ADUPuZrFissionGasRelease

Computes fission gas release for UPuZr metallic fuel

Description

UPuZrFissionGasRelease and its associated AD and non-AD objects contain a fission gas release model for uranium plutonium zirconium (UPuZr) fuel based on the current porosity of the fuel. The model is derived from historical Experimental Breeder Reactor II (EBR-II) post-irradiation examinations that showed that the fission gas release fraction (gas released over gas produced) quickly increased to about 80% between 1 to 2 atom percent burnup, and remained nearly constant throughout the remainder of the irradiation (Hofman et al., 1997). The step-like function of fission gas release is related to the interconnection of porosity, $var element = document.getElementById("moose-equation-5ed17844-72b2-4deb-8e36-e2558cd21002");katex.render("p", element, {displayMode:false,throwOnError:false});$ , as the porosity increases past a critical porosity $var element = document.getElementById("moose-equation-a0e91f79-e0b2-4bf4-afec-3a80eb62ae2e");katex.render("p_{critical}", element, {displayMode:false,throwOnError:false});$ , and becomes interconnected. From these observations, an extremely simple fission gas release model can be formulated in the absence of more advanced mechanistic models, $(1)var element = document.getElementById("moose-equation-a0e21ec8-a8fb-4a6e-901d-88b87dba2172");katex.render(" G_{released}(t+\\Delta t) = \\begin{cases} 0 & p < p_{critical} \\\\ 0.8 G_{produced}(t+\\Delta t) & p = p_{critical} \\\\ G_{released}(t) + [G_{produced}(t+\\Delta t) - G_{produced}(t)] & p > p_{critical} \\end{cases}", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-fcb8175f-d826-4c70-a173-6c2d80eafd45");katex.render("G_{released}(t+\\Delta t)", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-782c94e8-5461-475d-87fe-f3fb45258810");katex.render("G_{produced}(t+\\Delta t)", element, {displayMode:false,throwOnError:false});$ are the total gas density released and produced at time $var element = document.getElementById("moose-equation-af8f90c3-d305-4789-8d9f-06c9e939934e");katex.render("t+\\Delta t", element, {displayMode:false,throwOnError:false});$ , respectively, in (mols/m $var element = document.getElementById("moose-equation-f6dd43ad-a968-48c3-80ce-028f08fe541b");katex.render("^3", element, {displayMode:false,throwOnError:false});$ ). The porosity value utilized in Eq. (1) can be either the current or previous time step, depending on the value of the input parameter use_current_porosity.

The total fission gas produced is related to the fission rate density by, $(2)var element = document.getElementById("moose-equation-e1393471-fb79-4773-a373-f32187b7044e");katex.render(" G_{produced}(t+\\Delta t) = G_{produced}(t) + \\dot{F}_{avg} \\Delta t \\gamma / N_A,", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-f1b4670e-a105-4679-b0d2-6513de120342");katex.render("\\gamma", element, {displayMode:false,throwOnError:false});$ is the yield of fission gas atoms per fission, typically taken as $var element = document.getElementById("moose-equation-8a35f6b6-8c7b-43bb-bf35-8d10ded3e7fa");katex.render("\\gamma=0.3017", element, {displayMode:false,throwOnError:false});$ (gas atoms/m $var element = document.getElementById("moose-equation-a448ae00-b437-4e3a-b026-108f0fe45a2f");katex.render("^3", element, {displayMode:false,throwOnError:false});$ /s), and $var element = document.getElementById("moose-equation-d80fa416-61cd-4b6a-a255-0acb8d44cc9d");katex.render("N_A", element, {displayMode:false,throwOnError:false});$ is Avogadro's number ( $var element = document.getElementById("moose-equation-cc211694-a1b3-4ae0-89dd-d90992daf1e3");katex.render("6.022\\times 10^{23}", element, {displayMode:false,throwOnError:false});$ atoms/mol). Here, $var element = document.getElementById("moose-equation-7232c74e-41e1-4ff1-8655-d4037ce3cf3e");katex.render("\\dot{F}_{ave}", element, {displayMode:false,throwOnError:false});$ is $var element = document.getElementById("moose-equation-81b25b47-b8de-4665-aff3-356d5cac0bdd");katex.render("\\dot{F}_{ave} = \\frac{\\dot{F}(t) + \\dot{F}(t+\\Delta t)}{2}", element, {displayMode:true,throwOnError:false});$ Optionally, the value of the fission rate at the current time-step can be utilized instead of the average by setting time_average_fission_rate=false, such that $var element = document.getElementById("moose-equation-9b792436-fd5e-4e18-a9c8-9bff6dcf2a1b");katex.render("\\dot{F}_{avg}= \\dot{F}(t+\\Delta t)", element, {displayMode:false,throwOnError:false});$ in Eq. (2).

The critical porosity value nominally should occur around 25% porosity, corresponding to 33.3% volumetric swelling. The default value of 24% porosity is set to lie between the default interconnection_initiating_porosity=0.23 and interconnection_terminating_porosity=0.25 values set in UPuZrVolumetricSwellingEigenstrain to capture the concurrent fission gas release and swelling termination.

The initial fraction of fission gas released after the critical porosity value is reached and the fraction of the post-interconnection produced fission gas that is released to the plenum can be set using the following parameters, fractional_fgr_initial and fractional_fgr_post. The default values for these parameters are 0.8 and 1.0, respectively.

Example Input Syntax

[Materials<<<{"href": "../../syntax/Materials/index.html"}>>>]
  [fission_gas_release]
    type = ADUPuZrFissionGasRelease<<<{"description": "Computes fission gas release for UPuZr metallic fuel", "href": "UPuZrFissionGasRelease.html"}>>>
    fission_rate<<<{"description": "Fission rate material property name"}>>> = fission_rate
    porosity<<<{"description": "Porosity material property name"}>>> = porosity
    fractional_yield<<<{"description": "fraction yield of fission gas atoms per fission"}>>> = 0.25
    critical_porosity<<<{"description": "Porosity at which fission gas release initiates. This needs to be between the interconnection_initiating_porosity and interconnection_terminating_porosity in UPuZrVolumetricSwellingEigenstrain"}>>> = 0.20
    time_average_fission_rate<<<{"description": "Flag to average the fission rate with the previous time step instead of only using the current fission rate"}>>> = false
    use_old_porosity<<<{"description": "Flag to use old porosity."}>>> = false
    fractional_fgr_initial<<<{"description": "fraction of fission gas produced that is released once the critical porosity is reached"}>>> = 0.7
    fractional_fgr_post<<<{"description": "fraction of fission gas produced that is released after interconnection"}>>> = 0.9
  []
[]

