MetallicFuelLiquidCladdingPenetration

Computes loss of cladding thickness due to the liquid penetration into cladding during power transients.

Description

MetallicFuelLiquidCladdingPenetration finds the liquid penetration depth into the cladding near the fuel cladding interface in metallic fuels used in sodium-cooled fast reactor (SFR) under off-normal conditions. SFR metallic fuel usually adopts a binary (U-10Zr) or ternary (U-10Zr-xPu) fuel slug and a austenitic (316SS or D9) or martensitic (HT9) steel cladding. Thus, U and Pu in fuel tends to metallurgically interact with the stainless steel cladding. During steady-state operation, such interaction is solid-state in nature and can be handled by MetallicFuelWastage. On the other hand, at the elevated temperatures during off-normal transients, the interaction is dominated by liquid phase penetrating the stainless steel cladding, which would weaken the cladding enclosure and even compromise the fuel pin's integrity. Therefore, this phenomenon is one of the major causes of fuel failure at elevated temperature during power transients.

The IFR legacy single-parameter correlation (Tsai, 1990), established from Argonne National Laboratory (ANL) fuel behavior test apparatus (FBTA) EBR-II fuel/cladding eutectic test data available during its development period, is implemented to estimate eutectic liquid penetration rates. This bounding correlation is activated at a fixed threshold temperature of 700 °C. Also implemented is a set of improved correlations for evaluating eutectic liquid penetration under transient conditions, which have been recently developed, leveraging the OPTD (Shu et al., 2024). The OPTD, with over 150 records from ANL FBTA EBR-II/FFTF fuel/cladding eutectic tests, helps validate and refine these correlations for better model alignment with experimental results. The tested fuel/cladding combinations cover U-26Pu-10Zr/316SS, U-19Pu-10Zr/HT9, U-19Pu10Zr/D9, U-10Zr/HT9, U-10Zr/D9 and U-10Zr/316SS. The burnup values of these fuel specimens range from 3 to 17 atomic percent. The selected tests are of the constant-temperature type; the temperature and duration of the tests range from 620 to 850 $var element = document.getElementById("moose-equation-ac93ae23-6841-455c-994e-79ff8fe7199d");katex.render("^{\\circ}", element, {displayMode:false,throwOnError:false});$ C and 5 minutes to 32 hours, respectively. Fuel- and burnup-dependent threshold temperatures were used in this set of correlations.

Forms of the Correlation

Based on the available experiments, it was concluded that there exist an onset temperature of approximately 700 $var element = document.getElementById("moose-equation-9dd1a1ac-95b6-4fac-af9f-0ac80b8d767a");katex.render("\\sim", element, {displayMode:false,throwOnError:false});$ 725 $var element = document.getElementById("moose-equation-3365b440-4cbe-412d-842e-d5a672d82ff0");katex.render("^{\\circ}", element, {displayMode:false,throwOnError:false});$ C for liquid cladding penetration. When the temperature is lower than the onset temperature, no liquid penetration was observed. On the other hand, if the temperature exceeds the onset temperature, liquid penetration is activated and the penetration rate follows the Arrhenius law. That is, the linear penetration rate ( $var element = document.getElementById("moose-equation-bc2118e1-8472-45bf-afe3-4e65dd2d99d8");katex.render("S_{linear}", element, {displayMode:false,throwOnError:false});$ in $var element = document.getElementById("moose-equation-3cb16aca-9278-4a0d-8171-32f212368822");katex.render("\\mu", element, {displayMode:false,throwOnError:false});$ m/s) is dependent on the temperature with the following form:

(1)var element = document.getElementById("moose-equation-928f3e3b-c5c5-45f9-9ff2-b9d41d19030a");katex.render("S_{linear}(T) = \\begin{cases} \\exp{\\left(A-\\frac{Q}{RT}\\right)} & T>T_{onset},\\\\ 0 & T \\leq T_{onset}. \\end{cases}", element, {displayMode:true,throwOnError:false});

Parameter	Unit	Description
$var element = document.getElementById("moose-equation-3f9a9431-f91b-4e39-993c-7b70ae2cfaed");katex.render("A", element, {displayMode:false,throwOnError:false});$	n.a.	Coefficient
$var element = document.getElementById("moose-equation-faf975f5-246c-4a0c-bf15-4cb200416a9b");katex.render("\\frac{Q}{R}", element, {displayMode:false,throwOnError:false});$	K	Activation energy
$var element = document.getElementById("moose-equation-f551e769-7b3a-45df-a9ef-3f06b643556b");katex.render("T_{onset}", element, {displayMode:false,throwOnError:false});$	K	Onset temperature

The Eq. (1) assumes a linear growth kinetics for the liquid cladding penetration phenomenon. Recently detailed data analysis unveils that a parabolic kinetics matches the experimental data better, which has the following form as the temperature exceeds the onset temperature ( $var element = document.getElementById("moose-equation-2d0251a5-fca7-430c-8ec4-da83162e2e9b");katex.render("T_{onset}", element, {displayMode:false,throwOnError:false});$ ):

(2)var element = document.getElementById("moose-equation-df0c5edf-8436-4c40-a7b4-1d942a9d2e11");katex.render("S_{parabolic}(t) = C(T)t^{-\\frac12}", element, {displayMode:true,throwOnError:false});

or,

(3)var element = document.getElementById("moose-equation-14ca3d31-3851-4438-bcfb-0443945fddbb");katex.render("\\int_{0}^{t} dt S_{parabolic}(T, t) = 2C(T)t^{\\frac12},", element, {displayMode:true,throwOnError:false});

where C(T) is a temperature-dependent constant.

To make the definition of kinetic models consistent, as the majority of the experimental data were collected for a one-hour duration, it is assumed that both kinetics expressions should predict the same penetration depth at 1 hour.

(4)var element = document.getElementById("moose-equation-5e968996-3027-46bf-8a3a-2c59cd499cca");katex.render("\\int_{0}^{t=3600 s} dt S_{linear}(T) = \\int_{0}^{t=3600 s} dt S_{parabolic}(T, t)\\\\ S_{linear}(T) \\cdot 3600 = 2C(T)\\sqrt{3600}\\\\ C(T) = \\frac{S_{linear}(T)}{2/\\sqrt{3600}}=\\frac{\\exp{\\left(A-\\frac{Q}{RT}\\right)}}{2/\\sqrt{3600}}", element, {displayMode:true,throwOnError:false});

Therefore,

(5)var element = document.getElementById("moose-equation-e35daaab-69ec-4bd4-ab6c-b2007a8ffffa");katex.render("S_{parabolic}(t) = C(T)t^{-\\frac12} = \\frac{\\exp{\\left(A-\\frac{Q}{RT}\\right)}}{2\\sqrt{t/3600}}", element, {displayMode:true,throwOnError:false});

Eq. (5) allows using of a consistent set of coefficients ( $var element = document.getElementById("moose-equation-a97cdb78-4fba-45ff-bda1-a86e6c11a55c");katex.render("A", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-5c1b77a3-ab6e-47e8-9ee4-170b652ecf41");katex.render("Q/R", element, {displayMode:false,throwOnError:false});$ , and $var element = document.getElementById("moose-equation-733697ae-ce9d-4c21-b226-de252ba4e1f2");katex.render("T_{onset}", element, {displayMode:false,throwOnError:false});$ ) for both linear and parabolic kinetic form. Users have option to specify which kinetic form to use through "kinetic_model".

Legacy IFR Correlation by Tsai et al. (Tsai, 1990)

During the IFR program, the parameters were empirically fit based on the results of over fifty aforementioned FBTA experiment tests (Tsai, 1990). A summary of the correlation compared with representative test results can be found in Figure 1. It is clear that the empirical correlation provides a conservative estimate of the liquid phase penetration kinetics covering a variety of cladding and fuel compositions. The IFR legacy single-parameter correlation can be selected by choosing TSAI in "liquid_penetration_model". The model is a general model that does not distinguish Pu content and burnup effects. The default kinetic model to use this model is LINEAR.

Figure 1: The liquid penetration correlation compared with the FBTA test results (Tsai, 1990).

Recently Developed Model

Tsai et al.'s IFR legacy single-parameter correlation was developed during the FBTA projects, with additional tests and in-depth analyses conducted after its establishment. The enriched data set, along with detailed experimental notes, has been integrated into the OPTD. This facilitates the development of new correlations that differentiate between different fuels and, to a limited extent, burnup. Two types of correlations were developed: the least-squares fitting correlation and the conservative correlation. The former aims to provide a more accurate estimation of experimental data, while the latter is designed to be an upper bound of the experiments. Notably, both types of correlations share the same activation energy. The new ANL correlations can be selected by choosing ANL_LS and ANL_CONSERVATIVE in "liquid_penetration_model". A comparison between the legacy and updated correlation using binary fuel as an example can be found in Figure 2.

As the correlations are fuel- and burnup-dependent, users are also required to provide the information of initial Pu content in the fuel and the burnup through "fuel_pu" and "burnup". More description and performance of the updated correlation can be found in the reference that reports its development(Shu et al., 2024).

The default kinetic model to use this model is PARABOLIC.

Figure 2: The improvements made by the recent updated correlation.

Axial Effective Region

The liquid penetration should only occur in the region where fuel and cladding are both present and in contact. Thus, the calculation of this phenomenon should be disable in the axial positions without fuel in presence. To achieve this, the axial range where the fuel is in presence can be provided manually using "fuel_bottom_position" and "fuel_height". Any axial location from fuel_bottom_position to fuel_bottom_position + fuel_height is considered to have fuel present. Alternatively, if the mesh is generated by FIPDRodletMeshGenerator, the axial range can be obtained through the mesh metadata by provide "mesh_generator".

Additionally, as fuel length is subject to change during irradiation or out-of-pile furnace experiments, the axial effective region is also affected by this phenomenon. To capture this, users have an option to provide a postprocessor ("fuel_elongation_pp") that tracks the displacement of the fuel's top surface. Axial locations with fuel present will be from fuel_bottom_position to fuel_bottom_position + fuel_height + fuel_elongation_pp.

Melting Fuel

During the liquid cladding penetration procedure, the fuel also experiences melting. This MetallicFuelLiquidCladdingPenetration has a few correlations to calculate the thickness of the melting fuel zone from the outer surface of the fuel, which can be activated by "calculate_fuel_melting_thickness". The correlation options are as follows.

User Provided Ratio

The simplest correlation assumes a fixed fuel-to-cladding liquid volume ratio, which can be selected by setting "fuel_melting_model" as USER_PROVIDED_FACTOR. The ratio can be manually set through "fuel_to_cladding_melting_ratio", which should be based on empirical or mechanistic deduction.

Empirical Temperature/Pu/Burnup Dependent Correlations

A more complex set of empirical correlations were recently developed based on FBTA data, which can be selected by setting "fuel_melting_model" as INTRINSIC. Based on the trends shown in the FBTA data, the fuel-to-cladding melting ratio is fuel- and burnup-dependent. Similar to the cladding penetration correlations, the information of initial Pu content in the fuel and the burnup are required through "fuel_pu" and "burnup".

The empirical correlations are based on U-Pu-Fe ternary phase diagrams with correction factors to account for complexity in kinetics. The details can be found in the following reference (Miao et al., 2024). The correlations have the following form,

(6)var element = document.getElementById("moose-equation-39fd94cc-ee33-4005-9695-610eea0e1f70");katex.render("R = R_{vol} \\cdot K_{corr} \\cdot P_{U/Fe}(T)", element, {displayMode:true,throwOnError:false});

where $var element = document.getElementById("moose-equation-3e58f94e-e125-40b8-b7c1-56a58787c473");katex.render("P_{U/Fe}(T)", element, {displayMode:false,throwOnError:false});$ is the U-to-Fe weight ratio as derived from the U-rich side of the liquidus curves on the U-Fe(0Pu), U-Fe(19Pu) and U-Fe(26Pu) phase diagrams, respectively (see Figure 3), $var element = document.getElementById("moose-equation-0cdd1556-752d-4762-8bcb-ec9972ac253b");katex.render("K_{corr}", element, {displayMode:false,throwOnError:false});$ is the correction factor for the U/Fe ratio, and $var element = document.getElementById("moose-equation-7cceb5f0-c8ce-47a6-aec0-4b0b0fea3b2b");katex.render("R_{vol}", element, {displayMode:false,throwOnError:false});$ is the volume factor accounts for the fact that the fuel contains Pu and Zr in addition to U. The values of $var element = document.getElementById("moose-equation-a685e323-375d-4d54-9cbb-d0805f377031");katex.render("K_{corr}", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-5470e15d-e1e0-4493-834d-7bb543ac3976");katex.render("R_{vol}", element, {displayMode:false,throwOnError:false});$ for various Pu compositions and burnup levels are listed in Table 1.

Figure 3: The liquidus curve for U-Pu-Zr system with 0, 19, and 26 wt.% Pu content.

Table 1: $var element = document.getElementById("moose-equation-f0ea23ae-3888-4c58-8684-805ddac0d52f");katex.render("K_{corr}", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-aae8eb86-5483-45ca-852b-4f1e5eb35c8e");katex.render("R_{vol}", element, {displayMode:false,throwOnError:false});$ values for different Pu and burnup conditions.

Pu Content	Burnup	$var element = document.getElementById("moose-equation-1c9fa28a-ef49-491f-8adb-69e7efc602f6");katex.render("K_{corr}", element, {displayMode:false,throwOnError:false});$	$var element = document.getElementById("moose-equation-0320d15a-8819-4086-8201-747884668276");katex.render("R_{vol}", element, {displayMode:false,throwOnError:false});$
0 wt.%	No Dependence	0.61	2.3
19 wt.%	$var element = document.getElementById("moose-equation-418dc302-0ef3-4f72-8156-a93bf4ec168b");katex.render("<", element, {displayMode:false,throwOnError:false});$ 7 at.%	0.40	3.0
19 wt.%	$var element = document.getElementById("moose-equation-afba9e17-4bfb-478a-acdf-f0fa7619b529");katex.render("\\geq", element, {displayMode:false,throwOnError:false});$ 7 at.%	0.50	3.0
26 wt.%	No Dependence	0.90	3.3

The performance of the correlations is evaluated using the experiment results of the FBTA tests, as shown in Figure 4. The predictions of the correlations are generally conservative and consistent with the experimental observation.

Figure 4: The predicted molten fuel areas versus measured values for FBTA tests.

Example Input Syntax

[Materials<<<{"href": "../../syntax/Materials/index.html"}>>>]
  [liquid_penetration]
    type = MetallicFuelLiquidCladdingPenetration<<<{"description": "Computes loss of cladding thickness due to the liquid penetration into cladding during power transients.", "href": "MetallicFuelLiquidCladdingPenetration.html"}>>>
    temperature<<<{"description": "The coupled temperature (K)"}>>> = temp
    fuel_bottom_position<<<{"description": "The axial position of the bottom of the fuel slug."}>>> = 0.0
    fuel_height<<<{"description": "The height (axial length) of the fuel slug to be added to the slug bottom position to get the top axial position of the fuel."}>>> = 1.0
    outputs<<<{"description": "Vector of output names where you would like to restrict the output of variables(s) associated with this object"}>>> = all
  []
[]

Input Parameters

fuel_melting_modelUSER_PROVIDED_FACTORThe model used to calculate fuel melting fraction based on cladding penetration.
Default:USER_PROVIDED_FACTOR
C++ Type:MooseEnum
Options:INTRINSIC, USER_PROVIDED_FACTOR
Controllable:No
Description:The model used to calculate fuel melting fraction based on cladding penetration.
fuel_puGENERALFuel Pu concentration.
Default:GENERAL
C++ Type:MooseEnum
Options:Pu_0, Pu_19, Pu_26, GENERAL
Controllable:No
Description:Fuel Pu concentration.
kinetic_modelDEFAULTThe kinetic model use to predict liquid penetration depth.
Default:DEFAULT
C++ Type:MooseEnum
Options:LINEAR, PARABOLIC, DEFAULT
Controllable:No
Description:The kinetic model use to predict liquid penetration depth.
liquid_penetration_modelTSAIThe liquid penetration model.
Default:TSAI
C++ Type:MooseEnum
Options:TSAI, ANL_CONSERVATIVE, ANL_LS, CUSTOM
Controllable:No
Description:The liquid penetration model.
temperatureThe coupled temperature (K)
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The coupled temperature (K)

Required Parameters

AOptional user provided coefficient (must work with CUSTOM 'liquid_penetration_model')
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Optional user provided coefficient (must work with CUSTOM 'liquid_penetration_model')
QROptional user provided activation energy parameter (K) (must work with CUSTOM 'liquid_penetration_model')
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Optional user provided activation energy parameter (K) (must work with CUSTOM 'liquid_penetration_model')
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
burnupBurnup material name (only required by ANL_LS and ANL_CONSERVATIVE 'liquid_penetration_model' and INTRINSIC 'fuel_melting_model' with PU_19 'fuel_pu')
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:Burnup material name (only required by ANL_LS and ANL_CONSERVATIVE 'liquid_penetration_model' and INTRINSIC 'fuel_melting_model' with PU_19 'fuel_pu')
calculate_fuel_melting_thicknessFalseWhether to calculate the thickness of the fuel that has melted.
Default:False
C++ Type:bool
Controllable:No
Description:Whether to calculate the thickness of the fuel that has melted.
cladding_inner_radiusInner radius of the cladding.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Inner radius of the cladding.
computeTrueWhen false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
Default:True
C++ Type:bool
Controllable:No
Description:When false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
constant_onNONEWhen ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
Default:NONE
C++ Type:MooseEnum
Options:NONE, ELEMENT, SUBDOMAIN
Controllable:No
Description:When ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
declare_suffixAn optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:An optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.
fuel_bottom_positionThe axial position of the bottom of the fuel slug.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The axial position of the bottom of the fuel slug.
fuel_elongation_ppName of the Postprocessor that tracks fuel elongation.
C++ Type:PostprocessorName
Unit:(no unit assumed)
Controllable:No
Description:Name of the Postprocessor that tracks fuel elongation.
fuel_heightThe height (axial length) of the fuel slug to be added to the slug bottom position to get the top axial position of the fuel.
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The height (axial length) of the fuel slug to be added to the slug bottom position to get the top axial position of the fuel.
fuel_to_cladding_melting_ratio3.94Volume ratio of molten fuel to molten cladding.
Default:3.94
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Volume ratio of molten fuel to molten cladding.
mesh_generatorThe name of the generator to use as the prefix for mesh meta data about pin geometry parameters.
C++ Type:MeshGeneratorName
Controllable:No
Description:The name of the generator to use as the prefix for mesh meta data about pin geometry parameters.
onset_temperatureOptional user provided onset temperature (K) (must work with TSAI or CUSTOM 'liquid_penetration_model')
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Optional user provided onset temperature (K) (must work with TSAI or CUSTOM 'liquid_penetration_model')

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

(assessment/metallic_fuel/FBTA/analysis/fbta_run/FBTA_base.i)
(test/tests/metallic_fuel_liquid_cladding_penetration/liquid_penetration_anl.i)
(assessment/metallic_fuel/FBTA/analysis/steady_state/common_inputs/test_base.i)
(test/tests/metallic_fuel_liquid_cladding_penetration/liquid_penetration.i)
(test/tests/metallic_fuel_liquid_cladding_penetration/liquid_penetration_low_temp.i)
(test/tests/metallic_fuel_liquid_cladding_penetration/liquid_penetration_err.i)
(test/tests/metallic_fuel_liquid_cladding_penetration/liquid_penetration_mg.i)
(assessment/metallic_fuel/WPF/analysis/X425_T418/X425_base.i)
(test/tests/metallic_fuel_liquid_cladding_penetration/liquid_penetration_ad.i)
(assessment/metallic_fuel/WPF/analysis/FM-1/FM_base.i)

References

Y. Miao, A. Oaks, S. Shu, A. Yacout, C. Matthews, and S. Novascone. Metallic fuel liquid cladding penetration and fuel liquefication models evaluation based on comprehensive out-of-pile transient assessment case in BISON. Technical Report in preparation, Argonne National Laboratory, 2024.

@techreport{miao_et_al_2024,
    author = "Miao, Y. and Oaks, A. and Shu, S. and Yacout, A. and Matthews, C. and Novascone, S.",
    title = "{Metallic fuel liquid cladding penetration and fuel liquefication models evaluation based on comprehensive out-of-pile transient assessment case in BISON}",
    year = "2024",
    number = "in preparation",
    institution = "Argonne National Laboratory"
}

S. Shu, Y. Miao, A. Oaks, K. Mo, C. Tomchik, and A. M. Yacout. Improved correlations of the fuel/cladding liquid penetration rate with the out-of-pile transient database. Nuclear Engineering and Design, 417:112819, 2024.

