UPuZrVolumetricSwellingEigenstrainLM

Computes and sums the change in fuel pellet volume due to solid and gaseous (adopted LIFE-METAL model) fission product buildup in UPuZr.

Description

This model, UPuZrVolumetricSwellingEigenstrainLM, computes a volumetric strain to account for solid and gaseous swelling in U-Pu-Zr metal fuel systems. The solid swelling and gaseous swelling are optionally saved as a material property, named solid_swelling and gas_swelling, respectively. The gas_swelling can be further categorized into the swelling strain contributed by van der Waals volume of the the gas atoms (gas_swelling_vdw) and the swelling strain contributed by ideal gas (gas_swelling_ideal). Also, porosity (as-fabricated + gas swelling porosity) is available as a material property. This swelling model was originally developed for the LIFE-METAL fuel performance code by Argonne National Laboratory for the IFR program (Yacout and Billone, 2015). The original model was modified with more optional features and implemented into the BISON code by Argonne National Laboratory (an implementation report will be cited in a future version).

Gaseous Swelling

The gas swelling strain calculation is based on the amount of fission gas atoms ( $var element = document.getElementById("moose-equation-aef52c32-36a7-48f1-be34-f14336e73477");katex.render("mol/m^3", element, {displayMode:false,throwOnError:false});$ ) retained in the UPuZr fuel (fis_gas_ret), which is calculated by material property module FgrUPuZrLM. Therefore, the two modules must be used together.

The gaseous swelling in this model is divided into two components: (1)gas_swelling_vdw accounts for the swelling due to the van der Waals volume of the fission gas atoms, which is not compressible (i.e. independent to hydrostatic stress); (2) gas_swelling_ideal accounts for the swelling governed by ideal gas equation of state.

Van der Waals Swelling

The van der Waals swelling ( $var element = document.getElementById("moose-equation-58d6cb2e-cdc6-4fca-9fca-51185471aa5a");katex.render("\\Delta \\varepsilon_{vdw}", element, {displayMode:false,throwOnError:false});$ ) is proportional to the retained gas atoms ( $var element = document.getElementById("moose-equation-32a19e05-70d7-4bf9-a989-d29cd64dc640");katex.render("n_g", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-26da52f6-e2c0-4b37-9a07-554f788d3155");katex.render("mol/m^3", element, {displayMode:false,throwOnError:false});$ ): $(1)var element = document.getElementById("moose-equation-40271520-c678-4537-a5e4-06dd491d8c48");katex.render(" \\varepsilon_{vdw} = b_{\\nu} n_g", element, {displayMode:true,throwOnError:false});$ where, $var element = document.getElementById("moose-equation-9e5f8725-1c2c-474a-bb6e-980c2f648bc1");katex.render("b_{\\nu}", element, {displayMode:false,throwOnError:false});$ is the van der Waals volume of a mole of fission gas atoms ( $var element = document.getElementById("moose-equation-05a162e5-56a1-467f-821d-31d9c8028bc3");katex.render("m^3/mol", element, {displayMode:false,throwOnError:false});$ ).

Ideal Gas Swelling

For the ideal gas swelling ( $var element = document.getElementById("moose-equation-696fa420-9c3b-433f-86b2-f2c2d1d4b8a5");katex.render("\\varepsilon_{ideal}", element, {displayMode:false,throwOnError:false});$ ), the fission gas bubble density ( $var element = document.getElementById("moose-equation-e71d9e9e-b350-4e5e-b9d8-4d923034fa80");katex.render("n_{bub}", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-8886a529-b407-415a-ade9-a7f4a0080a0f");katex.render("m^{-3}", element, {displayMode:false,throwOnError:false});$ ) is calculated as a function of temperature: $(2)var element = document.getElementById("moose-equation-4b1d2002-4f99-4676-877d-8f49d3f9809f");katex.render(" n_{bub} = n_{bub,0}\\exp{\\left(\\frac{Q_{bd}}{RT}\\right)}", element, {displayMode:true,throwOnError:false});$ where, $var element = document.getElementById("moose-equation-732ce6fc-076a-4d5b-bd80-cf22a0330b52");katex.render("n_{bub,0}", element, {displayMode:false,throwOnError:false});$ ( $var element = document.getElementById("moose-equation-a316e0a9-5254-44c6-9763-fc73af80ed40");katex.render("m^{-3}", element, {displayMode:false,throwOnError:false});$ ) is a pre-exponential coefficient, while $var element = document.getElementById("moose-equation-1c76d0ad-80fa-402b-b400-903e55a60eef");katex.render("Q_{bd}", element, {displayMode:false,throwOnError:false});$ is an empirical constant in a nominal form of activation energy ( $var element = document.getElementById("moose-equation-bbc4a938-ecbd-489b-87ac-3ddf8c3be779");katex.render("J/mol", element, {displayMode:false,throwOnError:false});$ ). To prevent extraneous high bubble density at low temperatures. A maximum bubble density (bub_den_max) can be set up to provide an upper limit for this quantity.

According to ideal gas equation of state, the ideal swelling strain ( $var element = document.getElementById("moose-equation-1bb950f1-2440-4879-889d-752869e081ca");katex.render("\\varepsilon_{ideal,eq}", element, {displayMode:false,throwOnError:false});$ ) at equilibrium can be calculated as follows: $(3)var element = document.getElementById("moose-equation-e3b9e34b-60f5-4784-9d71-c5924979a869");katex.render(" \\varepsilon_{ideal,eq} = \\frac{n_g R T}{\\sigma_{pg}}", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-23111933-5ecb-409e-9604-aca224ddf967");katex.render("R", element, {displayMode:false,throwOnError:false});$ is the gas constant ( $var element = document.getElementById("moose-equation-865ab5e7-b9b5-451e-aa5e-0a4ff748b6e5");katex.render("J/mol \\cdot K", element, {displayMode:false,throwOnError:false});$ ) and $var element = document.getElementById("moose-equation-5d62cc5e-935c-47e2-9110-57f46b9073ba");katex.render("T", element, {displayMode:false,throwOnError:false});$ is the thermodynamic temperature ( $var element = document.getElementById("moose-equation-03b83a4e-fd20-4b5e-8ef3-9b4166463197");katex.render("K", element, {displayMode:false,throwOnError:false});$ ), and $var element = document.getElementById("moose-equation-c015441b-0412-4897-9f17-c7c17b559926");katex.render("\\sigma_{pg}", element, {displayMode:false,throwOnError:false});$ ( $var element = document.getElementById("moose-equation-3f23a6dd-c1a9-448d-a42f-4b5f2396812b");katex.render("Pa", element, {displayMode:false,throwOnError:false});$ ) is the sum of hydrostatic stress ( $var element = document.getElementById("moose-equation-150d83b0-acec-4c5f-b05b-8c1d8fd6a20a");katex.render("\\sigma_h", element, {displayMode:false,throwOnError:false});$ ) and surface tension ( $var element = document.getElementById("moose-equation-4dd0a417-2d34-48f8-aa37-22d1ea3aa2a7");katex.render("\\sigma_g", element, {displayMode:false,throwOnError:false});$ ) of a equilibrium bubble: $(4)var element = document.getElementById("moose-equation-562083f0-ecd6-4b6b-aab2-d83357df2d74");katex.render(" \\sigma_{pg} = \\sigma_h + \\sigma_g", element, {displayMode:true,throwOnError:false});$ And the ideal gas swelling strain ( $var element = document.getElementById("moose-equation-78fcfab6-1f7c-4bd1-8b5a-4635b70e8bea");katex.render("\\varepsilon_{ideal}", element, {displayMode:false,throwOnError:false});$ ) has the following expression: $(5)var element = document.getElementById("moose-equation-07eaa9e2-8040-46a9-a441-7b9c3dde168e");katex.render(" \\varepsilon_{ideal}(t+\\Delta t) = \\varepsilon_{ideal}(t) + \\left[ 1-\\exp{(-C_{decay})} \\right] \\left[\\varepsilon_{ideal,eq}-\\varepsilon_{ideal}(t) \\right]", element, {displayMode:true,throwOnError:false});$ where, $var element = document.getElementById("moose-equation-937d00de-3bad-49f5-b389-8fb7a74a8b1d");katex.render("C_{decay}", element, {displayMode:false,throwOnError:false});$ is a decay factor controlled by the creep of the UPuZr alloy around the bubble. The decay factor consists of two parts: $(6)var element = document.getElementById("moose-equation-7caef6aa-7c34-4498-b3dd-b2e9435c0c9a");katex.render(" C_{decay} = \\sigma_{pg}(C_4(Bu,\\dot{f}) + C_5(T,\\sigma_{pg},p_{gas},\\varepsilon_{ideal}(t)))\\Delta t", element, {displayMode:true,throwOnError:false});$ Meanwhile, $(7)var element = document.getElementById("moose-equation-1e1c5603-3de5-4cda-b713-e4e248ff93b2");katex.render(" C_4(Bu,\\dot{f}) = \\left[ C_1 + C_3 \\exp{\\left(-\\frac45Bu\\right)}\\right]C_6\\dot{F}", element, {displayMode:true,throwOnError:false});$ where, $var element = document.getElementById("moose-equation-c154d81e-ec62-4214-ad84-2a0ff7130675");katex.render("C_1", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-c244a184-3b5c-4ee4-aab8-c1dbd78c39ca");katex.render("C_3", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-c2116a1c-0870-4703-96d3-9ba6376a5e61");katex.render("C_6", element, {displayMode:false,throwOnError:false});$ are constants, $var element = document.getElementById("moose-equation-8ac4e82e-2536-47d7-af7a-8fb700a77d1a");katex.render("\\dot{F}", element, {displayMode:false,throwOnError:false});$ is fission density rate ( $var element = document.getElementById("moose-equation-a3bd8058-3773-4b5f-aada-a7e306389111");katex.render("fiss/m^3 \\cdot s", element, {displayMode:false,throwOnError:false});$ ). $(8)var element = document.getElementById("moose-equation-0a0f81e0-babe-4399-a4ff-323fa713fced");katex.render(" C_5(T,\\sigma_h,p_{gas},\\varepsilon_{ideal}(t)) = \\frac{1.5^{k_1+1}C_2\\exp{\\left(-\\frac{Q_2}{RT}\\right)}}{\\left(1-\\varepsilon_{ideal}(t)^\\frac{1}{k_1}\\right)^{k_1}} \\frac{1}{k_1}\\left(\\frac{|\\sigma_{pg}-p_{gas}|}{k_1}\\right)^{k_1}", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-886e0a71-7cfa-4aa0-b10d-3469ab87bb2a");katex.render("k_1", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-4132da6d-46b6-47de-a2a5-6907ad91cb2f");katex.render("Q_2", element, {displayMode:false,throwOnError:false});$ are constants, and $var element = document.getElementById("moose-equation-87776559-2bf1-4c3c-9975-acaa3272a238");katex.render("p_{gas}", element, {displayMode:false,throwOnError:false});$ has the following expression $(9)var element = document.getElementById("moose-equation-350888ab-90d7-43cf-b8a5-2c79947e2f2b");katex.render(" p_{gas} = \\frac{n_g R T}{\\varepsilon_{ideal}(t)}", element, {displayMode:true,throwOnError:false});$ the hydrostatic stress ( $var element = document.getElementById("moose-equation-6a4021f6-74fd-4f14-bbb0-77952e41e716");katex.render("\\sigma_h", element, {displayMode:false,throwOnError:false});$ ) can either be calculated by BISON's tensor mechanics model or use the plenum pressure of the fuel pin (controlled by Boolean variable use_plenum_pressure). The surface tension of an equilibrium fission gas bubble ( $var element = document.getElementById("moose-equation-8e608e8e-c4b6-4791-a18f-7c01b95c5349");katex.render("\\sigma_g", element, {displayMode:false,throwOnError:false});$ ) can be calculated using the surface energy of UPuZr ( $var element = document.getElementById("moose-equation-8529ce4a-7f56-4581-9a98-7863612006b4");katex.render("\\gamma", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-946dd2e1-9255-4980-aa69-f5a290f84d43");katex.render("J/m^2", element, {displayMode:false,throwOnError:false});$ ) and the equilibrium bubble radius ( $var element = document.getElementById("moose-equation-0ea867d3-8935-435d-9bc2-12c150ba8c71");katex.render("r_{eq}", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-fe371256-ce89-4b2d-b105-1b46c8f1d57c");katex.render("m", element, {displayMode:false,throwOnError:false});$ ): $(10)var element = document.getElementById("moose-equation-05891d7e-d5f6-47fc-bf0f-aec2d8be156a");katex.render(" \\sigma_g = 2\\gamma/r_{eq}", element, {displayMode:true,throwOnError:false});$