Input Parameters

blockThe list of blocks (ids or names) that this object will be applied
C++ Type:std::vector<SubdomainName>
Controllable:No
Description:The list of blocks (ids or names) that this object will be applied
boundaryThe list of boundaries (ids or names) from the mesh where this object applies
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:The list of boundaries (ids or names) from the mesh where this object applies
computeTrueWhen false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
Default:True
C++ Type:bool
Controllable:No
Description:When false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
constant_onNONEWhen ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
Default:NONE
C++ Type:MooseEnum
Options:NONE, ELEMENT, SUBDOMAIN
Controllable:No
Description:When ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
critical_porosity0.24Porosity at which fission gas release initiates. This needs to be between the interconnection_initiating_porosity and interconnection_terminating_porosity in UPuZrVolumetricSwellingEigenstrain
Default:0.24
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Porosity at which fission gas release initiates. This needs to be between the interconnection_initiating_porosity and interconnection_terminating_porosity in UPuZrVolumetricSwellingEigenstrain
declare_suffixAn optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:An optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.
fission_ratefission_rateFission rate material property name
Default:fission_rate
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:Fission rate material property name
fractional_fgr_initial0.8fraction of fission gas produced that is released once the critical porosity is reached
Default:0.8
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:fraction of fission gas produced that is released once the critical porosity is reached
fractional_fgr_post1fraction of fission gas produced that is released after interconnection
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:fraction of fission gas produced that is released after interconnection
fractional_yield0.3017fraction yield of fission gas atoms per fission
Default:0.3017
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:fraction yield of fission gas atoms per fission
porosityporosityPorosity material property name
Default:porosity
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:Porosity material property name
time_average_fission_rateTrueFlag to average the fission rate with the previous time step instead of only using the current fission rate
Default:True
C++ Type:bool
Controllable:No
Description:Flag to average the fission rate with the previous time step instead of only using the current fission rate
use_old_porosityFalseFlag to use old porosity.
Default:False
C++ Type:bool
Controllable:No
Description:Flag to use old porosity.

Optional Parameters

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

Advanced Parameters

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

Outputs Parameters

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

Material Property Retrieval Parameters

Input Files

(examples/constituent_redistribution/2d_thermo.i)
(test/tests/solid_mechanics/simple_fission_gas_viscoplasticity/old_method_comparison.i)
(test/tests/upuzr_fission_gas_release/ad/test.i)
(test/tests/solid_mechanics/upuzr_eigenstrains/ad_upuzr_gaseous_eigenstrain/test.i)
(test/tests/upuzr_fission_gas_release/ad/exact_1D.i)
(test/tests/upuzr_fission_gas_release/ad/exact_2D.i)

References

G L Hofman, L C Walters, and T H Bauer. Metallic fast reactor fuels. Progress in Nuclear Energy, 31(1-2):83–110, January 1997.

@article{Hofman:1997fg,
    author = "Hofman, G L and Walters, L C and Bauer, T H",
    title = "{Metallic fast reactor fuels}",
    journal = "Progress in Nuclear Energy",
    year = "1997",
    volume = "31",
    number = "1-2",
    pages = "83-110",
    month = "January"
}

(test/tests/upuzr_fission_gas_release/ad/test.i)

# This tests the fission gas produced and released postprocessors when coupled with thermo-mechanics.

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  coord_type = RZ
  [mesh]
    type = GeneratedMeshGenerator
    dim = 2
    xmax = 3e-3
    ymax = 3e-2
    nx = 6
    ny = 6
  []
[]

[Variables]
  [power]
    initial_condition = 50
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    add_variables = true
    strain = FINITE
    generate_output = 'stress_xx'
    use_automatic_differentiation = true
  []
[]

[Kernels]
  [power_diff]
    type = ADMatDiffusion
    variable = power
    diffusivity = 1e-3
    use_displaced_mesh = true
  []
  [power_dt]
    type = ADTimeDerivative
    variable = power
  []
[]

[BCs]
  [power_left]
    type = ADDirichletBC
    variable = power
    boundary = left
    value = 100
  []
  [power_right]
    type = ADDirichletBC
    variable = power
    boundary = right
    value = 10
  []
  [fixed_x]
    type = ADDirichletBC
    boundary = left
    variable = disp_x
    value = 0
  []
  [fixed_y]
    type = ADDirichletBC
    boundary = bottom
    variable = disp_y
    value = 0
  []
  [pressure]
    type = ADPressure
    variable = disp_x
    boundary = right
    postprocessor = gas_released
    factor = 1e20
  []
[]

[Materials]
  [fission_rate]
    type = ADPiecewiseLinearInterpolationMaterial
    property = fission_rate
    x = '1 100'
    y = '1e19 1e21'
    variable = power
    outputs = all
    output_properties = fission_rate
  []
  [porosity]
    type = ADPiecewiseLinearInterpolationMaterial
    property = porosity
    x = '1 100'
    y = '0.1 0.3'
    variable = power
    outputs = all
    output_properties = porosity
  []
  [fission_gas_release]
     type = ADUPuZrFissionGasRelease
     fission_rate = fission_rate
     porosity = porosity
     fractional_yield = 0.25
     critical_porosity = 0.20
     time_average_fission_rate = false
     use_old_porosity = false
     fractional_fgr_initial = 0.7
     fractional_fgr_post = 0.9
  []
  [tensor]
    type = ADComputeIsotropicElasticityTensor
    youngs_modulus = 1e9
    poissons_ratio = 0.1
  []
  [stress]
    type = ADComputeFiniteStrainElasticStress
  []
[]

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

[Executioner]
  type = Transient

  nl_abs_tol = 1e-10
  num_steps = 5
  dt = 0.01
[]

[Postprocessors]
  [power_avg]
    type = ElementAverageValue
    variable = power
  []
  [power_max]
    type = ElementExtremeValue
    variable = power
  []
  [power_min]
    type = ElementExtremeValue
    variable = power
    value_type = min
  []
  [fission_rate]
    type = ElementAverageValue
    variable = fission_rate
  []
  [gas_produced]
    type = ADElementIntegralMaterialProperty
    mat_prop = fis_gas_prod
  []
  [gas_released]
    type = ADElementIntegralMaterialProperty
    mat_prop = fis_gas_rel
  []
  [porosity]
    type = ElementAverageValue
    variable = porosity
  []
  [disp_x]
    type = ElementExtremeValue
    variable = disp_x
  []
  [stress_xx]
    type = ElementExtremeValue
    variable = stress_xx
  []
[]

[Outputs]
  exodus = true
[]

(examples/constituent_redistribution/2d_thermo.i)

# This example demonstrates how to loosely couple the metallic fuel constituent
# redistribution model provided by ADUPuZrPhaseLookup and ADUPuZrMobility to a
# thermo solve using the MultiApps system.  This file contains the AD thermo
# solve.  The composition solve is contained in 2d_composition.i, which is
# executed as a SubApp.  The MultiApps system allows for use of different mesh
# resolutions and solver options.  The problem simulates irradiation of
# Experimental Breeder Reactor II Fuel Element DP81.  The predicted zirconium
# profile (X_Zr) can be compared to the experimental EPMA scan stored in
# (X_Zr_ref) [1].  This example runs in about 4 minutes on 2 processors using
# the Newton method.