@article{SHU20230808,
    author = "Shu, S. and Miao, Y. and Oaks, A. and Mo, K. and Tomchik, C. and Yacout, A. M.",
    title = "Improved correlations of the fuel/cladding liquid penetration rate with the out-of-pile transient database",
    journal = "Nuclear Engineering and Design",
    volume = "417",
    pages = "112819",
    year = "2024",
    publisher = "Elsevier"
}

Hanchung Tsai. Fuel/cladding compatibility in irradiated metallic fuel pins at elevated temperatures. In 1990 International Fast Reactor Safety Meeting. August 12-16 1990.

@inproceedings{Tsai1990,
    author = "Tsai, Hanchung",
    booktitle = "1990 International Fast Reactor Safety Meeting",
    month = "August 12-16",
    title = "Fuel/cladding compatibility in irradiated metallic fuel pins at elevated temperatures",
    year = "1990"
}

(test/tests/metallic_fuel_liquid_cladding_penetration/liquid_penetration.i)

# This test is to verify the calculation in MetallicFuelLiquidCladdingPenetration

[Mesh]
  [mesh]
    type = GeneratedMeshGenerator
    dim = 1
  []
[]

[Problem]
  solve = false
[]

[AuxVariables]
  [temp]
    initial_condition = 1000
  []
[]

[AuxKernels]
  [temp]
    type = ConstantAux
    variable = temp
    value = 1000
  []
[]

[Materials]
  [mybu]
    type = GenericConstantMaterial
    prop_names = 'mybu'
    prop_values = '0.05' # in fraction
  []
  [liquid_penetration]
    type = MetallicFuelLiquidCladdingPenetration
    temperature = temp
    fuel_bottom_position = 0.0
    fuel_height = 1.0
    outputs = all
  []
[]

[Executioner]
  type = Transient
  num_steps = 15
  dt = 1000
[]

[Postprocessors]
  [penetration_avg]
    type = ElementAverageValue
    variable = liquid_penetration
  []
  [temp_avg]
    type = ElementAverageValue
    variable = temp
  []
  [fuel_melting_avg]
    type = ElementAverageValue
    variable = fuel_melting_thickness
    enable = false
  []
[]

[Outputs]
  [csv]
    type = CSV
    file_base = liquid_penetration_out
  []
[]

(assessment/metallic_fuel/FBTA/analysis/fbta_run/FBTA_base.i)

file_base_str = 'fbta_run/FBTA_output/${fbta_exp_id}/${fbta_exp_id}_1D_${pen_model_enum}'
fipd_submodule_dir = '../../../../../../../fipd-bison-integration-data/'

[Mesh]
  [fmg]
    type = FileMeshGenerator
    file = ${raw '../../../gold/fbta_initialization/load_params_inputs/ ${fbta_exp_id} _loading_params_out.e'}
    use_for_exodus_restart = 1
  []
  [gen]
    type = FIPDRodletMeshGenerator
    fipd_geom_file = ${raw ' ${fipd_submodule_dir} / ${exp_id} / ${pin_id} / ${pin_id} _design.csv'}

    gap_bottom_length = 0.31e-3 # arbitrary
    cladding_bottom_plug_length = 2.24e-3 # arbitrary
    cladding_top_plug_length = 2.24e-3 # arbitrary

    cladding_sidewall_radial_elements = 10
    cladding_sidewall_axial_element_numbers = '2 150 150'
    cladding_top_plug_radial_elements = 10
    cladding_top_plug_axial_elements = 5
    cladding_bottom_plug_radial_elements = 10
    cladding_bottom_plug_axial_elements = 5
    fuel_radial_elements = 6
    fuel_axial_element_intervals = '0 1'
    fuel_axial_element_numbers = '150'
    use_default_cladding_sidewall_axial_element_intervals = true
    elem_type = QUAD4
  []
  final_generator = fmg
  coord_type = RZ
[]

[GlobalParams]
  order = FIRST
  family = LAGRANGE
  displacements = 'disp_x disp_y'
  X_Pu = ${fuel_pu}
  X_Zr = ${fuel_zr}
[]

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

[Variables]
  [temp]
    initial_from_file_var = temp
    initial_from_file_timestep = LATEST
  []
[]

[Kernels]
  [heat]
    type = ADHeatConduction
    variable = temp
    extra_vector_tags = 'ref'
  []
  [heat_ie_f]
    type = ADHeatConductionTimeDerivative
    variable = temp
    extra_vector_tags = 'ref'
    block = 3
    density_name = density
  []
  [heat_ie_c]
    type = ADHeatConductionTimeDerivative
    variable = temp
    extra_vector_tags = 'ref'
    block = 1
    density_name = density
  []
[]

[ThermalContact]
  [thermal_contact]
    type = GapHeatTransfer
    variable = temp
    primary = cladding_left
    secondary = fuel_right
    quadrature = true
    gap_conductivity = 61.0
    min_gap = 0.5e-03
  []
[]

[BCs]
  [ext_temp]
    type = ADFunctionDirichletBC
    boundary = 'cladding_right'
    variable = temp
    function = outer_temp
  []
[]

[Functions]
  [outer_temp]
    type = ConstantFunction
    value = ${test_temp}
  []
  [clad_thick]
    type = MeshPropertyFunction
    mesh_generator = 'gen'
    mesh_property_name = 'cladding_thickness'
  []
  [id_pen_vpp_func]
    type = MetallicFuelWastageDegradationFunction
    vectorpostprocessor_name = id_pen_trans
    argument_column = y
    wastage_type = ID
    value_column = pen_thick_aux
    use_metadata = true
    degradation_factor = 0.001
    mesh_generator = 'gen'
    transition_width = 1E-4
  []
  [fuel_melt_func]
    type = MetallicFuelMeltingFunction
    vectorpostprocessor_name = fuel_melting
    argument_column = y
    value_column = melt_fuel_aux
    use_metadata = true
    mesh_generator = 'gen'
    transition_width = 2e-4
  []
[]

[AuxVariables]
  [disp_x]
    initial_from_file_var = disp_x
    initial_from_file_timestep = LATEST
  []
  # y and z seem needed for ParaView diplaced mesh visualization
  [disp_y]
  []
  [disp_z]
  []
  [porosity]
    family = MONOMIAL
    order = CONSTANT
    initial_from_file_var = porosity
    initial_from_file_timestep = LATEST
  []
  [burnup_aux]
    family = MONOMIAL
    order = CONSTANT
    initial_from_file_var = burnup
    initial_from_file_timestep = LATEST
  []
  [pen_thick_aux]
    family = MONOMIAL
    order = CONSTANT
  []
  [id_wast_ss_aux]
    family = MONOMIAL
    order = CONSTANT
    initial_from_file_var = id_wastage
    initial_from_file_timestep = LATEST
  []
  [od_wast_ss_aux]
    family = MONOMIAL
    order = CONSTANT
    initial_from_file_var = od_wastage
    initial_from_file_timestep = LATEST
  []
  [total_id_loss]
    family = MONOMIAL
    order = CONSTANT
  []
  [melt_fuel_aux]
    family = MONOMIAL
    order = CONSTANT
  []
  [func_val1]
    block = 1
  []
  [func_val3]
    block = 3
  []
[]

[AuxKernels]
  [assign_pen_thick_aux]
    type = ADMaterialRealAux
    variable = pen_thick_aux
    property = liquid_penetration
  []
  [assign_total_id_loss]
    type = ParsedAux
    variable = total_id_loss
    coupled_variables = 'id_wast_ss_aux pen_thick_aux'
    expression = 'id_wast_ss_aux + pen_thick_aux'
  []
  [assign_melt_fuel_aux]
    type = ADMaterialRealAux
    variable = melt_fuel_aux
    property = fuel_melting_thickness
  []
  [func_val1]
    type = FunctionAux
    function = id_pen_vpp_func
    variable = func_val1
    block = 1
  []
  [func_val3]
    type = FunctionAux
    function = fuel_melt_func
    variable = func_val3
    block = 3
  []
[]

[Materials]
  [burnup]
    type = ADParsedMaterial
    property_name = burnup
    coupled_variables = burnup_aux
    expression = burnup_aux
  []
  [pen_thick_rate]
    type = ADMetallicFuelLiquidCladdingPenetration
    liquid_penetration_model = ${pen_model_enum}
    fuel_pu = ${fuel_pu_enum}
    temperature = temp
    mesh_generator = gen
    burnup = burnup
    calculate_fuel_melting_thickness = true
    fuel_melting_model = INTRINSIC
  []
  [metal_fuel_thermal]
    type = ADUPuZrThermal
    block = 3
    spheat_model = savage
    thcond_model = lanl
    porosity = porosity
    temperature = temp
  []
  [fuel_density]
    type = ADStrainAdjustedDensity
    displacements = 'disp_x disp_y'
    block = 3
    strain_free_density = ${fuel_density}
  []
  [clad_thermal]
    type = ADHT9Thermal
    block = 1
    temperature = temp
  []
  [clad_density]
    type = ADStrainAdjustedDensity
    block = 1
    strain_free_density = 7874.0
  []
  [porosity]
    type = ADParsedMaterial
    coupled_variables = 'porosity'
    expression = 'porosity'
    property_name = porosity
  []
[]

[Preconditioning]
  [SMP]
    type = SMP
    full = true
    solve_type = 'PJFNK'
  []
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'
  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -ksp_gmres_restart'
  petsc_options_value = 'lu       superlu_dist                  101'
  line_search = 'none'

  end_time = ${run_time}
  dt = ${fparse max(1.0,floor(run_time/1000))}

  l_max_its = 100
  l_tol = 1e-3
  nl_max_its = 50
  nl_rel_tol = 1e-5
  nl_abs_tol = 1e-7
[]

[UserObjects]
  [clad_comsumption]
    type = Terminator
    expression = 'clad_total_id_loss >= clad_thick'
    execute_on = TIMESTEP_END
  []
[]

[Postprocessors]
  [clad_thick]
    type = FunctionValuePostprocessor
    function = clad_thick
    outputs = none
  []
  [clad_pen_thick]
    type = SideAverageValue
    variable = pen_thick_aux
    boundary = cladding_left
  []
  [fuel_melt_thick]
    type = SideAverageValue
    variable = melt_fuel_aux
    boundary = fuel_right
  []
  [clad_total_id_loss]
    type = SideAverageValue
    variable = total_id_loss
    boundary = cladding_left
  []
  [bu_min]
    type = ADElementExtremeMaterialProperty
    mat_prop = burnup
    value_type = min
    enable = false
  []
  [bu_max]
    type = ADElementExtremeMaterialProperty
    mat_prop = burnup
    value_type = max
    enable = false
  []
[]

[VectorPostprocessors]
  [id_pen_trans]
    type = SideValueSampler
    variable = pen_thick_aux
    boundary = cladding_left
    sort_by = y
    outputs = none
  []
  [id_wastage_ss]
    type = SideValueSampler
    variable = id_wast_ss_aux
    boundary = cladding_left
    sort_by = y
    outputs = none
  []
  [od_wastage_ss]
    type = SideValueSampler
    variable = od_wast_ss_aux
    boundary = cladding_right
    sort_by = y
    outputs = none
  []
  [id_total]
    type = SideValueSampler
    variable = total_id_loss
    boundary = cladding_left
    sort_by = y
    outputs = none
  []
  [fuel_melting]
    type = SideValueSampler
    variable = melt_fuel_aux
    boundary = fuel_right
    sort_by = y
    outputs = none
  []
[]

[Outputs]
  console = true
  [csv]
    type = CSV
    time_step_interval = 100
    file_base = ${file_base_str}
  []
  [exodus]
    type = Exodus
    time_step_interval = 100
    file_base = ${file_base_str}
    enable = false
  []
  [cp]
    type = Checkpoint
    wall_time_interval = 1e10
  []
[]

!include FBTA_RUNNING_PARAMS_FILE

(test/tests/metallic_fuel_liquid_cladding_penetration/liquid_penetration_anl.i)

# This test is to verify the calculation in MetallicFuelLiquidCladdingPenetration

[Mesh]
  [mesh]
    type = GeneratedMeshGenerator
    dim = 1
  []
[]

[Problem]
  solve = false
[]

[AuxVariables]
  [temp]
    initial_condition = 1073
  []
[]

[AuxKernels]
  [temp]
    type = ConstantAux
    variable = temp
    value = 1073
  []
[]

[Materials]
  [mybu]
    type = GenericConstantMaterial
    prop_names = 'mybu'
    prop_values = '0.12' # in fraction
  []
  [liquid_penetration]
    type = MetallicFuelLiquidCladdingPenetration
    liquid_penetration_model = ANL_CONSERVATIVE
    fuel_pu = Pu_0
    temperature = temp
    fuel_bottom_position = 0.0
    fuel_height = 1.0
    burnup = mybu
    outputs = all
  []
[]

[Executioner]
  type = Transient
  num_steps = 150
  dt = 100
[]

[Postprocessors]
  [penetration_avg]
    type = ElementAverageValue
    variable = liquid_penetration
  []
  [temp_avg]
    type = ElementAverageValue
    variable = temp
  []
[]

[Outputs]
  [csv]
    type = CSV
    file_base = liquid_penetration_anl_conserve_pu0
  []
[]

(assessment/metallic_fuel/FBTA/analysis/steady_state/common_inputs/test_base.i)

# IFR Steady State Irradiation Base Input File
# Inspired by X441 Assessment Case

fipd_submodule_dir = '../../../../../../../fipd-bison-integration-data/'

gap_bottom_length = 0.31e-3
top_bot_cladding_height = 2.24e-3
# calculations
cladding_ir = '${fparse fuel_radius + cladding_gap_width}'
gas_plenum_height = '${fparse plenum_volume / pi / cladding_ir^2}'
fuel_y_start = '${fparse gap_bottom_length + top_bot_cladding_height}'
alpha_start = 877
alpha_end = 936
bubble_concentration = 1e15

cladding_block = 'cladding'

clad_n_rad = 10

[GlobalParams]
  order = FIRST
  energy_per_fission = 3.2e-11 # J/fission
  displacements = 'disp_x disp_y'
  alpha_transition_end = ${alpha_end}
  alpha_transition_start = ${alpha_start}
[]

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

[Mesh]
  # Pin design parameters from FIPD database
  [gen]
    type = FIPDRodletMeshGenerator
    fipd_geom_file = ${raw ' ${fipd_submodule_dir} / ${exp_id} / ${pin_id} / ${pin_id} _design.csv'}

    gap_bottom_length = 0.31e-3 # arbitrary
    cladding_bottom_plug_length = 2.24e-3 # arbitrary
    cladding_top_plug_length = 2.24e-3 # arbitrary

    cladding_sidewall_radial_elements = ${clad_n_rad}
    cladding_sidewall_axial_element_numbers = '2 150 150'
    # use_tri_for_cladding_sidewall = '0 1 0'
    cladding_top_plug_radial_elements = 10
    cladding_top_plug_axial_elements = 5
    cladding_bottom_plug_axial_elements = 5
    fuel_radial_elements = 6
    fuel_axial_element_intervals = '0 1'
    fuel_axial_element_numbers = '250'

    use_default_cladding_sidewall_axial_element_intervals = true

    elem_type = QUAD4
    make_stand = true
    make_cap = true
    cap_axial_elements = 15
    stand_axial_elements = 15
  []

  [sodium_height]
    type = SideSetsFromBoundingBoxGenerator
    input = gen
    bottom_left = '0 0 0'
    top_right = '${fparse cladding_ir + cladding_thickness} ${fparse fuel_y_start + fuel_height} 0'
    included_boundaries = 'cladding_inside_right'
    boundary_new = '1005'
  []
  [gas_height]
    type = SideSetsFromBoundingBoxGenerator
    input = sodium_height
    bottom_left = '0 ${fparse fuel_y_start + fuel_height} 0'
    top_right = '${fparse cladding_ir + cladding_thickness} ${fparse fuel_y_start + fuel_height + gas_plenum_height + top_bot_cladding_height} 0'
    included_boundaries = 'cladding_inside_right'
    boundary_new = '1006'
  []
  [sodium_plenum_rename]
    type = RenameBoundaryGenerator
    input = gas_height
    old_boundary = '1005 1006'
    new_boundary = 'sodium_height gas_height'
  []

  patch_size = 40
  patch_update_strategy = always
  partitioner = centroid
  centroid_partitioner_direction = y
  coord_type = RZ
[]

[Variables]
  [temp]
    initial_condition = 298
    block = 'fuel ${cladding_block} cap stand'
  []
  [disp_x]
    block = 'fuel ${cladding_block} cap stand'
  []
  [disp_y]
    block = 'fuel ${cladding_block} cap stand'
  []
[]

[Functions]
  [fflux_axial_peaking_factors] # Fast flux peaking factor from FIPD database; used for fuel related simulations
    type = FIPDAxialProfileFunction
    data_file = ${raw ' ${fipd_submodule_dir} / ${exp_id} / ${pin_id} / peakingfactor_flux_relative_ ${pin_id} .csv'}
    use_metadata = true
    mesh_generator = gen
    zero_ends = true
    data_shift_type = peaking
    extrapolate_to_zero = true
  []
  [fflux_axial_peaking_factors_elongate] # Fast flux peaking factor from FIPD database; used for cladding related simulations
    type = FIPDAxialProfileFunction
    data_file = ${raw ' ${fipd_submodule_dir} / ${exp_id} / ${pin_id} / peakingfactor_flux_relative_ ${pin_id} .csv'}
    use_metadata = true
    mesh_generator = gen
    zero_ends = true
    data_shift_type = peaking
    extrapolate_to_zero = true
    fuel_elongation_pp = max_fuel_elongation # pp used to track fuel elongation
  []
  [flux_history] # Time-dependent pin average fast flux from FIPD database
    type = PiecewiseLinear
    data_file = ${raw ' ${fipd_submodule_dir} / ${exp_id} / ${pin_id} / flux_history_ ${pin_id} .csv'}
  []
  [clad_od_temp] # Time-dependent cladding OD temperature from FIPD database
    type = FIPDAxialProfileFunction
    data_file = ${raw ' ${fipd_submodule_dir} / ${exp_id} / ${pin_id} / clad_od_temp_history_ ${pin_id} .csv'}
    use_metadata = true
    mesh_generator = gen
  []
  [ab_sodium_vol]
    type = MeshPropertyFunction
    mesh_generator = gen
    mesh_property_name = sodium_volume
    scale_factor = -1.0
  []
  [sodium_volume]
    # Need to account for the factor that hot pressing is also occupying the open pores
    type = ParsedFunction
    symbol_names = 'porosity_sodium_logging_avg volume_fuel raw_sodium_vol temp_sodium_avg'
    symbol_values = 'porosity_sodium_logging_avg volume_fuel ab_sodium_vol temp_sodium_avg'
    # Note the the symbol before volume_fuel should be negative as volume_fuel itself is negative
    expression = 'raw_sodium_vol * 954 / (1102 - 0.23 * temp_sodium_avg) - volume_fuel * porosity_sodium_logging_avg'
  []
  [power_history] # Time-dependent pin average power from FIPD database
    type = PiecewiseLinear
    data_file = ${raw ' ${fipd_submodule_dir} / ${exp_id} / ${pin_id} / power_history_ ${pin_id} .csv'}
  []