Controlled by Boolean variable use_preset_bubble_size, the equilibrium bubble radius ( $var element = document.getElementById("moose-equation-aac00087-d103-4ea6-8f81-862543d2f156");katex.render("r_{eq}", element, {displayMode:false,throwOnError:false});$ ) can either be a preset value (preset_bub_size), or calculated by equation of state. To calculate $var element = document.getElementById("moose-equation-e54cf589-f7b1-4c5d-9ade-921bc8f74b40");katex.render("r_{eq}", element, {displayMode:false,throwOnError:false});$ , the average amount of fission gas atoms ( $var element = document.getElementById("moose-equation-e8c78800-b6d0-4bfd-8939-1a5da8871344");katex.render("mol", element, {displayMode:false,throwOnError:false});$ ) exist in a single bubble ( $var element = document.getElementById("moose-equation-4186d2b7-900e-4c32-81d9-7df346031e01");katex.render("N_g", element, {displayMode:false,throwOnError:false});$ ) needs to be calculated first: $(11)var element = document.getElementById("moose-equation-b0628c7c-c8d6-4e67-828d-623c37fd9303");katex.render(" N_g = \\frac{G_s}{n_{bub}}", element, {displayMode:true,throwOnError:false});$ where, $var element = document.getElementById("moose-equation-23d42c82-2f69-4e0a-9f23-7723aa6e91e5");katex.render("G_s", element, {displayMode:false,throwOnError:false});$ is the fission gas amount retained in the fuel as defined in FgrUPuZrLM, $var element = document.getElementById("moose-equation-faa62493-96d4-4714-8ca3-c329b5395ab1");katex.render("n_{bub}", element, {displayMode:false,throwOnError:false});$ is the number density of bubbles as mentioned above.

Knowing the amount of fission gas atoms in one bubble and the bubble density, the equilibrium of fission gas bubble is reached when the fission gas pressure is balanced with the sum of hydrostatic stress and surface tension: $(12)var element = document.getElementById("moose-equation-a25a33f8-ba0f-48be-8185-1394188a54c8");katex.render(" p = \\sigma_h + 2\\gamma/r_{eq}", element, {displayMode:true,throwOnError:false});$

Thus, the equilibrium radius of a fission gas bubble is calculated by solving the following equation using Newton's method: $(13)var element = document.getElementById("moose-equation-95b1536e-a755-4744-ae03-4487183d65e6");katex.render(" \\left(\\sigma_h + \\frac{2\\gamma}{r_{eq}}\\right)\\left(\\frac34 \\pi r_{eq}^3-N_gb_{\\nu}\\right)=N_g R T", element, {displayMode:true,throwOnError:false});$

Solid Swelling

Swelling due to solid fission products is assumed to be proportional to the burnup: $(14)var element = document.getElementById("moose-equation-ff97a5e9-fd5c-4645-8051-ab580f2f11ef");katex.render(" \\varepsilon_{solid} = C_{solid} Bu", element, {displayMode:true,throwOnError:false});$ $var element = document.getElementById("moose-equation-e884753d-39d9-43ab-a911-43212b88565f");katex.render("C_{solid}", element, {displayMode:false,throwOnError:false});$ is a constant with a typical value from 1.2% to 1.5% per 1% atomic burnup. In this model, 1.5% is used so that this solid fission product model is consistent with the other UPuZr models (UPuZrVolumetricSwellingEigenstrain) in BISON. If the dissolution of fission products into liquid sodium is taken into consideration, 1.2% may be a better approximation.

Total Volumetric Swelling

The total volumetric swelling is the summation of contributions from gaseous and solid swelling: $(15)var element = document.getElementById("moose-equation-239764e7-2be0-4735-86b3-986fee9533f9");katex.render(" \\varepsilon_{total} = \\varepsilon_{vdw} + \\varepsilon_{ideal} + \\varepsilon_{solid}", element, {displayMode:true,throwOnError:false});$

Anisotropic Swelling

A simplified anisotropic model based on an anisotropic factor $var element = document.getElementById("moose-equation-e866aabc-c22c-4d1a-bd7b-2e836c6f47a3");katex.render("f", element, {displayMode:false,throwOnError:false});$ is added to this swelling model to provide users a tool to adjust axial-to-radial swelling ratio to fit experiment observations. The volumetric swelling strain needs to be converted to logarithmic strain in three directions. If the swelling is isotropic: $(16)var element = document.getElementById("moose-equation-d9fc9156-dfc8-401b-9d39-60b4410188e2");katex.render(" \\varepsilon_{xx} = \\varepsilon_{yy} = \\varepsilon_{zz} = \\frac13 \\ln{(1+\\varepsilon_{total})}", element, {displayMode:true,throwOnError:false});$

When the anisotropic factor $var element = document.getElementById("moose-equation-9161752c-993d-417f-ba0f-02288136cd06");katex.render("f", element, {displayMode:false,throwOnError:false});$ is involved: $(17)var element = document.getElementById("moose-equation-1d1d4b0f-c9d6-41bf-8487-7febb65bdd74");katex.render(" \\varepsilon_{xx} = \\varepsilon_{zz} = \\frac{f}{3} \\ln{(1+\\varepsilon_{total})}", element, {displayMode:true,throwOnError:false});$ $(18)var element = document.getElementById("moose-equation-8bf51eca-ada0-4c65-8f25-4b37c9432021");katex.render(" \\varepsilon_{yy} = \\frac{3-2f}{3} \\ln{(1+\\varepsilon_{total})}", element, {displayMode:true,throwOnError:false});$

Example Input Syntax

[Materials<<<{"href": "../../../syntax/Materials/index.html"}>>>]
  [gas_swelling]
    type = UPuZrVolumetricSwellingEigenstrainLM<<<{"description": "Computes and sums the change in fuel pellet volume due to solid and gaseous (adopted LIFE-METAL model) fission product buildup in UPuZr.", "href": "UPuZrVolumetricSwellingEigenstrainLM.html"}>>>
    temperature<<<{"description": "Coupled temperature variable (K)"}>>> = temp
    use_plenum_pressure<<<{"description": "Flag to use the plenum pressure instead of the hydrostatic pressure for better stability"}>>> = false
    use_preset_bubble_size<<<{"description": "Flag to use a preset bubble size instead realtime calculationfor better stability and speed"}>>> = true
    initial_porosity<<<{"description": "Initial or fabrication porosity"}>>> = 0.1
    outputs<<<{"description": "Vector of output names where you would like to restrict the output of variables(s) associated with this object"}>>> = all
    output_properties<<<{"description": "List of material properties, from this material, to output (outputs must also be defined to an output type)"}>>> = 'porosity gaseous_porosity gas_swelling_vdw gas_swelling_ideal gas_swelling gas_bubble_radius gas_bubble_density'
    eigenstrain_name<<<{"description": "Material property name for the eigenstrain tensor computed by this model. IMPORTANT: The name of this property must also be provided to the strain calculator."}>>> = gas_swelling_eigenstrain
    anisotropic_factor<<<{"description": "Anisotropic swelling factor for the fuel"}>>> = 1.25
  []
[]

Input Parameters

eigenstrain_nameMaterial property name for the eigenstrain tensor computed by this model. IMPORTANT: The name of this property must also be provided to the strain calculator.
C++ Type:std::string
Controllable:No
Description:Material property name for the eigenstrain tensor computed by this model. IMPORTANT: The name of this property must also be provided to the strain calculator.
temperatureCoupled temperature variable (K)
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Coupled temperature variable (K)

Required Parameters

C_125Fitting parameter
Default:25
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Fitting parameter
C_28.5882e-31Thermal creep fitting factor
Default:8.5882e-31
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Thermal creep fitting factor
C_310Fitting parameter
Default:10
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Fitting parameter
C_67.65478e-35Radiation creep fitting factor
Default:7.65478e-35
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Radiation creep fitting factor
Q_2217568Creep activation energy
Default:217568
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Creep activation energy
Q_bd257734Bubble density formular activation energy
Default:257734
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Bubble density formular activation energy
R8.314Gas constant
Default:8.314
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Gas constant
anisotropic_factor1Anisotropic swelling factor for the fuel
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Anisotropic swelling factor for the fuel
b_v3.387e-05Van der Waals volume
Default:3.387e-05
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Van der Waals volume
base_nameOptional parameter that allows the user to define multiple mechanics material systems on the same block, i.e. for multiple phases
C++ Type:std::string
Controllable:No
Description:Optional parameter that allows the user to define multiple mechanics material systems on the same block, i.e. for multiple phases
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
bub_den_coeff10Bubble density formular coefficient
Default:10
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Bubble density formular coefficient
bub_den_max5e+16maximum bubble density
Default:5e+16
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:maximum bubble density
bub_size_residual_thres1e-12Convergence criteria threshold for buble size calculation use Newton's method
Default:1e-12
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Convergence criteria threshold for buble size calculation use Newton's method
burnupburnupburnup material property name
Default:burnup
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:burnup material property name
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.
fis_gas_retfis_gas_retretained fission gas material property name
Default:fis_gas_ret
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:retained fission gas material property name
fission_ratefission_rateFission rate material property name
Default:fission_rate
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:Fission rate material property name
gm0.8Surface tension of UPuZr
Default:0.8
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Surface tension of UPuZr
hydrostatic_stressCoupled hydrostatic stress variable
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Coupled hydrostatic stress variable
initial_porosity0Initial or fabrication porosity
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Initial or fabrication porosity
k_14.5Thermal creep exponent for porosity
Default:4.5
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Thermal creep exponent for porosity
plenum_pressureplenum_pressureplenum pressure used as hydrostatic pressure
Default:plenum_pressure
C++ Type:PostprocessorName
Unit:(no unit assumed)
Controllable:No
Description:plenum pressure used as hydrostatic pressure
preset_bub_size2.5e-06preset bubble radius
Default:2.5e-06
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:preset bubble radius
use_plenum_pressureTrueFlag to use the plenum pressure instead of the hydrostatic pressure for better stability
Default:True
C++ Type:bool
Controllable:No
Description:Flag to use the plenum pressure instead of the hydrostatic pressure for better stability
use_preset_bubble_sizeTrueFlag to use a preset bubble size instead realtime calculationfor better stability and speed
Default:True
C++ Type:bool
Controllable:No
Description:Flag to use a preset bubble size instead realtime calculationfor better stability and speed

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

gas_swelling_scale_factor1Scale factor to be applied to the gaseous swelling strain. Used for calibration and sensitivity studies
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Scale factor to be applied to the gaseous swelling strain. Used for calibration and sensitivity studies
solid_swelling_scale_factor1Scale factor to be applied to the solid swelling strain. Used for calibration and sensitivity studies
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Scale factor to be applied to the solid swelling strain. Used for calibration and sensitivity studies

Advanced: Scaling Factors 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

(test/tests/solid_mechanics/adupuzr_gas_LM/calc_rad.i)
(assessment/metallic_fuel/EBRII/X447/analysis/legacy/x447_base.i)
(test/tests/solid_mechanics/adupuzr_gas_LM/preset_rad.i)
(test/tests/solid_mechanics/upuzr_gas_LM/calc_rad.i)
(assessment/metallic_fuel/EBRII/X423/analysis/x423_lm_base.i)
(test/tests/solid_mechanics/upuzr_gas_LM/preset_rad.i)

References

AM Yacout and MC Billone. Current status of the life fast reactors fuel performance codes. In Fast Reactors and Related Fuel Cycles: Safe Technologies and Sustainable Scenarios (FR13). COMPANION CD-ROM. Proceedings of an International Conference. 2015.