# References
# [1]: Hofman, G. L., Hayes, S. L., and Petri, M. C.  Temperature Gradient
#      Driven Constituent Redistribution in U-Zr Alloys.  Journal of Nuclear
#      Materials 227 (1996).  277-286.

[Mesh]
  coord_type = RZ
  [smeared_pellet_mesh]
    type = FuelPinMeshGenerator
    clad_thickness = 3.810e-04
    pellet_outer_radius = 2.192e-03
    pellet_height = 3.428e-01
    clad_top_gap_height = 2.714e-01
    clad_gap_width = 3.480e-04
    bottom_clad_height = 2.240e-03
    top_clad_height = 2.240e-03
    clad_bot_gap_height = 3.100e-04
    clad_mesh_density = customize
    pellet_mesh_density = customize
    nx_p = 10
    ny_p = 260
    nx_c = 4
    ny_c = 260
    ny_cu = 3
    ny_cl = 3
    pellet_quantity = 1
    elem_type = QUAD8
  []
  [radial_slice]
    type = BoundingBoxNodeSetGenerator
    input = smeared_pellet_mesh
    new_boundary = radial_slice
    bottom_left = '-0.001e-03 2.688e-01 0'
    top_right = '2.193e-03 2.690e-01 0'
  []
  construct_side_list_from_node_list = true
[]

[MultiApps]
  [composition]
    type = TransientMultiApp
    app_type = BisonApp
    positions = '0 0 0'
    input_files = 2d_composition.i
    catch_up = true
    max_catch_up_steps = 2
 []
[]

[Transfers]
  [to_sub_T]
    type = MultiAppGeometricInterpolationTransfer
    to_multi_app = composition
    source_variable = T
    variable = T
  []
  [from_sub_xZr]
    type = MultiAppGeometricInterpolationTransfer
    from_multi_app = composition
    source_variable = X_Zr
    variable = X_Zr
  []
  [from_sub_alpha]
    type = MultiAppGeometricInterpolationTransfer
    from_multi_app = composition
    source_variable = alpha
    variable = alpha
  []
  [from_sub_beta]
    type = MultiAppGeometricInterpolationTransfer
    from_multi_app = composition
    source_variable = beta
    variable = beta
  []
  [from_sub_gamma]
    type = MultiAppGeometricInterpolationTransfer
    from_multi_app = composition
    source_variable = gamma
    variable = gamma
  []
  [from_sub_delta]
    type = MultiAppGeometricInterpolationTransfer
    from_multi_app = composition
    source_variable = delta
    variable = delta
  []
  [from_sub_zeta]
    type = MultiAppGeometricInterpolationTransfer
    from_multi_app = composition
    source_variable = zeta
    variable = zeta
  []
[]

[Variables]
  [T]
    order = SECOND
    family = LAGRANGE
    initial_condition = 298
  []
[]

[ThermalContact]
  [thermal_contact]
    type = GapHeatTransfer
    variable = T
    order = SECOND
    quadrature = true
    gap_conductivity = 61.0
    min_gap = 3.480e-04
    primary = 5
    secondary = 10
  []
[]

[CoolantChannel]
  [convective_clad_surface]
    variable = T
    inlet_temperature = f_T_coolant_in
    inlet_pressure = f_coolant_pressure
    inlet_massflux = 2.315e+03
    coolant_material = sodium
    linear_heat_rate = f_power
    axial_power_profile = f_axial_power
    subchannel_geometry = triangular
    rod_diameter = 5.842e-03
    rod_pitch = 6.909e-03
    thermal_conductivity = thermal_conductivity_reg
    boundary = '1 2 3'
  []
[]

[Kernels]
  # Transient heat generation and conduction
  [heat_dt]
    type = ADHeatConductionTimeDerivative
    variable = T
    specific_heat = specific_heat
    density_name = density
  []
  [heat_conduction]
    type = ADHeatConduction
    variable = T
    thermal_conductivity = thermal_conductivity
  []
  [heat_source]
    type = ADFissionRateHeatSource
    block = pellet
    variable = T
    fission_rate = fission_rate
  []
[]

