrheniusDiffusionCoef
    block = buffer
    d1 = 1.0e-12 # m^2/s
    q1 = 0.0
    d2 = 0.0
    q2 = 0.0
    gas_constant = 8.3143 # J/K-mol
    temperature = temp
  []
  [buffer_partial_pressure]
    type = SorptionPartialPressure
    A = 19.33
    B = -47290
    D = 1.518
    E = 4338
    d1 = 3.397
    d2 = 6.15e-4
    unit_scale = 1e3 # convert from mol to mmol
    density = density # convert from mmol/m^3 to mmol/kg
    concentration = conc
    temperature = temp
    block = 'buffer IPyC'
    outputs = 'all'
    output_properties = partial_pressure
  []
  [normal_vectors_triso]
    type = NormalVectorsTRISO
    block = 'IPyC OPyC buffer'
  []
  [IPyC_eigenstrain]
    type = PyCIrradiationEigenstrain
    block = IPyC
    pyc_type = dense
    eigenstrain_name = 'swelling_strain'
  []
  [IPyC_thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    block = IPyC
    thermal_expansion_coeff = 5.65e-6
    stress_free_temperature = 1500.0
    eigenstrain_name = thermal_strain
    temperature = temp
  []
  [IPyC_elasticity]
    type = ComputeIsotropicElasticityTensor
    block = IPyC
    youngs_modulus = 4.74e10
    poissons_ratio = .23
  []
  [IPyC_disp]
    type = PyCCreep
    block = 'IPyC OPyC'
    temperature = temp
  []
  [IPyC_temp]
    type = HeatConductionMaterial
    block = 'IPyC OPyC'
    thermal_conductivity = 4.0
    specific_heat = 720.0
  []
  [IPyC_den]
    type = StrainAdjustedDensity
    block = 'IPyC OPyC'
    strain_free_density = 1900.0
  []
  [IPyC_conc]
    type = ArrheniusDiffusionCoef
    block = IPyC
    d1 = 6.3e-8
    q1 = 222.0e+3
    d2 = 0.0
    q2 = 0.0
    gas_constant = 8.3143 # J/K-mol
    temperature = temp
  []
  [SiC_thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    block = SiC
    thermal_expansion_coeff = 4.9e-6
    stress_free_temperature = 1500.0
    eigenstrain_name = thermal_strain
    temperature = temp
  []
  [SiC_elasticity]
    type = ComputeIsotropicElasticityTensor
    block = SiC
    youngs_modulus = 3.4e11
    poissons_ratio = .13
  []
  [SiC_creep]
    type = MonolithicSiCCreepUpdate
    block = SiC
    temperature = temp
    k_function = k_function
  []
  [SiC_stress]
    type = ComputeMultipleInelasticStress
    block = SiC
    tangent_operator = elastic
    inelastic_models = 'SiC_creep'
  []
  [SiC_temp]
    type = HeatConductionMaterial
    block = SiC
    thermal_conductivity = 13.9 # J/m-s-K
    specific_heat = 620.0 # J/kg-K
  []
  [SiC_den]
    type = StrainAdjustedDensity
    strain_free_density = 3180.0 # kg/m^3
    block = SiC
  []
  [SiC_conc]
    type = ArrheniusDiffusionCoef
    block = SiC
    d1 = 5.5e-14 # m^2/s
    d1_function = d1_function
    d1_function_variable = fluence
    q1 = 125.0e+3 # J/mol
    d2 = 1.6e-2 # m^2/s
    q2 = 514.0e+3 # J/mol
    gas_constant = 8.3143 # J/K-mol
    temperature = temp
  []

  [OPyC_eigenstrain]
    type = PyCIrradiationEigenstrain
    block = OPyC
    pyc_type = dense
    eigenstrain_name = 'swelling_strain'
  []
  [OPyC_thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    block = OPyC
    thermal_expansion_coeff = 5.65e-6
    stress_free_temperature = 1500.0
    eigenstrain_name = thermal_strain
    temperature = temp
  []
  [OPyC_elasticity]
    type = ComputeIsotropicElasticityTensor
    block = OPyC
    youngs_modulus = 4.74e10
    poissons_ratio = .23
  []
  [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
    gas_constant = 8.3143 # J/K-mol
    temperature = temp
  []
[]

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

[Debug]
  show_var_residual_norms = true
[]

[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-4
  nl_abs_tol = 1e-9
  nl_max_its = 15

  l_tol = 1e-3
  l_max_its = 50

  start_time = 0.0
  end_time = 85.3682e6
  dt = 100

  dtmax = 2e6
  dtmin = 1

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

  [Predictor]
    type = SimplePredictor
    scale = 1
    skip_times_old = '0    76e6  76.001e6 84.641e6 84.6482e6'
  []
[]

[Outputs]
  perf_graph = true
  exodus = true
  [console]
    type = Console
    max_rows = 25
  []
  [csv]
    type = CSV
    sync_times = '100 6308007 75696087'
    sync_only = true
  []
[]

[Postprocessors]
  [Cs_release]
    type = SideIntegralMassFlux
    variable = conc
    boundary = exterior
    execute_on = timestep_end
  []
  [dt]
    type = TimestepSize
    execute_on = timestep_end
  []
  [fis_gas_produced] # fission gas produced (moles)
    type = ElementIntegralFisGasGeneratedSifgrs
    block = fuel
    execute_on = 'initial linear nonlinear timestep_begin timestep_end'
  []
  [fis_gas_released] # fission gas released to plenum (moles)
    type = ElementIntegralFisGasReleasedSifgrs
    block = fuel
    execute_on = 'initial linear nonlinear timestep_begin timestep_end'
  []
  [volumeTotal]
    type = InternalVolume
    boundary = exterior
    scale_factor = -1
    execute_on = 'initial timestep_end'
  []
  [volumeFuel]
    type = InternalVolume
    boundary = fuel_outer_boundary
    scale_factor = -1
    execute_on = 'initial timestep_end'
  []
  [volumeGas]
    type = InternalVolume
    boundary = 'buffer_IPyC IPyC_buffer'
    # ro = 3.125e-4
    # ri = 2.125e-4
    # vb = 4/3*pi*(ro^3-ri^3) = 8.76e-11
    # buffer density = 1000
    # PyC density    = 1900
    # fill ratio = 10/19
    # vb*10/19 = 4.6e-11
    # Must remove 4.6e-11 m^3 from the volume
    addition = -4.6e-11
    execute_on = 'initial linear nonlinear timestep_begin timestep_end'
  []
  [volumeBufferShell]
    type = InternalVolume
    boundary = 'buffer_IPyC IPyC_buffer'
    execute_on = 'initial timestep_end'
  []
  [ave_temp_interior]
    type = SideAverageValue
    boundary = 'buffer_IPyC IPyC_buffer'
    variable = temp
    execute_on = 'initial linear nonlinear timestep_begin timestep_end'
  []

  # Postprocessors for CO production

  [total_fission_rate]
    type = ElementIntegralPower
    variable = temp
    fission_rate = fission_rate
    block = fuel
    energy_per_fission = 1.0
    execute_on = 'initial linear nonlinear timestep_begin timestep_end'
  []
  [total_fissions]
    type = TimeIntegratedPostprocessor
    value = total_fission_rate
    execute_on = 'initial linear nonlinear timestep_begin timestep_end'
  []
  [avg_surface_temp]
    type = SideAverageValue
    variable = temp
    boundary = exterior
    execute_on = 'initial linear nonlinear timestep_begin timestep_end'
  []
  [time_int_surf_temp]
    type = TimeIntegratedPostprocessor
    value = avg_surface_temp
    execute_on = 'initial linear nonlinear timestep_begin timestep_end'
  []
  [co_production]
    type = CarbonMonoxideProduction
    total_fissions = total_fissions
    time_integrated_triso_temperature = time_int_surf_temp
    initial_enrichment = 0.14029
    execute_on = 'initial linear nonlinear timestep_begin timestep_end'
  []
  [num_lin_it]
    type = NumLinearIterations
  []
  [num_nonlin_it]
    type = NumNonlinearIterations
  []
  [tot_lin_it]
    type = CumulativeValuePostprocessor
    postprocessor = num_lin_it
  []
  [tot_nonlin_it]
    type = CumulativeValuePostprocessor
    postprocessor = num_nonlin_it
  []
  [alive_time]
    type = PerfGraphData
    section_name = Root
    data_type = TOTAL
  []