@inproceedings{yacout2015current,
    author = "Yacout, AM and Billone, MC",
    title = "Current Status of the LIFE Fast Reactors Fuel Performance Codes",
    booktitle = "Fast Reactors and Related Fuel Cycles: Safe Technologies and Sustainable Scenarios (FR13). COMPANION CD-ROM. Proceedings of an International Conference",
    year = "2015"
}

(test/tests/solid_mechanics/upuzr_gas_LM/preset_rad.i)

# This test is to verify the calculation in UPuZrVolumetricSwellingEigenstrainLM and
# FgrUPuZrLM (the preset bubble radius)

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

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

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

[AuxVariables]
  [temp]
    initial_condition = 1000
  []
  [volumetric_strain]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [temp]
    type = ConstantAux
    variable = temp
    value = 1000
  []
  [volumetric_strain]
    type = RankTwoScalarAux
    variable = volumetric_strain
    rank_two_tensor = total_strain
    scalar_type = VolumetricStrain
  []
[]

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

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

[Materials]
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 2.0e11
    poissons_ratio = 0.3
  []
  [fuel_stress]
    type = ComputeFiniteStrainElasticStress
  []
  [fission_rate]
    type = GenericFunctionMaterial
    prop_names = 'fission_rate'
    prop_values = 'fission_rate_func'
    outputs = all
  []
  [burnup]
    type = UPuZrBurnup
    density = 16000
    initial_X_Pu = 0.0
    initial_X_Zr = 0.225
    outputs = all
  []
  [gas_swelling]
    type = UPuZrVolumetricSwellingEigenstrainLM
    temperature = temp
    use_plenum_pressure = false
    use_preset_bubble_size = true
    initial_porosity = 0.1
    outputs = all
    output_properties = 'porosity gaseous_porosity gas_swelling_vdw gas_swelling_ideal gas_swelling gas_bubble_radius gas_bubble_density'
    eigenstrain_name = gas_swelling_eigenstrain
    anisotropic_factor = 1.25
  []

  [fission_gas_behavior]
    type = FgrUPuZrLM
    temperature = temp
    outputs = all
    output_properties = 'fis_gas_prod fis_gas_rel fis_gas_ret'
  []
[]

[Executioner]
  type = Transient

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

[Postprocessors]
  [gas_produced]
    type = ElementAverageValue
    variable = fis_gas_prod
  []
  [gas_released]
    type = ElementAverageValue
    variable = fis_gas_rel
  []
  [gas_retained]
    type = ElementAverageValue
    variable = fis_gas_ret
  []
  [fission_rate]
    type = ElementAverageValue
    variable = fission_rate
  []
  [hydrostatic_stress]
    type = ElementAverageValue
    variable = hydrostatic_stress
  []
  [porosity]
    type = ElementAverageValue
    variable = porosity
  []
  [gaseous_porosity]
    type = ElementAverageValue
    variable = gaseous_porosity
  []
  [gas_swell]
    type = ElementAverageValue
    variable = gas_swelling
  []
  [volumetric_strain]
    type = ElementAverageValue
    variable = volumetric_strain
  []
  [gas_swelling_vdw]
    type = ElementAverageValue
    variable = gas_swelling_vdw
  []
  [gas_swelling_ideal]
    type = ElementAverageValue
    variable = gas_swelling_ideal
  []
  [gas_bubble_radius]
    type = ElementAverageValue
    variable = gas_bubble_radius
  []
  [gas_bubble_density]
    type = ElementAverageValue
    variable = gas_bubble_density
  []
  [strain_xx]
    type = ElementAverageValue
    variable = strain_xx
  []
  [strain_yy]
    type = ElementAverageValue
    variable = strain_yy
  []
[]

[Outputs]
  csv = true
[]

(test/tests/solid_mechanics/adupuzr_gas_LM/calc_rad.i)

# This test is to verify the calculation in ADUPuZrVolumetricSwellingEigenstrainLM and
# ADFgrUPuZrLM (the real-time calculated bubble radius)

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

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

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


[AuxVariables]
  [temp]
    initial_condition = 1000
  []
  [volumetric_strain]
    order = CONSTANT
    family = MONOMIAL
  []
  [gas_swell]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [temp]
    type = ConstantAux
    variable = temp
    value = 1000
  []
  [volumetric_strain]
    type = ADRankTwoScalarAux
    variable = volumetric_strain
    rank_two_tensor = total_strain
    scalar_type = VolumetricStrain
  []
  [gas_swell_aux]
    type = ADMaterialRealAux
    variable = gas_swell
    property = gas_swelling
  []
[]

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

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

[Materials]
  [elasticity_tensor]
    type = ADComputeVariableIsotropicElasticityTensor
    youngs_modulus = 2.0e11
    poissons_ratio = 0.3
  []
  [fuel_stress]
    type = ADComputeFiniteStrainElasticStress
  []
  [fission_rate]
    type = ADGenericFunctionMaterial
    prop_names = 'fission_rate'
    prop_values = 'fission_rate_func'
    outputs = all
  []
  [burnup]
    type = ADUPuZrBurnup
    density = 16000
    initial_X_Pu = 0.0
    initial_X_Zr = 0.225
    outputs = all
  []
  [gas_swelling]
    type = ADUPuZrVolumetricSwellingEigenstrainLM
    temperature = temp
    use_plenum_pressure = false
    use_preset_bubble_size = false
    initial_porosity = 0.1
    outputs = all
    output_properties = 'porosity gaseous_porosity gas_swelling_vdw gas_swelling_ideal gas_swelling gas_bubble_radius gas_bubble_density'
    eigenstrain_name = gas_swelling_eigenstrain
    anisotropic_factor = 1.25
  []

  [fission_gas_behavior]
    type = ADFgrUPuZrLM
    temperature = temp
    outputs = all
    output_properties = 'fis_gas_prod fis_gas_rel fis_gas_ret'
  []
[]

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

[Executioner]
  type = Transient

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

[Postprocessors]
  [gas_produced]
    type = ElementAverageValue
    variable = fis_gas_prod
  []
  [gas_released]
    type = ElementAverageValue
    variable = fis_gas_rel
  []
  [gas_retained]
    type = ElementAverageValue
    variable = fis_gas_ret
  []
  [fission_rate]
    type = ElementAverageValue
    variable = fission_rate
  []
  [hydrostatic_stress]
    type = ElementAverageValue
    variable = hydrostatic_stress
  []
  [porosity]
    type = ElementAverageValue
    variable = porosity
  []
  [gaseous_porosity]
    type = ElementAverageValue
    variable = gaseous_porosity
  []
  [gas_swell]
    type = ElementAverageValue
    variable = gas_swelling
  []
  [volumetric_strain]
    type = ElementAverageValue
    variable = volumetric_strain
  []
  [gas_swelling_vdw]
    type = ElementAverageValue
    variable = gas_swelling_vdw
  []
  [gas_swelling_ideal]
    type = ElementAverageValue
    variable = gas_swelling_ideal
  []
  [gas_bubble_radius]
    type = ElementAverageValue
    variable = gas_bubble_radius
  []
  [gas_bubble_density]
    type = ElementAverageValue
    variable = gas_bubble_density
  []
  [strain_xx]
    type = ElementAverageValue
    variable = strain_xx
  []
  [strain_yy]
    type = ElementAverageValue
    variable = strain_yy
  []
[]

[Outputs]
  csv = true
[]

(assessment/metallic_fuel/EBRII/X447/analysis/legacy/x447_base.i)

[GlobalParams]
  density = ${fuel_density}
  order = FIRST
  family = LAGRANGE
  energy_per_fission = 3.2e-11 # J/fission
  volumetric_locking_correction = false
  displacements = 'disp_x disp_y' # RZ-2D
  X_Pu = ${fuel_pu}
  X_Zr = ${fuel_zr}
[]

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

[Mesh]
  coord_type = RZ
  # Pin design parameters from FIPD database
  [gen]
    type = FIPDRodletMeshGenerator
    fipd_geom_file = ${raw '../../../../../../../fipd-bison-integration-data/X447/ ${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
  []
[]

[Variables]
  [temp]
    initial_condition = 298
  []
[]

[AuxVariables]
  [creep_strain_mag]
    order = CONSTANT
    family = MONOMIAL
  []
  [gap_cond]
    order = CONSTANT
    family = MONOMIAL
  []
  [coolant_htc]
    order = CONSTANT
    family = MONOMIAL
  []
  [cumulative_damage_index]
    order = CONSTANT
    family = MONOMIAL
  []
  [element_failed]
    order = CONSTANT
    family = MONOMIAL
  []
  [solid_swell]
    block = fuel
    order = CONSTANT
    family = MONOMIAL
  []
  [gas_swell]
    block = fuel
    order = CONSTANT
    family = MONOMIAL
  []
  [total_hoop_strain]
    order = CONSTANT
    family = MONOMIAL
  []
  [func_val1] # Just for visualization
  []
  [func_val2] # Just for visualization
  []
  # AuxVariables used for thermal expansion correction
  [fuel_thermal_strain_xx]
    order = CONSTANT
    family = MONOMIAL
    block = fuel
  []
  [fuel_thm_exp]
    order = CONSTANT
    family = MONOMIAL
    block = fuel
  []
  [clad_thermal_eigenstrain_xx]
    order = CONSTANT
    family = MONOMIAL
    block = cladding
  []
  [clad_thm_exp]
    order = CONSTANT
    family = MONOMIAL
    block = cladding
  []
[]

[Functions]
  [clad_od_temp] # Time-dependent cladding OD temperature from FIPD database
    type = FIPDAxialProfileFunction
    data_file = ${raw '../../../../../../../fipd-bison-integration-data/X447/ ${pin_id} /clad_od_temp_history_ ${pin_id} .csv'}
    use_metadata = true
    mesh_generator = gen
  []
  [power_history] # Time-dependent pin average power from FIPD database
    type = PiecewiseLinear
    data_file = ${raw '../../../../../../../fipd-bison-integration-data/X447/ ${pin_id} /power_history_ ${pin_id} .csv'}
  []
  [pwr_axial_peaking_factors] # Power peaking factor from FIPD database; used for fuel related simulations
    type = FIPDAxialProfileFunction
    data_file = ${raw '../../../../../../../fipd-bison-integration-data/X447/ ${pin_id} /peakingfactor_power_relative_ ${pin_id} .csv'}
    use_metadata = true
    mesh_generator = gen
    zero_ends = true
    data_shift_type = peaking
  []
  [pwr_axial_peaking_factors_elongate] # Power peaking factor from FIPD database; used for cladding related simulations
    type = FIPDAxialProfileFunction
    data_file = ${raw '../../../../../../../fipd-bison-integration-data/X447/ ${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
  []
  [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/X447/ ${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/X447/ ${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/X447/ ${pin_id} /flux_history_ ${pin_id} .csv'}
  []
  [flow_rate_history] # Time-dependent flow mass flux from FIPD database; no longer needed if FIPD temperature is used as BC.
    type = PiecewiseLinear
    data_file = ${raw '../../../../../../../fipd-bison-integration-data/X447/ ${pin_id} /flow_history_ ${pin_id} .csv'}
  []
  [coolant_press_ramp]
    type = PiecewiseLinear
    x = '0 ${time_last}'
    y = '0.151e6 0.151e6'
  []
  [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
  []
  [ci_temp] # vpp_function used to track cladding ID temperature.
    type = PiecewiseLinearFromVectorPostprocessor
    argument_column = y
    component = y
    value_column = temp
    vectorpostprocessor_name = clad_inn_temp
  []
  [na_vol] # Get sodium volume from mesh generator
    type = MeshPropertyFunction
    mesh_generator = gen
    mesh_property_name = sodium_volume
    scale_factor = -1.0
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  temperature = temp
  add_variables = true
  [fuel]
    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 volumetric_strain'
    extra_vector_tags = 'ref'
    block = fuel
    eigenstrain_names = 'fuel_thermal_strain fuel_volumetric_strain'
  []
  [clad]
    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 hoop_stress hoop_creep_strain hoop_elastic_strain'
    extra_vector_tags = 'ref'
    block = cladding
    eigenstrain_names = 'clad_thermal_eigenstrain'
  []
[]