  [axial_peaking_factors]
    type = FIPDAxialProfileFunction
    data_file = ${raw ' ${fipd_submodule_dir} / ${exp_id} / ${pin_id} / peakingfactor_power_relative_ ${pin_id} .csv'}
    use_metadata = true
    mesh_generator = gen
    zero_ends = true
    data_shift_type = peaking
  []
  [axial_peaking_factors_extended]
    type = FIPDAxialProfileFunction
    data_file = ${raw ' ${fipd_submodule_dir} / ${exp_id} / ${pin_id} / peakingfactor_power_relative_ ${pin_id} .csv'}
    use_metadata = true
    mesh_generator = gen
    zero_ends = true
    data_shift_type = peaking
    fuel_elongation_pp = max_fuel_elongation # pp used to track fuel elongation
  []
  [anisotropic_swelling_factor]
    type = ParsedFunction
    symbol_names = 'disp_x_fuel_radial_surface_avg disp_y_fuel_top_surface_avg fuel_height fuel_radius'
    symbol_values = 'disp_x_fuel_radial_surface_avg disp_y_fuel_top_surface_avg ${fuel_height} ${fuel_radius}'
    expression = '(disp_x_fuel_radial_surface_avg / ${fuel_radius}) / (disp_y_fuel_top_surface_avg / ${fuel_height})'
  []
  [gap_thermal_conductivity]
    type = ParsedFunction
    expression = '124.67 - 0.11381 * t + 5.5226e-5 * t^2 - 1.1842e-8 * t^3'
  []
  [id_vpp_func] # vpp_function used to track FCCI-related cladding degradation.
    type = MetallicFuelWastageDegradationFunction
    vectorpostprocessor_name = id_wastage
    argument_column = y
    wastage_type = ID
    value_column = wastage_thickness
    use_metadata = true
    degradation_factor = 0.001
    mesh_generator = 'gen'
    transition_width = 1E-4
  []
  [od_vpp_func] # vpp_function used to track CCCI-related cladding degradation.
    type = MetallicFuelWastageDegradationFunction
    vectorpostprocessor_name = od_wastage
    argument_column = y
    wastage_type = OD
    value_column = cc_wastage_thickness
    use_metadata = true
    degradation_factor = 0.001
    mesh_generator = 'gen'
    transition_width = 1E-4
  []
  [fuel_melt_func]
    type = MetallicFuelMeltingFunction
    vectorpostprocessor_name = fuel_melting
    argument_column = y
    value_column = fuel_melting_thickness
    use_metadata = true
    mesh_generator = 'gen'
    transition_width = 2e-4
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [fuel]
    block = fuel
    strain = FINITE
    generate_output = 'firstinv_strain stress_xx stress_yy stress_zz vonmises_stress hydrostatic_stress creep_strain_xx creep_strain_yy creep_strain_zz elastic_strain_xx elastic_strain_yy elastic_strain_zz strain_xx strain_yy strain_zz'
    extra_vector_tags = 'ref'
    eigenstrain_names = 'fuel_thermal_strain solid_swelling_eigenstrain'
    use_automatic_differentiation = true
    volumetric_locking_correction = true
  []
[]

[Kernels]
  [gravity]
    type = ADGravity
    block = 'fuel ${cladding_block}'
    variable = disp_y
    value = -9.81
    extra_vector_tags = 'ref'
  []
  [heat]
    type = ADHeatConduction
    block = 'fuel ${cladding_block} cap stand'
    variable = temp
    extra_vector_tags = 'ref'
  []
  [heat_ie]
    type = ADHeatConductionTimeDerivative
    block = 'fuel ${cladding_block} cap stand'
    variable = temp
    extra_vector_tags = 'ref'
  []
  [heat_source]
    type = ADFissionRateHeatSource
    variable = temp
    block = 'fuel'
    fission_rate = fission_rate
    extra_vector_tags = 'ref'
    energy_deposited_in_fuel = 0.95
  []

  [disp_x_dt]
    type = ADTimeDerivative
    variable = disp_x
    block = 'cap stand'
    extra_vector_tags = 'ref'
  []
  [disp_y_dt]
    type = ADTimeDerivative
    variable = disp_y
    block = 'cap stand'
    extra_vector_tags = 'ref'
  []
  [disp_x_diff]
    type = ADMatAnisoDiffusion
    variable = disp_x
    block = 'cap stand'
    diffusivity = d_x
    extra_vector_tags = 'ref'
  []
  [disp_y_diff]
    type = ADMatDiffusion
    variable = disp_y
    block = 'cap stand'
    diffusivity = 1e8
    extra_vector_tags = 'ref'
  []
[]

[UserObjects]
  [pin_geometry]
    type = FuelPinGeometry
    clad_bottom = cladding_outside_bottom
    clad_inner_wall = cladding_inside_right
    clad_outer_wall = cladding_outside_right
    clad_top = cladding_outside_top
    pellet_exteriors = fuel_outside_all
  []
  [fuel_thm_exp]
    type = LayeredAverage
    variable = fuel_thermal_strain_xx
    direction = y
    num_layers = 1000
    block = fuel
  []
  [clad_thm_exp]
    type = LayeredAverage
    variable = clad_thermal_eigenstrain_xx
    direction = y
    num_layers = 1000
    block = ${cladding_block}
  []
[]

[Contact]
  [fuel_cladding_mechanical]
    primary = cladding_inside_right
    secondary = fuel_outer_radial_surface
    model = coulomb
    friction_coefficient = 0.1
    formulation = mortar
    c_normal = '${fparse 1e17 * magic_factor}'
    c_tangential = '${fparse 1e19 * magic_factor}'
    correct_edge_dropping = true
  []
[]

[MortarGapHeatTransfer]
  [inside2outside]
    temperature = temp
    boundary = 'cladding_inside_right'
    gap_conductivity_function = gap_thermal_conductivity
    gap_conductivity_function_variable = temp
    primary_boundary = cladding_inside_right
    secondary_boundary = fuel_contact_surfaces
    gap_flux_options = 'CONDUCTION'
    ghost_point_neighbors = true
  []
[]

[BCs]
  [no_x_all]
    type = ADDirichletBC
    variable = disp_x
    boundary = 'centerline cap_top'
    value = 0.0
    preset = false
  []
  [no_y_clad]
    type = ADDirichletBC
    variable = disp_y
    boundary = 'cladding_inside_bottom'
    value = 0.0
    preset = false
  []
  [Pressure]
    [coolantPressure]
      boundary = 'cladding_outside_right'
      factor = 0.151e6
      use_automatic_differentiation = true
    []
  []
  [PlenumPressure]
    [plenumPressure]
      boundary = 'inside_surfaces'
      initial_pressure = 84116 # in Pa, 12.2 psi
      startup_time = 0
      R = 8.3143
      temperature = temp_gas_avg
      volume = volume_plenum
      output = plenum_pressure
      material_input = fg_released
      use_automatic_differentiation = true
    []
  []
  [surf] # Setting temperature BC base on FIPD data
    type = ADFunctionDirichletBC
    variable = temp
    boundary = 'cladding_outside_bottom cladding_outside_right cladding_outside_top'
    function = clad_od_temp
  []
[]

[AuxVariables]
  [cumulative_damage_index]
    order = CONSTANT
    family = MONOMIAL
  []
  [relx]
  []
  [clad_thm_exp]
    order = CONSTANT
    family = MONOMIAL
    block = '${cladding_block}'
  []
  [clad_thermal_eigenstrain_xx]
    order = CONSTANT
    family = MONOMIAL
    block = '${cladding_block}'
  []
  [fuel_thermal_strain_xx]
    order = CONSTANT
    family = MONOMIAL
    block = fuel
  []
  [fuel_thermal_strain_yy]
    order = CONSTANT
    family = MONOMIAL
    block = fuel
  []
  [fuel_thm_exp]
    order = CONSTANT
    family = MONOMIAL
    block = fuel
  []
  [func_val1]
  []
  [func_val2]
  []
  [func_val3]
  []
  # OPTD Dummy during this stage
  [pen_thick_aux]
    family = MONOMIAL
    order = CONSTANT
    block = 'fuel ${cladding_block}'
  []
  [total_id_reduction]
    family = MONOMIAL
    order = CONSTANT
    block = 'fuel ${cladding_block}'
  []
  [fast_neutron_fluence_aux]
    order = CONSTANT
    family = MONOMIAL
    block = '${cladding_block}'
  []
[]

[AuxKernels]
  [func_val1]
    type = FunctionAux
    function = id_vpp_func
    variable = func_val1
    block = ${cladding_block}
  []
  [func_val2]
    type = FunctionAux
    function = od_vpp_func
    variable = func_val2
    block = ${cladding_block}
  []
  [func_val3]
    type = FunctionAux
    function = fuel_melt_func
    variable = func_val3
    block = fuel
  []
  [cdf_amount]
    block = '${cladding_block}'
    type = MaterialRealAux
    property = cdf_failure
    variable = cumulative_damage_index
  []
  [relx_aux]
    type = ParsedAux
    variable = relx
    block = fuel
    use_xyzt = true
    expression = 'x / ${fuel_radius}'
  []
  [clad_thm_exp]
    type = SpatialUserObjectAux
    variable = clad_thm_exp
    execute_on = 'initial timestep_end'
    user_object = clad_thm_exp
    block = '${cladding_block}'
  []
  [clad_thermal_eigenstrain_xx]
    type = ADRankTwoAux
    rank_two_tensor = cladding_thermal_eigenstrain
    variable = clad_thermal_eigenstrain_xx
    index_j = 0
    index_i = 0
    execute_on = 'initial timestep_end'
    block = '${cladding_block}'
  []
  [fuel_thermal_strain_xx]
    type = ADRankTwoAux
    rank_two_tensor = fuel_thermal_strain
    variable = fuel_thermal_strain_xx
    index_j = 0
    index_i = 0
    execute_on = 'initial timestep_end'
    block = fuel
  []
  [fuel_thermal_strain_yy]
    type = ADRankTwoAux
    rank_two_tensor = fuel_thermal_strain
    variable = fuel_thermal_strain_yy
    index_j = 1
    index_i = 1
    execute_on = 'initial timestep_end'
    block = fuel
  []
  [fuel_thm_exp]
    type = SpatialUserObjectAux
    variable = fuel_thm_exp
    execute_on = 'initial timestep_end'
    user_object = fuel_thm_exp
    block = fuel
  []

  # OPTD
  [assign_pen_thick_aux]
    type = ADMaterialRealAux
    variable = pen_thick_aux
    property = liquid_penetration
    block = 'fuel ${cladding_block}'
  []
  [assign_total_id_reduction]
    type = ParsedAux
    variable = total_id_reduction
    coupled_variables = 'pen_thick_aux wastage_thickness'
    expression = 'pen_thick_aux + wastage_thickness'
    block = 'fuel ${cladding_block}'
  []
[]

[Materials]
  [fuel_pen]
    type = ADMetallicFuelLiquidCladdingPenetration
    temperature = temp
    mesh_generator = gen
    fuel_elongation_pp = max_fuel_elongation
    liquid_penetration_model = 'ANL_CONSERVATIVE'
    fuel_pu = Pu_0
    burnup = burnup
    outputs = all
    calculate_fuel_melting_thickness = true
    block = 'fuel ${cladding_block}'
  []
  [d_x]
    type = ADConstantAnisotropicMobility
    tensor = '1e3 0 0
              0   1e6 0
              0   0 0'
    M_name = d_x
  []
  [cap_thcond]
    type = ADGenericConstantMaterial
    prop_names = 'thermal_conductivity specific_heat density'
    prop_values = '65 1200 830'
    block = 'cap stand'
    outputs = all
  []
  [interconnected_porosity]
    type = ADParsedMaterial
    block = 'fuel'
    property_name = interconnected_porosity
    material_property_names = 'porosity interconnectivity'
    expression = 'porosity * interconnectivity'
    outputs = all
  []

  [fission_rate]
    type = ADUPuZrFissionRate
    rod_linear_power = power_history
    axial_power_profile = axial_peaking_factors
    pellet_radius = ${fuel_radius}
    # initial_X_Zr=${initial_X_Zr}
    X_Zr = ${initial_X_Zr}
    X_Pu_function = ${X_Pu}
    block = 'fuel'
    outputs = all
  []
  [fission_rate_elongate]
    type = ADUPuZrFissionRate
    rod_linear_power = power_history
    axial_power_profile = axial_peaking_factors_extended
    pellet_radius = ${fuel_radius}
    # initial_X_Zr = ${initial_X_Zr}
    X_Zr = ${initial_X_Zr}
    X_Pu_function = ${X_Pu}
    block = '${cladding_block}'
    outputs = all
    fission_rate_name = fission_rate
  []
  [burnup]
    type = ADUPuZrBurnup
    initial_X_Zr = ${initial_X_Zr}
    initial_X_Pu = ${X_Pu}
    density = ${fuel_density}
    block = 'fuel'
    outputs = all
  []
  [burnup_elongate]
    type = ADUPuZrBurnup
    initial_X_Pu = ${X_Pu}
    initial_X_Zr = ${initial_X_Zr}
    outputs = all
    block = '${cladding_block}'
    density = ${fuel_density}
    burnup_name = burnup
  []
  [fuel_elastic_stress]
    type = ADComputeMultipleInelasticStress
    inelastic_models = 'hotpress fuel_upuzrcreep gas_swelling'
    block = 'fuel'
    outputs = all
  []
  [hotpress]
    type = ADUPuZrHotPressingStressUpdate
    block = 'fuel'
    outputs = all
    surface_energy = 1.6
    plenum_pressure = plenum_pressure
    porosity_name = porosity
    max_inelastic_increment = 1e-1
    interconnectivity = interconnectivity
    bubble_concentration = ${bubble_concentration}
    temperature = temp
    creep_model = MFH
    fission_rate = fission_rate
    atomic_volume = 2.15e-29
    porosity_start = 0.01
    porosity_end = 0
    grain_boundary_D0 = 4e-29
    grain_boundary_Q = 0
    absolute_tolerance = 1e-9
  []
  [porosity]
    type = ADPorosityFromStrain
    block = 'fuel'
    initial_porosity = 1e-10
    inelastic_strain = 'combined_inelastic_strain'
    outputs = all
  []
  [fuel_elasticity_tensor]
    type = ADUPuZrElasticityTensor
    X_Zr = ${initial_X_Zr}
    X_Pu = ${X_Pu}
    youngs_model = LANL
    block = 'fuel'
    temperature = temp
    use_old_porosity = true
    outputs = all
    output_properties = 'youngs_modulus poissons_ratio'
  []
  [fuel_upuzrcreep]
    type = ADUPuZrCreepUpdate
    block = 'fuel'
    temperature = temp
    porosity = porosity
    use_old_porosity = true
    max_inelastic_increment = 1e-3
    outputs = all
    automatic_differentiation_return_mapping = false
  []
  [fuel_thermal_expansion]
    type = ADUPuZrThermalExpansionEigenstrain
    block = 'fuel'
    temperature = temp
    stress_free_temperature = 298.0
    eigenstrain_name = fuel_thermal_strain
    outputs = all
    thermal_expansion_model = LANL
    X_Zr = ${initial_X_Zr}
    X_Pu = ${X_Pu}
  []
  [gas_swelling]
    type = ADSimpleFissionGasViscoplasticityStressUpdate
    temperature = temp
    outputs = all
    block = 'fuel'
    bubble_concentration = ${bubble_concentration}
    initial_bubble_concentration = ${bubble_concentration}
    compute_interconnectivity = true
    fission_gas_yield = 0.3017 #0.25
    fission_rate = fission_rate
    initial_atoms_per_bubble = 1e-05
    initial_bubble_radius = 1e-15
    initial_fgm_dissolved = 0
    interconnection_cutoff = 0.99
    interconnection_initiating_porosity = 0.23
    interconnection_terminating_porosity = 0.25
    max_inelastic_increment = 1e-2
    retained_gas_fraction = 0.25
    interconnection_dependent_retained_gas_fraction = 0.5
    surface_energy = 1.6
    anisotropic_factor = 0.26
    initial_porosity = 1e-10
    fuel_melting_function = fuel_melt_func
  []
  [solid_swelling]
    type = ADBurnupDependentEigenstrain
    eigenstrain_name = solid_swelling_eigenstrain
    block = 'fuel'
    swelling_name = 'solid_swelling'
    outputs = all
    anisotropic_factor = 0.26
  []
  [metal_fuel_thermal]
    type = ADUPuZrThermal
    block = 'fuel'
    X_Zr = ${initial_X_Zr}
    X_Pu = ${X_Pu}
    spheat_model = savage
    porosity = porosity
    temperature = temp
    outputs = all
    porosity_model = logged
    sodium_logged_porosity = sodium_logged_porosity
  []
  [sodium_logging]
    type = ADUPuZrSodiumLogging
    block = 'fuel'
    porosity = porosity
    interconnectivity = interconnectivity
    sodium_infiltration_fraction = 0.28
    outputs = all
  []
  [fuel_density]
    type = ADStrainAdjustedDensity
    block = 'fuel'
    strain_free_density = ${fuel_density}
    outputs = all
  []
  [fast_neutron_flux]
    type = ADFastNeutronFlux
    calculate_fluence = true
    axial_power_profile = fflux_axial_peaking_factors
    rod_ave_lin_pow = flux_history
    block = fuel
    factor = 1.0
    outputs = all
  []
  [fast_neutron_flux_elongate]
    type = ADFastNeutronFlux
    calculate_fluence = true
    axial_power_profile = fflux_axial_peaking_factors_elongate
    rod_ave_lin_pow = flux_history
    block = '${cladding_block}'
    factor = 1.0
    outputs = all
  []
[]

[Dampers]
  [disp_x]
    type = MaxIncrement
    variable = disp_x
    max_increment = 1e-4
  []
  [disp_y]
    type = MaxIncrement
    variable = disp_y
    max_increment = 1e-3
  []
  [temp]
    type = MaxIncrement
    variable = temp
    max_increment = 50
  []
[]

[Preconditioning]
  [vcp]
    type = VCP
    full = true
    primary_variable = 'disp_x disp_y temp'
    preconditioner = 'LU'
    adaptive_condensation = true
    lm_variable = 'fuel_cladding_mechanical_normal_lm fuel_cladding_mechanical_tangential_lm inside2outside_thermal_lm'
    is_lm_coupling_diagonal = true
  []
[]

[Executioner]
  type = Transient
  solve_type = 'NEWTON'
  petsc_options = '-snes_ksp_ew -snes_converged_reason -ksp_converged_reason'
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_type -mat_mffd_err -pc_factor_shift_type -pc_factor_shift_amount -snes_force_iteration'
  petsc_options_value = 'lu    superlu_dist   1e-5          NONZERO               1e-15 1'
  line_search = 'none'
  snesmf_reuse_base = false
  verbose = true

  l_max_its = 60
  nl_max_its = 20
  nl_rel_tol = 1e-7
  nl_abs_tol = 1e-8 #1e9

  end_time = ${run_time}
  dtmin = 1
  dtmax = ${max_time_step}

  automatic_scaling = true
  compute_scaling_once = false
  off_diagonals_in_auto_scaling = true
  ignore_variables_for_autoscaling = 'fuel_cladding_mechanical_normal_lm fuel_cladding_mechanical_tangential_lm inside2outside_thermal_lm'

  [TimeStepper]
    type = IterationAdaptiveDT
    timestep_limiting_postprocessor = time_step_limit
    force_step_every_function_point = true
    timestep_limiting_function = power_history
    dt = 1e2
    iteration_window = 4
    optimal_iterations = 10
  []
[]

[Postprocessors]
  [_dt]
    type = TimestepSize
  []
  # elemental temperatures
  [temp_fuel_avg]
    type = ElementAverageValue
    variable = temp
    block = 'fuel'
    execute_on = 'initial timestep_end'
  []
  [temp_fuel_max]
    type = ElementExtremeValue
    variable = temp
    block = 'fuel'
  []
  [temp_fuel_min]
    type = ElementExtremeValue
    variable = temp
    block = 'fuel'
    value_type = min
  []
  [temp_cladding_avg]
    type = ElementAverageValue
    variable = temp
    block = '${cladding_block}'
  []
  [temp_cladding_max]
    type = ElementExtremeValue
    variable = temp
    block = '${cladding_block}'
  []
  [temp_cladding_min]
    type = ElementExtremeValue
    variable = temp
    block = '${cladding_block}'
    value_type = min
  []

  # boundary temperatures
  [temp_gas_avg]
    type = SideAverageValue
    boundary = 'gas_height cladding_inside_top'
    variable = temp
    execute_on = 'initial timestep_end'
  []
  [temp_sodium_avg]
    type = ElementAverageValue
    block = 'cap'
    variable = temp
    execute_on = 'initial timestep_end'
  []
  [temp_inside_surfaces_avg]
    type = SideAverageValue
    boundary = 'inside_surfaces'
    variable = temp
    execute_on = 'initial timestep_end'
  []
  [temp_fuel_centerline_avg]
    type = AxisymmetricCenterlineAverageValue
    boundary = 'centerline'
    variable = temp
  []
  [temp_fuel_centerline_max]
    type = NodalExtremeValue
    boundary = 'centerline'
    variable = temp
  []
  [temp_fuel_centerline_min]
    type = NodalExtremeValue
    boundary = 'centerline'
    variable = temp
    value_type = min
  []
  [temp_fuel_surface_avg]
    type = SideAverageValue
    boundary = 'fuel_outer_radial_surface'
    variable = temp
  []
  [temp_fuel_surface_max]
    type = NodalExtremeValue
    boundary = 'fuel_outer_radial_surface'
    variable = temp
  []
  [temp_fuel_surface_min]
    type = NodalExtremeValue
    boundary = 'fuel_outer_radial_surface'
    variable = temp
    value_type = min
  []
  [temp_cladding_inside_right_avg]
    type = SideAverageValue
    boundary = 'cladding_inside_right'
    variable = temp
  []
  [temp_cladding_inside_right_max]
    type = NodalExtremeValue
    boundary = 'cladding_inside_right'
    variable = temp
  []
  [temp_cladding_outside_right_avg]
    type = SideAverageValue
    boundary = 'cladding_outside_right'
    variable = temp
  []