  [buffer_integral_flux]
    type = SideDiffusiveFluxIntegral
    variable = conc
    boundary = buffer_IPyC
    diffusivity = arrhenius_diffusion_coef
  []
  [IPyC_integral_flux]
    type = SideDiffusiveFluxIntegral
    variable = conc
    boundary = IPyC_buffer
    diffusivity = arrhenius_diffusion_coef
  []
  [buffer_partial_pressure]
    type = SideAverageMaterialProperty
    property = partial_pressure
    boundary = buffer_IPyC
  []
  [IPyC_partial_pressure]
    type = SideAverageMaterialProperty
    property = partial_pressure
    boundary = IPyC_buffer
  []
  [integral_flux_error]
    type = FunctionValuePostprocessor
    function = integral_flux_error
  []
  [partial_pressure_error]
    type = FunctionValuePostprocessor
    function = partial_pressure_error
  []
  [integral_Cs_release]
    type = TimeIntegratedPostprocessor
    value = Cs_release
  []
  [Cs_production]
    type = FunctionValuePostprocessor
    function = power_history
    scale_factor = 1.22e-5 # units of moles/m**3-s
  []
  [time_integral_Cs_production]
    type = TimeIntegratedPostprocessor
    value = Cs_production
  []
  [volumeFuel_initial]
    type = InternalVolume
    boundary = fuel_outer_boundary
    scale_factor = -1
    execute_on = initial
  []
  [integral_Cs_production]
    type = ParsedPostprocessor
    pp_names = 'time_integral_Cs_production volumeFuel_initial'
    expression = 'time_integral_Cs_production * volumeFuel_initial'
  []
  [Cs_release_fraction]
    type = ParsedPostprocessor
    pp_names = 'integral_Cs_release integral_Cs_production'
    expression = 'integral_Cs_release / integral_Cs_production'
  []
[]

[VectorPostprocessors]
  [temperaturevpp]
    type = SideValueSampler
    boundary = 11
    variable = temp
    sort_by = x
    outputs = 'csv'
    use_displaced_mesh = true
  []
[]

(test/tests/triso/base_irradiation/triso1D_accident_action.i)

[GlobalParams]
  density = 11000.0 # kg/m^3
  order = SECOND
  displacements = 'disp_x'
  temperature = temperature
  energy_per_fission = 3.2e-11
  stress_free_temperature = '1500'
[]

[Mesh]
  coord_type = RSPHERICAL
  [mesh]
    type = FileMeshGenerator
    file = triso1DFineTruss3.e
  []
[]

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

[AuxVariables]
  [gap_condSlave]
    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'
  []
[]

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

[Contact]
  [pellet_clad_mechanical]
    primary = 15
    secondary = 17
    penalty = 1e5
    model = frictionless
    formulation = kinematic
  []
[]

[ThermalContact]
  [thermal_contact]
    type = GasGapHeatTransfer
    variable = temperature
    primary = 15
    secondary = 17
    initial_moles = initial_moles # coupling to a postprocessor which supplies the initial plenum/gap gas mass
    gas_released = 'fis_gas_released co_production' # coupling to postprocessors which supply the fission gas addition, co addition
    released_gas_types = 'Kr Xe;
                          CO'
    released_fractions = '0.153 0.847;
                          1'
    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_Cs
    primary = 15
    secondary = 17
    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
    boundary = exterior
    function = temp_bc
  []

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

  # apply plenum pressure on clad inner walls and pellet surfaces
  [PlenumPressure]
    [plenumPressure]
      boundary = BufferGapVol
      initial_pressure = 100
      startup_time = 0
      R = 8.3145
      output_initial_moles = initial_moles
      temperature = ave_temp_interior
      volume = volumeGas
      material_input = 'fis_gas_released co_production'
      output = plenum_pressure
    []
  []
[]

[NuclearMaterials]
  physics = 'Mechanics Thermal'
  fission_operation = 'Normal'
  initial_temperature = 1500
  elements_tracked = 'Cs'
  element_decay_constants = '7.297e-10'
  elements_initial_concentration = '0.0'
  element_scaling = '1e18'
  use_automatic_differentiation = false
  add_variables = true
  flux_factor = 5e17
  flux_function = 'power_history'
  strain = 'FINITE'
  extra_vector_tags = 'ref'
  generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz strain_xx
    strain_yy strain_zz'
  [ParticleFuel]
    [UO2]
      block = fuel
      fuel_type = 'UO2'
      flux_factor = 5e17
      flux_function = 'power_history'
      fission_rate_function = fission_rate
      initial_porosity = 0.0
      youngs_modulus = 2.2e11
      poissons_ratio = 0.345
      concentration_density = 1.22e-5 # units of mol/m**3-s
      gas_constant = 8.3143
      particle_fuel_models = 'Burnup Diffusion Swelling Creep ThermalExpansion'
      diffusion_1st_coefficients = '5.6e-8'
      diffusion_2nd_coefficients = '5.2e-4'
      diffusion_1st_activation_energies = '209.0e+3'
      diffusion_2nd_activation_energies = '362.0e+3'
      initial_density = 11000.0
      average_grain_radius = 10e-6
      triso_geometry = particle_geometry
      thermal_conductivity_model = FINK_LUCUTA
    []
  []
  [ParticleLayers]
    layers_models = 'Diffusion IrradiationGrowth ThermalExpansion Creep'
    fuel_type = 'UO2'
    [IPyC]
      [IPyC_layer]
        block = IPyC
        additional_generate_output = 'creep_strain_xx creep_strain_yy
          creep_strain_zz'
        diffusion_1st_coefficients = '6.3e-8'
        diffusion_1st_activation_energies = '222.0e+3'
        initial_density = 1900.0
        youngs_modulus = 4.74e10
        poissons_ratio = 0.23
        thermal_conductivity = 4.0
        specific_heat = 720.0
        thermal_expansion_coeff = 5.65e-6
      []
    []
    [OPyC]
      [OPyC_layer]
        block = OPyC
        additional_generate_output = 'creep_strain_xx creep_strain_yy
          creep_strain_zz'
        diffusion_1st_coefficients = '6.3e-8'
        diffusion_1st_activation_energies = '222.0e+3'
        initial_density = 1900.0
        thermal_conductivity = 4.0
        specific_heat = 720.0
        youngs_modulus = 4.74e10
        poissons_ratio = 0.23
        thermal_expansion_coeff = 5.65e-6
      []
    []
    [SiC]
      [SiC_layer]
        block = SiC
        additional_generate_output = 'creep_strain_xx creep_strain_yy
          creep_strain_zz'
        diffusion_1st_coefficients = '5.5e-14'
        diffusion_1st_activation_energies = '125.0e+3'
        d1_function = d1_function
        d1_function_variable = fast_neutron_fluence
        diffusion_2nd_coefficients = '1.6e-2'
        diffusion_2nd_activation_energies = 514.0e3
        initial_density = 3180.0
        thermal_conductivity = 13.9
        specific_heat = 620.0
        youngs_modulus = 3.4e11
        poissons_ratio = 0.13
        thermal_expansion_coeff = 4.9e-6
      []
    []
    [Buffer]
      [Buffer_layer]
        block = buffer
        diffusion_1st_coefficients = '1e-12'
        diffusion_1st_activation_energies = '0'
        initial_density = 1000.0
        youngs_modulus = 2.0e10
        poissons_ratio = 0.23
        thermal_conductivity = 0.5
        specific_heat = 720.0
        thermal_expansion_coeff = 5.65e-6
        additional_generate_output = 'creep_strain_xx creep_strain_yy
          creep_strain_zz'
      []
    []
  []
[]