[AuxVariables]
  [gap_conductance_aux]
    order = CONSTANT
    family = MONOMIAL
  []
  [X_Pu]
    block = pellet
  []
  [X_Zr]
    block = pellet
  []
  [X_Zr_ref]
    block = pellet
    [InitialCondition]
      type = FunctionIC
      function = f_X_Zr_ref
    []
  []
  [alpha]
    block = pellet
    order = CONSTANT
    family = MONOMIAL
  []
  [beta]
    block = pellet
    order = CONSTANT
    family = MONOMIAL
  []
  [gamma]
    block = pellet
    order = CONSTANT
    family = MONOMIAL
  []
  [delta]
    block = pellet
    order = CONSTANT
    family = MONOMIAL
  []
  [zeta]
    block = pellet
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [f_power]
    type = PiecewiseLinear
    x = '0 100000 4420000 5111200 11504800 18157600 24969600'
    y = '0 31816 30504 29848 30504 29192 29192'
  []
  [f_coolant_pressure]
    type = PiecewiseLinear
    x = '0 24969600'
    y = '0.151e6 0.151e6'
  []
  [f_T_coolant_in]
    type = PiecewiseLinear
    x = '0 1e5 24959600 24969600'
    y = '298.0 644.0 644.0 644.0'
  []
  [f_axial_power]
    type = PowerPeakingFunction
    fit = EBRII_ROW_4
    pellet_length = 3.428e-01
    pellet_y_start = 2.440e-03
  []
  [f_X_Zr_ref]
    type = SplineFunction
    x = '0.000e+00 1.099e-05 2.197e-05 3.296e-05 4.394e-05 5.493e-05 6.591e-05 7.690e-05 8.788e-05 9.887e-05 1.099e-04 1.208e-04 1.318e-04 1.428e-04 1.538e-04 1.648e-04 1.758e-04 1.867e-04 1.977e-04 2.087e-04 2.197e-04 2.307e-04 2.417e-04 2.527e-04 2.636e-04 2.746e-04 2.856e-04 2.966e-04 3.076e-04 3.186e-04 3.296e-04 3.405e-04 3.515e-04 3.625e-04 3.735e-04 3.845e-04 3.955e-04 4.064e-04 4.174e-04 4.284e-04 4.394e-04 4.504e-04 4.614e-04 4.724e-04 4.833e-04 4.943e-04 5.053e-04 5.163e-04 5.273e-04 5.383e-04 5.493e-04 5.602e-04 5.712e-04 5.822e-04 5.932e-04 6.042e-04 6.152e-04 6.261e-04 6.371e-04 6.481e-04 6.591e-04 6.701e-04 6.811e-04 6.921e-04 7.030e-04 7.140e-04 7.250e-04 7.360e-04 7.470e-04 7.580e-04 7.690e-04 7.799e-04 7.909e-04 8.019e-04 8.129e-04 8.239e-04 8.349e-04 8.458e-04 8.568e-04 8.678e-04 8.788e-04 8.898e-04 9.008e-04 9.118e-04 9.227e-04 9.337e-04 9.447e-04 9.557e-04 9.667e-04 9.777e-04 9.887e-04 9.996e-04 1.011e-03 1.022e-03 1.033e-03 1.044e-03 1.055e-03 1.066e-03 1.077e-03 1.088e-03 1.099e-03 1.109e-03 1.120e-03 1.131e-03 1.142e-03 1.153e-03 1.164e-03 1.175e-03 1.186e-03 1.197e-03 1.208e-03 1.219e-03 1.230e-03 1.241e-03 1.252e-03 1.263e-03 1.274e-03 1.285e-03 1.296e-03 1.307e-03 1.318e-03 1.329e-03 1.340e-03 1.351e-03 1.362e-03 1.373e-03 1.384e-03 1.395e-03 1.406e-03 1.417e-03 1.428e-03 1.439e-03 1.450e-03 1.461e-03 1.472e-03 1.483e-03 1.494e-03 1.505e-03 1.516e-03 1.527e-03 1.538e-03 1.549e-03 1.560e-03 1.571e-03 1.582e-03 1.593e-03 1.604e-03 1.615e-03 1.626e-03 1.637e-03 1.648e-03 1.659e-03 1.670e-03 1.681e-03 1.692e-03 1.703e-03 1.714e-03 1.725e-03 1.736e-03 1.747e-03 1.758e-03 1.769e-03 1.780e-03 1.791e-03 1.802e-03 1.813e-03 1.824e-03 1.834e-03 1.845e-03 1.856e-03 1.867e-03 1.878e-03 1.889e-03 1.900e-03 1.911e-03 1.922e-03 1.933e-03 1.944e-03 1.955e-03 1.966e-03 1.977e-03 1.988e-03 1.999e-03 2.010e-03 2.021e-03 2.032e-03 2.043e-03 2.054e-03 2.065e-03 2.076e-03 2.087e-03 2.098e-03 2.109e-03 2.120e-03 2.131e-03 2.142e-03 2.153e-03 2.164e-03 2.175e-03 2.186e-03'
    y = '3.885e-01 3.885e-01 3.734e-01 3.590e-01 3.453e-01 3.801e-01 4.422e-01 4.596e-01 4.215e-01 3.965e-01 3.933e-01 4.167e-01 4.431e-01 4.037e-01 4.095e-01 4.104e-01 4.010e-01 3.799e-01 3.995e-01 4.261e-01 4.421e-01 4.450e-01 4.256e-01 4.510e-01 5.115e-01 4.718e-01 4.138e-01 4.158e-01 4.454e-01 3.952e-01 2.708e-01 1.811e-01 2.932e-01 3.956e-01 4.010e-01 4.438e-01 4.706e-01 4.574e-01 3.943e-01 3.271e-01 3.642e-01 4.024e-01 3.875e-01 3.970e-01 4.123e-01 4.326e-01 4.353e-01 4.202e-01 3.674e-01 3.546e-01 3.746e-01 4.111e-01 4.174e-01 3.858e-01 3.380e-01 3.172e-01 3.418e-01 3.884e-01 4.080e-01 3.816e-01 3.655e-01 3.654e-01 3.654e-01 3.677e-01 3.751e-01 3.649e-01 3.557e-01 3.597e-01 3.655e-01 3.656e-01 3.542e-01 3.659e-01 3.575e-01 3.202e-01 2.908e-01 3.047e-01 3.069e-01 3.287e-01 3.847e-01 3.949e-01 3.514e-01 3.297e-01 3.263e-01 3.546e-01 3.581e-01 3.608e-01 3.121e-01 2.694e-01 2.931e-01 3.235e-01 2.970e-01 2.552e-01 2.159e-01 1.917e-01 2.040e-01 2.168e-01 1.825e-01 1.284e-01 7.370e-02 4.785e-02 1.842e-02 7.600e-03 7.420e-03 1.751e-02 6.518e-02 7.871e-02 7.470e-02 6.046e-02 1.203e-01 2.068e-01 1.903e-01 8.591e-02 4.031e-02 2.911e-02 5.307e-02 8.001e-02 1.061e-01 1.072e-01 7.464e-02 4.104e-02 3.966e-02 7.244e-02 8.140e-02 7.180e-02 9.492e-02 1.281e-01 1.213e-01 1.188e-01 1.617e-01 2.258e-01 2.321e-01 1.980e-01 1.650e-01 1.621e-01 2.045e-01 2.132e-01 1.669e-01 1.865e-01 2.431e-01 2.144e-01 1.597e-01 1.821e-01 1.962e-01 1.905e-01 2.026e-01 2.446e-01 2.788e-01 2.705e-01 2.518e-01 2.454e-01 2.472e-01 2.465e-01 2.963e-01 3.190e-01 2.726e-01 2.280e-01 2.382e-01 2.713e-01 2.889e-01 2.408e-01 2.094e-01 2.454e-01 2.894e-01 2.808e-01 2.695e-01 2.769e-01 2.813e-01 2.802e-01 2.810e-01 3.856e-01 4.359e-01 3.762e-01 4.293e-01 4.049e-01 3.155e-01 2.501e-01 2.662e-01 3.887e-01 4.248e-01 3.808e-01 3.120e-01 2.897e-01 2.816e-01 2.762e-01 2.350e-01 2.032e-01 2.147e-01 2.246e-01 3.273e-01 3.938e-01 3.301e-01 2.641e-01 2.351e-01 2.482e-01 2.716e-01 2.403e-01 2.083e-01 1.802e-01 1.772e-01 2.982e-01'
  []
[]