[Kernels]
  [gravity]
    type = Gravity
    variable = disp_y
    value = -9.81
    extra_vector_tags = 'ref'
  []
  [heat]
    type = HeatConduction
    variable = temp
    extra_vector_tags = 'ref'
  []
  [heat_ie_f]
    type = HeatConductionTimeDerivative
    variable = temp
    extra_vector_tags = 'ref'
    block = fuel
  []
  [heat_ie_c]
    type = HeatConductionTimeDerivative
    variable = temp
    extra_vector_tags = 'ref'
    block = cladding
  []
  [heat_source]
    type = FissionRateHeatSource
    variable = temp
    fission_rate = fission_rate
    block = fuel
    extra_vector_tags = 'ref'
  []
[]

[AuxKernels]
  [conductance]
    type = MaterialRealAux
    property = gap_conductance
    variable = gap_cond
    boundary = fuel_outer_radial_surface
  []
  [cdf_amount]
    block = cladding
    type = MaterialRealAux
    property = cdf_failure
    variable = cumulative_damage_index
  []
  [failed_element]
    block = cladding
    type = MaterialRealAux
    property = failed
    variable = element_failed
  []
  [gas_swell]
    type = MaterialRealAux
    variable = gas_swell
    property = gas_swelling
    execute_on = timestep_end
  []
  [solid_swell]
    type = MaterialRealAux
    variable = solid_swell
    property = solid_swelling
    execute_on = timestep_end
  []
  [total_hoop_strain]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = total_hoop_strain
    index_j = 2
    index_i = 2
    execute_on = timestep_end
    block = cladding
  []
  [func_val1]
    type = FunctionAux
    function = id_vpp_func
    variable = func_val1
    block = cladding
  []
  [func_val2]
    type = FunctionAux
    function = od_vpp_func
    variable = func_val2
    block = cladding
  []
  # AuxKernels used to correct thermal expansion
  [fuel_thermal_strain_xx]
    type = RankTwoAux
    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_thm_exp]
    type = SpatialUserObjectAux
    variable = fuel_thm_exp
    execute_on = 'initial timestep_end'
    user_object = fuel_thm_exp
    block = fuel
  []
  [clad_thermal_eigenstrain_xx]
    type = RankTwoAux
    rank_two_tensor = clad_thermal_eigenstrain
    variable = clad_thermal_eigenstrain_xx
    index_j = 0
    index_i = 0
    execute_on = 'initial timestep_end'
    block = cladding
  []
  [clad_thm_exp]
    type = SpatialUserObjectAux
    variable = clad_thm_exp
    execute_on = 'initial timestep_end'
    user_object = clad_thm_exp
    block = cladding
  []
[]

[Contact]
  [pellet_clad_mechanical]
    primary = cladding_inside_right
    secondary = fuel_outer_radial_surface
    penalty = 1e12
    model = frictionless
    normalize_penalty = true
    tangential_tolerance = 1e-3
    normal_smoothing_distance = 0.1
  []
[]

[ThermalContact]
  [thermal_contact]
    type = GapHeatTransfer
    variable = temp
    primary = cladding_inside_right
    secondary = fuel_outer_radial_surface
    quadrature = true
    gap_conductivity = 61.0
    min_gap = 0.5e-03 # Adjustable
  []
[]

[BCs]
  [no_x_all]
    type = DirichletBC
    variable = disp_x
    boundary = centerline
    value = 0.0
  []
  [no_y_fuel]
    type = DirichletBC
    variable = disp_y
    boundary = fuel_bottom
    value = 0.0
  []
  [no_y_clad]
    type = DirichletBC
    variable = disp_y
    boundary = cladding_outside_bottom
    value = 0.0
  []
  [fuel_top_temp] # Artificially set fuel top temperature; this could also be a Robin BC. Helps to avoid superhigh fuel top temperature in some extreme cases
    type = FunctionDirichletBC
    boundary = fuel_top
    variable = temp
    function = ci_temp
  []
  [surf] # Setting temperature BC base on FIPD data
    type = FunctionDirichletBC
    variable = temp
    boundary = 'cladding_outside_bottom cladding_outside_right cladding_outside_top'
    function = clad_od_temp
  []
  [Pressure]
    [coolantPressure]
      boundary = 'cladding_outside_bottom cladding_outside_right cladding_outside_top'
      function = coolant_press_ramp
    []
  []
  [PlenumPressure]
    [plenumPressure]
      boundary = 'fuel_outside_all cladding_inside_all'
      initial_pressure = 0.084e6 # Pa
      startup_time = 0
      R = 8.3143
      temperature = ave_temp_interior
      volume = gas_volume
      output = plenum_pressure
      material_input = fis_gas_released
    []
  []
[]

[Materials]
  [fission_rate]
    type = UPuZrFissionRate
    block = fuel
    rod_linear_power = power_history
    axial_power_profile = pwr_axial_peaking_factors
    use_metadata = true
    mesh_generator = gen
    outputs = all
  []
  [fission_rate_elongate]
    type = UPuZrFissionRate
    block = cladding
    fission_rate_name = fission_rate
    rod_linear_power = power_history
    axial_power_profile = pwr_axial_peaking_factors_elongate
    use_metadata = true
    mesh_generator = gen
    outputs = all
  []
  [burnup]
    type = UPuZrBurnup
    initial_X_Pu = ${fuel_pu}
    initial_X_Zr = ${fuel_zr}
    outputs = all
    block = fuel
  []
  [burnup_elongate]
    type = UPuZrBurnup
    initial_X_Pu = ${fuel_pu}
    initial_X_Zr = ${fuel_zr}
    outputs = all
    block = cladding
    burnup_name = burnup
  []
  [fast_neutron_flux]
    type = FastNeutronFlux
    calculate_fluence = true
    rod_ave_lin_pow = flux_history
    axial_power_profile = fflux_axial_peaking_factors
    block = fuel
    factor = 1.0
    outputs = all
  []
  [fast_neutron_flux_elongate]
    type = FastNeutronFlux
    calculate_fluence = true
    rod_ave_lin_pow = flux_history
    axial_power_profile = fflux_axial_peaking_factors_elongate
    block = cladding
    factor = 1.0
    outputs = all
  []
  [fuel_elasticity_tensor]
    type = UPuZrElasticityTensor
    block = fuel
    temperature = temp
  []
  [fuel_elastic_stress]
    type = ComputeMultipleInelasticStress
    tangent_operator = nonlinear
    inelastic_models = 'fuel_upuzrcreep'
    block = fuel
  []
  [fuel_upuzrcreep]
    type = UPuZrCreepUpdate
    block = fuel
    temperature = temp
    porosity = porosity
    max_inelastic_increment = 2e-3
  []
  [fuel_thermal_expansion]
    type = ComputeThermalExpansionEigenstrain
    block = fuel
    thermal_expansion_coeff = 1.18e-5
    temperature = temp
    stress_free_temperature = 295.0
    eigenstrain_name = fuel_thermal_strain
    outputs = all
  []
  [fuel_volumetric_swelling] # Use LIFE-METAL Empirical model
    type = UPuZrVolumetricSwellingEigenstrainLM
    block = fuel
    use_preset_bubble_size = true
    anisotropic_factor = 1.26
    temperature = temp
    fission_rate = fission_rate
    burnup = burnup
    fis_gas_ret = fis_gas_ret
    hydrostatic_stress = hydrostatic_stress
    eigenstrain_name = fuel_volumetric_strain
    gas_swelling_scale_factor = 1.0
    outputs = all
  []
  [metal_fuel_thermal]
    type = UPuZrThermal
    block = fuel
    spheat_model = savage
    thcond_model = lanl
    porosity = porosity
    temperature = temp
  []
  [fuel_density]
    type = StrainAdjustedDensity
    displacements = 'disp_x disp_y'
    block = fuel
    strain_free_density = ${fuel_density}
  []
  [fission_gas_behavior]
    type = FgrUPuZrLM
    block = fuel
    temperature = temp
    fission_rate = fission_rate
    epsilon_c = 0.36
  []
  [clad_elasticity_tensor]
    type = HT9ElasticityTensor
    temperature = temp
    id_wastage_degradation_function = id_vpp_func
    od_wastage_degradation_function = od_vpp_func
    block = cladding
  []
  [clad_stress]
    type = ComputeMultipleInelasticStress
    tangent_operator = nonlinear
    inelastic_models = 'clad_ht9creep'
    block = cladding
  []
  [clad_ht9creep]
    type = HT9CreepUpdate
    block = cladding
    temperature = temp
    fast_neutron_flux = fast_neutron_flux
    id_wastage_degradation_function = id_vpp_func
    od_wastage_degradation_function = od_vpp_func
  []
  [thermal_expansion]
    type = ComputeThermalExpansionEigenstrain
    block = cladding
    thermal_expansion_coeff = 1.2e-5
    temperature = temp
    stress_free_temperature = 295.0
    eigenstrain_name = clad_thermal_eigenstrain
    outputs = all
  []
  [clad_thermal]
    type = HT9Thermal
    block = cladding
    temperature = temp
  []
  [clad_density]
    type = StrainAdjustedDensity
    block = cladding
    strain_free_density = 7874.0
  []
  [longHT9_failure]
    type = HT9FailureClad
    block = cladding
    method = cdf_long
    temperature = temp
    outputs = all
    hoop_stress = stress_zz # Since 2D-RZ
  []
  [wastage_thickness]
    type = MetallicFuelWastage
    method = burnup_ht9_opt
    burnup = burnup
    temperature = temp
    scale_factor = 1
    boundary = cladding_inside_right
    outputs = all
  []
  [cc_wastage_thickness]
    type = MetallicFuelCoolantWastage
    clad_material = HT9
    use_effective_method = true
    temperature = temp
    scale_factor = 1
    boundary = cladding_outside_right
    outputs = all
  []
[]

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

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

[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' #51
  line_search = 'none'

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

  end_time = ${time_last}
  dtmin = 1
  dtmax = ${max_dt}

  [Quadrature]
    order = fifth
    side_order = seventh
  []
  [TimeStepper]
    type = IterationAdaptiveDT
    timestep_limiting_function = power_history
    max_function_change = 300
    timestep_limiting_postprocessor = creep_timestep
    dt = 100
    time_t = '0 9300'
    time_dt = '100 100'
    iteration_window = 2
    optimal_iterations = 10
    force_step_every_function_point = true
  []
[]