  # stresses
  [stress_vonmises_fuel_avg]
    type = ElementAverageValue
    variable = vonmises_stress
    block = 'fuel'
  []
  [stress_vonmises_fuel_max]
    type = ElementExtremeValue
    variable = vonmises_stress
    block = 'fuel'
  []
  [stress_vonmises_fuel_min]
    type = ElementExtremeValue
    variable = vonmises_stress
    value_type = min
    block = 'fuel'
  []
  [stress_hydro_fuel_avg]
    type = ElementAverageValue
    variable = hydrostatic_stress
    block = 'fuel'
  []
  [stress_hydro_fuel_max]
    type = ElementExtremeValue
    variable = hydrostatic_stress
    block = 'fuel'
  []
  [stress_hydro_fuel_min]
    type = ElementExtremeValue
    variable = hydrostatic_stress
    value_type = min
    block = 'fuel'
  []
  [stress_vonmises_cladding_avg]
    type = ElementAverageValue
    variable = vonmises_stress
    block = '${cladding_block}'
  []
  [stress_vonmises_cladding_max]
    type = ElementExtremeValue
    variable = vonmises_stress
    block = '${cladding_block}'
  []
  [stress_vonmises_cladding_min]
    type = ElementExtremeValue
    variable = vonmises_stress
    value_type = min
    block = '${cladding_block}'
  []
  [stress_hydro_cladding_avg]
    type = ElementAverageValue
    variable = hydrostatic_stress
    block = '${cladding_block}'
  []
  [stress_hydro_cladding_max]
    type = ElementExtremeValue
    variable = hydrostatic_stress
    block = '${cladding_block}'
  []
  [stress_hydro_cladding_min]
    type = ElementExtremeValue
    variable = hydrostatic_stress
    value_type = min
    block = '${cladding_block}'
  []
  [contact_pressure_max]
    type = NodalExtremeValue
    variable = fuel_cladding_mechanical_normal_lm
    boundary = 'fuel_outer_radial_surface'
  []

  # strain information
  [strain_solid_swelling_fuel_avg]
    type = ElementAverageValue
    variable = solid_swelling
    block = 'fuel'
  []
  [strain_gas_swelling_fuel_avg]
    type = ElementAverageValue
    variable = effective_fission_gas_strain
    block = 'fuel'
  []
  [strain_hot_pressing_fuel_avg]
    type = ElementAverageValue
    variable = effective_hot_pressing_strain
    block = 'fuel'
  []
  [strain_volumetric_fuel_avg]
    type = ElementAverageValue
    variable = firstinv_strain
    block = 'fuel'
  []
  [strain_axial_fuel_avg]
    type = ParsedPostprocessor
    pp_names = 'disp_y_fuel_top_surface_avg disp_y_fuel_bottom_surface_avg'
    expression = '(disp_y_fuel_top_surface_avg - disp_y_fuel_bottom_surface_avg) / ${fuel_height}'
  []
  [disp_y_fuel_top_surface_avg]
    type = SideAverageValue
    variable = disp_y
    boundary = 'fuel_top'
  []
  [disp_y_fuel_top_surface_max]
    type = NodalExtremeValue
    variable = disp_y
    boundary = 'fuel_top'
  []
  [disp_y_fuel_bottom_surface_avg]
    type = SideAverageValue
    variable = disp_y
    boundary = 'fuel_bottom'
  []
  [disp_y_fuel_bottom_surface_max]
    type = NodalExtremeValue
    variable = disp_y
    boundary = 'fuel_bottom'
  []
  [disp_x_fuel_radial_surface_max]
    type = NodalExtremeValue
    variable = disp_x
    boundary = 'fuel_outer_radial_surface'
  []
  [disp_x_fuel_radial_surface_avg]
    type = SideAverageValue
    variable = disp_x
    boundary = 'fuel_outer_radial_surface'
  []
  [disp_x_cladding_interior_max]
    type = NodalExtremeValue
    variable = disp_x
    boundary = 'cladding_inside_right'
  []
  [disp_x_cladding_interior_min]
    type = NodalExtremeValue
    variable = disp_x
    boundary = 'cladding_inside_right'
    value_type = min
  []
  [disp_x_cladding_interior_avg]
    type = SideAverageValue
    variable = disp_x
    boundary = 'cladding_inside_right'
  []
  [disp_x_cladding_exterior_max]
    type = NodalExtremeValue
    variable = disp_x
    boundary = 'cladding_outside_right'
  []
  [disp_x_cladding_exterior_avg]
    type = SideAverageValue
    variable = disp_x
    boundary = 'cladding_outside_right'
  []
  [anisotropic_swelling_factor]
    type = FunctionValuePostprocessor
    function = anisotropic_swelling_factor
  []
  [max_fuel_elongation]
    type = NodalExtremeValue
    variable = disp_y
    boundary = fuel_outside_all
  []

  # geometric information
  [volume_cladding_interior]
    type = InternalVolume
    boundary = 'cladding_inside_all'
  []
  [volume_fuel]
    type = InternalVolume
    boundary = 'fuel_outside_all'
    execute_on = 'initial timestep_end'
  []
  [volume_plenum]
    type = InternalVolume
    boundary = 'inside_surfaces'
    execute_on = 'initial timestep_end'
    addition = sodium_volume
  []
  [plenum_ratio]
    type = ParsedPostprocessor
    pp_names = 'volume_plenum volume_fuel'
    expression = 'volume_plenum / volume_fuel'
    execute_on = 'initial timestep_end'
  []
  [volume_sodium]
    type = FunctionValuePostprocessor
    function = sodium_volume
    execute_on = 'initial timestep_end'
  []

  # energy information
  [flux_clad]
    type = ADSideDiffusiveFluxIntegral
    variable = temp
    boundary = 'cladding_inside_right'
    diffusivity = thermal_conductivity
  []
  [flux_fuel]
    type = ADSideDiffusiveFluxIntegral
    variable = temp
    boundary = 'fuel_contact_surfaces'
    diffusivity = thermal_conductivity
  []
  [power_integral]
    type = ADElementIntegralPower
    variable = temp
    use_material_fission_rate = true
    fission_rate_material = fission_rate
    block = fuel
  []
  [linear_heat_generation_rate]
    type = FunctionValuePostprocessor
    function = power_history
    scale_factor = 0.01
  []
  [burnup_avg]
    type = ElementAverageValue
    block = fuel
    variable = burnup
  []
  [burnup_max]
    type = ElementExtremeValue
    block = fuel
    variable = burnup
  []
  [fission_rate_avg]
    type = ElementAverageValue
    variable = fission_rate
    block = fuel
  []

  # fission gas information
  [fg_produced]
    type = ADElementIntegralMaterialProperty
    mat_prop = fgm_produced
    block = fuel
  []
  [fg_released]
    type = ADElementIntegralMaterialProperty
    mat_prop = fgm_released
    block = fuel
    execute_on = 'initial timestep_end'
  []
  [fg_percent]
    type = FGRPercent
    fission_gas_released = fg_released
    fission_gas_generated = fg_produced
  []
  [interconnected_porosity_fuel_avg]
    type = ElementAverageValue
    variable = interconnected_porosity
    block = fuel
    execute_on = 'initial timestep_end'
  []
  [porosity_fuel_avg]
    type = ElementAverageValue
    variable = porosity
    block = fuel
  []
  [porosity_fuel_max]
    type = ElementExtremeValue
    variable = porosity
    block = fuel
  []
  [porosity_fuel_min]
    type = ElementExtremeValue
    variable = porosity
    value_type = min
    block = fuel
  []
  [porosity_sodium_logging_avg]
    type = ElementAverageValue
    variable = sodium_logged_porosity
    block = fuel
  []

  # extras
  [actual_time_step_limit]
    type = MaterialTimeStepPostprocessor
    block = 'fuel ${cladding_block}'
    outputs = none
  []
  [time_step_limit]
    type = ParsedPostprocessor
    expression = 'if(actual_time_step_limit > 1e6, 1e6, actual_time_step_limit)'
    pp_names = 'actual_time_step_limit'
  []
  [max_wastagethickness]
    type = ElementExtremeValue
    value_type = max
    variable = wastage_thickness
    # outputs = 'console'
  []
  [max_wst_temp]
    type = ElementExtremeValue
    value_type = max
    variable = temp
    proxy_variable = wastage_thickness
    block = '${cladding_block}'
  []
  [max_wst_burnup]
    type = ElementExtremeValue
    value_type = max
    variable = burnup
    proxy_variable = wastage_thickness
    block = '${cladding_block}'
  []
  [max_cdf]
    type = ElementExtremeValue
    value_type = max
    variable = cumulative_damage_index
  []
[]

[VectorPostprocessors]
  [id_wastage]
    type = FuelRodLineValueSampler
    variable = wastage_thickness
    material = 'clad'
    fraction = 0.0
    num_points = 600
    orientation = 'vertical'
    fuel_pin_geometry = 'pin_geometry'
    execute_on = 'initial timestep_end'
    allow_duplicate_execution_on_initial = true
    outputs = csv_wst_a
  []
  [id_pen_total]
    type = FuelRodLineValueSampler
    variable = total_id_reduction
    material = 'clad'
    fraction = 0.0
    num_points = 600
    orientation = 'vertical'
    fuel_pin_geometry = 'pin_geometry'
    execute_on = 'initial timestep_end'
    allow_duplicate_execution_on_initial = true
    outputs = none
  []
  [od_wastage]
    type = FuelRodLineValueSampler
    variable = cc_wastage_thickness
    material = 'clad'
    fraction = 1.0
    num_points = 600
    orientation = 'vertical'
    fuel_pin_geometry = 'pin_geometry'
    execute_on = 'initial timestep_end'
    allow_duplicate_execution_on_initial = true
    outputs = none
  []
  [fuel_melting]
    type = FuelRodLineValueSampler
    variable = fuel_melting_thickness
    material = 'fuel'
    fraction = 1.0
    num_points = 600
    orientation = 'vertical'
    fuel_pin_geometry = 'pin_geometry'
    execute_on = 'initial timestep_end'
    allow_duplicate_execution_on_initial = true
    outputs = none
  []
[]

[PerformanceMetricOutputs]
  outputs = 'console'
[]

[Outputs]
  # print_linear_residuals = true
  # color = true
  # perf_graph = true
  # sync_times = ${time_spots}

  [checkpoint]
    type = Checkpoint
    time_step_interval = 1
    enable = false
  []
  [exodus]
    type = Exodus
    sync_only = true
    sync_times = ${time_spots}
    enable = false
    additional_execute_on = 'FAILED'
  []
  [exodus_final]
    type = Exodus
    execute_on = 'FINAL'
  []
  [console]
    type = Console
    show = 'time_step_size temp_fuel_avg temp_fuel_centerline_max temp_cladding_avg temp_cladding_max stress_vonmises_fuel_max stress_hydro_fuel_max stress_hydro_fuel_min contact_pressure_max strain_axial_fuel_avg power_integral burnup_avg fission_rate_avg fg_percent porosity_fuel_avg time_step_limit anisotropic_swelling_factor plenum_ratio volume_fuel volume_plenum max_wastagethickness max_cdf'
  []
  [csv_wst_a]
    type = CSV
    sync_only = true
    sync_times = ${time_spots_a}
    enable = ${enable_a}
    execute_postprocessors_on = none
    create_latest_symlink = true
  []
  [csv_general]
    type = CSV
    sync_only = true
    sync_times = ${time_spots}
    enable = true
  []
[]

[Debug]
  show_var_residual = 'disp_x disp_y temp'
  show_var_residual_norms = true
[]

(test/tests/metallic_fuel_liquid_cladding_penetration/liquid_penetration.i)

# This test is to verify the calculation in MetallicFuelLiquidCladdingPenetration

[Mesh]
  [mesh]
    type = GeneratedMeshGenerator
    dim = 1
  []
[]

[Problem]
  solve = false
[]

[AuxVariables]
  [temp]
    initial_condition = 1000
  []
[]

[AuxKernels]
  [temp]
    type = ConstantAux
    variable = temp
    value = 1000
  []
[]

[Materials]
  [mybu]
    type = GenericConstantMaterial
    prop_names = 'mybu'
    prop_values = '0.05' # in fraction
  []
  [liquid_penetration]
    type = MetallicFuelLiquidCladdingPenetration
    temperature = temp
    fuel_bottom_position = 0.0
    fuel_height = 1.0
    outputs = all
  []
[]

[Executioner]
  type = Transient
  num_steps = 15
  dt = 1000
[]

[Postprocessors]
  [penetration_avg]
    type = ElementAverageValue
    variable = liquid_penetration
  []
  [temp_avg]
    type = ElementAverageValue
    variable = temp
  []
  [fuel_melting_avg]
    type = ElementAverageValue
    variable = fuel_melting_thickness
    enable = false
  []
[]

[Outputs]
  [csv]
    type = CSV
    file_base = liquid_penetration_out
  []
[]

(test/tests/metallic_fuel_liquid_cladding_penetration/liquid_penetration_low_temp.i)

# This test is to verify the calculation in MetallicFuelLiquidCladdingPenetration

[Mesh]
  [mesh]
    type = GeneratedMeshGenerator
    dim = 1
  []
[]

[Problem]
  solve = false
[]

[AuxVariables]
  [temp]
    initial_condition = 900
  []
[]

[AuxKernels]
  [temp]
    type = ConstantAux
    variable = temp
    value = 900
  []
[]

[Materials]
  [liquid_penetration]
    type = MetallicFuelLiquidCladdingPenetration
    temperature = temp
    fuel_bottom_position = 0.0
    fuel_height = 1.0
    outputs = all
  []
[]

[Executioner]
  type = Transient
  num_steps = 15
  dt = 1000
[]

[Postprocessors]
  [penetration_avg]
    type = ElementAverageValue
    variable = liquid_penetration
  []
  [temp_avg]
    type = ElementAverageValue
    variable = temp
  []
[]

[Outputs]
  csv = true
[]

(test/tests/metallic_fuel_liquid_cladding_penetration/liquid_penetration_err.i)

# This test is to verify the calculation in MetallicFuelLiquidCladdingPenetration

[Mesh]
  [mesh]
    type = GeneratedMeshGenerator
    dim = 1
  []
[]

[Problem]
  solve = false
[]

[AuxVariables]
  [temp]
    initial_condition = 1000
  []
[]

[AuxKernels]
  [temp]
    type = ConstantAux
    variable = temp
    value = 1000
  []
[]

[Materials]
  [liquid_penetration]
    type = MetallicFuelLiquidCladdingPenetration
    temperature = temp
    # fuel_bottom_position = 0.0
    # fuel_height = 1.0
    outputs = all
  []
[]

[Executioner]
  type = Transient
  num_steps = 1
  dt = 1000
[]

(test/tests/metallic_fuel_liquid_cladding_penetration/liquid_penetration_mg.i)

# This test is to verify the calculation in MetallicFuelLiquidCladdingPenetration

[Mesh]
  [mesh]
    type = GeneratedMeshGenerator
    dim = 2
    ny = 10
  []
  [amd]
    type = AddMetaDataGenerator
    input = mesh
    real_scalar_metadata_names = 'cladding_start cladding_bottom_gap_width fuel_height'
    real_scalar_metadata_values = '0.0 0.1 0.4'
  []
[]

[Functions]
  [fuel_elong]
    type = ParsedFunction
    expression = 't/1000/15*0.5'
  []
[]

[Problem]
  solve = false
[]

[AuxVariables]
  [temp]
    initial_condition = 1000
  []
[]

[AuxKernels]
  [temp]
    type = ConstantAux
    variable = temp
    value = 1000
  []
[]

[Materials]
  [liquid_penetration]
    type = MetallicFuelLiquidCladdingPenetration
    temperature = temp
    mesh_generator = amd
    fuel_elongation_pp = fuel_elong_pp
    outputs = all
  []
[]

[Executioner]
  type = Transient
  num_steps = 15
  dt = 1000
[]

[Postprocessors]
  [penetration_avg]
    type = ElementAverageValue
    variable = liquid_penetration
  []
  [penetration_min]
    type = ElementExtremeValue
    variable = liquid_penetration
    value_type = min
  []
  [penetration_max]
    type = ElementExtremeValue
    variable = liquid_penetration
  []
  [temp_avg]
    type = ElementAverageValue
    variable = temp
  []
  [fuel_elong_pp]
    type = FunctionValuePostprocessor
    function = fuel_elong
  []
[]

[Outputs]
  csv = true
[]

(assessment/metallic_fuel/WPF/analysis/X425_T418/X425_base.i)

# X425 Steady State Irradiation Base Input File

gap_bottom_length = 0.31e-3
top_bot_cladding_height = 2.24e-3
# calculations
cladding_ir = '${fparse fuel_radius + cladding_gap_width}'
gas_plenum_height = '${fparse plenum_volume / pi / cladding_ir^2}'
fuel_y_start = '${fparse gap_bottom_length + top_bot_cladding_height}'
alpha_start = 877
alpha_end = 936
bubble_concentration = 1e15

cladding_block = 'cladding cladding_tri'

# A relatively coarse radial mesh density can be used
# since localized refining is done by TRI3 elements
clad_n_rad = 10

[GlobalParams]
  order = FIRST
  energy_per_fission = 3.2e-11 # J/fission
  displacements = 'disp_x disp_y'
  alpha_transition_end = ${alpha_end}
  alpha_transition_start = ${alpha_start}
[]

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

[Mesh]
  # Pin design parameters from FIPD database
  [gen]
    type = FIPDRodletMeshGenerator
    fipd_geom_file = ${raw '../../../../../fipd-bison-integration-data/ ${exp_id} / ${pin_id} / ${pin_id} _design.csv'}

    gap_bottom_length = 0.31e-3 # arbitrary
    cladding_bottom_plug_length = 2.24e-3 # arbitrary
    cladding_top_plug_length = 2.24e-3 # arbitrary

    cladding_sidewall_radial_elements = ${clad_n_rad}
    cladding_sidewall_axial_element_intervals = '0 0.540 0.625 1.0'
    cladding_sidewall_axial_element_numbers = '150 1000 150'
    use_tri_for_cladding_sidewall = '0 1 0'
    cladding_top_plug_radial_elements = 10
    cladding_top_plug_axial_elements = 5
    cladding_bottom_plug_axial_elements = 5
    fuel_radial_elements = 10
    fuel_axial_element_intervals = '0 1'
    fuel_axial_element_numbers = '1000'
    tri_element_size_factor = 0.4
    elem_type = QUAD4
    make_stand = true
    make_cap = true
    cap_axial_elements = 15
    stand_axial_elements = 15
  []
  [sodium_height]
    type = SideSetsFromBoundingBoxGenerator
    input = gen
    bottom_left = '0 0 0'
    top_right = '${fparse cladding_ir + cladding_thickness} ${fparse fuel_y_start + fuel_height} 0'
    included_boundaries = 'cladding_inside_right'
    boundary_new = '1005'
  []
  [gas_height]
    type = SideSetsFromBoundingBoxGenerator
    input = sodium_height
    bottom_left = '0 ${fparse fuel_y_start + fuel_height} 0'
    top_right = '${fparse cladding_ir + cladding_thickness} ${fparse fuel_y_start + fuel_height + gas_plenum_height + top_bot_cladding_height} 0'
    included_boundaries = 'cladding_inside_right'
    boundary_new = '1006'
  []
  [sodium_plenum_rename]
    type = RenameBoundaryGenerator
    input = gas_height
    old_boundary = '1005 1006'
    new_boundary = 'sodium_height gas_height'
  []

  patch_size = 40
  patch_update_strategy = always
  partitioner = centroid
  centroid_partitioner_direction = y
  coord_type = RZ
[]

[Variables]
  [temp]
    initial_condition = 298
    block = 'fuel ${cladding_block} cap stand'
  []
  [disp_x]
    block = 'fuel ${cladding_block} cap stand'
  []
  [disp_y]
    block = 'fuel ${cladding_block} cap stand'
  []
[]

