UO2PulverizationMesoscale

Determines whether or not the fuel has pulverized into small fragments during a Loss of Coolant Accident using a mesoscale-informed pulverization criterion.

Description

The UO2PulverizationMesoscale material computes whether or not the UO $var element = document.getElementById("moose-equation-068df594-a3f0-489f-8c50-ec7836341775");katex.render("_2", element, {displayMode:false,throwOnError:false});$ fuel has disintegrated into fine fragments. There are two criteria available for pulverization, one of which is based on an analytical derivation and one of which is based on fits to data from a phase-field fracture model. The critical bubble pressure for pulverization is computed by one of these criteria, selected by the user. The model also computes the current pressure of the statistically most likely bubble size in the HBS region and compares current bubble pressure to the critical pressure. If the current bubble pressure is greater than the critical pressure, pulverization is deemed to have occurred and the material property _pulverized is changed from 0 to 1. Further details on the model are available in INL technical reports (Aagesen et al., 2021; Aagesen et al., 2022).

Analytical criterion for pulverization

The analytical criterion for pulverization is based on an expression that was originally developed for fragmentation along grain boundaries for lenticular bubbles in UO $var element = document.getElementById("moose-equation-aa714a2f-8221-4d69-ba8f-42a4b544b159");katex.render("_2", element, {displayMode:false,throwOnError:false});$ (Olander, 1997). Because pulverization is predominantly observed to occur in regions where the high burnup structure (HBS) in UO $var element = document.getElementById("moose-equation-249d45bb-a063-46e4-afcd-581898f810d6");katex.render("_2", element, {displayMode:false,throwOnError:false});$ fuel has formed, the analytical model has been adapted to apply to the morphology of bubbles in the HBS region. These bubbles are approximately spherical and their sizes can be described by a log-normal distribution. The criterion for fine fragmentation to occur is met when the gas pressure $var element = document.getElementById("moose-equation-a6b47621-b966-441a-ac4a-b0296718bde2");katex.render("P_g", element, {displayMode:false,throwOnError:false});$ inside the statistically most common bubble (i.e., bubble with the statistically most common size) exceeds the critical pressure $var element = document.getElementById("moose-equation-144f8503-275e-4e77-b667-54407199c0a2");katex.render("P_g^{cr}", element, {displayMode:false,throwOnError:false});$ : $var element = document.getElementById("moose-equation-11dcf710-9d40-4008-9a09-b99065f85d05");katex.render("P_g^{cr} = \\frac{2\\gamma}{r} + \\frac{\\sigma_{gb}^{cr} (1-\\phi_2) - \\sigma_H}{\\phi_2}", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-b7d52fa7-7adb-4b89-a77b-ac441cbcf5e4");katex.render("\\gamma", element, {displayMode:false,throwOnError:false});$ is the surface tension of the bubble-fuel interface, $var element = document.getElementById("moose-equation-d2e4b31b-61ee-43a0-a82d-f05e745729a1");katex.render("r", element, {displayMode:false,throwOnError:false});$ is the bubble radius, $var element = document.getElementById("moose-equation-cfcf92c1-f857-449a-b435-5597222fff05");katex.render("\\sigma_{gb}^{cr}", element, {displayMode:false,throwOnError:false});$ is the critical fracture stress of the grain boundaries intersecting the bubble, $var element = document.getElementById("moose-equation-4758e21d-dd36-4430-be69-1566343b5dc0");katex.render("\\phi_2", element, {displayMode:false,throwOnError:false});$ is areal fraction of the grain boundary occupied by the bubble, and $var element = document.getElementById("moose-equation-c8e05dcc-390f-4c5b-87d3-e6e838b2a2f5");katex.render("\\sigma_H", element, {displayMode:false,throwOnError:false});$ is the local hydrostatic stress. In applying this equation, it is assumed that there is a a uniform array of the statistically most likely bubbles and that a flat grain boundary intersects each bubble; this neglects the more complex actual morphology of the bubbles and of the grain boundaries in the HBS. The statistically most common bubble size is $var element = document.getElementById("moose-equation-8de60da3-dfbd-4c4e-883e-fe513e4fb217");katex.render("r \\approx 0.5", element, {displayMode:false,throwOnError:false});$ $var element = document.getElementById("moose-equation-3254e283-fd0d-4927-b81c-11c498bfa68d");katex.render("\\mu", element, {displayMode:false,throwOnError:false});$ m (Kulacsy, 2015). Additionally, it is assumed that the local volume fraction of HBS formation must be greater than a threshold value (user-definable with a default of 0.17 (Biswas et al., 2023)) for pulverization to occur.

Given the assumed geometry, $var element = document.getElementById("moose-equation-6e3b4771-09a7-4dee-aee1-7b1814c48cff");katex.render("\\phi_2", element, {displayMode:false,throwOnError:false});$ can be calculated from the local porosity in the HBS structure, $var element = document.getElementById("moose-equation-9cc56122-6c34-496d-9243-d1b3c3cec32e");katex.render("p", element, {displayMode:false,throwOnError:false});$ , using $var element = document.getElementById("moose-equation-b834a38b-9fd6-444f-80ee-496a4c7b6ddd");katex.render("\\phi_2 = \\left( \\frac{3p \\sqrt{\\pi}}{4} \\right)^{2/3}.", element, {displayMode:true,throwOnError:false});$ This criterion is used by default (pulverization_criterion_type = Analytical).