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

[Debug]
  show_var_residual_norms = 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-8
  l_max_its = 50

  start_time = 0.0
  #end_time = 85.3682e6
  end_time = 1e3
  num_steps = 1000

  dtmax = 2e6
  dtmin = 1

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

  [Quadrature]
    order = THIRD
  []
[]

[Postprocessors]
  [Int_Cs_release]
    type = TimeIntegratedPostprocessor
    value = release_Cs_inc
  []
  [Int_Cs_release_fuel]
    type = TimeIntegratedPostprocessor
    value = release_fuel_Cs
  []
  [Int_Cs_release_PyCGapBndry]
    type = TimeIntegratedPostprocessor
    value = release_PyCGapBndry_Cs
  []
  [fis_gas_produced]
    type = ElementIntegralFisGasGeneratedSifgrs
    block = fuel
    execute_on = linear
  []
  [fis_gas_released]
    type = ElementIntegralFisGasReleasedSifgrs
    block = fuel
    execute_on = linear
  []
  [volumeTotal]
    type = InternalVolume
    boundary = exterior
    execute_on = 'initial timestep_end'
  []
  [volumeFuel]
    type = InternalVolume
    boundary = fuel
    execute_on = 'initial timestep_end'
  []
  [volumeGas]
    type = InternalVolume
    boundary = BufferGapVol
    addition = -4.6e-11
    execute_on = 'initial linear'
  []
  [volumeBufferShell]
    type = InternalVolume
    boundary = BufferGapVol
    execute_on = 'initial timestep_end'
  []
  [ave_temp_interior]
    type = SideAverageValue
    boundary = BufferGapVol
    variable = temperature
    execute_on = 'initial timestep_end'
  []

  # Postprocessors for CO production
  [total_fission_rate]
    type = ElementIntegralPower
    variable = temperature
    fission_rate = fission_rate
    block = fuel
    energy_per_fission = 1.0
    outputs = exodus
    execute_on = 'initial linear'
  []
  [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'
  []
  [co_production]
    type = CarbonMonoxideProduction
    total_fissions = total_fissions
    time_integrated_triso_temperature = time_int_surf_temp
    initial_enrichment = 0.14029
    execute_on = 'initial nonlinear'
  []
[]

[Outputs]
  print_linear_residuals = false
  [console]
    type = Console
    max_rows = 5
    outlier_variable_norms = false
  []
  [exodus]
    type = Exodus
    file_base = triso1D_accident_action_out
  []
[]

(examples/NuclearMaterialActions/TRISO/full_particle_action.i)


initial_fuel_density = 10810.0

[GlobalParams]
  density = ${initial_fuel_density}
  order = SECOND
  family = LAGRANGE
  displacements = 'disp_x disp_y'
  energy_per_fission = 3.2e-11
  volumetric_locking_correction = false
[]

[Mesh]
  coord_type = RZ
  [mesh]
    type = FileMeshGenerator
    file = full_particle.e
  []
[]

[AuxVariables]
  [grain_radius]
    initial_condition = 5.0e-6
  []
[]

[Functions]
  [fast_neutron_flux]
    type = ParsedFunction
    expression = 1.708707e18
  []
  [fission_rate]
    type = ParsedFunction
    expression = 7.75e19
  []
[]

[AuxKernels]
  [grain_radius]
    type = GrainRadiusAux
    block = fuel
    variable = grain_radius
    temperature = temperature
    execute_on = linear
  []
[]

[Contact]
  [pellet_clad_mechanical]
    primary = 15
    secondary = 17
    penalty = 1e5
    model = frictionless
    formulation = penalty
  []
[]

[ThermalContact]
  [thermal_contact]
    type = GasGapHeatTransfer
    variable = temperature
    primary = 15
    secondary = 17
    initial_moles = initial_moles
    released_gas_types = 'Kr Xe;
                          CO'
    released_fractions = '0.153 0.847;
                          1'
  []
[]

[BCs]
  [no_disp_x]
    type = DirichletBC
    variable = disp_x
    boundary = xzero
    value = 0.0
  []
  [no_disp_y]
    type = DirichletBC
    variable = disp_y
    boundary = yzero
    value = 0.0
  []
  [freesurf_temperature]
    type = DirichletBC
    variable = temperature
    boundary = exterior
    value = 1346
  []
  [exterior_pressure_x]
    type = Pressure
    variable = disp_x
    boundary = exterior
    factor = 0.1e6
  []
  [exterior_pressure_y]
    type = Pressure
    variable = disp_y
    boundary = exterior
    factor = 0.1e6
  []
  [PlenumPressure]
    [plenumPressure]
      boundary = 'PyCGapBndry BufferGapBndry'
      initial_pressure = 0
      startup_time = 1.0e4
      R = 8.3143
      output_initial_moles = initial_moles
      temperature = ave_temp_interior
      volume = volumeGas
      material_input = 'fis_gas_released co_production'
      output = plenum_pressure
    []
  []
[]

[NuclearMaterials]
  fission_operation = 'Normal'
  physics = 'Thermal Mechanics'
  initial_temperature = 1346.0
  strain = FINITE
  generate_output = 'hydrostatic_stress stress_xx stress_yy stress_zz
    strain_xx strain_yy strain_zz stress_xy stress_yz stress_xz strain_xy
     strain_yz strain_xz'
  add_variables = true
  stress_free_temperature = 1346.0
  [ParticleFuel]
    [UO2]
      block = fuel
      fuel_type = 'UO2'
      youngs_modulus = 2.0e8
      poissons_ratio = 0.345
      particle_fuel_models = 'Burnup ThermalExpansion'
      fission_rate_function = fission_rate
      flux_factor = 1.708707e18
      initial_density = 10810.0
      average_grain_radius = 5e-6
      initial_porosity = 0.0
    []
  []
  [ParticleLayers]
    fuel_type = 'UO2'
    stress_free_temperature = 1346.0
    [SiC]
      [SiC_layer]
        block = SiC
        layers_models = 'ThermalExpansion IrradiationGrowth'
        initial_density = 3200.0
        youngs_modulus = 3.7e11
        poissons_ratio = 0.13
        thermal_conductivity = 13.9
        specific_heat = 620.0
        thermal_expansion_coeff = 4.9e-06
        thermal_conductivity_model = miller
      []
    []
    [IPyC]
      [IPyC_layer]
        block = IPyC
        layers_models = 'Creep ThermalExpansion IrradiationGrowth'
        youngs_modulus = 3.96e10
        poissons_ratio = 0.33
        initial_density = 1880.0
        thermal_conductivity = 4.0
        specific_heat = 720.0
        thermal_expansion_coeff = 5.5e-06
      []
    []
    [OPyC]
      [OPyC_layer]
        block = OPyC
        layers_models = 'Creep ThermalExpansion IrradiationGrowth'
        poissons_ratio = 0.33
        youngs_modulus = 3.96e10
        initial_density = 1880.0
        thermal_expansion_coeff = 5.5e-6
        thermal_conductivity = 4.0
        specific_heat = 720.0
      []
    []
    [Buffer]
      [Buffer_layer]
        block = buffer
        layers_models = 'ThermalExpansion IrradiationGrowth'
        thermal_conductivity = 0.5
        thermal_expansion_coeff = 5.5e-06
        specific_heat = 720.0
        youngs_modulus = 2.0e8
        poissons_ratio = 0.345
        initial_density = 1000.0
      []
    []
  []
[]