[Functions]
  [fflux_axial_peaking_factors] # Fast flux peaking factor from FIPD database; used for fuel related simulations
    type = FIPDAxialProfileFunction
    data_file = ${raw '../../../../../fipd-bison-integration-data/ ${exp_id} / ${pin_id} /peakingfactor_flux_relative_ ${pin_id} .csv'}
    use_metadata = true
    mesh_generator = gen
    zero_ends = true
    data_shift_type = peaking
    extrapolate_to_zero = true
  []
  [fflux_axial_peaking_factors_elongate] # Fast flux peaking factor from FIPD database; used for cladding related simulations
    type = FIPDAxialProfileFunction
    data_file = ${raw '../../../../../fipd-bison-integration-data/ ${exp_id} / ${pin_id} /peakingfactor_flux_relative_ ${pin_id} .csv'}
    use_metadata = true
    mesh_generator = gen
    zero_ends = true
    data_shift_type = peaking
    extrapolate_to_zero = true
    fuel_elongation_pp = max_fuel_elongation # pp used to track fuel elongation
  []
  [flux_history] # Time-dependent pin average fast flux from FIPD database
    type = PiecewiseLinear
    data_file = ${raw '../../../../../fipd-bison-integration-data/ ${exp_id} / ${pin_id} /flux_history_ ${pin_id} .csv'}
  []
  [clad_od_temp] # Time-dependent cladding OD temperature from FIPD database
    type = FIPDAxialProfileFunction
    data_file = ${raw '../../../../../fipd-bison-integration-data/ ${exp_id} / ${pin_id} /clad_od_temp_history_ ${pin_id} .csv'}
    use_metadata = true
    mesh_generator = gen
  []
  [ab_sodium_vol]
    type = MeshPropertyFunction
    mesh_generator = gen
    mesh_property_name = sodium_volume
    scale_factor = -1.0
  []
  [sodium_volume]
    # Need to account for the factor that hot pressing is also occupying the open pores
    type = ParsedFunction
    symbol_names = 'porosity_sodium_logging_avg volume_fuel raw_sodium_vol temp_sodium_avg'
    symbol_values = 'porosity_sodium_logging_avg volume_fuel ab_sodium_vol temp_sodium_avg'
    # Note the the symbol before volume_fuel should be negative as volume_fuel itself is negative
    expression = 'raw_sodium_vol * 954 / (1012 - 0.23 * temp_sodium_avg) - volume_fuel * porosity_sodium_logging_avg'
  []
  [power_history] # Time-dependent pin average power from FIPD database
    type = PiecewiseLinear
    data_file = ${raw '../../../../../fipd-bison-integration-data/ ${exp_id} / ${pin_id} /power_history_ ${pin_id} .csv'}
  []

  [axial_peaking_factors]
    type = FIPDAxialProfileFunction
    data_file = ${raw '../../../../../fipd-bison-integration-data/ ${exp_id} / ${pin_id} /peakingfactor_power_relative_ ${pin_id} .csv'}
    use_metadata = true
    mesh_generator = gen
    zero_ends = true
    data_shift_type = peaking
  []
  [axial_peaking_factors_extended]
    type = FIPDAxialProfileFunction
    data_file = ${raw '../../../../../fipd-bison-integration-data/ ${exp_id} / ${pin_id} /peakingfactor_power_relative_ ${pin_id} .csv'}
    use_metadata = true
    mesh_generator = gen
    zero_ends = true
    data_shift_type = peaking
    fuel_elongation_pp = max_fuel_elongation # pp used to track fuel elongation
  []
  [anisotropic_swelling_factor]
    type = ParsedFunction
    symbol_names = 'disp_x_fuel_radial_surface_avg disp_y_fuel_top_surface_avg fuel_height fuel_radius'
    symbol_values = 'disp_x_fuel_radial_surface_avg disp_y_fuel_top_surface_avg ${fuel_height} ${fuel_radius}'
    expression = '(disp_x_fuel_radial_surface_avg / ${fuel_radius}) / (disp_y_fuel_top_surface_avg / ${fuel_height})'
  []
  [gap_thermal_conductivity]
    type = ParsedFunction
    expression = '124.67 - 0.11381 * t + 5.5226e-5 * t^2 - 1.1842e-8 * t^3'
  []
  [id_vpp_func] # vpp_function used to track FCCI-related cladding degradation.
    type = MetallicFuelWastageDegradationFunction
    vectorpostprocessor_name = id_wastage
    argument_column = y
    wastage_type = ID
    value_column = wastage_thickness
    use_metadata = true
    degradation_factor = 0.001
    mesh_generator = 'gen'
    transition_width = 1E-4
  []
  [od_vpp_func] # vpp_function used to track CCCI-related cladding degradation.
    type = MetallicFuelWastageDegradationFunction
    vectorpostprocessor_name = od_wastage
    argument_column = y
    wastage_type = OD
    value_column = cc_wastage_thickness
    use_metadata = true
    degradation_factor = 0.001
    mesh_generator = 'gen'
    transition_width = 1E-4
  []
  [fuel_melt_func]
    type = MetallicFuelMeltingFunction
    vectorpostprocessor_name = fuel_melting
    argument_column = y
    value_column = fuel_melting_thickness
    use_metadata = true
    mesh_generator = 'gen'
    transition_width = 2e-4
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [fuel]
    block = fuel
    strain = FINITE
    generate_output = 'firstinv_strain stress_xx stress_yy stress_zz vonmises_stress hydrostatic_stress creep_strain_xx creep_strain_yy creep_strain_zz elastic_strain_xx elastic_strain_yy elastic_strain_zz strain_xx strain_yy strain_zz'
    extra_vector_tags = 'ref'
    eigenstrain_names = 'fuel_thermal_strain solid_swelling_eigenstrain'
    use_automatic_differentiation = true
    volumetric_locking_correction = true
  []
  [cladding]
    strain = FINITE
    generate_output = 'stress_xx stress_yy stress_zz vonmises_stress hydrostatic_stress creep_strain_xx creep_strain_yy creep_strain_zz elastic_strain_xx elastic_strain_yy elastic_strain_zz strain_xx strain_yy strain_zz'
    extra_vector_tags = 'ref'
    block = '${cladding_block}'
    eigenstrain_names = 'cladding_thermal_eigenstrain'
    use_automatic_differentiation = true
    volumetric_locking_correction = true
  []
[]

[Kernels]
  [gravity]
    type = ADGravity
    block = 'fuel ${cladding_block}'
    variable = disp_y
    value = -9.81
    extra_vector_tags = 'ref'
  []
  [heat]
    type = ADHeatConduction
    block = 'fuel ${cladding_block} cap stand'
    variable = temp
    extra_vector_tags = 'ref'
  []
  [heat_ie]
    type = ADHeatConductionTimeDerivative
    block = 'fuel ${cladding_block} cap stand'
    variable = temp
    extra_vector_tags = 'ref'
  []
  [heat_source]
    type = ADFissionRateHeatSource
    variable = temp
    block = 'fuel'
    fission_rate = fission_rate
    extra_vector_tags = 'ref'
    energy_deposited_in_fuel = 0.95
  []

  [disp_x_dt]
    type = ADTimeDerivative
    variable = disp_x
    block = ' cap stand'
    extra_vector_tags = 'ref'
  []
  [disp_y_dt]
    type = ADTimeDerivative
    variable = disp_y
    block = 'cap stand'
    extra_vector_tags = 'ref'
  []
  [disp_x_diff]
    type = ADMatAnisoDiffusion
    variable = disp_x
    block = 'cap stand'
    diffusivity = d_x
    extra_vector_tags = 'ref'
  []
  [disp_y_diff]
    type = ADMatDiffusion
    variable = disp_y
    block = 'cap stand'
    diffusivity = 1e8
    extra_vector_tags = 'ref'
  []
[]

[UserObjects]
  [pin_geometry]
    type = FuelPinGeometry
    clad_bottom = cladding_outside_bottom
    clad_inner_wall = cladding_inside_right
    clad_outer_wall = cladding_outside_right
    clad_top = cladding_outside_top
    pellet_exteriors = fuel_outside_all
  []
  [fuel_thm_exp]
    type = LayeredAverage
    variable = fuel_thermal_strain_xx
    direction = y
    num_layers = 1000
    block = fuel
  []
  [clad_thm_exp]
    type = LayeredAverage
    variable = clad_thermal_eigenstrain_xx
    direction = y
    num_layers = 1000
    block = ${cladding_block}
  []
[]

[Contact]
  [fuel_cladding_mechanical]
    primary = cladding_inside_right
    secondary = fuel_outer_radial_surface
    model = coulomb
    friction_coefficient = 0.1
    formulation = mortar
    c_normal = '${fparse 1e17 * magic_factor}'
    c_tangential = '${fparse 1e19 * magic_factor}'
    correct_edge_dropping = true
  []
[]

[MortarGapHeatTransfer]
  [inside2outside]
    temperature = temp
    boundary = 'cladding_inside_right'
    gap_conductivity_function = gap_thermal_conductivity
    gap_conductivity_function_variable = temp
    primary_boundary = cladding_inside_right
    secondary_boundary = fuel_contact_surfaces
    gap_flux_options = 'CONDUCTION'
    ghost_point_neighbors = true
  []
[]

[BCs]
  [no_x_all]
    type = ADDirichletBC
    variable = disp_x
    boundary = 'centerline cap_top'
    value = 0.0
    preset = false
  []
  [no_y_clad]
    type = ADDirichletBC
    variable = disp_y
    boundary = 'cladding_inside_bottom'
    value = 0.0
    preset = false
  []
  [Pressure]
    [coolantPressure]
      boundary = 'cladding_outside_right'
      factor = 0.151e6
      use_automatic_differentiation = true
    []
  []
  [PlenumPressure]
    [plenumPressure]
      boundary = 'inside_surfaces'
      initial_pressure = 84116 # in Pa, 12.2 psi
      startup_time = 0
      R = 8.3143
      temperature = temp_gas_avg
      volume = volume_plenum
      output = plenum_pressure
      material_input = fg_released
      use_automatic_differentiation = true
    []
  []
  [surf] # Setting temperature BC base on FIPD data
    type = ADFunctionDirichletBC
    variable = temp
    boundary = 'cladding_outside_bottom cladding_outside_right cladding_outside_top'
    function = clad_od_temp
  []
[]

[AuxVariables]
  [cumulative_damage_index]
    order = CONSTANT
    family = MONOMIAL
  []
  [relx]
  []
  [clad_thm_exp]
    order = CONSTANT
    family = MONOMIAL
    block = '${cladding_block}'
  []
  [clad_thermal_eigenstrain_xx]
    order = CONSTANT
    family = MONOMIAL
    block = '${cladding_block}'
  []
  [fuel_thermal_strain_xx]
    order = CONSTANT
    family = MONOMIAL
    block = fuel
  []
  [fuel_thermal_strain_yy]
    order = CONSTANT
    family = MONOMIAL
    block = fuel
  []
  [fuel_thm_exp]
    order = CONSTANT
    family = MONOMIAL
    block = fuel
  []
  [func_val1]
  []
  [func_val2]
  []
  [func_val3]
  []
  # OPTD Dummy during this stage
  [pen_thick_aux]
    family = MONOMIAL
    order = CONSTANT
    block = 'fuel ${cladding_block}'
  []
  [total_id_reduction]
    family = MONOMIAL
    order = CONSTANT
    block = 'fuel ${cladding_block}'
  []
  [fast_neutron_fluence_aux]
    order = CONSTANT
    family = MONOMIAL
    block = '${cladding_block}'
  []
[]

[AuxKernels]
  [func_val1]
    type = FunctionAux
    function = id_vpp_func
    variable = func_val1
    block = 'cladding cladding_tri'
  []
  [func_val2]
    type = FunctionAux
    function = od_vpp_func
    variable = func_val2
    block = 'cladding cladding_tri'
  []
  [func_val3]
    type = FunctionAux
    function = fuel_melt_func
    variable = func_val3
    block = fuel
  []
  [cdf_amount]
    block = '${cladding_block}'
    type = MaterialRealAux
    property = cdf_failure
    variable = cumulative_damage_index
  []
  [relx_aux]
    type = ParsedAux
    variable = relx
    block = fuel
    use_xyzt = true
    expression = 'x / ${fuel_radius}'
  []
  [clad_thm_exp]
    type = SpatialUserObjectAux
    variable = clad_thm_exp
    execute_on = 'initial timestep_end'
    user_object = clad_thm_exp
    block = '${cladding_block}'
  []
  [clad_thermal_eigenstrain_xx]
    type = ADRankTwoAux
    rank_two_tensor = cladding_thermal_eigenstrain
    variable = clad_thermal_eigenstrain_xx
    index_j = 0
    index_i = 0
    execute_on = 'initial timestep_end'
    block = '${cladding_block}'
  []
  [fuel_thermal_strain_xx]
    type = ADRankTwoAux
    rank_two_tensor = fuel_thermal_strain
    variable = fuel_thermal_strain_xx
    index_j = 0
    index_i = 0
    execute_on = 'initial timestep_end'
    block = fuel
  []
  [fuel_thermal_strain_yy]
    type = ADRankTwoAux
    rank_two_tensor = fuel_thermal_strain
    variable = fuel_thermal_strain_yy
    index_j = 1
    index_i = 1
    execute_on = 'initial timestep_end'
    block = fuel
  []
  [fuel_thm_exp]
    type = SpatialUserObjectAux
    variable = fuel_thm_exp
    execute_on = 'initial timestep_end'
    user_object = fuel_thm_exp
    block = fuel
  []

  # OPTD
  [assign_pen_thick_aux]
    type = ADMaterialRealAux
    variable = pen_thick_aux
    property = liquid_penetration
    block = 'fuel ${cladding_block}'
  []
  [assign_total_id_reduction]
    type = ParsedAux
    variable = total_id_reduction
    coupled_variables = 'pen_thick_aux wastage_thickness'
    expression = 'pen_thick_aux + wastage_thickness'
    block = 'fuel ${cladding_block}'
  []
[]

[Materials]
  [fuel_pen]
    type = ADMetallicFuelLiquidCladdingPenetration
    temperature = temp
    mesh_generator = gen
    fuel_elongation_pp = max_fuel_elongation
    liquid_penetration_model = 'ANL_CONSERVATIVE'
    fuel_pu = Pu_0
    burnup = burnup
    outputs = all
    calculate_fuel_melting_thickness = true
    block = 'fuel ${cladding_block}'
  []
  [longHT9_failure]
    type = HT9FailureClad
    block = '${cladding_block}'
    method = cdf_long
    temperature = temp
    outputs = all
    hoop_stress = stress_zz # Since 2D-RZ
  []
  [d_x]
    type = ADConstantAnisotropicMobility
    tensor = '1e3 0 0
              0   1e6 0
              0   0 0'
    M_name = d_x
  []
  [cap_thcond]
    type = ADGenericConstantMaterial
    prop_names = 'thermal_conductivity specific_heat density'
    prop_values = '65 1200 830'
    block = 'cap stand'
    outputs = all
  []
  [interconnected_porosity]
    type = ADParsedMaterial
    block = 'fuel'
    property_name = interconnected_porosity
    material_property_names = 'porosity interconnectivity'
    expression = 'porosity * interconnectivity'
    outputs = all
  []

  [fission_rate]
    type = ADUPuZrFissionRate
    rod_linear_power = power_history
    axial_power_profile = axial_peaking_factors
    pellet_radius = ${fuel_radius}
    X_Zr = ${initial_X_Zr}
    X_Pu_function = ${X_Pu}
    block = 'fuel'
    outputs = all
  []
  [fission_rate_elongate]
    type = ADUPuZrFissionRate
    rod_linear_power = power_history
    axial_power_profile = axial_peaking_factors_extended
    pellet_radius = ${fuel_radius}
    X_Zr = ${initial_X_Zr}
    X_Pu_function = ${X_Pu}
    block = '${cladding_block}'
    outputs = all
    fission_rate_name = fission_rate
  []
  [burnup]
    type = ADUPuZrBurnup
    initial_X_Zr = ${initial_X_Zr}
    initial_X_Pu = ${X_Pu}
    density = ${fuel_density}
    block = 'fuel'
    outputs = all
  []
  [burnup_elongate]
    type = ADUPuZrBurnup
    initial_X_Pu = ${X_Pu}
    initial_X_Zr = ${initial_X_Zr}
    outputs = all
    block = '${cladding_block}'
    density = ${fuel_density}
    burnup_name = burnup
  []
  [fuel_elastic_stress]
    type = ADComputeMultipleInelasticStress
    inelastic_models = 'hotpress fuel_upuzrcreep gas_swelling'
    block = 'fuel'
    outputs = all
  []
  [hotpress]
    type = ADUPuZrHotPressingStressUpdate
    block = 'fuel'
    outputs = all
    surface_energy = 1.6
    plenum_pressure = plenum_pressure
    porosity_name = porosity
    max_inelastic_increment = 1e-1
    interconnectivity = interconnectivity
    bubble_concentration = ${bubble_concentration}
    temperature = temp
    creep_model = MFH
    fission_rate = fission_rate
    atomic_volume = 2.15e-29
    porosity_start = 0.01
    porosity_end = 0
    grain_boundary_D0 = 4e-29
    grain_boundary_Q = 0
    absolute_tolerance = 1e-9
  []
  [porosity]
    type = ADPorosityFromStrain
    block = 'fuel'
    initial_porosity = 1e-10
    inelastic_strain = 'combined_inelastic_strain'
    outputs = all
  []
  [fuel_elasticity_tensor]
    type = ADUPuZrElasticityTensor
    X_Zr = ${initial_X_Zr}
    X_Pu = ${X_Pu}
    youngs_model = LANL
    block = 'fuel'
    temperature = temp
    use_old_porosity = true
    outputs = all
    output_properties = 'youngs_modulus poissons_ratio'
  []
  [fuel_upuzrcreep]
    type = ADUPuZrCreepUpdate
    block = 'fuel'
    temperature = temp
    porosity = porosity
    use_old_porosity = true
    max_inelastic_increment = 1e-1
    outputs = all
    automatic_differentiation_return_mapping = false
  []
  [fuel_thermal_expansion]
    type = ADUPuZrThermalExpansionEigenstrain
    block = 'fuel'
    temperature = temp
    stress_free_temperature = 298.0
    eigenstrain_name = fuel_thermal_strain
    outputs = all
    thermal_expansion_model = LANL
    X_Zr = ${initial_X_Zr}
    X_Pu = ${X_Pu}
  []
  [gas_swelling]
    type = ADSimpleFissionGasViscoplasticityStressUpdate
    temperature = temp
    outputs = all
    block = 'fuel'
    bubble_concentration = ${bubble_concentration}
    initial_bubble_concentration = ${bubble_concentration}
    compute_interconnectivity = true
    fission_gas_yield = 0.3017
    fission_rate = fission_rate
    initial_atoms_per_bubble = 1e-05
    initial_bubble_radius = 1e-15
    initial_fgm_dissolved = 0
    interconnection_cutoff = 0.99
    interconnection_initiating_porosity = 0.23
    interconnection_terminating_porosity = 0.25
    max_inelastic_increment = 1e-2
    retained_gas_fraction = 0.25
    interconnection_dependent_retained_gas_fraction = 0.5
    surface_energy = 1.6
    anisotropic_factor = 0.26
    initial_porosity = 1e-10
    fuel_melting_function = fuel_melt_func
  []
  [solid_swelling]
    type = ADBurnupDependentEigenstrain
    eigenstrain_name = solid_swelling_eigenstrain
    block = 'fuel'
    swelling_name = 'solid_swelling'
    outputs = all
    anisotropic_factor = 0.26
  []
  [metal_fuel_thermal]
    type = ADUPuZrThermal
    block = 'fuel'
    X_Zr = ${initial_X_Zr}
    X_Pu = ${X_Pu}
    spheat_model = savage
    porosity = porosity
    temperature = temp
    outputs = all
    porosity_model = logged
    sodium_logged_porosity = sodium_logged_porosity
  []
  [sodium_logging]
    type = ADUPuZrSodiumLogging
    block = 'fuel'
    porosity = porosity
    interconnectivity = interconnectivity
    sodium_infiltration_fraction = 0.28
    outputs = all
  []
  [fuel_density]
    type = ADStrainAdjustedDensity
    block = 'fuel'
    strain_free_density = ${fuel_density}
    outputs = all
  []
  [fast_neutron_flux]
    type = ADFastNeutronFlux
    calculate_fluence = true
    axial_power_profile = fflux_axial_peaking_factors
    rod_ave_lin_pow = flux_history
    block = fuel
    factor = 1.0
    outputs = all
  []
  [fast_neutron_flux_elongate]
    type = ADFastNeutronFlux
    calculate_fluence = true
    axial_power_profile = fflux_axial_peaking_factors_elongate
    rod_ave_lin_pow = flux_history
    block = '${cladding_block}'
    factor = 1.0
    outputs = all
  []
  [cladding_elasticity_tensor]
    type = ADHT9ElasticityTensor
    temperature = temp
    block = '${cladding_block}'
    outputs = all
    id_wastage_degradation_function = id_vpp_func
    od_wastage_degradation_function = od_vpp_func
    output_properties = 'youngs_modulus poissons_ratio'
  []
  [cladding_stress]
    type = ADComputeMultipleInelasticStress
    inelastic_models = 'cladding_creep'
    block = '${cladding_block}'
    outputs = all
  []
  [cladding_creep]
    type = ADHT9CreepUpdate
    block = '${cladding_block}'
    temperature = temp
    outputs = all
    primary_creep_model = MFH
    secondary_creep_model = MFH
    irradiation_creep_model = MFH
    fast_neutron_flux = fast_neutron_flux
  []
  [thermal_expansion]
    type = ADHT9ThermalExpansionEigenstrain
    block = '${cladding_block}'
    temperature = temp
    stress_free_temperature = 298.0
    eigenstrain_name = cladding_thermal_eigenstrain
    outputs = all
  []
  [cladding_thermal]
    type = ADHT9Thermal
    block = '${cladding_block}'
    temperature = temp
    outputs = all
  []
  [cladding_density]
    type = ADStrainAdjustedDensity
    block = '${cladding_block}'
    strain_free_density = '${clad_density}'
    outputs = all
  []
  [wastage_thickness]
    type = ADMetallicFuelWastage
    method = burnup_ht9_opt
    burnup = burnup
    temperature = temp
    scale_factor = 1
    block = '${cladding_block}'
    outputs = all
  []
  [cc_wastage_thickness]
    type = ADMetallicFuelCoolantWastage
    clad_material = HT9
    use_effective_method = true
    temperature = temp
    scale_factor = 1
    block = '${cladding_block}'
    outputs = all
  []
[]