[Materials]
  [fuel_density]
    type = ADGenericConstantMaterial
    block = pellet
    prop_names = density
    prop_values = 1.580e+04
  []

  # Heat generation and conduction
  [fission_rate]
    type = ADUPuZrFissionRate
    block = pellet
    X_Pu_function = 0
    initial_X_Zr = 0.225
    X_Zr = X_Zr
    rod_linear_power = f_power
    axial_power_profile = f_axial_power
    pellet_radius = 2.192e-03
  []
  [burnup]
    type = ADUPuZrBurnup
    block = pellet
    initial_X_Pu = 0
    initial_X_Zr = 0.225
    density = 1.580e+04
    outputs = all
  []
  [gaseous_swelling]
    type = ADUPuZrGaseousEigenstrain
    block = pellet
    eigenstrain_name = gaseous_swelling_eigenstrain
    temperature = T
    initial_porosity = 0
    bubble_number_density = 1e20
    outputs = 'all'
    output_properties = 'gaseous_porosity porosity gas_swelling'
  []
  [solid_swelling]
    type = ADBurnupDependentEigenstrain
    block = pellet
    eigenstrain_name = solid_swelling_eigenstrain
    swelling_name = solid_swelling
    outputs = all
  []
  [sodium_logging]
    type = ADUPuZrSodiumLogging
    block = pellet
    porosity = porosity
    interconnectivity = interconnectivity
    sodium_infiltration_fraction = 0.08
    outputs = all
  []
  [fuel_thermal_conductivity]
    type = ADUPuZrThermal
    block = pellet
    temperature = T
    X_Zr = X_Zr
    X_Pu = X_Pu
    thcond_model = lanl
    porosity_model = logged
    porosity = porosity
    sodium_logged_porosity = sodium_logged_porosity
    spheat_model = savage
  []
  [fission_gas_release]
    type = ADUPuZrFissionGasRelease
    block = pellet
    fission_rate = fission_rate
    porosity = porosity
  []
  [clad_density]
    type = ADGenericConstantMaterial
    block = clad
    prop_names = density
    prop_values = 7874.0
  []
  [clad_thermal_conductivity]
    type = ADHT9Thermal
    block = clad
    temperature = T
  []
  [clad_thermal_conductivity_converter]
    # This material creates a non-AD version of the cladding thermal
    # conductivity, which is used by the CoolantChannel model.
    type = MaterialADConverter
    block = clad
    ad_props_in = thermal_conductivity
    reg_props_out = thermal_conductivity_reg
  []
[]

[AuxKernels]
  [gap_conductance_aux]
    type = MaterialRealAux
    variable = gap_conductance_aux
    property = gap_conductance
    boundary = 10
  []
[]

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

[Executioner]
  type = Transient
  solve_type = NEWTON
  automatic_scaling = true
  compute_scaling_once = false
  scheme = bdf2
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'
  line_search = none
  l_max_its = 15
  l_tol = 1e-3
  nl_max_its = 15
  nl_rel_tol = 1e-6
  nl_abs_tol = 1e-6
  dtmin = 10
  dtmax = 1e6
  end_time = 24969600
  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 1e5
    iteration_window = 2
    optimal_iterations = 9
    growth_factor = 1.1
    cutback_factor = 0.5
  []
[]

[Postprocessors]
  [T_cl]
    type = PointValue
    variable = T
    point = '0 2.689e-01 0'
  []
  [burnup_avg]
    type = SideAverageValue
    variable = burnup
    boundary = radial_slice
  []
  [porosity_avg]
    type = SideAverageValue
    variable = porosity
    boundary = radial_slice
  []
  [logged_sodium_avg]
    type = SideAverageValue
    variable = sodium_logged_porosity
    boundary = radial_slice
  []
  [gas_porosity_avg]
    type = SideAverageValue
    variable = gaseous_porosity
    boundary = radial_slice
  []
  [solid_swelling_avg]
    type = SideAverageValue
    variable = solid_swelling
    boundary = radial_slice
  []
  [gaseous_swelling_avg]
    type = SideAverageValue
    variable = gas_swelling
    boundary = radial_slice
  []
  [fis_gas_produced]
    type = ADElementIntegralMaterialProperty
    block = pellet
    mat_prop = fis_gas_prod
  []
  [fis_gas_released]
    type = ADElementIntegralMaterialProperty
    block = pellet
    mat_prop = fis_gas_rel
    execute_on = 'initial timestep_end'
  []
  [fis_gas_percent]
    type = FGRPercent
    fission_gas_released = fis_gas_released
    fission_gas_generated = fis_gas_produced
  []
[]

[VectorPostprocessors]
  [profiles]
    type = LineValueSampler
    variable = 'T X_Pu X_Zr X_Zr_ref alpha beta gamma delta zeta'
    sort_by = x
    start_point = '0 2.689e-01 0'
    end_point = '2.192e-03 2.689e-01 0'
    num_points = 11
  []
[]

[Outputs]
  perf_graph = true
  exodus = true
  [csv]
    type = CSV
    execute_vector_postprocessors_on = final
  []
[]

(test/tests/solid_mechanics/simple_fission_gas_viscoplasticity/old_method_comparison.i)

# This test ensures that shows the differences between the old fission gas swelling and fission
# gas release model with the new combined model. Note, the method for calculating porosity
# is different between the two methods, so the final interconnection and porosities are different.
# What should be similar is the amount of fission gas produced and final radius. Also note, the
# old models do not keep track of the dissolved fission gas or gas in bubbles. Other small differences
# are due to small numerical differences in constants.