[Dampers]
  [temperature]
    type = MaxIncrement
    variable = temperature
    max_increment = 20
  []
[]

[Executioner]
  type = Transient
  petsc_options = '-snes_ksp_ew'
  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-10
  nl_max_its = 15
  l_tol = 1e-3
  l_max_its = 50
  start_time = 0.0
  end_time = 3.10176e7
  dtmax = 2e5
  dtmin = 1
  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 10
    optimal_iterations = 8
    iteration_window = 2
    linear_iteration_ratio = 100
  []
  [Quadrature]
    order = FIFTH
    side_order = SEVENTH
  []
[]

[Postprocessors]
  [max_xx_IPyC]
    type = ElementExtremeValue
    variable = stress_xx
    block = IPyC
  []
  [max_yy_IPyC]
    type = ElementExtremeValue
    variable = stress_yy
    block = IPyC
  []
  [min_zz_IPyC]
    type = ElementExtremeValue
    variable = stress_zz
    block = IPyC
    value_type = min
  []
  [max_xx_SiC]
    type = ElementExtremeValue
    variable = stress_xx
    block = SiC
  []
  [max_yy_SiC]
    type = ElementExtremeValue
    variable = stress_yy
    block = SiC
  []
  [min_zz_SiC]
    type = ElementExtremeValue
    variable = stress_zz
    block = SiC
    value_type = min
  []
  [max_xx_OPyC]
    type = ElementExtremeValue
    variable = stress_xx
    block = OPyC
  []
  [max_yy_OPyC]
    type = ElementExtremeValue
    variable = stress_yy
    block = OPyC
  []
  [min_zz_OPyC]
    type = ElementExtremeValue
    variable = stress_zz
    block = OPyC
    value_type = min
  []
  [fis_gas_produced]
    type = ElementIntegralFisGasGeneratedSifgrs
    block = fuel
    execute_on = 'initial linear'
  []
  [fis_gas_released]
    type = ElementIntegralFisGasReleasedSifgrs
    block = fuel
    execute_on = 'initial linear'
  []
  [volumeTotal]
    type = InternalVolume
    boundary = exterior
    execute_on = 'initial TIMESTEP_END'
  []
  [volumeFuel]
    type = InternalVolume
    boundary = fuel
    execute_on = 'initial TIMESTEP_END'
  []
  [volumeGas]
    type = InternalVolume
    boundary = BufferGapVol
    addition = -5.53e-11
    execute_on = 'initial TIMESTEP_END'
  []
  [volumeBufferShell]
    type = InternalVolume
    boundary = BufferGapVol
    execute_on = 'initial TIMESTEP_END'
  []
  [ave_temp_interior]
    type = SideAverageValue
    boundary = BufferGapVol
    variable = temperature
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [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'
  []
  [avg_surface_temperature]
    type = SideAverageValue
    variable = temperature
    boundary = exterior
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [time_int_surf_temperature]
    type = TimeIntegratedPostprocessor
    value = avg_surface_temperature
    execute_on = 'INITIAL TIMESTEP_END'
  []
  [co_production]
    type = CarbonMonoxideProduction
    total_fissions = total_fissions
    time_integrated_triso_temperature = time_int_surf_temperature
    initial_enrichment = 0.14029
    execute_on = 'INITIAL TIMESTEP_END'
  []
[]

[PerformanceMetricOutputs]
[]

[Outputs]
  perf_graph = true
  exodus = true
  csv = true
  [chkfile]
    type = CSV
    execute_on = Final
    show = 'max_xx_IPyC max_yy_IPyC min_zz_IPyC max_xx_SiC max_yy_SiC min_zz_SiC co_production fis_gas_released avg_surface_temperature'
  []
[]

(examples/TRISO/accident_simulation/triso2D_accident_ad.i)

# This example is 2D-RZ analysis of a TRISO fuel particle. Fully coupled
# heat transfer and solid mechanics, plus diffusion of the fission product
# species cesium (Cs) are simulated.  The mesh includes contact surfaces
# between the buffer and IPyC layers to facilitate a gap opening between
# these layers. These surfaces are initially in mechanical contact but
# are assumed to have no strength in tension. A coarse mesh is used to
# provide a short run time.

# The calculation simulates fuel-life in three steps. The first step is an
# irradiation period, where constant power and a fixed particle surface
# temperature (1500 K) are assumed over a lifetime of 76 Ms (2.4 yrs).
# For the second step, fuel removal and storage are simulated by setting
# the reactor power and Cs source terms to zero, reducing the particle
# surface temperature to ambient (300 K), and then holding it
# for 100 days. A third and final step simulates accident
# behavior by increasing the particle surface temperature from ambient
# to 2073 K over 2 hrs, and then holding it at this elevated temperature
# for an additional 200 hrs. At the particle outer boundary, the Cs
# concentration is held at zero and the pressure at ambient during the
# entire simulation. The particle is assumed to be stress-free at an
# initial temperature of 1500 K.
#
# Details about this simulation are given in Section 4 of the following
# article: J. D. Hales, R. L. Williamson, S. R. Novascone, D. M. Perez,
# B. W. Spencer and G. Pastore, "Multidimensional multiphysics simulation
# of TRISO particle fuel", Journal of Nuclear Materials, Vol. 443, p. 531,
# 2013.

# This is a version using a thermomechanical mortar approach. It uses
# Automatic Differentiation classes and models gap mass transfer using
# flux preserving and sorption mortar constraints. Sorption constants are
# given in Table 1 of the following article: A. Londono-Hurtado, I.
# Szlufarska, R. Bratton and D. Morgan, "A review of fission product
# sorption in carbon structures", Journal of Nuclear Materials, Vol. 426,
# p. 254, 2012.


initial_fuel_density = 11000.0

[GlobalParams]
  order = SECOND
  family = LAGRANGE
  displacements = 'disp_x disp_y'
  flux_conversion_factor = 0.85
  use_automatic_differentiation = true
[]

[Mesh]
  coord_type = RZ
  [file]
    type = FileMeshGenerator
    file = triso2Dmed.e
  []
[]

[Problem]
  type = ReferenceResidualProblem
  reference_vector = 'ref'
  extra_tag_vectors = 'ref'
  converge_on = 'disp_x disp_y temp conc'
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [temp]
    initial_condition = 1500.0
  []
  [conc]
    initial_condition = 0.0
  []
  [conc_lm]
    block = pellet_clad_mechanical_secondary_subdomain
  []
  [conc_dx_lm]
    block = pellet_clad_mechanical_secondary_subdomain
  []
  [conc_dy_lm]
    block = pellet_clad_mechanical_secondary_subdomain
  []
[]

[AuxVariables]
  [fission_rate]
    block = fuel
    order = CONSTANT
    family = MONOMIAL
  []
  [fluence]
    order = CONSTANT
    family = MONOMIAL
  []
  [burnup]
    block = fuel
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_xx]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_yy]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_zz]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [power_history]
    type = PiecewiseLinear
    x = '0 76e6 76.001e6'
    y = '1 1     0'
  []
  [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)'
  []
  [integral_flux_error]
    type = ParsedFunction
    symbol_names = 'buffer_integral_flux IPyC_integral_flux'
    symbol_values = 'buffer_integral_flux IPyC_integral_flux'
    expression = 'IPyC_integral_flux + buffer_integral_flux'
  []
  [partial_pressure_error]
    type = ParsedFunction
    symbol_names = 'buffer_partial_pressure IPyC_partial_pressure'
    symbol_values = 'buffer_partial_pressure IPyC_partial_pressure'
    expression = 'IPyC_partial_pressure - buffer_partial_pressure'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  generate_output = 'stress_xx stress_yy stress_zz stress_xy stress_yz stress_zx hydrostatic_stress'
  strain = FINITE
  incremental = true
  add_variables = false
  [default]
    block = 'fuel buffer IPyC OPyC'
    eigenstrain_names = 'thermal_strain swelling_strain'
    extra_vector_tags = 'ref'
  []
  [SiC]
    block = 'SiC'
    eigenstrain_names = 'thermal_strain'
    extra_vector_tags = 'ref'
  []
[]