[Dampers]
  [disp_x]
    type = MaxIncrement
    variable = disp_x
    max_increment = 1e-4
  []
  [disp_y]
    type = MaxIncrement
    variable = disp_y
    max_increment = 1e-3
  []
  [temp]
    type = MaxIncrement
    variable = temp
    max_increment = 50
  []
[]

[Preconditioning]
  [vcp]
    type = VCP
    full = true
    primary_variable = 'disp_x disp_y temp'
    preconditioner = 'LU'
    adaptive_condensation = true
    lm_variable = 'fuel_cladding_mechanical_normal_lm fuel_cladding_mechanical_tangential_lm inside2outside_thermal_lm'
    is_lm_coupling_diagonal = true
  []
[]

[Executioner]
  type = Transient
  solve_type = 'NEWTON'
  petsc_options = '-snes_ksp_ew -snes_converged_reason -ksp_converged_reason'
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_type -mat_mffd_err -pc_factor_shift_type -pc_factor_shift_amount -snes_force_iteration'
  petsc_options_value = 'lu    superlu_dist   1e-5          NONZERO               1e-15 1'
  line_search = 'none'
  snesmf_reuse_base = false
  verbose = true

  l_max_its = 60
  nl_max_its = 20
  nl_rel_tol = 1e-7
  nl_abs_tol = 1e-9

  end_time = ${run_time}
  dtmin = 1e-100
  dtmax = ${max_time_step}

  automatic_scaling = true
  compute_scaling_once = false
  off_diagonals_in_auto_scaling = true
  ignore_variables_for_autoscaling = 'fuel_cladding_mechanical_normal_lm fuel_cladding_mechanical_tangential_lm inside2outside_thermal_lm'

  [TimeStepper]
    type = IterationAdaptiveDT
    timestep_limiting_postprocessor = time_step_limit
    force_step_every_function_point = true
    timestep_limiting_function = power_history
    dt = 1e2
    iteration_window = 4
    optimal_iterations = 10
  []
[]

[Postprocessors]
  [_dt]
    type = TimestepSize
  []
  # elemental temperatures
  [temp_fuel_avg]
    type = ElementAverageValue
    variable = temp
    block = 'fuel'
    execute_on = 'initial timestep_end'
  []
  [temp_fuel_max]
    type = ElementExtremeValue
    variable = temp
    block = 'fuel'
  []
  [temp_fuel_min]
    type = ElementExtremeValue
    variable = temp
    block = 'fuel'
    value_type = min
  []
  [temp_cladding_avg]
    type = ElementAverageValue
    variable = temp
    block = '${cladding_block}'
  []
  [temp_cladding_max]
    type = ElementExtremeValue
    variable = temp
    block = '${cladding_block}'
  []
  [temp_cladding_min]
    type = ElementExtremeValue
    variable = temp
    block = '${cladding_block}'
    value_type = min
  []

  # boundary temperatures
  [temp_gas_avg]
    type = SideAverageValue
    boundary = 'gas_height cladding_inside_top'
    variable = temp
    execute_on = 'initial timestep_end'
  []
  [temp_sodium_avg]
    type = ElementAverageValue
    block = 'cap'
    variable = temp
    execute_on = 'initial timestep_end'
  []
  [temp_inside_surfaces_avg]
    type = SideAverageValue
    boundary = 'inside_surfaces'
    variable = temp
    execute_on = 'initial timestep_end'
  []
  [temp_fuel_centerline_avg]
    type = AxisymmetricCenterlineAverageValue
    boundary = 'centerline'
    variable = temp
  []
  [temp_fuel_centerline_max]
    type = NodalExtremeValue
    boundary = 'centerline'
    variable = temp
  []
  [temp_fuel_centerline_min]
    type = NodalExtremeValue
    boundary = 'centerline'
    variable = temp
    value_type = min
  []
  [temp_fuel_surface_avg]
    type = SideAverageValue
    boundary = 'fuel_outer_radial_surface'
    variable = temp
  []
  [temp_fuel_surface_max]
    type = NodalExtremeValue
    boundary = 'fuel_outer_radial_surface'
    variable = temp
  []
  [temp_fuel_surface_min]
    type = NodalExtremeValue
    boundary = 'fuel_outer_radial_surface'
    variable = temp
    value_type = min
  []
  [temp_cladding_inside_right_avg]
    type = SideAverageValue
    boundary = 'cladding_inside_right'
    variable = temp
  []
  [temp_cladding_inside_right_max]
    type = NodalExtremeValue
    boundary = 'cladding_inside_right'
    variable = temp
  []
  [temp_cladding_outside_right_avg]
    type = SideAverageValue
    boundary = 'cladding_outside_right'
    variable = temp
  []

  # stresses
  [stress_vonmises_fuel_avg]
    type = ElementAverageValue
    variable = vonmises_stress
    block = 'fuel'
  []
  [stress_vonmises_fuel_max]
    type = ElementExtremeValue
    variable = vonmises_stress
    block = 'fuel'
  []
  [stress_vonmises_fuel_min]
    type = ElementExtremeValue
    variable = vonmises_stress
    value_type = min
    block = 'fuel'
  []
  [stress_hydro_fuel_avg]
    type = ElementAverageValue
    variable = hydrostatic_stress
    block = 'fuel'
  []
  [stress_hydro_fuel_max]
    type = ElementExtremeValue
    variable = hydrostatic_stress
    block = 'fuel'
  []
  [stress_hydro_fuel_min]
    type = ElementExtremeValue
    variable = hydrostatic_stress
    value_type = min
    block = 'fuel'
  []
  [stress_vonmises_cladding_avg]
    type = ElementAverageValue
    variable = vonmises_stress
    block = '${cladding_block}'
  []
  [stress_vonmises_cladding_max]
    type = ElementExtremeValue
    variable = vonmises_stress
    block = '${cladding_block}'
  []
  [stress_vonmises_cladding_min]
    type = ElementExtremeValue
    variable = vonmises_stress
    value_type = min
    block = '${cladding_block}'
  []
  [stress_hydro_cladding_avg]
    type = ElementAverageValue
    variable = hydrostatic_stress
    block = '${cladding_block}'
  []
  [stress_hydro_cladding_max]
    type = ElementExtremeValue
    variable = hydrostatic_stress
    block = '${cladding_block}'
  []
  [stress_hydro_cladding_min]
    type = ElementExtremeValue
    variable = hydrostatic_stress
    value_type = min
    block = '${cladding_block}'
  []
  [contact_pressure_max]
    type = NodalExtremeValue
    variable = fuel_cladding_mechanical_normal_lm
    boundary = 'fuel_outer_radial_surface'
  []

  # strain information
  [strain_solid_swelling_fuel_avg]
    type = ElementAverageValue
    variable = solid_swelling
    block = 'fuel'
  []
  [strain_gas_swelling_fuel_avg]
    type = ElementAverageValue
    variable = effective_fission_gas_strain
    block = 'fuel'
  []
  [strain_hot_pressing_fuel_avg]
    type = ElementAverageValue
    variable = effective_hot_pressing_strain
    block = 'fuel'
  []
  [strain_volumetric_fuel_avg]
    type = ElementAverageValue
    variable = firstinv_strain
    block = 'fuel'
  []
  [strain_axial_fuel_avg]
    type = ParsedPostprocessor
    pp_names = 'disp_y_fuel_top_surface_avg disp_y_fuel_bottom_surface_avg'
    expression = '(disp_y_fuel_top_surface_avg - disp_y_fuel_bottom_surface_avg) / ${fuel_height}'
  []
  [disp_y_fuel_top_surface_avg]
    type = SideAverageValue
    variable = disp_y
    boundary = 'fuel_top'
  []
  [disp_y_fuel_top_surface_max]
    type = NodalExtremeValue
    variable = disp_y
    boundary = 'fuel_top'
  []
  [disp_y_fuel_bottom_surface_avg]
    type = SideAverageValue
    variable = disp_y
    boundary = 'fuel_bottom'
  []
  [disp_y_fuel_bottom_surface_max]
    type = NodalExtremeValue
    variable = disp_y
    boundary = 'fuel_bottom'
  []
  [disp_x_fuel_radial_surface_max]
    type = NodalExtremeValue
    variable = disp_x
    boundary = 'fuel_outer_radial_surface'
  []
  [disp_x_fuel_radial_surface_avg]
    type = SideAverageValue
    variable = disp_x
    boundary = 'fuel_outer_radial_surface'
  []
  [disp_x_cladding_interior_max]
    type = NodalExtremeValue
    variable = disp_x
    boundary = 'cladding_inside_right'
  []
  [disp_x_cladding_interior_min]
    type = NodalExtremeValue
    variable = disp_x
    boundary = 'cladding_inside_right'
    value_type = min
  []
  [disp_x_cladding_interior_avg]
    type = SideAverageValue
    variable = disp_x
    boundary = 'cladding_inside_right'
  []
  [disp_x_cladding_exterior_max]
    type = NodalExtremeValue
    variable = disp_x
    boundary = 'cladding_outside_right'
  []
  [disp_x_cladding_exterior_avg]
    type = SideAverageValue
    variable = disp_x
    boundary = 'cladding_outside_right'
  []
  [anisotropic_swelling_factor]
    type = FunctionValuePostprocessor
    function = anisotropic_swelling_factor
  []
  [max_fuel_elongation]
    type = NodalExtremeValue
    variable = disp_y
    boundary = fuel_outside_all
  []

  # geometric information
  [volume_cladding_interior]
    type = InternalVolume
    boundary = 'cladding_inside_all'
  []
  [volume_fuel]
    type = InternalVolume
    boundary = 'fuel_outside_all'
    execute_on = 'initial timestep_end'
  []
  [volume_plenum]
    type = InternalVolume
    boundary = 'inside_surfaces'
    execute_on = 'initial timestep_end'
    addition = sodium_volume
  []
  [plenum_ratio]
    type = ParsedPostprocessor
    pp_names = 'volume_plenum volume_fuel'
    expression = 'volume_plenum / volume_fuel'
    execute_on = 'initial timestep_end'
  []
  [volume_sodium]
    type = FunctionValuePostprocessor
    function = sodium_volume
    execute_on = 'initial timestep_end'
  []

  # energy information
  [flux_clad]
    type = ADSideDiffusiveFluxIntegral
    variable = temp
    boundary = 'cladding_inside_right'
    diffusivity = thermal_conductivity
  []
  [flux_fuel]
    type = ADSideDiffusiveFluxIntegral
    variable = temp
    boundary = 'fuel_contact_surfaces'
    diffusivity = thermal_conductivity
  []
  [power_integral]
    type = ADElementIntegralPower
    variable = temp
    use_material_fission_rate = true
    fission_rate_material = fission_rate
    block = fuel
  []
  [linear_heat_generation_rate]
    type = FunctionValuePostprocessor
    function = power_history
    scale_factor = 0.01
  []
  [burnup_avg]
    type = ElementAverageValue
    block = fuel
    variable = burnup
  []
  [burnup_max]
    type = ElementExtremeValue
    block = fuel
    variable = burnup
  []
  [fission_rate_avg]
    type = ElementAverageValue
    variable = fission_rate
    block = fuel
  []

  # fission gas information
  [fg_produced]
    type = ADElementIntegralMaterialProperty
    mat_prop = fgm_produced
    block = fuel
  []
  [fg_released]
    type = ADElementIntegralMaterialProperty
    mat_prop = fgm_released
    block = fuel
    execute_on = 'initial timestep_end'
  []
  [fg_percent]
    type = FGRPercent
    fission_gas_released = fg_released
    fission_gas_generated = fg_produced
  []
  [interconnected_porosity_fuel_avg]
    type = ElementAverageValue
    variable = interconnected_porosity
    block = fuel
    execute_on = 'initial timestep_end'
  []
  [porosity_fuel_avg]
    type = ElementAverageValue
    variable = porosity
    block = fuel
  []
  [porosity_fuel_max]
    type = ElementExtremeValue
    variable = porosity
    block = fuel
  []
  [porosity_fuel_min]
    type = ElementExtremeValue
    variable = porosity
    value_type = min
    block = fuel
  []
  [porosity_sodium_logging_avg]
    type = ElementAverageValue
    variable = sodium_logged_porosity
    block = fuel
  []

  # extras
  [actual_time_step_limit]
    type = MaterialTimeStepPostprocessor
    block = 'fuel ${cladding_block}'
    outputs = none
  []
  [time_step_limit]
    type = ParsedPostprocessor
    expression = 'if(actual_time_step_limit > 1e6, 1e6, actual_time_step_limit)'
    pp_names = 'actual_time_step_limit'
  []
  [max_wastagethickness]
    type = ElementExtremeValue
    value_type = max
    variable = wastage_thickness
    # outputs = 'console'
  []
  [max_wst_temp]
    type = ElementExtremeValue
    value_type = max
    variable = temp
    proxy_variable = wastage_thickness
    block = '${cladding_block}'
  []
  [max_wst_burnup]
    type = ElementExtremeValue
    value_type = max
    variable = burnup
    proxy_variable = wastage_thickness
    block = '${cladding_block}'
  []
  [max_cdf]
    type = ElementExtremeValue
    value_type = max
    variable = cumulative_damage_index
  []
[]

[VectorPostprocessors]
  [id_wastage]
    type = FuelRodLineValueSampler
    variable = wastage_thickness
    material = 'clad'
    fraction = 0.0
    num_points = 600
    orientation = 'vertical'
    fuel_pin_geometry = 'pin_geometry'
    execute_on = 'initial timestep_end'
    allow_duplicate_execution_on_initial = true
    outputs = csv_wst_a
  []
  [id_pen_total]
    type = FuelRodLineValueSampler
    variable = total_id_reduction
    material = 'clad'
    fraction = 0.0
    num_points = 600
    orientation = 'vertical'
    fuel_pin_geometry = 'pin_geometry'
    execute_on = 'initial timestep_end'
    allow_duplicate_execution_on_initial = true
    outputs = none
  []
  [od_wastage]
    type = FuelRodLineValueSampler
    variable = cc_wastage_thickness
    material = 'clad'
    fraction = 1.0
    num_points = 600
    orientation = 'vertical'
    fuel_pin_geometry = 'pin_geometry'
    execute_on = 'initial timestep_end'
    allow_duplicate_execution_on_initial = true
    outputs = none
  []
  [fuel_melting]
    type = FuelRodLineValueSampler
    variable = fuel_melting_thickness
    material = 'fuel'
    fraction = 1.0
    num_points = 600
    orientation = 'vertical'
    fuel_pin_geometry = 'pin_geometry'
    execute_on = 'initial timestep_end'
    allow_duplicate_execution_on_initial = true
    outputs = none
  []
[]

[PerformanceMetricOutputs]
  outputs = 'console'
[]

[Outputs]
  print_linear_residuals = true
  color = true
  perf_graph = true
  sync_times = ${time_spots}

  [checkpoint]
    type = Checkpoint
    time_step_interval =  1
  []
  [exodus]
    type = Exodus
    time_step_interval =  500
    sync_times = ${time_spots}
    enable = false
  []
  [console]
    type = Console
    show = 'time_step_size temp_fuel_avg temp_fuel_centerline_max temp_cladding_avg temp_cladding_max stress_vonmises_fuel_max stress_hydro_fuel_max stress_hydro_fuel_min contact_pressure_max strain_axial_fuel_avg power_integral burnup_avg fission_rate_avg fg_percent porosity_fuel_avg time_step_limit anisotropic_swelling_factor plenum_ratio volume_fuel volume_plenum max_wastagethickness max_cdf'
  []
  [csv_wst_a]
    type = CSV
    sync_only = true
    sync_times = ${time_spots_a}
    enable = ${enable_a}
    execute_postprocessors_on = none
    create_latest_symlink = true
  []
  [csv_general]
    type = CSV
    sync_only = true
    sync_times = ${time_spots}
    enable = true
  []
[]

[Debug]
  show_var_residual = 'disp_x disp_y temp'
  show_var_residual_norms = true
[]

(test/tests/metallic_fuel_liquid_cladding_penetration/liquid_penetration_ad.i)

# This test is to verify the calculation in MetallicFuelLiquidCladdingPenetration

[Mesh]
  [mesh]
    type = GeneratedMeshGenerator
    dim = 1
  []
[]

[Problem]
  solve = false
[]

[AuxVariables]
  [temp]
    initial_condition = 1000
  []
[]

[AuxKernels]
  [temp]
    type = ConstantAux
    variable = temp
    value = 1000
  []
[]

[Materials]
  [liquid_penetration]
    type = ADMetallicFuelLiquidCladdingPenetration
    temperature = temp
    fuel_bottom_position = 0.0
    fuel_height = 1.0
    outputs = all
  []
[]

[Executioner]
  type = Transient
  num_steps = 15
  dt = 1000
[]

[Postprocessors]
  [penetration_avg]
    type = ElementAverageValue
    variable = liquid_penetration
  []
  [temp_avg]
    type = ElementAverageValue
    variable = temp
  []
[]

[Outputs]
  csv = true
[]

(assessment/metallic_fuel/WPF/analysis/FM-1/FM_base.i)

# FM-1 Base Input File

gap_bottom_length = 0.31e-3
top_bot_cladding_height = 2.24e-3
# calculations
cladding_ir = '${fparse fuel_radius + cladding_gap_width}'
gas_plenum_height = '${fparse plenum_volume / pi / cladding_ir^2}'
fuel_y_start = '${fparse gap_bottom_length + top_bot_cladding_height}'
alpha_start = 877
alpha_end = 936
bubble_concentration = 1e15

cladding_block = 'cladding cladding_tri'

y_tc1 = '${fparse 2.55e-3+22.0*0.0254}'
y_tc2 = '${fparse y_tc1-4.5*0.0254}'
y_tc3 = '${fparse y_tc2-3.5*0.0254}'
y_tc4 = '${fparse y_tc3-2.0*0.0254}'
y_tc5 = '${fparse y_tc4-3.0*0.0254}'
y_tc6 = '${fparse y_tc1-4.0*0.0254}'

x_tc = 0.002920

p_tc1 = '${x_tc} ${y_tc1} 0.0'
p_tc2 = '${x_tc} ${y_tc2} 0.0'
p_tc3 = '${x_tc} ${y_tc3} 0.0'
p_tc4 = '${x_tc} ${y_tc4} 0.0'
p_tc5 = '${x_tc} ${y_tc5} 0.0'
p_tc6 = '${x_tc} ${y_tc6} 0.0'

# A relatively coarse radial mesh density can be used
# since localized refining is done by TRI3 elements
clad_n_rad = 10

[GlobalParams]
  order = FIRST
  energy_per_fission = 3.2e-11 # J/fission
  displacements = 'disp_x disp_y'
  alpha_transition_end = ${alpha_end}
  alpha_transition_start = ${alpha_start}
[]