[Postprocessors]
  [ave_temp_interior]
    type = SideAverageValue
    boundary = cladding_inside_top
    variable = temp
    execute_on = 'initial linear'
  []
  [approx_FCT]
    type = AverageNodalVariableValue
    boundary = centerline
    variable = temp
  []
  [max_approx_FCT]
    type = TimeExtremeValue
    value_type = max
    postprocessor = approx_FCT
  []
  [ave_FST]
    type = SideAverageValue
    boundary = fuel_outer_radial_surface
    variable = temp
  []
  [max_ave_FST]
    type = TimeExtremeValue
    value_type = max
    postprocessor = ave_FST
  []
  [ave_CIT]
    type = SideAverageValue
    boundary = cladding_inside_right
    variable = temp
  []
  [max_ave_CIT]
    type = TimeExtremeValue
    value_type = max
    postprocessor = ave_CIT
  []
  [avg_clad_temp]
    type = ElementAverageValue
    variable = temp
    block = cladding
  []
  [peak_clad_temp]
    type = ElementExtremeValue
    variable = temp
    value_type = max
    block = cladding
  []
  [peak_fuel_temp]
    type = ElementExtremeValue
    variable = temp
    value_type = max
    block = fuel
  []
  [max_hydro]
    type = ElementExtremeValue
    variable = hydrostatic_stress
    value_type = max
    block = fuel
  []
  [min_hydro]
    type = ElementExtremeValue
    variable = hydrostatic_stress
    value_type = min
    block = fuel
  []
  [avg_hydro]
    type = ElementAverageValue
    variable = hydrostatic_stress
    block = fuel
  []
  [peak_porosity]
    type = ElementExtremeValue
    variable = porosity
    value_type = max
    block = fuel
  []
  [clad_inner_vol]
    type = InternalVolume
    boundary = cladding_inside_all
  []
  [pellet_volume]
    type = InternalVolume
    boundary = fuel_outside_all
  []
  [gas_volume]
    type = InternalVolume
    boundary = 'fuel_outside_all cladding_inside_all'
    execute_on = 'initial timestep_end'
    addition = na_vol
  []
  [clad_fuel_gap]
    type = NodalExtremeValue
    variable = penetration
    boundary = fuel_outer_radial_surface
  []
  [max_cont_press]
    type = NodalExtremeValue
    variable = contact_pressure
    boundary = fuel_outer_radial_surface
  []
  [flux_from_clad]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = cladding_inside_right
    diffusivity = thermal_conductivity
  []
  [flux_from_fuel]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = fuel_outer_radial_surface
    diffusivity = thermal_conductivity
  []
  [rod_total_power]
    type = ElementIntegralPower
    variable = temp
    use_material_fission_rate = true
    fission_rate_material = fission_rate
    block = fuel
  []
  [LHGR_W_per_cm]
    type = FunctionValuePostprocessor
    function = power_history
    scale_factor = 0.01
  []
  [average_burnup]
    type = ElementAverageValue
    block = fuel
    variable = burnup
  []
  [max_cdf]
    type = ElementExtremeValue
    value_type = max
    variable = cumulative_damage_index
  []
  [fis_gas_produced]
    type = ElementIntegralMaterialProperty
    mat_prop = fis_gas_prod
    block = fuel
  []
  [fis_gas_released]
    type = ElementIntegralMaterialProperty
    mat_prop = fis_gas_rel
    block = fuel
    execute_on = 'initial timestep_end'
  []
  [creep_timestep]
    type = MaterialTimeStepPostprocessor
    block = fuel
  []
  [hydrostatic_stress]
    type = ElementAverageValue
    variable = hydrostatic_stress
    execute_on = 'initial timestep_end'
    block = fuel
  []
  [solid_swelling]
    type = ElementAverageValue
    variable = solid_swell
    block = fuel
  []
  [gas_swelling]
    type = ElementAverageValue
    variable = gas_swell
    block = fuel
  []
  [volumetric_strain]
    type = ElementAverageValue
    variable = volumetric_strain
    block = fuel
  []
  [fission_rate]
    type = ElementAverageValue
    variable = fission_rate
    block = fuel
  []
  [porosity]
    type = ElementAverageValue
    variable = porosity
    block = fuel
  []
  [gaseous_porosity]
    type = ElementAverageValue
    variable = gaseous_porosity
    block = fuel
  []
  [fis_gas_percent]
    type = FGRPercent
    fission_gas_released = fis_gas_released
    fission_gas_generated = fis_gas_produced
  []
  [max_clad_hoop_creep]
    type = ElementExtremeValue
    value_type = max
    block = cladding
    variable = hoop_creep_strain
  []
  [max_clad_creep_strain_mag]
    type = ElementExtremeValue
    value_type = max
    block = cladding
    variable = creep_strain_mag
  []
  [max_total_hoop_strain]
    type = ElementExtremeValue
    value_type = max
    block = cladding
    variable = total_hoop_strain
  []
  [max_fuel_elongation]
    type = NodalExtremeValue
    variable = disp_y
    boundary = fuel_outside_all
  []
  [max_clad_elongation]
    type = NodalExtremeValue
    variable = disp_y
    boundary = 'cladding_outside_top cladding_outside_right'
  []
  [max_wastagethickness]
    type = ElementExtremeValue
    value_type = max
    variable = wastage_thickness
    outputs = 'console'
  []
  [avg_fuel_temp]
    type = ElementAverageValue
    variable = temp
    block = fuel
    execute_on = 'initial timestep_end'
    allow_duplicate_execution_on_initial = true
  []
[]

[VectorPostprocessors]
  [clad_x_disp]
    type = NodalValueSampler
    variable = disp_x
    boundary = cladding_outside_right
    sort_by = y
    outputs = none
  []
  [fuel_cl_temp]
    type = NodalValueSampler
    variable = temp
    boundary = centerline
    sort_by = y
    outputs = none
  []
  [fuel_surf_temp]
    type = NodalValueSampler
    variable = temp
    boundary = fuel_outer_radial_surface
    sort_by = y
    outputs = none
  []
  [clad_inn_temp]
    type = NodalValueSampler
    variable = temp
    boundary = cladding_inside_right
    sort_by = y
    execute_on = 'initial timestep_end'
    allow_duplicate_execution_on_initial = true
    outputs = none
  []
  [clad_out_temp]
    type = NodalValueSampler
    variable = temp
    boundary = cladding_outside_right
    sort_by = y
    outputs = none
  []
  [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
  []
  [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
  []
  [nrad_comparison_a]
    type = FIPDAxialPIEComparison
    boundary = cladding_outside_right
    sort_by = y
    csv_file = ${raw '../../../../../../../fipd-bison-integration-data/X447/ ${pin_id} /X447A_ ${pin_id} _PR.csv'}
    variable = disp_x
    thermal_strain_variable = clad_thm_exp
    involved_component = cladding
    mesh_generator = gen
    series_type_to_read = 'Cladding O.D. (mils)'
    outputs = csv_vpp_a
    enable = ${enable_a}
  []
[]

[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
  []
[]

[Outputs]
  perf_graph = true
  checkpoint = false
  color = true
  [console]
    type = Console
    max_rows = 25
    time_step_interval =  1
    output_linear = true
    sync_times = ${time_spots}
  []
  [csv_vpp_a]
    type = CSV
    sync_only = true
    sync_times = ${time_spots_a}
    enable = ${enable_a}
    execute_postprocessors_on = none
    create_latest_symlink = true
  []
  [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
  []
  [exodus]
    type = Exodus
    time_step_interval =  20
    sync_times = ${time_spots}
    enable = false
  []
[]

(test/tests/solid_mechanics/adupuzr_gas_LM/preset_rad.i)

# This test is to verify the calculation in ADUPuZrVolumetricSwellingEigenstrainLM and
# ADFgrUPuZrLM (the preset bubble radius)

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

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

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


[AuxVariables]
  [temp]
    initial_condition = 1000
  []
  [volumetric_strain]
    order = CONSTANT
    family = MONOMIAL
  []
  [gas_swell]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [temp]
    type = ConstantAux
    variable = temp
    value = 1000
  []
  [volumetric_strain]
    type = ADRankTwoScalarAux
    variable = volumetric_strain
    rank_two_tensor = total_strain
    scalar_type = VolumetricStrain
  []
  [gas_swell_aux]
    type = ADMaterialRealAux
    variable = gas_swell
    property = gas_swelling
  []
[]

[Functions]
  [fission_rate_func]
    type = PiecewiseLinear
    x = '0 7e7'
    y = '0 2.5e19'
  []
  [pressure_func]
    type = PiecewiseLinear
    x = '0 7e7'
    y = '0 1e6'
  []
  [fuel_melting_func]
    type = PiecewiseLinear
    x = '0 3e7 5e7 7e7'
    y = '1 1 0 0'
  []
[]

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

[Materials]
  [elasticity_tensor]
    type = ADComputeVariableIsotropicElasticityTensor
    youngs_modulus = 2.0e11
    poissons_ratio = 0.3
  []
  [fuel_stress]
    type = ADComputeFiniteStrainElasticStress
  []
  [fission_rate]
    type = ADGenericFunctionMaterial
    prop_names = 'fission_rate'
    prop_values = 'fission_rate_func'
    outputs = all
  []
  [burnup]
    type = ADUPuZrBurnup
    density = 16000
    initial_X_Pu = 0.0
    initial_X_Zr = 0.225
    outputs = all
  []
  [gas_swelling]
    type = ADUPuZrVolumetricSwellingEigenstrainLM
    temperature = temp
    use_plenum_pressure = false
    use_preset_bubble_size = true
    initial_porosity = 0.1
    outputs = all
    output_properties = 'porosity gaseous_porosity gas_swelling_vdw gas_swelling_ideal gas_swelling gas_bubble_radius gas_bubble_density'
    eigenstrain_name = gas_swelling_eigenstrain
    anisotropic_factor = 1.25
  []

  [fission_gas_behavior]
    type = ADFgrUPuZrLM
    temperature = temp
    outputs = all
    output_properties = 'fis_gas_prod fis_gas_rel fis_gas_ret'
  []
[]

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

[Executioner]
  type = Transient

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

[Postprocessors]
  [gas_produced]
    type = ElementAverageValue
    variable = fis_gas_prod
  []
  [gas_released]
    type = ElementAverageValue
    variable = fis_gas_rel
  []
  [gas_retained]
    type = ElementAverageValue
    variable = fis_gas_ret
  []
  [fission_rate]
    type = ElementAverageValue
    variable = fission_rate
  []
  [hydrostatic_stress]
    type = ElementAverageValue
    variable = hydrostatic_stress
  []
  [porosity]
    type = ElementAverageValue
    variable = porosity
  []
  [gaseous_porosity]
    type = ElementAverageValue
    variable = gaseous_porosity
  []
  [gas_swell]
    type = ElementAverageValue
    variable = gas_swelling
  []
  [volumetric_strain]
    type = ElementAverageValue
    variable = volumetric_strain
  []
  [gas_swelling_vdw]
    type = ElementAverageValue
    variable = gas_swelling_vdw
  []
  [gas_swelling_ideal]
    type = ElementAverageValue
    variable = gas_swelling_ideal
  []
  [gas_bubble_radius]
    type = ElementAverageValue
    variable = gas_bubble_radius
  []
  [gas_bubble_density]
    type = ElementAverageValue
    variable = gas_bubble_density
  []
  [strain_xx]
    type = ElementAverageValue
    variable = strain_xx
  []
  [strain_yy]
    type = ElementAverageValue
    variable = strain_yy
  []
[]

[Outputs]
  csv = true
[]

(test/tests/solid_mechanics/upuzr_gas_LM/calc_rad.i)

# This test is to verify the calculation in UPuZrVolumetricSwellingEigenstrainLM and
# FgrUPuZrLM (the real-time calculated bubble radius)

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

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

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

[AuxVariables]
  [temp]
    initial_condition = 1000
  []
  [volumetric_strain]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [temp]
    type = ConstantAux
    variable = temp
    value = 1000
  []
  [volumetric_strain]
    type = RankTwoScalarAux
    variable = volumetric_strain
    rank_two_tensor = total_strain
    scalar_type = VolumetricStrain
  []
[]