[Kernels]
  [heat_ie]
    type = ADHeatConductionTimeDerivative
    variable = temp
    extra_vector_tags = 'ref'
    block = 'fuel buffer IPyC SiC OPyC'
  []
  [heat]
    type = ADHeatConduction
    variable = temp
    extra_vector_tags = 'ref'
    block = 'fuel buffer IPyC SiC OPyC'
  []
  [heat_source]
    type = ADNeutronHeatSource
    variable = temp
    block = fuel
    energy_per_fission = 3.2e-11 # units of J/fission
    fission_rate = fission_rate
    extra_vector_tags = 'ref'
  []
  [mass_ie]
    type = ADTimeDerivative
    variable = conc
    extra_vector_tags = 'ref'
    block = 'fuel buffer IPyC SiC OPyC'
  []
  [mass]
    type = ADArrheniusDiffusion
    variable = conc
    extra_vector_tags = 'ref'
    block = 'fuel buffer IPyC SiC OPyC'
  []
  [mass_source]
    type = ADBodyForce
    variable = conc
    function = power_history
    value = 1.22e-5 # units of moles/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
    block = 'fuel buffer IPyC SiC OPyC'
    extra_vector_tags = 'ref'
  []
[]

[AuxKernels]
  [fission_rate]
    type = FissionRateGeneral
    fission_rate_formulation = GENERIC
    variable = fission_rate
    block = fuel
    fission_rate_function = power_history
    value = 3.89e19
    execute_on = timestep_begin
  []
  [fluence]
    type = ADMaterialRealAux
    property = fast_neutron_fluence
    variable = fluence
  []
  [burnup]
    type = ADBurnupAux
    variable = burnup
    block = fuel
    fission_rate = fission_rate
    molecular_weight = 0.270 # units of kg/mole
    execute_on = timestep_begin
    density = ${initial_fuel_density}
  []
  [creep_xx]
    type = ADRankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_xx
    index_i = 0
    index_j = 0
    block = 'buffer IPyC SiC OPyC'
    execute_on = timestep_end
  []
  [creep_yy]
    type = ADRankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_yy
    index_i = 1
    index_j = 1
    block = 'buffer IPyC SiC OPyC'
    execute_on = timestep_end
  []
  [creep_zz]
    type = ADRankTwoAux
    rank_two_tensor = creep_strain
    variable = creep_zz
    index_i = 2
    index_j = 2
    block = 'buffer IPyC SiC OPyC'
    execute_on = timestep_end
  []
[]

[ThermalContactMortar]
  [thermal]
    secondary_variable = temp
    primary_boundary = 15
    secondary_boundary = 17

    initial_moles = initial_moles # coupling to a postprocessor which supplies the initial plenum/gap gas mass
    gas_released = 'fis_gas_released co_production' # coupling to postprocessors which supply the fission gas addition, co addition
    released_gas_types = 'Kr Xe;
                          CO'
    released_fractions = '0.153 0.847;
                          1'
    gap_geometry_type = CYLINDER
    min_gap = 1e-7
    max_gap = 50e-6
    roughness_coef = 0.0
    correct_edge_dropping = true
  []
[]

[Contact]
  [pellet_clad_mechanical]
    primary = 15
    secondary = 17
    model = frictionless
    formulation = mortar
    c_normal = 1.0e8
    correct_edge_dropping = true
  []
[]

[Constraints]
    [cesium_gap_value]
      type = MassSorptionConstraint
      variable = conc_lm
      primary_variable = conc
      primary_boundary = 15
      primary_subdomain = pellet_clad_mechanical_primary_subdomain
      secondary_variable = conc
      secondary_boundary = 17
      secondary_subdomain = pellet_clad_mechanical_secondary_subdomain
      partial_pressure_name = partial_pressure
      epsilon = 1e-4
      correct_edge_dropping = true
    []
    [cesium_gap_flux_x]
      type = MassFluxConstraint
      variable = conc_dx_lm
      primary_variable = conc
      diffusivity_primary = arrhenius_diffusion_coef
      primary_boundary = 15
      primary_subdomain = pellet_clad_mechanical_primary_subdomain
      secondary_variable = conc
      diffusivity_secondary = arrhenius_diffusion_coef
      secondary_boundary = 17
      secondary_subdomain = pellet_clad_mechanical_secondary_subdomain
      component = 0
      epsilon = 1e-5
      correct_edge_dropping = true
    []
    [cesium_gap_flux_y]
      type = MassFluxConstraint
      variable = conc_dy_lm
      primary_variable = conc
      diffusivity_primary = arrhenius_diffusion_coef
      primary_boundary = 15
      primary_subdomain = pellet_clad_mechanical_primary_subdomain
      secondary_variable = conc
      diffusivity_secondary = arrhenius_diffusion_coef
      secondary_boundary = 17
      secondary_subdomain = pellet_clad_mechanical_secondary_subdomain
      component = 1
      epsilon = 1e-5
      correct_edge_dropping = true
    []
  []

[BCs]
  # pin particle along symmetry planes
  [no_disp_x]
    type = ADDirichletBC
    variable = disp_x
    boundary = xzero
    value = 0.0
    extra_vector_tags = 'ref'
  []
  [no_disp_y]
    type = ADDirichletBC
    variable = disp_y
    boundary = yzero
    value = 0.0
    extra_vector_tags = 'ref'
  []
  # fix temperature on free surface
  [freesurf_temp]
    type = ADFunctionDirichletBC
    variable = temp
    boundary = exterior
    function = temp_bc
    extra_vector_tags = 'ref'
  []
  # fix concentration on free surface
  [freesurf_conc]
    type = ADDirichletBC
    variable = conc
    boundary = exterior
    value = 0.0
    extra_vector_tags = 'ref'
  []
  [PlenumPressure] #  apply plenum pressure on clad inner walls and pellet surfaces
    [plenumPressure]
      boundary = BufferGapVol
      initial_pressure = 0
      startup_time = 1.0e4
      R = 8.3145
      output_initial_moles = initial_moles # coupling to post processor to get initial fill gas mass
      temperature = ave_temp_interior # coupling to post processor to get gas temperature approximation
      volume = volumeGas # coupling to post processor to get gas volume
      material_input = 'fis_gas_released co_production' # coupling to post processor to get fission gas added, co added
      output = plenum_pressure # coupling to post processor to output plenum/gap pressure
    []
  []
[]

[Materials]
  [flux]
    type = ADFastNeutronFlux
    calculate_fluence = true
    factor = 5e17
  []

  [fission_gas_release] # Sifgrs fission gas release mode
    type = ADUO2Sifgrs
    block = fuel
    temperature = temp
    fission_rate = fission_rate # coupling to fission_rate aux variable
    grain_radius_const = 5.0e-6
  []

  [fuel_thermal]
    type = ADUO2Thermal
    thermal_conductivity_model = FINK_LUCUTA
    block = fuel
    temperature = temp
    burnup = burnup
    initial_porosity = 0.0
  []
  [fuel_swelling]
    type = ADUO2VolumetricSwellingEigenstrain
    gas_swelling_model_type = MATPRO
    block = fuel
    temperature = temp
    burnup = burnup
    eigenstrain_name = 'swelling_strain'
    initial_fuel_density = ${initial_fuel_density}
  []
  [fuel_stress]
    type = ADComputeFiniteStrainElasticStress
    block = 'fuel'
  []
  [fuel_elasticity]
    type = ADComputeIsotropicElasticityTensor
    block = fuel
    youngs_modulus = 2.2e11
    poissons_ratio = .345
  []
  [fuel_thermal_strain]
    type = ADComputeThermalExpansionEigenstrain
    block = fuel
    thermal_expansion_coeff = 10e-6
    stress_free_temperature = 1500.0
    eigenstrain_name = thermal_strain
    temperature = temp
  []
  [fuel_den]
    type = ADStrainAdjustedDensity
    block = fuel
    strain_free_density = ${initial_fuel_density} # kg/m^3
  []
  [fuel_conc]
    type = ADArrheniusDiffusionCoef
    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
    gas_constant = 8.3143 # J/K-mol
    temperature = temp
  []