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

[Mesh]
  # Pin design parameters from FIPD database
  [gen]
    type = FIPDRodletMeshGenerator
    fipd_geom_file = ${raw '../../../../../fipd-bison-integration-data/ ${exp_id} / ${pin_id} / ${pin_id} _design.csv'}

    gap_bottom_length = 0.31e-3 # arbitrary
    cladding_bottom_plug_length = 2.24e-3 # arbitrary
    cladding_top_plug_length = 2.24e-3 # arbitrary

    cladding_sidewall_radial_elements = ${clad_n_rad}
    cladding_sidewall_axial_element_intervals = '0 0.540 0.625 1.0'
    cladding_sidewall_axial_element_numbers = '150 1000 150'
    use_tri_for_cladding_sidewall = '0 1 0'
    cladding_top_plug_radial_elements = 10
    cladding_top_plug_axial_elements = 5
    cladding_bottom_plug_axial_elements = 5
    fuel_radial_elements = 10
    fuel_axial_element_intervals = '0 1'
    fuel_axial_element_numbers = '1000'
    tri_element_size_factor = 0.4
    elem_type = QUAD4
    make_stand = true
    make_cap = true
    cap_axial_elements = 15
    stand_axial_elements = 15
  []
  [sodium_height]
    type = SideSetsFromBoundingBoxGenerator
    input = gen
    bottom_left = '0 0 0'
    top_right = '${fparse cladding_ir + cladding_thickness} ${fparse fuel_y_start + fuel_height} 0'
    included_boundaries = 'cladding_inside_right'
    boundary_new = '1005'
  []
  [gas_height]
    type = SideSetsFromBoundingBoxGenerator
    input = sodium_height
    bottom_left = '0 ${fparse fuel_y_start + fuel_height} 0'
    top_right = '${fparse cladding_ir + cladding_thickness} ${fparse fuel_y_start + fuel_height + gas_plenum_height + top_bot_cladding_height} 0'
    included_boundaries = 'cladding_inside_right'
    boundary_new = '1006'
  []
  [sodium_plenum_rename]
    type = RenameBoundaryGenerator
    input = gas_height
    old_boundary = '1005 1006'
    new_boundary = 'sodium_height gas_height'
  []

  patch_size = 40
  patch_update_strategy = always
  partitioner = centroid
  centroid_partitioner_direction = y
  coord_type = RZ
[]

[Variables]
  [temp]
    initial_condition = 298
    block = 'fuel ${cladding_block} cap stand'
  []
  [disp_x]
    block = 'fuel ${cladding_block} cap stand'
  []
  [disp_y]
    block = 'fuel ${cladding_block} cap stand'
  []
[]

[Functions]
  [fflux_axial_peaking_factors]
    type = ConstantFunction
    value = 0.0
  []
  [fflux_axial_peaking_factors_elongate]
    type = ConstantFunction
    value = 0.0
  []
  [flux_history] # Time-dependent pin average fast flux from FIPD database
    type = ConstantFunction
    value = 0.0
  []
  [clad_od_temp]
    type = PiecewiseBilinear
    data_file = './data/temp_hist.csv'
    xaxis = 1
  []
  [ab_sodium_vol]
    type = MeshPropertyFunction
    mesh_generator = gen
    mesh_property_name = sodium_volume
    scale_factor = -1.0
  []
  [sodium_volume]
    # Need to account for the factor that hot pressing is also occupying the open pores
    type = ParsedFunction
    symbol_names = 'porosity_sodium_logging_avg volume_fuel raw_sodium_vol temp_sodium_avg'
    symbol_values = 'porosity_sodium_logging_avg volume_fuel ab_sodium_vol temp_sodium_avg'
    # Note the the symbol before volume_fuel should be negative as volume_fuel itself is negative
    expression = 'raw_sodium_vol * 954 / (1012 - 0.23 * temp_sodium_avg) - volume_fuel * porosity_sodium_logging_avg'
  []
  [power_history]
    type = ConstantFunction
    value = 0.0
  []
  [axial_peaking_factors]
    type = ConstantFunction
    value = 0.0
  []
  [axial_peaking_factors_extended]
    type = ConstantFunction
    value = 0.0
  []
  [anisotropic_swelling_factor]
    type = ParsedFunction
    symbol_names = 'disp_x_fuel_radial_surface_avg disp_y_fuel_top_surface_avg fuel_height fuel_radius'
    symbol_values = 'disp_x_fuel_radial_surface_avg disp_y_fuel_top_surface_avg ${fuel_height} ${fuel_radius}'
    expression = '(disp_x_fuel_radial_surface_avg / ${fuel_radius}) / (disp_y_fuel_top_surface_avg / ${fuel_height})'
  []
  [gap_thermal_conductivity]
    type = ParsedFunction
    expression = '124.67 - 0.11381 * t + 5.5226e-5 * t^2 - 1.1842e-8 * t^3'
  []
  [id_vpp_func] # vpp_function used to track FCCI-related cladding degradation.
    type = MetallicFuelWastageDegradationFunction
    vectorpostprocessor_name = id_pen_total
    argument_column = y
    wastage_type = ID
    value_column = total_id_reduction
    use_metadata = true
    degradation_factor = 0.001
    mesh_generator = 'gen'
    transition_width = 1E-4
  []
  [od_vpp_func] # vpp_function used to track CCCI-related cladding degradation.
    type = MetallicFuelWastageDegradationFunction
    vectorpostprocessor_name = od_wastage
    argument_column = y
    wastage_type = OD
    value_column = cc_wastage_thickness
    use_metadata = true
    degradation_factor = 0.001
    mesh_generator = 'gen'
    transition_width = 1E-4
  []

  [fuel_melt_func]
    type = MetallicFuelMeltingFunction
    vectorpostprocessor_name = fuel_melting
    argument_column = y
    value_column = fuel_melting_thickness
    use_metadata = true
    mesh_generator = 'gen'
    transition_width = 2e-4
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [fuel]
    block = fuel
    strain = FINITE
    generate_output = 'firstinv_strain stress_xx stress_yy stress_zz vonmises_stress hydrostatic_stress creep_strain_xx creep_strain_yy creep_strain_zz elastic_strain_xx elastic_strain_yy elastic_strain_zz strain_xx strain_yy strain_zz'
    extra_vector_tags = 'ref'
    eigenstrain_names = 'fuel_thermal_strain solid_swelling_eigenstrain'
    use_automatic_differentiation = true
    volumetric_locking_correction = true
  []
  [cladding]
    strain = FINITE
    generate_output = 'stress_xx stress_yy stress_zz vonmises_stress hydrostatic_stress creep_strain_xx creep_strain_yy creep_strain_zz elastic_strain_xx elastic_strain_yy elastic_strain_zz strain_xx strain_yy strain_zz'
    extra_vector_tags = 'ref'
    block = '${cladding_block}'
    eigenstrain_names = 'cladding_thermal_eigenstrain'
    use_automatic_differentiation = true
    volumetric_locking_correction = true
  []
[]

[Kernels]
  [gravity]
    type = ADGravity
    block = 'fuel ${cladding_block}'
    variable = disp_y
    value = -9.81
    extra_vector_tags = 'ref'
  []
  [heat]
    type = ADHeatConduction
    block = 'fuel ${cladding_block} cap stand'
    variable = temp
    extra_vector_tags = 'ref'
  []
  [heat_ie]
    type = ADHeatConductionTimeDerivative
    block = 'fuel ${cladding_block} cap stand'
    variable = temp
    extra_vector_tags = 'ref'
  []
  [heat_source]
    type = ADFissionRateHeatSource
    variable = temp
    block = 'fuel'
    fission_rate = fission_rate
    extra_vector_tags = 'ref'
    energy_deposited_in_fuel = 0.95
  []
  [disp_x_dt]
    type = ADTimeDerivative
    variable = disp_x
    block = ' cap stand'
    extra_vector_tags = 'ref'
  []
  [disp_y_dt]
    type = ADTimeDerivative
    variable = disp_y
    block = 'cap stand'
    extra_vector_tags = 'ref'
  []
  [disp_x_diff]
    type = ADMatAnisoDiffusion
    variable = disp_x
    block = 'cap stand'
    diffusivity = d_x
    extra_vector_tags = 'ref'
  []
  [disp_y_diff]
    type = ADMatDiffusion
    variable = disp_y
    block = 'cap stand'
    diffusivity = 1e8
    extra_vector_tags = 'ref'
  []
[]

[UserObjects]
  [pin_geometry]
    type = FuelPinGeometry
    clad_bottom = cladding_outside_bottom
    clad_inner_wall = cladding_inside_right
    clad_outer_wall = cladding_outside_right
    clad_top = cladding_outside_top
    pellet_exteriors = fuel_outside_all
  []
  [fuel_thm_exp]
    type = LayeredAverage
    variable = fuel_thermal_strain_xx
    direction = y
    num_layers = 1000
    block = fuel
  []
  [clad_thm_exp]
    type = LayeredAverage
    variable = clad_thermal_eigenstrain_xx
    direction = y
    num_layers = 1000
    block = ${cladding_block}
  []
[]

[Contact]
  [fuel_cladding_mechanical]
    primary = cladding_inside_right
    secondary = fuel_outer_radial_surface
    model = coulomb
    friction_coefficient = 0.1
    formulation = mortar
    c_normal = '${fparse 1e17 * magic_factor}'
    c_tangential = '${fparse 1e19 * magic_factor}'
    correct_edge_dropping = true
  []
[]

[MortarGapHeatTransfer]
  [inside2outside]
    temperature = temp
    boundary = 'cladding_inside_right'
    gap_conductivity_function = gap_thermal_conductivity
    gap_conductivity_function_variable = temp
    primary_boundary = cladding_inside_right
    secondary_boundary = fuel_contact_surfaces
    gap_flux_options = 'CONDUCTION'
    ghost_point_neighbors = true
  []
[]

[BCs]
  [no_x_all]
    type = ADDirichletBC
    variable = disp_x
    boundary = 'centerline cap_top'
    value = 0.0
    preset = false
  []
  [no_y_clad]
    type = ADDirichletBC
    variable = disp_y
    boundary = 'cladding_inside_bottom'
    value = 0.0
    preset = false
  []
  [Pressure]
    [coolantPressure]
      boundary = 'cladding_outside_right'
      factor = 1378.95 # in Pa, 0.2 psia as measured by transducer
      use_automatic_differentiation = true
    []
  []
  [PlenumPressure]
    [plenumPressure]
      boundary = 'inside_surfaces'
      initial_pressure = 84116 # in Pa, 12.2 psi
      startup_time = 0
      R = 8.3143
      temperature = temp_gas_avg
      volume = volume_plenum
      output = plenum_pressure
      material_input = fg_released
      use_automatic_differentiation = true
    []
  []
  [surf] # Setting temperature BC base on FIPD data
    type = ADFunctionDirichletBC
    variable = temp
    boundary = 'cladding_outside_bottom cladding_outside_right cladding_outside_top'
    function = clad_od_temp
  []
[]

[AuxVariables]
  [dummy_hoop_stress]
    order = CONSTANT
    family = MONOMIAL
  []
  [cumulative_damage_index]
    order = CONSTANT
    family = MONOMIAL
  []
  [relx]
  []
  [clad_thm_exp]
    order = CONSTANT
    family = MONOMIAL
    block = '${cladding_block}'
  []
  [clad_thermal_eigenstrain_xx]
    order = CONSTANT
    family = MONOMIAL
    block = '${cladding_block}'
  []
  [fuel_thermal_strain_xx]
    order = CONSTANT
    family = MONOMIAL
    block = fuel
  []
  [fuel_thermal_strain_yy]
    order = CONSTANT
    family = MONOMIAL
    block = fuel
  []
  [fuel_thm_exp]
    order = CONSTANT
    family = MONOMIAL
    block = fuel
  []
  [func_val1]
  []
  [func_val2]
  []
  [func_val3]
  []
  # OPTD Active during this stage
  [pen_thick_aux]
    family = MONOMIAL
    order = CONSTANT
    block = 'fuel ${cladding_block}'
  []
  [total_id_reduction]
    family = MONOMIAL
    order = CONSTANT
    block = 'fuel ${cladding_block}'
  []
  [fast_neutron_fluence_aux]
    order = CONSTANT
    family = MONOMIAL
    block = '${cladding_block}'
  []
[]

[AuxKernels]
  [func_val1]
    type = FunctionAux
    function = id_vpp_func
    variable = func_val1
    block = 'cladding cladding_tri'
  []
  [func_val2]
    type = FunctionAux
    function = od_vpp_func
    variable = func_val2
    block = 'cladding cladding_tri'
  []
  [func_val3]
    type = FunctionAux
    function = fuel_melt_func
    variable = func_val3
    block = fuel
  []
  [cdf_amount]
    block = '${cladding_block}'
    type = MaterialRealAux
    property = cdf_failure
    variable = cumulative_damage_index
  []
  [relx_aux]
    type = ParsedAux
    variable = relx
    block = fuel
    use_xyzt = true
    expression = 'x / ${fuel_radius}'
  []
  [clad_thm_exp]
    type = SpatialUserObjectAux
    variable = clad_thm_exp
    execute_on = 'initial timestep_end'
    user_object = clad_thm_exp
    block = '${cladding_block}'
  []
  [clad_thermal_eigenstrain_xx]
    type = ADRankTwoAux
    rank_two_tensor = cladding_thermal_eigenstrain
    variable = clad_thermal_eigenstrain_xx
    index_j = 0
    index_i = 0
    execute_on = 'initial timestep_end'
    block = '${cladding_block}'
  []
  [fuel_thermal_strain_xx]
    type = ADRankTwoAux
    rank_two_tensor = fuel_thermal_strain
    variable = fuel_thermal_strain_xx
    index_j = 0
    index_i = 0
    execute_on = 'initial timestep_end'
    block = fuel
  []
  [fuel_thermal_strain_yy]
    type = ADRankTwoAux
    rank_two_tensor = fuel_thermal_strain
    variable = fuel_thermal_strain_yy
    index_j = 1
    index_i = 1
    execute_on = 'initial timestep_end'
    block = fuel
  []
  [fuel_thm_exp]
    type = SpatialUserObjectAux
    variable = fuel_thm_exp
    execute_on = 'initial timestep_end'
    user_object = fuel_thm_exp
    block = fuel
  []
  #OPTD
  [assign_pen_thick_aux]
    type = ADMaterialRealAux
    variable = pen_thick_aux
    property = liquid_penetration
    block = 'fuel ${cladding_block}'
  []
  [assign_total_id_reduction]
    type = ParsedAux
    variable = total_id_reduction
    coupled_variables = 'pen_thick_aux wastage_thickness'
    expression = 'pen_thick_aux + wastage_thickness'
    block = 'fuel ${cladding_block}'
  []
[]

[Materials]
  [fuel_pen]
    type = ADMetallicFuelLiquidCladdingPenetration
    temperature = temp
    mesh_generator = gen
    fuel_elongation_pp = max_fuel_elongation
    liquid_penetration_model = 'ANL_CONSERVATIVE'
    fuel_pu = Pu_0
    burnup = burnup
    outputs = all
    calculate_fuel_melting_thickness = true
    block = 'fuel ${cladding_block}'
  []
  [longHT9_failure]
    type = HT9FailureClad
    block = '${cladding_block}'
    method = cdf_long
    temperature = temp
    outputs = all
    hoop_stress = stress_zz # Since 2D-RZ
  []
  [d_x]
    type = ADConstantAnisotropicMobility
    tensor = '1e3 0 0
              0   1e6 0
              0   0 0'
    M_name = d_x
  []
  [cap_thcond]
    type = ADGenericConstantMaterial
    prop_names = 'thermal_conductivity specific_heat density'
    prop_values = '65 1200 830'
    block = 'cap stand'
    outputs = all
  []
  [interconnected_porosity]
    type = ADParsedMaterial
    block = 'fuel'
    property_name = interconnected_porosity
    material_property_names = 'porosity interconnectivity'
    expression = 'porosity * interconnectivity'
    outputs = all
  []

  [fission_rate]
    type = ADUPuZrFissionRate
    rod_linear_power = power_history
    axial_power_profile = axial_peaking_factors
    pellet_radius = ${fuel_radius}
    X_Zr = ${initial_X_Zr}
    X_Pu_function = ${X_Pu}
    block = 'fuel'
    outputs = all
  []
  [fission_rate_elongate]
    type = ADUPuZrFissionRate
    rod_linear_power = power_history
    axial_power_profile = axial_peaking_factors_extended
    pellet_radius = ${fuel_radius}
    X_Zr = ${initial_X_Zr}
    X_Pu_function = ${X_Pu}
    block = '${cladding_block}'
    outputs = all
    fission_rate_name = fission_rate
  []
  [burnup]
    type = ADUPuZrBurnup
    initial_X_Zr = ${initial_X_Zr}
    initial_X_Pu = ${X_Pu}
    density = ${fuel_density}
    block = 'fuel'
    outputs = all
  []
  [burnup_elongate]
    type = ADUPuZrBurnup
    initial_X_Pu = ${X_Pu}
    initial_X_Zr = ${initial_X_Zr}
    outputs = all
    block = '${cladding_block}'
    density = ${fuel_density}
    burnup_name = burnup
  []
  [fuel_elastic_stress]
    type = ADComputeMultipleInelasticStress
    inelastic_models = 'hotpress fuel_upuzrcreep gas_swelling'
    block = 'fuel'
    outputs = all
  []
  [hotpress]
    type = ADUPuZrHotPressingStressUpdate
    block = 'fuel'
    outputs = all
    surface_energy = 1.6
    plenum_pressure = plenum_pressure
    porosity_name = porosity
    max_inelastic_increment = 1e-1
    interconnectivity = interconnectivity
    bubble_concentration = ${bubble_concentration}
    temperature = temp
    creep_model = MFH
    fission_rate = fission_rate
    atomic_volume = 2.15e-29
    porosity_start = 0.01
    porosity_end = 0
    grain_boundary_D0 = 4e-29
    grain_boundary_Q = 0
    absolute_tolerance = 1e-9
  []
  [porosity]
    type = ADPorosityFromStrain
    block = 'fuel'
    initial_porosity = 1e-10
    inelastic_strain = 'combined_inelastic_strain'
    outputs = all
  []
  [fuel_elasticity_tensor]
    type = ADUPuZrElasticityTensor
    X_Zr = ${initial_X_Zr}
    X_Pu = ${X_Pu}
    youngs_model = LANL
    block = 'fuel'
    temperature = temp
    use_old_porosity = true
    outputs = all
    output_properties = 'youngs_modulus poissons_ratio'
  []
  [fuel_upuzrcreep]
    type = ADUPuZrCreepUpdate
    block = 'fuel'
    temperature = temp
    porosity = porosity
    use_old_porosity = true
    max_inelastic_increment = 1e-1
    outputs = all
    automatic_differentiation_return_mapping = false
  []
  [fuel_thermal_expansion]
    type = ADUPuZrThermalExpansionEigenstrain
    block = 'fuel'
    temperature = temp
    stress_free_temperature = 298.0
    eigenstrain_name = fuel_thermal_strain
    outputs = all
    thermal_expansion_model = LANL
    X_Zr = ${initial_X_Zr}
    X_Pu = ${X_Pu}
  []
  [gas_swelling]
    type = ADSimpleFissionGasViscoplasticityStressUpdate
    temperature = temp
    outputs = all
    block = 'fuel'
    bubble_concentration = ${bubble_concentration}
    initial_bubble_concentration = ${bubble_concentration}
    compute_interconnectivity = true
    fission_gas_yield = 0.3017
    fission_rate = fission_rate
    initial_atoms_per_bubble = 1e-05
    initial_bubble_radius = 1e-15
    initial_fgm_dissolved = 0
    interconnection_cutoff = 0.99
    interconnection_initiating_porosity = 0.23
    interconnection_terminating_porosity = 0.25
    max_inelastic_increment = 1e-2
    retained_gas_fraction = 0.25
    interconnection_dependent_retained_gas_fraction = 0.5
    surface_energy = 1.6
    anisotropic_factor = 0.26
    initial_porosity = 1e-10
    fuel_melting_function = fuel_melt_func
  []
  [solid_swelling]
    type = ADBurnupDependentEigenstrain
    eigenstrain_name = solid_swelling_eigenstrain
    block = 'fuel'
    swelling_name = 'solid_swelling'
    outputs = all
    anisotropic_factor = 0.26
  []
  [metal_fuel_thermal]
    type = ADUPuZrThermal
    block = 'fuel'
    X_Zr = ${initial_X_Zr}
    X_Pu = ${X_Pu}
    spheat_model = savage
    porosity = porosity
    temperature = temp
    outputs = all
    porosity_model = logged
    sodium_logged_porosity = sodium_logged_porosity
  []
  [sodium_logging]
    type = ADUPuZrSodiumLogging
    block = 'fuel'
    porosity = porosity
    interconnectivity = interconnectivity
    sodium_infiltration_fraction = 0.28
    outputs = all
  []
  [fuel_density]
    type = ADStrainAdjustedDensity
    block = 'fuel'
    strain_free_density = ${fuel_density}
    outputs = all
  []
  [fast_neutron_flux]
    type = ADFastNeutronFlux
    calculate_fluence = true
    axial_power_profile = fflux_axial_peaking_factors
    rod_ave_lin_pow = flux_history
    block = fuel
    factor = 1.0
    outputs = all
  []
  [fast_neutron_flux_elongate]
    type = ADFastNeutronFlux
    calculate_fluence = true
    axial_power_profile = fflux_axial_peaking_factors_elongate
    rod_ave_lin_pow = flux_history
    block = '${cladding_block}'
    factor = 1.0
    outputs = all
  []
  [cladding_elasticity_tensor]
    type = ADHT9ElasticityTensor
    temperature = temp
    block = '${cladding_block}'
    outputs = all
    id_wastage_degradation_function = id_vpp_func
    od_wastage_degradation_function = od_vpp_func
    output_properties = 'youngs_modulus poissons_ratio'
  []
  [cladding_stress]
    type = ADComputeMultipleInelasticStress
    inelastic_models = 'cladding_creep'
    block = '${cladding_block}'
    outputs = all
  []
  [cladding_creep]
    type = ADHT9CreepUpdate
    block = '${cladding_block}'
    temperature = temp
    outputs = all
    primary_creep_model = MFH
    secondary_creep_model = MFH
    irradiation_creep_model = MFH
    fast_neutron_flux = fast_neutron_flux
  []
  [thermal_expansion]
    type = ADHT9ThermalExpansionEigenstrain
    block = '${cladding_block}'
    temperature = temp
    stress_free_temperature = 298.0
    eigenstrain_name = cladding_thermal_eigenstrain
    outputs = all
  []
  [cladding_thermal]
    type = ADHT9Thermal
    block = '${cladding_block}'
    temperature = temp
    outputs = all
  []
  [cladding_density]
    type = ADStrainAdjustedDensity
    block = '${cladding_block}'
    strain_free_density = '${clad_density}'
    outputs = all
  []
  [wastage_thickness]
    type = ADMetallicFuelWastage
    method = burnup_ht9_opt
    burnup = burnup
    temperature = temp
    scale_factor = 1
    block = '${cladding_block}'
    outputs = all
  []
  [cc_wastage_thickness]
    type = ADMetallicFuelCoolantWastage
    clad_material = HT9
    use_effective_method = true
    temperature = temp
    scale_factor = 1
    block = '${cladding_block}'
    outputs = all
  []
[]