[GlobalParams]
  displacements = 'disp_x'
[]

[Mesh]
  [left]
    type = GeneratedMeshGenerator
    dim = 1
    nx = 4
    xmin = 0
    xmax = 1
  []
  [left_id]
    type = SubdomainIDGenerator
    input = left
    subdomain_id = 1
  []

  [right]
    type = GeneratedMeshGenerator
    dim = 1
    nx = 4
    xmin = 2
    xmax = 3
  []
  [right_id]
    type = SubdomainIDGenerator
    input = right
    subdomain_id = 2
  []

  [combined]
    type = MeshCollectionGenerator
    inputs = 'left_id right_id'
  []
  [block_rename]
    type = RenameBlockGenerator
    input = combined
    old_block_id = '1 2'
    new_block_name = 'left right'
  []
  [block_sidesets]
    type = SideSetsFromPointsGenerator
    input = block_rename
    points = '3 0 0'
    new_boundary = 'far_right'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [left]
    add_variables = true
    strain = FINITE
    use_automatic_differentiation = true
    block = left
  []
  [right]
    add_variables = true
    strain = FINITE
    use_automatic_differentiation = true
    block = right
    eigenstrain_names = 'gas_swelling_eigenstrain'
  []
[]

[AuxVariables]
  [temp]
    initial_condition = 1700
  []
[]

[AuxKernels]
  [temp_aux]
    type = FunctionAux
    variable = temp
    function = temp_fcn
  []
[]

[BCs]
  [no_x]
    type = DirichletBC
    variable = disp_x
    boundary = 'left far_right'
    value = 0
  []
[]

[Functions]
  [temp_fcn]
    type = PiecewiseLinear
    x = '0   1e7  1.1e7 3e7'
    y = '100 1000 500   1000'
  []
  [fsnrate_fcn]
    type = PiecewiseConstant
    x = '0    1e7 1.1e7 3e7'
    y = '1e19 0   1e21  1e20'
  []
  [fg_check_left]
    type = ParsedFunction
    symbol_values = 'fgm_produced_avg_left fgm_released_avg_left fgm_captured_avg_left fgm_dissolved_avg_left'
    symbol_names = 'fgm_produced_avg_left fgm_released_avg_left fgm_captured_avg_left fgm_dissolved_avg_left'
    expression = 'fgm_produced_avg_left-fgm_released_avg_left-fgm_captured_avg_left-fgm_dissolved_avg_left'
  []
  [fg_check_right]
    type = ParsedFunction
    symbol_values = 'fgm_produced_avg_right fgm_released_avg_right fgm_captured_avg_right fgm_dissolved_avg_right'
    symbol_names = 'fgm_produced_avg_right fgm_released_avg_right fgm_captured_avg_right fgm_dissolved_avg_right'
    expression = 'fgm_produced_avg_right-fgm_released_avg_right-fgm_captured_avg_right-fgm_dissolved_avg_right'
  []
[]

[Materials]
  [elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    youngs_modulus = 1
    poissons_ratio = 0.3
  []
  [fission_rate]
    type = ADGenericFunctionMaterial
    prop_names = 'fission_rate'
    prop_values = 'fsnrate_fcn'
    outputs = all
  []
  [left_fuel_stress]
    type = ADComputeMultipleInelasticStress
    block = left
    inelastic_models = 'left_gas_swelling'
  []
  [porosity]
    type = ADPorosityFromStrain
    block = left
    initial_porosity = 0.1
    inelastic_strain = 'combined_inelastic_strain'
    outputs = all
  []
  [left_gas_swelling]
    type = ADSimpleFissionGasViscoplasticityStressUpdate
    block = left
    fission_rate = fission_rate
    temperature = temp
    bubble_concentration = 1e20
    initial_bubble_concentration = 1e20
    interconnection_initiating_porosity = 0.15
    interconnection_terminating_porosity = 0.2
    compute_interconnectivity = true
    scalar = 0.8
    initial_fgm_dissolved = 0
    initial_atoms_per_bubble = 1e-5
    surface_energy = 1.2
    fission_gas_yield = 0.15
    retained_gas_fraction = 0.2
    outputs = all
  []

  [right_fuel_stress]
    type = ADComputeFiniteStrainElasticStress
    block = right
  []
  [right_gas_swelling]
    type = ADUPuZrGaseousEigenstrain
    block = right
    temperature = temp
    initial_porosity = 0.1
    bubble_number_density = 1e20
    interconnection_initiating_porosity = 0.15
    interconnection_terminating_porosity = 0.2
    scalar = 0.8
    surface_energy = 1.2
    fission_gas_yield = 0.15
    retained_gas_fraction = 0.2
    outputs = all
    eigenstrain_name = gas_swelling_eigenstrain
  []
  [fission_gas_release]
    type = ADUPuZrFissionGasRelease
    block = right
    fission_rate = fission_rate
    porosity = porosity
    fractional_yield = 0.15
    critical_porosity = 0.20
    time_average_fission_rate = false
    use_old_porosity = false
    outputs = all
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  line_search = 'none'

  end_time = 2e7
  dt = 5e5
  dtmin = 1
  nl_abs_tol = 1e-15
[]

[Postprocessors]
  [fission_rate]
    type = ElementAverageValue
    variable = fission_rate
  []
  [temp]
    type = ElementAverageValue
    variable = temp
  []

  [atoms_left]
    type = ElementAverageValue
    variable = fgm_per_bubble
    block = left
  []
  [porosity_left]
    type = ElementAverageValue
    variable = porosity
    block = left
  []
  [gas_swelling_left]
    type = ElementAverageValue
    variable = effective_fission_gas_strain
    block = left
  []
  [radius_left]
    type = ElementAverageValue
    variable = radius
    block = left
  []
  [interconnectivity_left]
    type = ElementAverageValue
    variable = interconnectivity
    block = left
  []
  [fgm_produced_avg_left]
    type = ElementAverageValue
    variable = fgm_produced
    block = left
  []
  [fgm_released_avg_left]
    type = ElementAverageValue
    variable = fgm_released
    block = left
  []
  [fgm_captured_avg_left]
    type = ElementAverageValue
    variable = fgm_captured
    block = left
  []
  [fgm_dissolved_avg_left]
    type = ElementAverageValue
    variable = fgm_dissolved
    block = left
  []
  [fg_check_left]
    type = FunctionValuePostprocessor
    function = fg_check_left
  []

  [atoms_right]
    type = ElementAverageValue
    variable = atoms_per_bubble
    block = right
  []
  [porosity_right]
    type = ElementAverageValue
    variable = porosity
    block = right
  []
  [gas_swelling_right]
    type = ElementAverageValue
    variable = gas_swelling
    block = right
  []
  [radius_right]
    type = ElementAverageValue
    variable = radius
    block = right
  []
  [interconnectivity_right]
    type = ElementAverageValue
    variable = interconnectivity
    block = right
  []
  [fgm_produced_avg_right]
    type = ElementAverageValue
    variable = fis_gas_prod
    block = right
  []
  [fgm_released_avg_right]
    type = ElementAverageValue
    variable = fis_gas_rel
    block = right
  []
  [fgm_captured_avg_right]
    type = ElementAverageValue
    variable = fgm_captured
    block = right
  []
  [fgm_dissolved_avg_right]
    type = ElementAverageValue
    variable = fgm_dissolved
    block = right
  []
  [fg_check_right]
    type = FunctionValuePostprocessor
    function = fg_check_right
  []
[]