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

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

[Materials]
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 2.0e11
    poissons_ratio = 0.3
  []
  [fuel_stress]
    type = ComputeFiniteStrainElasticStress
  []
  [fission_rate]
    type = GenericFunctionMaterial
    prop_names = 'fission_rate'
    prop_values = 'fission_rate_func'
    outputs = all
  []
  [burnup]
    type = UPuZrBurnup
    density = 16000
    initial_X_Pu = 0.0
    initial_X_Zr = 0.225
    outputs = all
  []
  [gas_swelling]
    type = UPuZrVolumetricSwellingEigenstrainLM
    temperature = temp
    use_plenum_pressure = false
    use_preset_bubble_size = false
    initial_porosity = 0.1
    outputs = all
    output_properties = 'porosity gaseous_porosity gas_swelling_vdw gas_swelling_ideal gas_swelling gas_bubble_radius gas_bubble_density'
    eigenstrain_name = gas_swelling_eigenstrain
    anisotropic_factor = 1.25
  []

  [fission_gas_behavior]
    type = FgrUPuZrLM
    temperature = temp
    outputs = all
    output_properties = 'fis_gas_prod fis_gas_rel fis_gas_ret'
  []
[]

[Executioner]
  type = Transient

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

[Postprocessors]
  [gas_produced]
    type = ElementAverageValue
    variable = fis_gas_prod
  []
  [gas_released]
    type = ElementAverageValue
    variable = fis_gas_rel
  []
  [gas_retained]
    type = ElementAverageValue
    variable = fis_gas_ret
  []
  [fission_rate]
    type = ElementAverageValue
    variable = fission_rate
  []
  [hydrostatic_stress]
    type = ElementAverageValue
    variable = hydrostatic_stress
  []
  [porosity]
    type = ElementAverageValue
    variable = porosity
  []
  [gaseous_porosity]
    type = ElementAverageValue
    variable = gaseous_porosity
  []
  [gas_swell]
    type = ElementAverageValue
    variable = gas_swelling
  []
  [volumetric_strain]
    type = ElementAverageValue
    variable = volumetric_strain
  []
  [gas_swelling_vdw]
    type = ElementAverageValue
    variable = gas_swelling_vdw
  []
  [gas_swelling_ideal]
    type = ElementAverageValue
    variable = gas_swelling_ideal
  []
  [gas_bubble_radius]
    type = ElementAverageValue
    variable = gas_bubble_radius
  []
  [gas_bubble_density]
    type = ElementAverageValue
    variable = gas_bubble_density
  []
  [strain_xx]
    type = ElementAverageValue
    variable = strain_xx
  []
  [strain_yy]
    type = ElementAverageValue
    variable = strain_yy
  []
[]

[Outputs]
  csv = true
[]

(assessment/metallic_fuel/EBRII/X423/analysis/x423_lm_base.i)

[GlobalParams]
  density = ${fuel_density}
  order = FIRST
  family = LAGRANGE
  energy_per_fission = 3.2e-11  # J/fission
  volumetric_locking_correction = true
  displacements = 'disp_x disp_y'
  X_Pu = ${fuel_pu}
  X_Zr = ${fuel_zr}
[]

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

[Mesh]
  coord_type = RZ
  [gen]
    type = FIPDRodletMeshGenerator
    fipd_geom_file = ${raw '../../../../../../fipd-bison-integration-data/X423/ ${pin_id} / ${pin_id} _design.csv'}
    fipd_as_fabricated_file = ${raw '../../../../../../fipd-bison-integration-data/X423/ ${pin_id} / ${pin_id} _as_fabricated.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
  []
[]

[Variables]
  [temp]
    initial_condition = 298
  []
[]

[AuxVariables]
  # Aux variables for output
  [creep_strain_mag]
    order = CONSTANT
    family = MONOMIAL
  []
  [gap_cond]
    order = CONSTANT
    family = MONOMIAL
  []
  [coolant_htc]
    order = CONSTANT
    family = MONOMIAL
  []
  [cumulative_damage_index]
    order = CONSTANT
    family = MONOMIAL
  []
  [element_failed]
    order = CONSTANT
    family = MONOMIAL
  []
  [solid_swell]
    block = fuel
    order = CONSTANT
    family = MONOMIAL
  []
  [gas_swell]
    block = fuel
    order = CONSTANT
    family = MONOMIAL
  []
  [volumetric_strain]
    block = fuel
    order = CONSTANT
    family = MONOMIAL
  []
  [hoop_stress]
    order = CONSTANT
    family = MONOMIAL
  []
  [hoop_creep_strain]
    order = CONSTANT
    family = MONOMIAL
  []
  [hoop_elastic_strain]
    order = CONSTANT
    family = MONOMIAL
  []
  [total_hoop_strain]
    order = CONSTANT
    family = MONOMIAL
  []
  [func_val1]
  []
  [func_val2]
  []
  # AuxVariables used for thermal expansion correction
  [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
  []
  [clad_thermal_eigenstrain_xx]
    order = CONSTANT
    family = MONOMIAL
    block = cladding
  []
  [clad_thm_exp]
    order = CONSTANT
    family = MONOMIAL
    block = cladding
  []
[]

[Functions]  #copied from fipd-tdep
  [clad_od_temp]
    type =  FIPDAxialProfileFunction
    data_file = ${raw '../../../../../../fipd-bison-integration-data/X423/ ${pin_id} /clad_od_temp_history_ ${pin_id} .csv'}
    use_metadata = true
    mesh_generator = gen
  []
  [power_history]
    type = PiecewiseLinear
    data_file = ${raw '../../../../../../fipd-bison-integration-data/X423/ ${pin_id} /power_history_ ${pin_id} .csv'}
  []
  [pwr_axial_peaking_factors]
    type = FIPDAxialProfileFunction
    data_file = ${raw '../../../../../../fipd-bison-integration-data/X423/ ${pin_id} /peakingfactor_power_relative_ ${pin_id} .csv'}
    use_metadata = true
    mesh_generator = gen
    zero_ends = true
    data_shift_type = peaking
  []
  [pwr_axial_peaking_factors_elongate]
    type = FIPDAxialProfileFunction
    data_file = ${raw '../../../../../../fipd-bison-integration-data/X423/ ${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
  []
  [fflux_axial_peaking_factors]
    type = FIPDAxialProfileFunction
    data_file = ${raw '../../../../../../fipd-bison-integration-data/X423/ ${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]
    type = FIPDAxialProfileFunction
    data_file = ${raw '../../../../../../fipd-bison-integration-data/X423/ ${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
  []
  [flux_history]
    type = PiecewiseLinear
    data_file = ${raw '../../../../../../fipd-bison-integration-data/X423/ ${pin_id} /flux_history_ ${pin_id} .csv'}
  []
  [coolant_press_ramp]
    type = PiecewiseLinear
    x = '0 56465640'
    y = '0.151e6 0.151e6'
  []
  [id_vpp_func]
    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]
    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
  []
  [ci_temp]
    type = PiecewiseLinearFromVectorPostprocessor
    argument_column = y
    component = y
    value_column = temp
    vectorpostprocessor_name = clad_inn_temp
  []
  [na_vol]
    type = MeshPropertyFunction
    mesh_generator = gen
    mesh_property_name = sodium_volume
    scale_factor = -1.0
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  temperature = temp
  [fuel]
    strain = FINITE
    add_variables = true
    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 = fuel
    eigenstrain_names = 'fuel_thermal_strain fuel_volumetric_strain'
  []
  [clad]
    strain = FINITE
    add_variables = true
    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
    eigenstrain_names = 'clad_swelling clad_thermal_eigenstrain'
  []
[]

[Kernels]
  # Define kernels for the various terms in the PDE system
  [gravity]
    type = Gravity
    variable = disp_y
    value = -9.81
    extra_vector_tags = 'ref'
  []
  [heat]
    type = HeatConduction
    variable = temp
    extra_vector_tags = 'ref'
  []
  [heat_ie_f]
    type = HeatConductionTimeDerivative
    variable = temp
    extra_vector_tags = 'ref'
    block = fuel
    density_name = density
  []
  [heat_ie_c]
    type = HeatConductionTimeDerivative
    variable = temp
    extra_vector_tags = 'ref'
    block = cladding
    density_name = density
  []
  [heat_source]
    type = FissionRateHeatSource
    variable = temp
    fission_rate = fission_rate
    block = fuel
    extra_vector_tags = 'ref'
  []
[]

[AuxKernels]
  [conductance]
    type = MaterialRealAux
    property = gap_conductance
    variable = gap_cond
    boundary = fuel_outer_radial_surface
  []
  [cdf_amount]
    block = cladding
    type = MaterialRealAux
    property = cdf_failure
    variable = cumulative_damage_index
  []
  [failed_element]
    boundary = 'cladding_outside_right'
    type = MaterialRealAux
    property = failed
    variable = element_failed
  []
  [gas_swell]
    type = MaterialRealAux
    variable = gas_swell
    property = gas_swelling
    execute_on = timestep_end
  []
  [solid_swell]
    type = MaterialRealAux
    variable = solid_swell
    property = solid_swelling
    execute_on = timestep_end
  []
  [volumetric_strain]
    type = RankTwoScalarAux
    rank_two_tensor = total_strain
    variable = volumetric_strain
    scalar_type = VolumetricStrain
    execute_on = timestep_end
    block = fuel
  []
  [hoop_stress]
    type = RankTwoAux
    rank_two_tensor = stress
    variable = hoop_stress
    index_j = 2
    index_i = 2
    execute_on = timestep_end
  []
  [hoop_creep_strain]
    type = RankTwoAux
    rank_two_tensor = creep_strain
    variable = hoop_creep_strain
    index_j = 2
    index_i = 2
    execute_on = timestep_end
    block = cladding
  []
  [hoop_elastic_strain]
    type = RankTwoAux
    rank_two_tensor = elastic_strain
    variable = hoop_elastic_strain
    index_j = 2
    index_i = 2
    execute_on = timestep_end
    block = cladding
  []
  [total_hoop_strain]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = total_hoop_strain
    index_j = 2
    index_i = 2
    execute_on = timestep_end
    block = cladding
  []
  [func_val1]
    type = FunctionAux
    function = id_vpp_func
    variable = func_val1
    block = cladding
  []
  [func_val2]
    type = FunctionAux
    function = od_vpp_func
    variable = func_val2
    block = cladding
  []
  # AuxKernels used to correct thermal expansion
  [fuel_thermal_strain_xx]
    type = RankTwoAux
    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 = RankTwoAux
    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
  []
  [clad_thermal_eigenstrain_xx]
    type = RankTwoAux
    rank_two_tensor = clad_thermal_eigenstrain
    variable = clad_thermal_eigenstrain_xx
    index_j = 0
    index_i = 0
    execute_on = 'initial timestep_end'
    block = cladding
  []
  [clad_thm_exp]
    type = SpatialUserObjectAux
    variable = clad_thm_exp
    execute_on = 'initial timestep_end'
    user_object = clad_thm_exp
    block = cladding
  []
[]

[Contact]
  [pellet_clad_mechanical]
    primary = cladding_inside_right
    secondary = fuel_outer_radial_surface
    penalty = 1e12
    model = frictionless
    normalize_penalty = true
    tangential_tolerance = 1e-3
    normal_smoothing_distance = 0.1
  []
[]

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

[BCs]
  [no_x_all]
    type = DirichletBC
    variable = disp_x
    boundary = centerline
    value = 0.0
  []
  [no_y_fuel]
    type = DirichletBC
    variable = disp_y
    boundary = fuel_bottom
    value = 0.0
  []
  [no_y_clad]
    type = DirichletBC
    variable = disp_y
    boundary = cladding_outside_bottom
    value = 0.0
  []
  [fuel_top_temp]
    type = FunctionDirichletBC
    boundary = fuel_top
    variable = temp
    function = ci_temp
  []
  [surf] #copied from fipd-tdep
    type = FunctionDirichletBC
    variable = temp
    boundary = 'cladding_outside_bottom cladding_outside_right cladding_outside_top'
    function = clad_od_temp
  []
  [Pressure]
    [coolantPressure]
      boundary = 'cladding_outside_bottom cladding_outside_right cladding_outside_top'
      function = coolant_press_ramp
    []
  []
  [PlenumPressure]
    [plenumPressure]
      boundary = 'fuel_outside_all cladding_inside_all'
      initial_pressure = 0.084e6 # Pa
      startup_time = 0
      R = 8.3143
      temperature = ave_temp_interior
      volume = gas_volume
      output = plenum_pressure
      material_input = fis_gas_released
    []
  []
[]