  [buffer_eigenstrain]
    type = ADPyCIrradiationEigenstrain
    block = buffer
    pyc_type = buffer
    eigenstrain_name = 'swelling_strain'
  []
  [buffer_thermal_strain]
    type = ADComputeThermalExpansionEigenstrain
    block = buffer
    thermal_expansion_coeff = 5.65e-6
    stress_free_temperature = 1500.0
    eigenstrain_name = thermal_strain
    temperature = temp
  []
  [buffer_elasticity]
    type = ADComputeIsotropicElasticityTensor
    block = buffer
    youngs_modulus = 2e10
    poissons_ratio = .23
  []
  [buffer_stress]
    type = ADPyCCreep
    block = buffer
    temperature = temp
  []
  [buffer_temp]
    type = ADHeatConductionMaterial
    block = buffer
    thermal_conductivity = 0.5 # J/m-s-K
    specific_heat = 720.0 # J/kg-K
  []
  [buffer_den]
    type = ADStrainAdjustedDensity
    strain_free_density = 1000.0 #kg/m^3
    block = buffer
  []
  [buffer_conc]
    type = ADArrheniusDiffusionCoef
    block = buffer
    d1 = 1.0e-12 # m^2/s
    q1 = 0.0
    d2 = 0.0
    q2 = 0.0
    gas_constant = 8.3143 # J/K-mol
    temperature = temp
  []
  [buffer_partial_pressure]
    type = ADSorptionPartialPressure
    A = 19.33
    B = -47290
    D = 1.518
    E = 4338
    d1 = 3.397
    d2 = 6.15e-4
    unit_scale = 1e3 # convert from mol to mmol
    density = 1000 # convert from mmol/m^3 to mmol/kg, using constant for compatibility with default AD derivative container size
    concentration = conc
    temperature = temp
    block = buffer
    outputs = 'all'
    output_properties = partial_pressure
  []
  [normal_vectors_triso]
    type = NormalVectorsTRISO
    block = 'IPyC OPyC buffer'
  []
  [IPyC_eigenstrain]
    type = ADPyCIrradiationEigenstrain
    block = IPyC
    pyc_type = dense
    eigenstrain_name = 'swelling_strain'
  []
  [IPyC_thermal_strain]
    type = ADComputeThermalExpansionEigenstrain
    block = IPyC
    thermal_expansion_coeff = 5.65e-6
    stress_free_temperature = 1500.0
    eigenstrain_name = thermal_strain
    temperature = temp
  []
  [IPyC_elasticity]
    type = ADComputeIsotropicElasticityTensor
    block = IPyC
    youngs_modulus = 4.74e10
    poissons_ratio = .23
  []
  [IPyC_disp]
    type = ADPyCCreep
    block = 'IPyC OPyC'
    temperature = temp
  []
  [IPyC_temp]
    type = ADHeatConductionMaterial
    block = 'IPyC OPyC'
    thermal_conductivity = 4.0
    specific_heat = 720.0
  []
  [IPyC_den]
    type = ADStrainAdjustedDensity
    block = 'IPyC OPyC'
    strain_free_density = 1900.0
  []
  [IPyC_conc]
    type = ADArrheniusDiffusionCoef
    block = IPyC
    d1 = 6.3e-8
    q1 = 222.0e+3
    d2 = 0.0
    q2 = 0.0
    gas_constant = 8.3143 # J/K-mol
    temperature = temp
  []
  [IPyC_partial_pressure]
    type = ADSorptionPartialPressure
    A = 19.33
    B = -47290
    D = 1.518
    E = 4338
    d1 = 3.397
    d2 = 6.15e-4
    unit_scale = 1e3 # convert from mol to mmol
    density = 1900 # convert from mmol/m^3 to mmol/kg, using constant for compatibility with default AD derivative container size
    concentration = conc
    temperature = temp
    block = IPyC
    outputs = 'all'
    output_properties = partial_pressure
  []
  [SiC_thermal_strain]
    type = ADComputeThermalExpansionEigenstrain
    block = SiC
    thermal_expansion_coeff = 4.9e-6
    stress_free_temperature = 1500.0
    eigenstrain_name = thermal_strain
    temperature = temp
  []
  [SiC_elasticity]
    type = ADComputeIsotropicElasticityTensor
    block = SiC
    youngs_modulus = 3.4e11
    poissons_ratio = .13
  []
  [SiC_creep]
    type = ADMonolithicSiCCreepUpdate
    block = SiC
    temperature = temp
    k_function = k_function
  []
  [SiC_stress]
    type = ADComputeMultipleInelasticStress
    block = SiC
    inelastic_models = 'SiC_creep'
  []
  [SiC_temp]
    type = ADHeatConductionMaterial
    block = SiC
    thermal_conductivity = 13.9 # J/m-s-K
    specific_heat = 620.0 # J/kg-K
  []
  [SiC_den]
    type = ADStrainAdjustedDensity
    strain_free_density = 3180.0 # kg/m^3
    block = SiC
  []
  [SiC_conc]
    type = ADArrheniusDiffusionCoef
    block = SiC
    d1 = 5.5e-14 # m^2/s
    d1_function = d1_function
    d1_function_variable = fluence
    q1 = 125.0e+3 # J/mol
    d2 = 1.6e-2 # m^2/s
    q2 = 514.0e+3 # J/mol
    gas_constant = 8.3143 # J/K-mol
    temperature = temp
  []

  [OPyC_eigenstrain]
    type = ADPyCIrradiationEigenstrain
    block = OPyC
    pyc_type = dense
    eigenstrain_name = 'swelling_strain'
  []
  [OPyC_thermal_strain]
    type = ADComputeThermalExpansionEigenstrain
    block = OPyC
    thermal_expansion_coeff = 5.65e-6
    stress_free_temperature = 1500.0
    eigenstrain_name = thermal_strain
    temperature = temp
  []
  [OPyC_elasticity]
    type = ADComputeIsotropicElasticityTensor
    block = OPyC
    youngs_modulus = 4.74e10
    poissons_ratio = .23
  []
  [OPyC_conc]
    type = ADArrheniusDiffusionCoef
    block = OPyC
    d1 = 6.3e-8 # m^2/s
    q1 = 222.0e+3 # J/mol
    d2 = 0.0
    q2 = 0.0
    gas_constant = 8.3143 # J/K-mol
    temperature = temp
  []
[]

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

[Debug]
  show_var_residual_norms = true
[]

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

[Executioner]
  type = Transient
  solve_type = 'NEWTON'
  petsc_options = '-snes_converged_reason -ksp_converged_reason -snes_ksp_ew'
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -mat_mffd_err -pc_factor_shift_type -pc_factor_shift_amount'
  petsc_options_value = 'lu    superlu_dist   1e-5          NONZERO               1e-14'

  snesmf_reuse_base = false

  line_search = 'none'
  nl_rel_tol = 5e-4
  nl_abs_tol = 1e-10
  nl_max_its = 20
  l_max_its = 8

  start_time = 0.0
  end_time = 85.3682e6
  dt = 100

  dtmax = 2e6
  dtmin = 1

  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 100
    optimal_iterations = 10
    growth_factor = 1.5
    linear_iteration_ratio = 100
    time_t = '0    76e6  76.001e6 84.641e6 84.6482e6'
    time_dt = '20  20     20      20       20'
  []