[Outputs]
  csv = true
  exodus = true
[]

(test/tests/upuzr_fission_gas_release/ad/test.i)

# This tests the fission gas produced and released postprocessors when coupled with thermo-mechanics.

[GlobalParams]
  displacements = 'disp_x disp_y'
[]

[Mesh]
  coord_type = RZ
  [mesh]
    type = GeneratedMeshGenerator
    dim = 2
    xmax = 3e-3
    ymax = 3e-2
    nx = 6
    ny = 6
  []
[]

[Variables]
  [power]
    initial_condition = 50
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    add_variables = true
    strain = FINITE
    generate_output = 'stress_xx'
    use_automatic_differentiation = true
  []
[]

[Kernels]
  [power_diff]
    type = ADMatDiffusion
    variable = power
    diffusivity = 1e-3
    use_displaced_mesh = true
  []
  [power_dt]
    type = ADTimeDerivative
    variable = power
  []
[]

[BCs]
  [power_left]
    type = ADDirichletBC
    variable = power
    boundary = left
    value = 100
  []
  [power_right]
    type = ADDirichletBC
    variable = power
    boundary = right
    value = 10
  []
  [fixed_x]
    type = ADDirichletBC
    boundary = left
    variable = disp_x
    value = 0
  []
  [fixed_y]
    type = ADDirichletBC
    boundary = bottom
    variable = disp_y
    value = 0
  []
  [pressure]
    type = ADPressure
    variable = disp_x
    boundary = right
    postprocessor = gas_released
    factor = 1e20
  []
[]

[Materials]
  [fission_rate]
    type = ADPiecewiseLinearInterpolationMaterial
    property = fission_rate
    x = '1 100'
    y = '1e19 1e21'
    variable = power
    outputs = all
    output_properties = fission_rate
  []
  [porosity]
    type = ADPiecewiseLinearInterpolationMaterial
    property = porosity
    x = '1 100'
    y = '0.1 0.3'
    variable = power
    outputs = all
    output_properties = porosity
  []
  [fission_gas_release]
     type = ADUPuZrFissionGasRelease
     fission_rate = fission_rate
     porosity = porosity
     fractional_yield = 0.25
     critical_porosity = 0.20
     time_average_fission_rate = false
     use_old_porosity = false
     fractional_fgr_initial = 0.7
     fractional_fgr_post = 0.9
  []
  [tensor]
    type = ADComputeIsotropicElasticityTensor
    youngs_modulus = 1e9
    poissons_ratio = 0.1
  []
  [stress]
    type = ADComputeFiniteStrainElasticStress
  []
[]

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

[Executioner]
  type = Transient

  nl_abs_tol = 1e-10
  num_steps = 5
  dt = 0.01
[]

[Postprocessors]
  [power_avg]
    type = ElementAverageValue
    variable = power
  []
  [power_max]
    type = ElementExtremeValue
    variable = power
  []
  [power_min]
    type = ElementExtremeValue
    variable = power
    value_type = min
  []
  [fission_rate]
    type = ElementAverageValue
    variable = fission_rate
  []
  [gas_produced]
    type = ADElementIntegralMaterialProperty
    mat_prop = fis_gas_prod
  []
  [gas_released]
    type = ADElementIntegralMaterialProperty
    mat_prop = fis_gas_rel
  []
  [porosity]
    type = ElementAverageValue
    variable = porosity
  []
  [disp_x]
    type = ElementExtremeValue
    variable = disp_x
  []
  [stress_xx]
    type = ElementExtremeValue
    variable = stress_xx
  []
[]

[Outputs]
  exodus = true
[]

(test/tests/solid_mechanics/upuzr_eigenstrains/ad_upuzr_gaseous_eigenstrain/test.i)

# @Requirement F4.40
# This tests UPuZrGaseousEigenstrain, a swelling model for UPuZr metal fuel
# that allows for variation in bubble radius, as well as to the fission gas release
# model for UPuZr fuel.
#
# The swelling model is based on Eq. (13.146) in "Fundamental aspects of nuclear
# reactor fuel elements" by Olander.
#
# The fission gas that is released is based on an empirical model
# which states that once the gaseous swelling reaches a value of
# 0.33 (corresponding to a porosity of 0.24812), 80% of the fission gas so far
# produced is immediately released. After that, 100% of the gas produced is released.
# For information regarding swelling and porosity, see the above reference or the
# following reference:
# Karahan A., Modeling of Thermo Mechanical and Irradiation Behavior of Metallic
# and Oxide Fuels for Sodium Fast Reactors, Thesis, Massachusetts Institute of Technology 2009.
#

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
[]

[Mesh]
  [mesh]
    type = GeneratedMeshGenerator
    dim = 3
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = FINITE
    add_variables = true
    eigenstrain_names = 'gas_swelling_eigenstrain'
    generate_output = 'stress_xx stress_yy stress_zz hydrostatic_stress strain_xx strain_yy'
    use_automatic_differentiation = true
  []
[]

[AuxVariables]
  [temp]
  []
  [volumetric_strain]
    order = CONSTANT
    family = MONOMIAL
  []
  [gas_swell]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [fission_rate_func]
    type = PiecewiseLinear
    x = '0 7e7'
    y = '0 2.5e19'
  []
  [pressure_func]
    type = PiecewiseLinear
    x = '0 7e7'
    y = '0 1e6'
  []
[]

[AuxKernels]
  [temp]
    type = ConstantAux
    variable = temp
    value = 1700
  []
  [volumetric_strain]
    type = ADRankTwoScalarAux
    variable = volumetric_strain
    rank_two_tensor = total_strain
    scalar_type = VolumetricStrain
  []
  [gas_swell_aux]
    type = ADMaterialRealAux
    variable = gas_swell
    property = gas_swelling
  []
[]

[BCs]
  [no_x]
    type = ADDirichletBC
    variable = disp_x
    boundary = left
    value = 0
  []
  [no_y]
    type = ADDirichletBC
    variable = disp_y
    boundary = bottom
    value = 0
  []
  [no_z]
    type = ADDirichletBC
    variable = disp_z
    boundary = back
    value = 0
  []
  [Pressure]
    [Side]
      boundary = 'right top front'
      function = pressure_func
      use_automatic_differentiation = true
    []
  []
[]