[Dampers]
  [disp_x]
    type = MaxIncrement
    variable = disp_x
    max_increment = 1e-3
  []
  [disp_y]
    type = MaxIncrement
    variable = disp_y
    max_increment = 1e-3
  []
  [temp]
    type = MaxIncrement
    variable = temp
    max_increment = 100
  []
[]

[Preconditioning]
  [vcp]
    type = VCP
    full = true
    primary_variable = 'disp_x disp_y temp'
    preconditioner = 'LU'
    adaptive_condensation = true
    lm_variable = 'fuel_cladding_mechanical_normal_lm fuel_cladding_mechanical_tangential_lm inside2outside_thermal_lm'
    is_lm_coupling_diagonal = true
  []
[]

[Executioner]
  type = Transient
  solve_type = 'NEWTON'
  petsc_options = '-snes_ksp_ew -snes_converged_reason -ksp_converged_reason'
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_type -mat_mffd_err -pc_factor_shift_type -pc_factor_shift_amount -snes_force_iteration'
  petsc_options_value = 'lu    superlu_dist   1e-5          NONZERO               1e-15 1'
  line_search = 'none'
  snesmf_reuse_base = false
  verbose = true

  l_max_its = 60
  nl_max_its = 100
  nl_rel_tol = 5e-6
  nl_abs_tol = 5e-9

  end_time = '${fparse run_time + total_transient_time}'
  dtmin = 1e-5
  dtmax = 5.0

  automatic_scaling = true
  compute_scaling_once = false
  off_diagonals_in_auto_scaling = true
  ignore_variables_for_autoscaling = 'fuel_cladding_mechanical_normal_lm fuel_cladding_mechanical_tangential_lm inside2outside_thermal_lm'

  [TimeStepper]
    type = IterationAdaptiveDT
    timestep_limiting_postprocessor = actual_cladding_time_step_limit

    dt = 0.01
    iteration_window = 4
    optimal_iterations = 10
    cutback_factor_at_failure = 0.9
    growth_factor = 2
  []
[]

[Postprocessors]
  [_dt]
    type = TimestepSize
  []
  [_transient_t]
    type = ParsedPostprocessor
    pp_names = ''
    expression = 't-t0'
    use_t = true
    constant_names = 't0'
    constant_expressions = '${run_time}'
  []
  # elemental temperatures
  [temp_fuel_avg]
    type = ElementAverageValue
    variable = temp
    block = 'fuel'
    execute_on = 'initial timestep_end'
  []
  [temp_fuel_max]
    type = ElementExtremeValue
    variable = temp
    block = 'fuel'
  []
  [temp_fuel_min]
    type = ElementExtremeValue
    variable = temp
    block = 'fuel'
    value_type = min
  []
  [temp_cladding_avg]
    type = ElementAverageValue
    variable = temp
    block = '${cladding_block}'
  []
  [temp_cladding_max]
    type = ElementExtremeValue
    variable = temp
    block = '${cladding_block}'
  []
  [temp_cladding_min]
    type = ElementExtremeValue
    variable = temp
    block = '${cladding_block}'
    value_type = min
  []

  # boundary temperatures
  [temp_gas_avg]
    type = SideAverageValue
    boundary = 'gas_height cladding_inside_top'
    variable = temp
    execute_on = 'initial timestep_end'
  []

  # Beyond gap closure, sodium temperarture is almost the same as the cap.
  [temp_sodium_avg]
    type = ElementAverageValue
    block = 'cap'
    variable = temp
    execute_on = 'initial timestep_end'
  []
  [temp_inside_surfaces_avg]
    type = SideAverageValue
    boundary = 'inside_surfaces'
    variable = temp
    execute_on = 'initial timestep_end'
  []
  [temp_fuel_centerline_avg]
    type = AxisymmetricCenterlineAverageValue
    boundary = 'centerline'
    variable = temp
  []
  [temp_fuel_centerline_max]
    type = NodalExtremeValue
    boundary = 'centerline'
    variable = temp
  []
  [temp_fuel_centerline_min]
    type = NodalExtremeValue
    boundary = 'centerline'
    variable = temp
    value_type = min
  []
  [temp_fuel_surface_avg]
    type = SideAverageValue
    boundary = 'fuel_outer_radial_surface'
    variable = temp
  []
  [temp_fuel_surface_max]
    type = NodalExtremeValue
    boundary = 'fuel_outer_radial_surface'
    variable = temp
  []
  [temp_fuel_surface_min]
    type = NodalExtremeValue
    boundary = 'fuel_outer_radial_surface'
    variable = temp
    value_type = min
  []
  [temp_cladding_inside_right_avg]
    type = SideAverageValue
    boundary = 'cladding_inside_right'
    variable = temp
  []
  [temp_cladding_inside_right_max]
    type = NodalExtremeValue
    boundary = 'cladding_inside_right'
    variable = temp
  []
  [temp_cladding_outside_right_avg]
    type = SideAverageValue
    boundary = 'cladding_outside_right'
    variable = temp
  []

  # stresses
  [stress_vonmises_fuel_avg]
    type = ElementAverageValue
    variable = vonmises_stress
    block = 'fuel'
  []
  [stress_vonmises_fuel_max]
    type = ElementExtremeValue
    variable = vonmises_stress
    block = 'fuel'
  []
  [stress_vonmises_fuel_min]
    type = ElementExtremeValue
    variable = vonmises_stress
    value_type = min
    block = 'fuel'
  []
  [stress_hydro_fuel_avg]
    type = ElementAverageValue
    variable = hydrostatic_stress
    block = 'fuel'
  []
  [stress_hydro_fuel_max]
    type = ElementExtremeValue
    variable = hydrostatic_stress
    block = 'fuel'
  []
  [stress_hydro_fuel_min]
    type = ElementExtremeValue
    variable = hydrostatic_stress
    value_type = min
    block = 'fuel'
  []
  [stress_vonmises_cladding_avg]
    type = ElementAverageValue
    variable = vonmises_stress
    block = '${cladding_block}'
  []
  [stress_vonmises_cladding_max]
    type = ElementExtremeValue
    variable = vonmises_stress
    block = '${cladding_block}'
  []
  [stress_vonmises_cladding_min]
    type = ElementExtremeValue
    variable = vonmises_stress
    value_type = min
    block = '${cladding_block}'
  []
  [stress_hydro_cladding_avg]
    type = ElementAverageValue
    variable = hydrostatic_stress
    block = '${cladding_block}'
  []
  [stress_hydro_cladding_max]
    type = ElementExtremeValue
    variable = hydrostatic_stress
    block = '${cladding_block}'
  []
  [stress_hydro_cladding_min]
    type = ElementExtremeValue
    variable = hydrostatic_stress
    value_type = min
    block = '${cladding_block}'
  []
  [contact_pressure_max]
    type = NodalExtremeValue
    variable = fuel_cladding_mechanical_normal_lm
    boundary = 'fuel_outer_radial_surface'
  []

  # strain information
  [strain_solid_swelling_fuel_avg]
    type = ElementAverageValue
    variable = solid_swelling
    block = 'fuel'
  []
  [strain_gas_swelling_fuel_avg]
    type = ElementAverageValue
    variable = effective_fission_gas_strain
    block = 'fuel'
  []
  [strain_hot_pressing_fuel_avg]
    type = ElementAverageValue
    variable = effective_hot_pressing_strain
    block = 'fuel'
  []
  [strain_volumetric_fuel_avg]
    type = ElementAverageValue
    variable = firstinv_strain
    block = 'fuel'
  []
  [strain_axial_fuel_avg]
    type = ParsedPostprocessor
    pp_names = 'disp_y_fuel_top_surface_avg disp_y_fuel_bottom_surface_avg'
    expression = '(disp_y_fuel_top_surface_avg - disp_y_fuel_bottom_surface_avg) / ${fuel_height}'
  []
  [disp_y_fuel_top_surface_avg]
    type = SideAverageValue
    variable = disp_y
    boundary = 'fuel_top'
  []
  [disp_y_fuel_top_surface_max]
    type = NodalExtremeValue
    variable = disp_y
    boundary = 'fuel_top'
  []
  [disp_y_fuel_bottom_surface_avg]
    type = SideAverageValue
    variable = disp_y
    boundary = 'fuel_bottom'
  []
  [disp_y_fuel_bottom_surface_max]
    type = NodalExtremeValue
    variable = disp_y
    boundary = 'fuel_bottom'
  []
  [disp_x_fuel_radial_surface_max]
    type = NodalExtremeValue
    variable = disp_x
    boundary = 'fuel_outer_radial_surface'
  []
  [disp_x_fuel_radial_surface_avg]
    type = SideAverageValue
    variable = disp_x
    boundary = 'fuel_outer_radial_surface'
  []
  [disp_x_cladding_interior_max]
    type = NodalExtremeValue
    variable = disp_x
    boundary = 'cladding_inside_right'
  []
  [disp_x_cladding_interior_min]
    type = NodalExtremeValue
    variable = disp_x
    boundary = 'cladding_inside_right'
    value_type = min
  []
  [disp_x_cladding_interior_avg]
    type = SideAverageValue
    variable = disp_x
    boundary = 'cladding_inside_right'
  []
  [disp_x_cladding_exterior_max]
    type = NodalExtremeValue
    variable = disp_x
    boundary = 'cladding_outside_right'
  []
  [disp_x_cladding_exterior_avg]
    type = SideAverageValue
    variable = disp_x
    boundary = 'cladding_outside_right'
  []
  [anisotropic_swelling_factor]
    type = FunctionValuePostprocessor
    function = anisotropic_swelling_factor
  []
  [max_fuel_elongation]
    type = NodalExtremeValue
    variable = disp_y
    boundary = fuel_outside_all
  []

  # geometric information
  [volume_cladding_interior]
    type = InternalVolume
    boundary = 'cladding_inside_all'
  []
  [volume_fuel]
    type = InternalVolume
    boundary = 'fuel_outside_all'
    execute_on = 'initial timestep_end'
  []
  [volume_plenum]
    type = InternalVolume
    boundary = 'inside_surfaces'
    execute_on = 'initial timestep_end'
    addition = sodium_volume
  []
  [plenum_ratio]
    type = ParsedPostprocessor
    pp_names = 'volume_plenum volume_fuel'
    expression = 'volume_plenum / volume_fuel'
    execute_on = 'initial timestep_end'
  []
  [volume_sodium]
    type = FunctionValuePostprocessor
    function = sodium_volume
    execute_on = 'initial timestep_end'
  []

  # energy information
  [flux_clad]
    type = ADSideDiffusiveFluxIntegral
    variable = temp
    boundary = 'cladding_inside_right'
    diffusivity = thermal_conductivity
  []
  [flux_fuel]
    type = ADSideDiffusiveFluxIntegral
    variable = temp
    boundary = 'fuel_contact_surfaces'
    diffusivity = thermal_conductivity
  []
  [power_integral]
    type = ADElementIntegralPower
    variable = temp
    use_material_fission_rate = true
    fission_rate_material = fission_rate
    block = fuel
  []
  [linear_heat_generation_rate]
    type = FunctionValuePostprocessor
    function = power_history
    scale_factor = 0.01
  []
  [burnup_avg]
    type = ElementAverageValue
    block = fuel
    variable = burnup
  []
  [burnup_max]
    type = ElementExtremeValue
    block = fuel
    variable = burnup
  []
  [fission_rate_avg]
    type = ElementAverageValue
    variable = fission_rate
    block = fuel
  []

  # fission gas information
  [fg_produced]
    type = ADElementIntegralMaterialProperty
    mat_prop = fgm_produced
    block = fuel
  []
  [fg_released]
    type = ADElementIntegralMaterialProperty
    mat_prop = fgm_released
    block = fuel
    execute_on = 'initial timestep_end'
  []
  [fg_percent]
    type = FGRPercent
    fission_gas_released = fg_released
    fission_gas_generated = fg_produced
  []
  [interconnected_porosity_fuel_avg]
    type = ElementAverageValue
    variable = interconnected_porosity
    block = fuel
    execute_on = 'initial timestep_end'
  []
  [porosity_fuel_avg]
    type = ElementAverageValue
    variable = porosity
    block = fuel
  []
  [porosity_fuel_max]
    type = ElementExtremeValue
    variable = porosity
    block = fuel
  []
  [porosity_fuel_min]
    type = ElementExtremeValue
    variable = porosity
    value_type = min
    block = fuel
  []
  [porosity_sodium_logging_avg]
    type = ElementAverageValue
    variable = sodium_logged_porosity
    block = fuel
  []

  # extras
  [actual_time_step_limit]
    type = MaterialTimeStepPostprocessor
    block = 'fuel ${cladding_block}'
    outputs = none
  []
  [actual_fuel_time_step_limit]
    type = MaterialTimeStepPostprocessor
    block = 'fuel'
    outputs = 'console'
  []
  [actual_cladding_time_step_limit]
    type = MaterialTimeStepPostprocessor
    block = '${cladding_block}'
    outputs = 'console'
  []
  [time_step_limit]
    type = ParsedPostprocessor
    expression = 'if(actual_time_step_limit > 1e6, 1e6, actual_time_step_limit)'
    pp_names = 'actual_time_step_limit'
  []
  [max_wastagethickness]
    type = ElementExtremeValue
    value_type = max
    variable = wastage_thickness
  []
  [max_wst_temp]
    type = ElementExtremeValue
    value_type = max
    variable = temp
    proxy_variable = wastage_thickness
    block = '${cladding_block}'
  []
  [max_wst_burnup]
    type = ElementExtremeValue
    value_type = max
    variable = burnup
    proxy_variable = wastage_thickness
    block = '${cladding_block}'
  []
  [max_cdf]
    type = ElementExtremeValue
    value_type = max
    variable = cumulative_damage_index
  []

  # OPTD
  [temp_tc1]
    type = PointValue
    point = ${p_tc1}
    variable = temp
  []
  [temp_tc2]
    type = PointValue
    point = ${p_tc2}
    variable = temp
  []
  [temp_tc3]
    type = PointValue
    point = ${p_tc3}
    variable = temp
  []
  [temp_tc4]
    type = PointValue
    point = ${p_tc4}
    variable = temp
  []
  [temp_tc5]
    type = PointValue
    point = ${p_tc5}
    variable = temp
  []
  [temp_tc6]
    type = PointValue
    point = ${p_tc6}
    variable = temp
  []
  [max_vm]
    type = ElementExtremeValue
    value_type = max
    block = cladding
    variable = vonmises_stress
  []
  [max_pen_total]
    type = VectorPostprocessorReductionValue
    vector_name = total_id_reduction
    vectorpostprocessor = id_pen_total
    value_type = max
  []
[]

[VectorPostprocessors]
  [id_wastage]
    type = FuelRodLineValueSampler
    variable = wastage_thickness
    material = 'clad'
    fraction = 0.0
    num_points = 600
    orientation = 'vertical'
    fuel_pin_geometry = 'pin_geometry'
    execute_on = 'initial timestep_end'
    allow_duplicate_execution_on_initial = true
    outputs = none
  []
  [id_pen_total]
    type = FuelRodLineValueSampler
    variable = total_id_reduction
    material = 'clad'
    fraction = 0.0
    num_points = 600
    orientation = 'vertical'
    fuel_pin_geometry = 'pin_geometry'
    execute_on = 'initial timestep_end'
    allow_duplicate_execution_on_initial = true
    outputs = none
  []
  [od_wastage]
    type = FuelRodLineValueSampler
    variable = cc_wastage_thickness
    material = 'clad'
    fraction = 1.0
    num_points = 600
    orientation = 'vertical'
    fuel_pin_geometry = 'pin_geometry'
    execute_on = 'initial timestep_end'
    allow_duplicate_execution_on_initial = true
    outputs = none
  []
  [fuel_melting]
    type = FuelRodLineValueSampler
    variable = fuel_melting_thickness
    material = 'fuel'
    fraction = 1.0
    num_points = 600
    orientation = 'vertical'
    fuel_pin_geometry = 'pin_geometry'
    execute_on = 'initial timestep_end'
    allow_duplicate_execution_on_initial = true
    outputs = none
  []
[]

[PerformanceMetricOutputs]
  outputs = 'console'
[]

[Outputs]
  print_linear_residuals = true
  color = true
  perf_graph = true
  sync_times = ${time_spots}

  [checkpoint]
    type = Checkpoint
    time_step_interval =  1
    enable = false
  []
  [exodus]
    type = Exodus
    time_step_interval =  500
    sync_times = ${time_spots}
    enable = false
  []
  [ext]
    type = Exodus
    time_step_interval =  5
    enable = true
  []
  [console]
    type = Console
    show = 'time_step_size temp_fuel_avg temp_fuel_centerline_max temp_cladding_avg temp_cladding_max stress_vonmises_fuel_max stress_hydro_fuel_max stress_hydro_fuel_min contact_pressure_max strain_axial_fuel_avg power_integral burnup_avg fission_rate_avg fg_percent porosity_fuel_avg time_step_limit anisotropic_swelling_factor plenum_ratio volume_fuel volume_plenum max_wastagethickness temp_tc1 temp_tc2 temp_tc3 temp_tc4 temp_tc5 temp_tc6 _transient_t max_vm max_pen_total actual_fuel_time_step_limit actual_cladding_time_step_limit max_cdf'
  []
  [csv_general]
    type = CSV
    file_base = 'FM-1/FM-1_csv_general'
  []
  [csv_gold]
    type = CSV
    show = 'temp_tc1 temp_tc2 temp_tc3 temp_tc4 temp_tc5 temp_tc6 _transient_t max_vm max_pen_total max_cdf'
    sync_only = true
    sync_times = '${fparse run_time+10} ${fparse run_time+20} ${fparse run_time+50} ${fparse run_time+100} ${fparse run_time+200}
                  ${fparse run_time+500} ${fparse run_time+1000} ${fparse run_time+2000} ${fparse run_time+3000} ${fparse run_time+4000}
                  ${fparse run_time+5000} ${fparse run_time+6000}'
    file_base = 'FM-1/FM-1_gold'
  []
[]

[Debug]
  show_var_residual = 'disp_x disp_y temp'
  show_var_residual_norms = true
[]

Description
Axial Effective Region
Melting Fuel
Example Input Syntax
Input Parameters
Input Files
References