  [Predictor]
    type = SimplePredictor
    scale = 0.5
    skip_times_old = '0    76e6  76.001e6 84.641e6 84.6482e6'
  []
[]

[Outputs]
  perf_graph = true
  exodus = true
  [console]
    type = Console
    max_rows = 25
  []
  [csv]
    type = CSV
    sync_times = '100 6308007 75696087'
    sync_only = true
  []
[]

[Postprocessors]
  [Cs_release]
    type = ADSideDiffusiveFluxIntegral
    variable = conc
    diffusivity = arrhenius_diffusion_coef
    boundary = exterior
    execute_on = timestep_end
  []
  [dt]
    type = TimestepSize
    execute_on = timestep_end
  []
  [fis_gas_produced] # fission gas produced (moles)
    type = ADElementIntegralFisGasGeneratedSifgrs
    block = fuel
    execute_on = 'initial linear nonlinear timestep_begin timestep_end'
  []
  [fis_gas_released] # fission gas released to plenum (moles)
    type = ADElementIntegralFisGasReleasedSifgrs
    block = fuel
    execute_on = 'initial linear nonlinear timestep_begin timestep_end'
  []
  [volumeTotal]
    type = InternalVolume
    boundary = exterior
    execute_on = 'initial timestep_end'
  []
  [volumeFuel]
    type = InternalVolume
    boundary = fuel
    execute_on = 'initial timestep_end'
  []
  [volumeGas]
    type = InternalVolume
    boundary = BufferGapVol
    # ro = 3.125e-4
    # ri = 2.125e-4
    # vb = 4/3*pi*(ro^3-ri^3) = 8.76e-11
    # buffer density = 1000
    # PyC density    = 1900
    # fill ratio = 10/19
    # vb*10/19 = 4.6e-11
    # Must remove 4.6e-11 m^3 from the volume
    addition = -4.6e-11
    execute_on = 'initial linear nonlinear timestep_begin timestep_end'
  []
  [volumeBufferShell]
    type = InternalVolume
    boundary = BufferGapVol
    execute_on = 'initial timestep_end'
  []
  [ave_temp_interior]
    type = SideAverageValue
    boundary = BufferGapVol
    variable = temp
    execute_on = 'initial linear nonlinear timestep_begin timestep_end'
  []

  # Postprocessors for CO production

  [total_fission_rate]
    type = ElementIntegralPower
    variable = temp
    fission_rate = fission_rate
    block = fuel
    energy_per_fission = 1.0
    execute_on = 'initial linear nonlinear timestep_begin timestep_end'
  []
  [total_fissions]
    type = TimeIntegratedPostprocessor
    value = total_fission_rate
    execute_on = 'initial linear nonlinear timestep_begin timestep_end'
  []
  [avg_surface_temp]
    type = SideAverageValue
    variable = temp
    boundary = exterior
    execute_on = 'initial linear nonlinear timestep_begin timestep_end'
  []
  [time_int_surf_temp]
    type = TimeIntegratedPostprocessor
    value = avg_surface_temp
    execute_on = 'initial linear nonlinear timestep_begin timestep_end'
  []
  [co_production]
    type = CarbonMonoxideProduction
    total_fissions = total_fissions
    time_integrated_triso_temperature = time_int_surf_temp
    initial_enrichment = 0.14029
    execute_on = 'initial linear nonlinear timestep_begin timestep_end'
  []
  [num_lin_it]
    type = NumLinearIterations
  []
  [num_nonlin_it]
    type = NumNonlinearIterations
  []
  [tot_lin_it]
    type = CumulativeValuePostprocessor
    postprocessor = num_lin_it
  []
  [tot_nonlin_it]
    type = CumulativeValuePostprocessor
    postprocessor = num_nonlin_it
  []
  [alive_time]
    type = PerfGraphData
    section_name = Root
    data_type = TOTAL
  []

  [buffer_integral_flux]
    type = ADSideDiffusiveFluxIntegral
    variable = conc
    boundary = 17
    diffusivity = arrhenius_diffusion_coef
  []
  [IPyC_integral_flux]
    type = ADSideDiffusiveFluxIntegral
    variable = conc
    boundary = 15
    diffusivity = arrhenius_diffusion_coef
  []
  [buffer_partial_pressure]
    type = ADSideAverageMaterialProperty
    property = partial_pressure
    boundary = 17
  []
  [IPyC_partial_pressure]
    type = ADSideAverageMaterialProperty
    property = partial_pressure
    boundary = 15
  []
  [integral_flux_error]
    type = FunctionValuePostprocessor
    function = integral_flux_error
  []
  [partial_pressure_error]
    type = FunctionValuePostprocessor
    function = partial_pressure_error
  []
  [integral_Cs_release]
    type = TimeIntegratedPostprocessor
    value = Cs_release
  []
  [Cs_production]
    type = FunctionValuePostprocessor
    function = power_history
    scale_factor = 1.22e-5 # units of moles/m**3-s
  []
  [time_integral_Cs_production]
    type = TimeIntegratedPostprocessor
    value = Cs_production
  []
  [volumeFuel_initial]
    type = InternalVolume
    boundary = fuel
    execute_on = initial
  []
  [integral_Cs_production]
    type = ParsedPostprocessor
    pp_names = 'time_integral_Cs_production volumeFuel_initial'
    expression = 'time_integral_Cs_production * volumeFuel_initial'
  []
  [Cs_release_fraction]
    type = ParsedPostprocessor
    pp_names = 'integral_Cs_release integral_Cs_production'
    expression = 'integral_Cs_release / integral_Cs_production'
  []
[]

[VectorPostprocessors]
  [temperaturevpp]
    type = SideValueSampler
    boundary = 11
    variable = temp
    sort_by = x
    outputs = 'csv'
    use_displaced_mesh = true
  []
[]

(assessment/TRISO/benchmark/IAEA_CRP-6/fuel_performance/case_10/case_10_1D.i)

#
# This case is taken from Advances in high temperature gas cooled reactor fuel
# technology. Technical Report IAEA-TECDOC-1674, International Atomic Energy
# Agency, 2012.
#
# See also Hales, et al., Multidimensional multiphysics simulation of TRISO
# particle fuel, JNM, 443, 2013.  https://doi.org/10.1016/j.jnucmat.2013.07.070
#
# The correctness of the results computed by this case must be checked against
# results from the IAEA benchmark.  The best way to do this is to compare
# results with information in the JNM article.
#

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

[Mesh]
  coord_type = RSPHERICAL
  [gen]
    type = TRISO1DMeshGenerator
    elem_type = EDGE3
    coordinates = '0 2.485e-4 3.425e-4 3.425e-4 3.835e-4 4.195e-4 4.595e-4'
    mesh_density = '6 6 0 6 8 6'
    block_names = 'fuel buffer IPyC SiC OPyC'
  []
[]

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

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

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

[Physics/SolidMechanics/QuasiStatic]
  [IPyC_OPyC]
    block = 'IPyC OPyC'
    strain = finite
    eigenstrain_names = 'thermal_strain pyc_eigenstrain'
  []
  [rest]
    block = 'fuel buffer SiC'
    strain = finite
    eigenstrain_names = thermal_strain
  []
[]

[Kernels]
  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temperature
  []
  [heat]
    type = HeatConduction
    variable = temperature
  []
  [heat_source]
    type = NeutronHeatSource
    variable = temperature
    block = fuel
    energy_per_fission = 3.2e-11 # units of J/fission
    fission_rate = fission_rate
  []
[]