[Materials]
  [elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    youngs_modulus = 2.0e11
    poissons_ratio = 0.3
  []
  [fuel_stress]
    type = ADComputeFiniteStrainElasticStress
  []
  [fission_rate]
    type = ADGenericFunctionMaterial
    prop_names = 'fission_rate'
    prop_values = 'fission_rate_func'
    outputs = all
  []
  [gas_swelling]
    type = ADUPuZrGaseousEigenstrain
    temperature = temp
    initial_porosity = 0.1
    outputs = all
    output_properties = 'porosity gaseous_porosity'
    bubble_number_density = 1e+20
    eigenstrain_name = gas_swelling_eigenstrain
    anisotropic_factor = 0.3
  []

  [fission_gas_behavior]
    type = ADUPuZrFissionGasRelease
    fission_rate = 'fission_rate'
    outputs = all
    output_properties = 'fis_gas_prod fis_gas_rel'
  []
[]

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

[Executioner]
  type = Transient

  l_max_its = 60
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-4
  l_tol = 1e-5
  num_steps = 70
  dt = 1e6
  dtmin = 1e6
[]

[Postprocessors]
  [gas_produced]
    type = ElementAverageValue
    variable = fis_gas_prod
  []
  [gas_released]
    type = ElementAverageValue
    variable = fis_gas_rel
  []
  [fission_rate]
    type = ElementAverageValue
    variable = fission_rate
  []
  [hydrostatic_stress]
    type = ElementAverageValue
    variable = hydrostatic_stress
  []
  [porosity]
    type = ElementAverageValue
    variable = porosity
  []
  [gaseous_porosity]
    type = ElementAverageValue
    variable = gaseous_porosity
  []
  [gas_swell]
    type = ElementAverageValue
    variable = gas_swell
  []
  [volumetric_strain]
    type = ElementAverageValue
    variable = volumetric_strain
  []
  [strain_xx]
    type = ElementAverageValue
    variable = strain_xx
  []
  [strain_yy]
    type = ElementAverageValue
    variable = strain_yy
  []
[]

[Outputs]
  exodus = true
[]

(test/tests/upuzr_fission_gas_release/ad/exact_1D.i)

# This tests the fission gas produced and released postprocessors
# and for 1d and 2d models with the same volume.
# The reported values should be the same for the
# 1d and 2d cases. See corresponding excel calculation
# in this directory.

[Problem]
  solve = false
[]

[UserObjects]
  [pin_geometry]
    type = Layered1DFuelPinGeometry
    include_clad = false
    mesh_generator = layered1D_mesh
  []
[]

[Mesh]
  coord_type = RZ
  [layered1D_mesh]
    type = Layered1DMeshGenerator
    include_clad = false
    include_plenum = false
    slices_per_block = 1
    fuel_height = 3e-3
    pellet_outer_radius = 3e-3
    pellet_bottom_coor = 0.0
    pellet_mesh_density = customize
    nx_p = 4
    elem_type = EDGE2
  []
[]

[Functions]
  [fission_rate_func]
    type = PiecewiseLinear
    x = '0    1e7'
    y = '1e20 1e18'
  []
  [porosity_func]
    type = PiecewiseLinear
    x = '0    1e7'
    y = '0.15 0.25'
  []
[]

[Variables]
  [temp]
    initial_condition = 1700
  []
[]

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

[Materials]
  [ad_properties]
    type = ADGenericFunctionMaterial
    prop_names  = 'fission_rate'
    prop_values = 'fission_rate_func'
    outputs = all
  []
  [properties]
    type = ADGenericFunctionMaterial
    prop_names  = 'porosity'
    prop_values = 'porosity_func'
    outputs = all
  []
  [fission_gas_release]
   type = ADUPuZrFissionGasRelease
   fission_rate = fission_rate
   fractional_yield = 0.3017
   critical_porosity = 0.2
   use_old_porosity = false
   time_average_fission_rate = false
  []
[]

[Executioner]
  type = Transient

  dt = 1e6
  end_time = 1e7
[]

[Postprocessors]
  [fission_rate]
    type = ElementAverageValue
    variable = fission_rate
  []
  [gas_produced]
    type = ADLayeredElementIntegralFisGasProducePostprocessor
    fuel_pin_geometry = pin_geometry
  []
  [gas_released]
    type = ADLayeredElementIntegralFisGasReleasePostprocessor
    fuel_pin_geometry = pin_geometry
  []
  [porosity]
    type = ElementAverageValue
    variable = porosity
  []
[]

[Outputs]
  csv = true
  file_base = exact_out
[]

(test/tests/upuzr_fission_gas_release/ad/exact_2D.i)

# This tests the fission gas produced and released postprocessors
# and for 1d and 2d models with the same volume.
# The reported values should be the same for the
# 1d and 2d cases. See corresponding excel calculation
# in this directory.

[Problem]
  solve = false
[]

[Mesh]
  coord_type = RZ
  [mesh]
    type = GeneratedMeshGenerator
    dim = 2
    xmax = 3e-3
    ymax = 3e-3
    nx = 4
    ny = 4
  []
[]

[Functions]
  [fission_rate_func]
    type = PiecewiseLinear
    x = '0    1e7'
    y = '1e20 1e18'
  []
  [porosity_func]
    type = PiecewiseLinear
    x = '0    1e7'
    y = '0.15 0.25'
  []
[]

[Variables]
  [temp]
    initial_condition = 1700
  []
[]

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

[Materials]
  [properties]
    type = ADGenericFunctionMaterial
    prop_names  = 'fission_rate'
    prop_values = 'fission_rate_func'
    outputs = all
  []
  [reg_properties]
    type = ADGenericFunctionMaterial
    prop_names = 'porosity'
    prop_values = 'porosity_func'
    outputs = all
  []
  [fission_gas_release]
   type = ADUPuZrFissionGasRelease
   fission_rate = fission_rate
   porosity = porosity
   fractional_yield = 0.3017
   critical_porosity = 0.2
   use_old_porosity = false
   time_average_fission_rate = false
  []
[]

[Executioner]
  type = Transient

  nl_abs_tol = 1e-10
  dt = 1e6
  end_time = 1e7
[]

[Postprocessors]
  [fission_rate]
    type = ElementAverageValue
    variable = fission_rate
  []
  [gas_produced]
    type = ADElementIntegralMaterialProperty
    mat_prop = fis_gas_prod
  []
  [gas_released]
    type = ADElementIntegralMaterialProperty
    mat_prop = fis_gas_rel
  []
  [porosity]
    type = ElementAverageValue
    variable = porosity
  []
[]

[Outputs]
  csv = true
  file_base = exact_out
[]

Description
Example Input Syntax
Input Parameters
Input Files
References