[Materials]
  [fission_rate]
    type = UPuZrFissionRate
    block = fuel
    rod_linear_power = power_history
    axial_power_profile = pwr_axial_peaking_factors
    use_metadata = true
    mesh_generator = gen
    outputs = all
  []
  [fission_rate_elongate]
    type = UPuZrFissionRate
    block = cladding
    fission_rate_name = fission_rate
    rod_linear_power = power_history
    axial_power_profile = pwr_axial_peaking_factors_elongate
    use_metadata = true
    mesh_generator = gen
    outputs = all
  []
  [burnup]
    type = UPuZrBurnup
    initial_X_Pu = ${fuel_pu}
    initial_X_Zr = ${fuel_zr}
    density = ${fuel_density}
    outputs = all
    block = fuel
  []
  [burnup_elongate]
    type = UPuZrBurnup
    initial_X_Pu = ${fuel_pu}
    initial_X_Zr = ${fuel_zr}
    density = ${fuel_density}
    outputs = all
    block = cladding
    burnup_name = burnup
  []
  [fast_neutron_flux]
    type = FastNeutronFlux
    calculate_fluence = true
    rod_ave_lin_pow = flux_history
    axial_power_profile = fflux_axial_peaking_factors
    block = fuel
    factor = 1.0
    outputs = all
  []
  [fast_neutron_flux_elongate]
    type = FastNeutronFlux
    calculate_fluence = true
    rod_ave_lin_pow = flux_history
    axial_power_profile = fflux_axial_peaking_factors_elongate
    block = cladding
    factor = 1.0
    outputs = all
  []
  [fuel_elasticity_tensor]
    type = UPuZrElasticityTensor
    block = fuel
    temperature = temp
  []
  [fuel_elastic_stress]
    type = ComputeMultipleInelasticStress
    tangent_operator = nonlinear
    inelastic_models = 'fuel_upuzrcreep'
    block = fuel
  []
  [fuel_upuzrcreep]
    type = UPuZrCreepUpdate
    block = fuel
    temperature = temp
    porosity = porosity
    max_inelastic_increment = 2e-3
  []
  [fuel_thermal_expansion]
    type = ComputeThermalExpansionEigenstrain
    block = fuel
    thermal_expansion_coeff = 1.18e-5
    temperature = temp
    stress_free_temperature = 295.0
    eigenstrain_name = fuel_thermal_strain
  []
  [fuel_volumetric_swelling]
    type = UPuZrVolumetricSwellingEigenstrainLM
    block = fuel
    use_preset_bubble_size = true
    anisotropic_factor = 1.26
    temperature = temp
    fission_rate = fission_rate
    burnup = burnup
    fis_gas_ret = fis_gas_ret
    hydrostatic_stress = hydrostatic_stress
    eigenstrain_name = fuel_volumetric_strain
    gas_swelling_scale_factor = 1.0
    outputs = all
  []
  [metal_fuel_thermal]
    type = UPuZrThermal
    block = fuel
    spheat_model = savage
    thcond_model = lanl
    porosity = porosity
    temperature = temp
  []
  [fuel_density]
    type = StrainAdjustedDensity
    displacements = 'disp_x disp_y'
    block = fuel
    strain_free_density = ${fuel_density}
  []
  [fission_gas_behavior]
    type = FgrUPuZrLM
    block = fuel
    temperature = temp
    fission_rate = fission_rate
    epsilon_c = 0.36
  []
  [clad_elasticity_tensor]
    type = SS316ElasticityTensor
    temperature = temp
    id_wastage_degradation_function = id_vpp_func
    od_wastage_degradation_function = od_vpp_func
    block = cladding
    elastic_constants_model = legacy_ifr
  []
  [clad_stress]
    type = ComputeMultipleInelasticStress
    tangent_operator = nonlinear
    inelastic_models = 'clad_ss316creep'
    block = cladding
  []
  [clad_ss316creep]
    type = SS316CreepUpdate
    block = cladding
    temperature = temp
    fast_neutron_flux = fast_neutron_flux
    id_wastage_degradation_function = id_vpp_func
    od_wastage_degradation_function = od_vpp_func
  []
  [clad_swelling]
    type = SS316VolumetricSwellingEigenstrain
    eigenstrain_name = clad_swelling
    fast_neutron_fluence = fast_neutron_fluence
    fast_neutron_flux = fast_neutron_flux
    temperature = temp
    outputs = all
  []
  [thermal_expansion]
    type = SS316ThermalExpansionEigenstrain
    block = cladding
    temperature = temp
    stress_free_temperature = 295.0
    eigenstrain_name = clad_thermal_eigenstrain
  []
  [clad_thermal]
    type = SS316Thermal
    block = cladding
    temperature = temp
  []
  [clad_density]
    type = StrainAdjustedDensity
    block = cladding
    strain_free_density = 7874.0
  []
  [longSS316_failure]
    type = D9FailureClad
    block = cladding
    method = steady_state
    temperature = temp
    outputs = all
    hoop_stress = stress_zz # Since 2D-RZ
  []
  [wastage_thickness]
    type = MetallicFuelWastage
    method = flux_ss316
    temperature = temp
    scale_factor = 1
    boundary = cladding_inside_right
    outputs = all
  []
  [cc_wastage_thickness]
    type = MetallicFuelCoolantWastage
    clad_material = SS316
    use_effective_method = true
    temperature = temp
    scale_factor = 1
    boundary = cladding_outside_right
    outputs = all
  []
[]

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

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

[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                  51'
  line_search = 'none'

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

  end_time = ${time_last}
  dtmin = 1
  dtmax = ${max_dt}

  [Quadrature]
    order = fifth
    side_order = seventh
  []
  [TimeStepper]
    type = IterationAdaptiveDT
    timestep_limiting_function = power_history
    #max_function_change = 300 # Removed to decrease run time
    timestep_limiting_postprocessor = creep_timestep
    dt = 100
    iteration_window = 2
    optimal_iterations = 10
    force_step_every_function_point = true
  []
[]

[Postprocessors]
  [_dt]
    type = TimestepSize
    outputs = 'csv_general console'
  []
  [num_lin_it]
    type = NumLinearIterations
    outputs = csv_general
  []
  [num_nonlin_it]
    type = NumNonlinearIterations
    outputs = csv_general
  []
  [tot_lin_it]
    type = CumulativeValuePostprocessor
    postprocessor = num_lin_it
    outputs = csv_general
  []
  [tot_nonlin_it]
    type = CumulativeValuePostprocessor
    postprocessor = num_nonlin_it
    outputs = csv_general
  []
  [alive_time]
    type = PerfGraphData
    section_name = Root
    data_type = TOTAL
    outputs = csv_general
  []
  [ave_temp_interior]
    type = SideAverageValue
    boundary = cladding_inside_top
    variable = temp
    execute_on = 'initial linear'
    outputs = csv_general
  []
  [approx_FCT]
    type = AverageNodalVariableValue
    boundary = centerline
    variable = temp
    outputs = csv_general
  []
  [max_approx_FCT]
    type = TimeExtremeValue
    value_type = max
    postprocessor = approx_FCT
    outputs = csv_general
  []
  [ave_FST]
    type = SideAverageValue
    boundary = fuel_outer_radial_surface
    variable = temp
    outputs = csv_general
  []
  [max_ave_FST]
    type = TimeExtremeValue
    value_type = max
    postprocessor = ave_FST
    outputs = csv_general
  []
  [ave_CIT]
    type = SideAverageValue
    boundary = cladding_inside_right
    variable = temp
    outputs = csv_general
  []
  [max_ave_CIT]
    type = TimeExtremeValue
    value_type = max
    postprocessor = ave_CIT
    outputs = csv_general
  []
  [avg_clad_temp]
    type = ElementAverageValue
    variable = temp
    block = cladding
    outputs = csv_general
  []
  [peak_clad_temp]
    type = ElementExtremeValue
    variable = temp
    value_type = max
    block = cladding
    outputs = csv_general
  []
  [peak_fuel_temp]
    type = ElementExtremeValue
    variable = temp
    value_type = max
    block = fuel
    outputs = csv_general
  []
  [max_hydro]
    type = ElementExtremeValue
    variable = hydrostatic_stress
    value_type = max
    block = fuel
    outputs = csv_general
  []
  [min_hydro]
    type = ElementExtremeValue
    variable = hydrostatic_stress
    value_type = min
    block = fuel
    outputs = csv_general
  []
  [avg_hydro]
    type = ElementAverageValue
    variable = hydrostatic_stress
    block = fuel
    outputs = csv_general
  []
  [peak_porosity]
    type = ElementExtremeValue
    variable = porosity
    value_type = max
    block = fuel
    outputs = csv_general
  []
  [clad_inner_vol]
    type = InternalVolume
    boundary = cladding_inside_all
    outputs = csv_general
  []
  [pellet_volume]
    type = InternalVolume
    boundary = fuel_outside_all
    outputs = csv_general
  []
  [gas_volume]
    type = InternalVolume
    boundary = 'fuel_outside_all cladding_inside_all'
    execute_on = 'initial timestep_end'
    addition = na_vol
    outputs = csv_general
  []
  [clad_fuel_gap]
    type = NodalExtremeValue
    variable = penetration
    boundary = fuel_outer_radial_surface
    outputs = csv_general
  []
  [max_cont_press]
    type = NodalExtremeValue
    variable = contact_pressure
    boundary = fuel_outer_radial_surface
    outputs = csv_general
  []
  [flux_from_clad]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = cladding_inside_right
    diffusivity = thermal_conductivity
    outputs = csv_general
  []
  [flux_from_fuel]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = fuel_outer_radial_surface
    diffusivity = thermal_conductivity
    outputs = csv_general
  []
  [rod_total_power]
    type = ElementIntegralPower
    variable = temp
    use_material_fission_rate = true
    fission_rate_material = fission_rate
    block = fuel
    outputs = csv_general
  []
  [LHGR_W_per_cm]
    type = FunctionValuePostprocessor
    function = power_history
    scale_factor = 0.01
    outputs = csv_general
  []
  [average_burnup]
    type = ElementAverageValue
    block = fuel
    variable = burnup
    outputs = csv_general
  []
  [max_cdf]
    type = ElementExtremeValue
    value_type = max
    variable = cumulative_damage_index
    outputs = csv_general
  []
  [fis_gas_produced]
    type = ElementIntegralMaterialProperty
    mat_prop = fis_gas_prod
    block = fuel
    outputs = csv_general
  []
  [fis_gas_released]
    type = ElementIntegralMaterialProperty
    mat_prop = fis_gas_rel
    block = fuel
    execute_on = 'initial timestep_end'
    outputs = csv_general
  []
  [creep_timestep]
    type = MaterialTimeStepPostprocessor
    block = fuel
    outputs = 'csv_general console'
  []
  [hydrostatic_stress]
    type = ElementAverageValue
    variable = hydrostatic_stress
    execute_on = 'initial timestep_end'
    block = fuel
    outputs = csv_general
  []
  [solid_swelling]
    type = ElementAverageValue
    variable = solid_swell
    block = fuel
    outputs = csv_general
  []
  [gas_swelling]
    type = ElementAverageValue
    variable = gas_swell
    block = fuel
    outputs = csv_general
  []
  [volumetric_strain]
    type = ElementAverageValue
    variable = volumetric_strain
    block = fuel
    outputs = csv_general
  []
  [fission_rate]
    type = ElementAverageValue
    variable = fission_rate
    block = fuel
    outputs = csv_general
  []
  [porosity]
    type = ElementAverageValue
    variable = porosity
    block = fuel
    outputs = csv_general
  []
  [gaseous_porosity]
    type = ElementAverageValue
    variable = gaseous_porosity
    block = fuel
    outputs = csv_general
  []
  [fis_gas_percent]
    type = FGRPercent
    fission_gas_released = fis_gas_released
    fission_gas_generated = fis_gas_produced
    outputs = csv_general
  []
  [max_clad_hoop_creep]
    type = ElementExtremeValue
    value_type = max
    block = cladding
    variable = hoop_creep_strain
    outputs = csv_general
  []
  [max_clad_creep_strain_mag]
    type = ElementExtremeValue
    value_type = max
    block = cladding
    variable = creep_strain_mag
    outputs = csv_general
  []
  [max_total_hoop_strain]
    type = ElementExtremeValue
    value_type = max
    block = cladding
    variable = total_hoop_strain
    outputs = csv_general
  []
  [max_fuel_elongation]
    type = NodalExtremeValue
    variable = disp_y
    boundary = fuel_top
    outputs = csv_general
  []
  [avg_fuel_ax_thm_str]
    type = AxisymmetricCenterlineAverageValue
    variable = fuel_thermal_strain_yy
    boundary = fuel_inner_radial_surface
    outputs = csv_general
  []
  [max_clad_elongation]
    type = NodalExtremeValue
    variable = disp_y
    boundary = 'cladding_outside_top cladding_outside_right'
    outputs = csv_general
  []
  [max_wastagethickness]
    type = ElementExtremeValue
    value_type = max
    variable = wastage_thickness
    outputs = 'console'
  []
  [avg_fuel_temp]
    type = ElementAverageValue
    variable = temp
    block = fuel
    execute_on = 'initial timestep_end'
    allow_duplicate_execution_on_initial = true
    outputs = csv_general
  []
[]