[AuxKernels]
  [stress_yy]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = stress_yy
    index_i = 1
    index_j = 1
    execute_on = timestep_end
  []
  [fission_rate]
    type = FunctionAux
    variable = fission_rate
    block = fuel
    function = fission_rate
  []
  [burnup]
    type = BurnupAux
    variable = burnup
    block = fuel
    fission_rate = fission_rate
    density = 10810.0
    molecular_weight = 0.270 # units of kg/mole
  []
[]

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

[ThermalContact]
  [thermal_contact]
    type = GasGapHeatTransfer
    variable = temperature
    primary = IPyC_inner_boundary
    secondary = buffer_outer_boundary
    initial_moles = initial_moles # coupling to a postprocessor which supplies the initial plenum/gap gas mass
    gas_released = 'fis_gas_released co_production' # coupling to postprocessors which supply the fission gas addition, co addition
    released_gas_types = 'Kr Xe;
                          CO'
    released_fractions = '0.153 0.847;
                          1'
    tangential_tolerance = 1e-6
    #    contact_pressure_input = 10e6
    #    quadrature = true
  []
[]

[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_temperature]
    type = DirichletBC
    variable = temperature
    boundary = exterior
    value = 1346.0
  []

  # 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 = 0
      startup_time = 1.0e4
      R = 8.3143
      output_initial_moles = initial_moles # coupling to post processor to get initial fill gas mass
      temperature = ave_temp_interior # coupling to post processor to get gas temperature approximation
      volume = volumeGas # coupling to post processor to get gas volume
      material_input = 'fis_gas_released co_production' # coupling to post processor to get fission gas added, co added
      output = plenum_pressure # coupling to post processor to output plenum/gap pressure
    []
  []

[]

[Materials]

  [flux]
    type = FastNeutronFlux
    calculate_fluence = true
    factor = 1.708707e18 # n/m^2-sec
  []

  [fission_gas_release] # Sifgr fission gas release mode
    type = UO2Sifgrs
    block = fuel
    temperature = temperature
    fission_rate = fission_rate # coupling to fission_rate aux variable
    grain_radius_const = 5.0e-6
  []

  [stress]
    type = ComputeFiniteStrainElasticStress
    block = 'fuel buffer SiC'
  []
  [PyC_stress]
    type = PyCCreep
    block = 'IPyC OPyC'
    k = k_function
    poissons_ratio = 0.4
    temperature = temperature
  []
  [normal_vectors_triso]
    type = NormalVectorsTRISO
    block = 'IPyC OPyC'
  []
  [PyC_eigenstrain]
    type = PyCIrradiationEigenstrain
    block = 'IPyC OPyC'
    radial_eigenstrain_function = radial_eigenstrain
    tangential_eigenstrain_function = tangential_eigenstrain
    eigenstrain_name = pyc_eigenstrain
  []

  [fuel_thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    block = fuel
    thermal_expansion_coeff = 10e-6
    stress_free_temperature = 1346.0
    eigenstrain_name = thermal_strain
    temperature = temperature
  []
  [PyC_thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    block = 'buffer IPyC OPyC'
    thermal_expansion_coeff = 5.5e-6
    stress_free_temperature = 1346.0
    eigenstrain_name = thermal_strain
    temperature = temperature
  []
  [SiC_thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    block = SiC
    thermal_expansion_coeff = 4.9e-6
    stress_free_temperature = 1346.0
    eigenstrain_name = thermal_strain
    temperature = temperature
  []

  [fuel_thermal] # temperature and burnup dependent thermal properties of UO2 (BISON kernel)
    type = UO2Thermal
    thermal_conductivity_model = FINK_LUCUTA
    block = fuel
    temperature = temperature
    burnup = burnup
  []

  [fuel_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = fuel
    youngs_modulus = 2e8
    poissons_ratio = 0.345
  []

  [fuel_den]
    type = StrainAdjustedDensity
    block = fuel
    strain_free_density = 10810.0
  []

  [buffer_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = buffer
    youngs_modulus = 2e8
    poissons_ratio = 0.345
  []

  [buffer_temperature]
    type = HeatConductionMaterial
    block = buffer
    thermal_conductivity = 0.5 # J/m-s-K
    specific_heat = 720.0 # J/kg-K
  []

  [buffer_den]
    type = StrainAdjustedDensity
    strain_free_density = 1000 #kg/m^3
    block = buffer
  []

  [PyC_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = 'IPyC OPyC'
    youngs_modulus = 3.96e10
    poissons_ratio = 0.33
  []

  [PyC_temperature]
    type = HeatConductionMaterial
    block = 'IPyC OPyC'
    thermal_conductivity = 4.0 # J/m-s-K
    specific_heat = 720.0 # J/kg-K
  []

  [PyC_den]
    type = StrainAdjustedDensity
    strain_free_density = 1880.0 # kg/m^3
    block = 'IPyC OPyC'
  []

  [SiC_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = SiC
    youngs_modulus = 3.7e11
    poissons_ratio = 0.13
  []

  [SiC_temperature]
    type = HeatConductionMaterial
    block = SiC
    thermal_conductivity = 13.9 # J/m-s-K
    specific_heat = 620.0 # J/kg-K
  []

  [SiC_den]
    type = StrainAdjustedDensity
    strain_free_density = 3200.0 # kg/m^3
    block = SiC
  []
[]

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

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

[Debug]
  show_var_residual_norms = true
[]

[Executioner]
  type = Transient

  petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
  petsc_options_value = '201                hypre    boomeramg      4'

  line_search = 'none'

  solve_type = 'PJFNK'

  nl_rel_tol = 1e-7
  nl_abs_tol = 1e-10
  nl_max_its = 15

  l_tol = 1e-3
  l_max_its = 50

  start_time = 0.0
  end_time = 3.10176e7

  dtmax = 2e5
  dtmin = 1
  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 20
    optimal_iterations = 6
    iteration_window = 2
    linear_iteration_ratio = 100
  []
[]

[Postprocessors]
  [burnup]
    type = ElementExtremeValue
    block = fuel
    variable = burnup
  []
  [fis_gas_produced] # fission gas produced (moles)
    type = ElementIntegralFisGasGeneratedSifgrs
    block = fuel
  []

  [fis_gas_released] # fission gas released to plenum (moles)
    type = ElementIntegralFisGasReleasedSifgrs
    block = fuel
  []
  [volumeTotal]
    type = InternalVolume
    boundary = exterior
  []
  [volumeFuel]
    type = InternalVolume
    boundary = fuel_outer_boundary
  []
  [volumeGas]
    type = InternalVolume
    boundary = 'fuel_outer_boundary IPyC_inner_boundary'
    addition = -5.53e-11
    execute_on = 'initial timestep_end'
  []
  [volumeBufferShell]
    type = InternalVolume
    boundary = buffer_IPyC_boundary
  []
  [ave_temp_interior]
    type = SideAverageValue
    boundary = buffer_IPyC_boundary
    variable = temperature
    execute_on = 'initial timestep_end'
  []

  # Postprocessors for CO production

  [total_fission_rate]
    type = ElementIntegralPower
    variable = temperature
    fission_rate = fission_rate
    block = fuel
    energy_per_fission = 1.0
  []

  [total_fissions]
    type = TimeIntegratedPostprocessor
    value = total_fission_rate
  []

  [avg_surface_temp]
    type = SideAverageValue
    variable = temperature
    boundary = exterior
  []

  [time_int_surf_temp]
    type = TimeIntegratedPostprocessor
    value = avg_surface_temp
  []

  [co_production]
    type = CarbonMonoxideProduction
    total_fissions = total_fissions
    time_integrated_triso_temperature = time_int_surf_temp
    initial_enrichment = 0.14029
  []

  [tang_SiC]
    type = ElementalVariableValue
    variable = stress_yy
    elementid = 18
  []
[]

[PerformanceMetricOutputs]
[]

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

GA model
Proksch model
CO Production
Example Input Syntax
Input Files
References