[VectorPostprocessors]
  [clad_x_disp]
    type = NodalValueSampler
    variable = disp_x
    boundary = cladding_outside_right
    sort_by = y
    outputs = none
  []
  [fuel_cl_temp]
    type = NodalValueSampler
    variable = temp
    boundary = centerline
    sort_by = y
    outputs = none
  []
  [fuel_surf_temp]
    type = NodalValueSampler
    variable = temp
    boundary = fuel_outer_radial_surface
    sort_by = y
    outputs = none
  []
  [clad_inn_temp]
    type = NodalValueSampler
    variable = temp
    boundary = cladding_inside_right
    sort_by = y
    execute_on = 'initial timestep_end'
    allow_duplicate_execution_on_initial = true
    outputs = none
  []
  [clad_out_temp]
    type = NodalValueSampler
    variable = temp
    boundary = cladding_outside_right
    sort_by = y
    outputs = none
  []
  [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
  []
  [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
  []
  # PIE Comparison VPPs
  [nrad_comparison_0]
    type = FIPDAxialPIEComparison
    boundary = fuel_outer_radial_surface
    sort_by = y
    csv_file = ${raw '../../../../../../fipd-bison-integration-data/X423/ ${pin_id} /X423_ ${pin_id} _NRAD.csv'}
    variable = disp_x
    thermal_strain_variable = fuel_thm_exp
    involved_component = fuel
    mesh_generator = gen
    series_type_to_read = 'Fuel O.D. (mils)'
    outputs = csv_vpp_0
    enable = ${enable_0}
    execute_on = 'initial timestep_end'
    extra_pp_output_name = 'extra_csv extra_csv_0'
    max_fuel_elongation_pp_name = max_fuel_elongation
    avg_fuel_ax_thm_str_pp_name = avg_fuel_ax_thm_str
    gas_swelling_pp_name = gas_swelling
    solid_swelling_pp_name = solid_swelling
  []
  [nrad_comparison_a]
    type = FIPDAxialPIEComparison
    boundary = fuel_outer_radial_surface
    sort_by = y
    csv_file = ${raw '../../../../../../fipd-bison-integration-data/X423/ ${pin_id} /X423A_ ${pin_id} _NRAD.csv'}
    variable = disp_x
    thermal_strain_variable = fuel_thm_exp
    involved_component = fuel
    mesh_generator = gen
    series_type_to_read = 'Fuel O.D. (mils)'
    outputs = csv_vpp_a
    enable = ${enable_a}
    execute_on = 'initial timestep_end'
    extra_pp_output_name = 'extra_csv extra_csv_a'
    max_fuel_elongation_pp_name = max_fuel_elongation
    avg_fuel_ax_thm_str_pp_name = avg_fuel_ax_thm_str
    gas_swelling_pp_name = gas_swelling
    solid_swelling_pp_name = solid_swelling
  []
  [nrad_comparison_b]
    type = FIPDAxialPIEComparison
    boundary = fuel_outer_radial_surface
    sort_by = y
    csv_file = ${raw '../../../../../../fipd-bison-integration-data/X423/ ${pin_id} /X423B_ ${pin_id} _NRAD.csv'}
    variable = disp_x
    thermal_strain_variable = fuel_thm_exp
    involved_component = fuel
    mesh_generator = gen
    series_type_to_read = 'Fuel O.D. (mils)'
    outputs = csv_vpp_b
    enable = ${enable_b}
    execute_on = 'initial timestep_end'
    extra_pp_output_name = 'extra_csv extra_csv_b'
    max_fuel_elongation_pp_name = max_fuel_elongation
    avg_fuel_ax_thm_str_pp_name = avg_fuel_ax_thm_str
    gas_swelling_pp_name = gas_swelling
    solid_swelling_pp_name = solid_swelling
  []
  [nrad_comparison_c]
    type = FIPDAxialPIEComparison
    boundary = fuel_outer_radial_surface
    sort_by = y
    csv_file = ${raw '../../../../../../fipd-bison-integration-data/X423/ ${pin_id} /X423C_ ${pin_id} _NRAD.csv'}
    variable = disp_x
    thermal_strain_variable = fuel_thm_exp
    involved_component = fuel
    mesh_generator = gen
    series_type_to_read = 'Fuel O.D. (mils)'
    outputs = csv_vpp_c
    enable = ${enable_c}
    execute_on = 'initial timestep_end'
    extra_pp_output_name = 'extra_csv extra_csv_c'
    max_fuel_elongation_pp_name = max_fuel_elongation
    avg_fuel_ax_thm_str_pp_name = avg_fuel_ax_thm_str
    gas_swelling_pp_name = gas_swelling
    solid_swelling_pp_name = solid_swelling
  []
[]

[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
  []
[]

[Outputs]
  perf_graph = true
  color = false
  [console]
    type = Console
    max_rows = 25
    time_step_interval =  1
    output_linear = true
    sync_times = ${time_spots}
  []
  [csv_vpp_0]
    type = CSV
    sync_only = true
    sync_times = ${time_spots_0}
    enable = ${enable_0}
    create_latest_symlink = true
  []
  [csv_vpp_a]
    type = CSV
    sync_only = true
    sync_times = ${time_spots_a}
    enable = ${enable_a}
    create_latest_symlink = true
  []
  [csv_vpp_b]
    type = CSV
    sync_only = true
    sync_times = ${time_spots_b}
    enable = ${enable_b}
    create_latest_symlink = true
  []
  [csv_vpp_c]
    type = CSV
    sync_only = true
    sync_times = ${time_spots_c}
    enable = ${enable_c}
    create_latest_symlink = true
  []
  [csv_general]
    type = CSV
    sync_times = ${time_spots}
  []
  [extra_csv]
    type = CSV
    sync_only = true
    sync_times = ${time_spots_extra}
  []
  [extra_csv_0]
    type = CSV
    sync_only = true
    sync_times = ${time_spots_0}
    enable = ${enable_0}
  []
  [extra_csv_a]
    type = CSV
    sync_only = true
    sync_times = ${time_spots_a}
    enable = ${enable_a}
  []
  [extra_csv_b]
    type = CSV
    sync_only = true
    sync_times = ${time_spots_b}
    enable = ${enable_b}
  []
  [extra_csv_c]
    type = CSV
    sync_only = true
    sync_times = ${time_spots_c}
    enable = ${enable_c}
  []
  [exodus]
    type = Exodus
    sync_only = true
    sync_times = ${time_spots}
  []
[]

(test/tests/solid_mechanics/upuzr_gas_LM/preset_rad.i)

# This test is to verify the calculation in UPuZrVolumetricSwellingEigenstrainLM and
# FgrUPuZrLM (the preset bubble radius)

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

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

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

[AuxVariables]
  [temp]
    initial_condition = 1000
  []
  [volumetric_strain]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[AuxKernels]
  [temp]
    type = ConstantAux
    variable = temp
    value = 1000
  []
  [volumetric_strain]
    type = RankTwoScalarAux
    variable = volumetric_strain
    rank_two_tensor = total_strain
    scalar_type = VolumetricStrain
  []
[]

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

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

[Materials]
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 2.0e11
    poissons_ratio = 0.3
  []
  [fuel_stress]
    type = ComputeFiniteStrainElasticStress
  []
  [fission_rate]
    type = GenericFunctionMaterial
    prop_names = 'fission_rate'
    prop_values = 'fission_rate_func'
    outputs = all
  []
  [burnup]
    type = UPuZrBurnup
    density = 16000
    initial_X_Pu = 0.0
    initial_X_Zr = 0.225
    outputs = all
  []
  [gas_swelling]
    type = UPuZrVolumetricSwellingEigenstrainLM
    temperature = temp
    use_plenum_pressure = false
    use_preset_bubble_size = true
    initial_porosity = 0.1
    outputs = all
    output_properties = 'porosity gaseous_porosity gas_swelling_vdw gas_swelling_ideal gas_swelling gas_bubble_radius gas_bubble_density'
    eigenstrain_name = gas_swelling_eigenstrain
    anisotropic_factor = 1.25
  []

  [fission_gas_behavior]
    type = FgrUPuZrLM
    temperature = temp
    outputs = all
    output_properties = 'fis_gas_prod fis_gas_rel fis_gas_ret'
  []
[]

[Executioner]
  type = Transient

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

[Postprocessors]
  [gas_produced]
    type = ElementAverageValue
    variable = fis_gas_prod
  []
  [gas_released]
    type = ElementAverageValue
    variable = fis_gas_rel
  []
  [gas_retained]
    type = ElementAverageValue
    variable = fis_gas_ret
  []
  [fission_rate]
    type = ElementAverageValue
    variable = fission_rate
  []
  [hydrostatic_stress]
    type = ElementAverageValue
    variable = hydrostatic_stress
  []
  [porosity]
    type = ElementAverageValue
    variable = porosity
  []
  [gaseous_porosity]
    type = ElementAverageValue
    variable = gaseous_porosity
  []
  [gas_swell]
    type = ElementAverageValue
    variable = gas_swelling
  []
  [volumetric_strain]
    type = ElementAverageValue
    variable = volumetric_strain
  []
  [gas_swelling_vdw]
    type = ElementAverageValue
    variable = gas_swelling_vdw
  []
  [gas_swelling_ideal]
    type = ElementAverageValue
    variable = gas_swelling_ideal
  []
  [gas_bubble_radius]
    type = ElementAverageValue
    variable = gas_bubble_radius
  []
  [gas_bubble_density]
    type = ElementAverageValue
    variable = gas_bubble_density
  []
  [strain_xx]
    type = ElementAverageValue
    variable = strain_xx
  []
  [strain_yy]
    type = ElementAverageValue
    variable = strain_yy
  []
[]

[Outputs]
  csv = true
[]

Description
Gaseous Swelling
Solid Swelling
Total Volumetric Swelling
Anisotropic Swelling
Example Input Syntax
Input Parameters
Input Files
References