Phase-field fracture criterion for pulverization

$var element = document.getElementById("moose-equation-68512546-6b67-43e2-ad0c-984a2d336f1f");katex.render("P_g^{cr}", element, {displayMode:false,throwOnError:false});$ can also be determined based on a phase-field fracture model-based criterion. The phase-field criterion was derived from simulations of fragmentation of a pressurized gas bubble in the HBS region. The grain structure is assumed to be fully restructured with an average grain size of 200 nm. The most common bubble size of $var element = document.getElementById("moose-equation-df3e41da-fef2-447f-a013-696b2fdfd0eb");katex.render("r = 0.5", element, {displayMode:false,throwOnError:false});$ $var element = document.getElementById("moose-equation-3d0ec6bf-e7c8-4b93-b456-6e69ec912bd3");katex.render("\\mu", element, {displayMode:false,throwOnError:false});$ m was used in a phase-field fracture model with periodic boundary conditions. Different values of porosity, external pressure, and critical fracture stress were explored to derive a phase-field criterion dependent on these factors.

Three different criteria were developed over time and are available to use:

The first criterion was derived using 2D phase field simulations (Aagesen et al., 2021) and can be selected using pulverization_criterion_type = Phase_field_2D. It provides $var element = document.getElementById("moose-equation-f48efe94-b5d8-433f-9615-825f911eb10c");katex.render("P_g^{cr}", element, {displayMode:false,throwOnError:false});$ in Pa as $(1)var element = document.getElementById("moose-equation-e6c53ad3-2922-437d-813e-49fa9050a820");katex.render("P_g^{cr} = 1.0 \\times 10^6 \\left[\\left(124.17 + 0.43858 \\left(\\sigma_{gb}^{cr} - 130\\right)\\right) \\left(1-p\\right) - 1.0178 \\sigma_H \\right]", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-c7fd5d6e-11d3-4dc3-853b-6d78f9f23160");katex.render("\\sigma_{gb}^{cr}", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-ce3edb8a-cc90-40f1-a0ae-71309387cf94");katex.render("\\sigma_H", element, {displayMode:false,throwOnError:false});$ are in MPa. $var element = document.getElementById("moose-equation-2cde8885-def5-43e4-92c9-9bdd99a85e50");katex.render("\\sigma_{gb}^{cr}", element, {displayMode:false,throwOnError:false});$ defaults to 130 MPa but can be updated using critical_gb_stress.

The second criterion is similar to the 2D one above, but is based on 3D phase field simulations (Aagesen et al., 2022). It can be selected using pulverization_criterion_type = Phase_field_3D. The equation for $var element = document.getElementById("moose-equation-9894c27e-7c7c-4262-9c2a-6015bacf3ecc");katex.render("P_g^{cr}", element, {displayMode:false,throwOnError:false});$ in Pa becomes $(2)var element = document.getElementById("moose-equation-13e0887c-7e2b-4de0-840b-93a213643c86");katex.render(" P_g^{cr} = 1.0 \\times 10^6 \\left[\\left(175.987 + 0.5035 \\left(\\sigma_{gb}^{cr} - 130\\right)\\right) \\left(1 - 1.582p\\right) - 1.089 \\sigma_H \\right].", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-4e784a72-5899-4df6-8d85-d872836abce7");katex.render("\\sigma_{gb}^{cr}", element, {displayMode:false,throwOnError:false});$ defaults to 130 MPa but can be updated using critical_gb_stress.

The third criterion leveraged molecular dynamic simulations to determine the critical fracture stress of the grain boundaries intersecting the bubble (Biswas et al., 2023). As such, the pulverization criteria is expressed in terms of porosity and external load only since it implicitly accounts for temperature and bubble configuration on the critical fracture stress. Variations in critical fracture stress are therefore considered as uncertainties. The new criteria is derived from 2D phase-field simulations (Biswas et al., 2023). This criterion can be used by setting pulverization_criterion_type = phase_field_2D_multiscale. The equation for $var element = document.getElementById("moose-equation-9ba3587c-1525-488b-9781-b59f7957c56b");katex.render("P_g^{cr}", element, {displayMode:false,throwOnError:false});$ in Pa becomes

$(3)var element = document.getElementById("moose-equation-4bf22808-0c18-4347-8c71-03c7ca5ae8d6");katex.render(" P_g^{cr} = 1.0 \\times 10^6 \\left(201.222 - 50.933p - 0.115 \\sigma_H \\right)", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-64c21d21-7aa4-4863-8c3b-471002a44acb");katex.render("\\sigma_H", element, {displayMode:false,throwOnError:false});$ is in MPa.

It is important to note that the references (Aagesen et al., 2021; Aagesen et al., 2022) refer to external pressure ( $var element = document.getElementById("moose-equation-6c728209-ed48-4160-bf5c-1ceea664bc42");katex.render("P_{ext}", element, {displayMode:false,throwOnError:false});$ ) when defining the equations for $var element = document.getElementById("moose-equation-e0e4124a-731d-4119-80ab-40522f0934c3");katex.render("P_g^{cr}", element, {displayMode:false,throwOnError:false});$ . In Eq. (1) and Eq. (2) the definition of $var element = document.getElementById("moose-equation-4643b563-675f-4b21-80fe-c09f5b67b9e2");katex.render("P_{ext}=-\\sigma_H", element, {displayMode:false,throwOnError:false});$ is used.

Note that it is possible to use the input scalar_critical_pressure, which defaults as 1, as a multiplicative scalar for $var element = document.getElementById("moose-equation-106e5552-8c77-409f-85d0-8c5ccd908038");katex.render("P_g^{cr}", element, {displayMode:false,throwOnError:false});$ . This enables sensitivity studies or adjustments of $var element = document.getElementById("moose-equation-27d2a7c5-1586-4aa7-ab1a-bfb5370ece09");katex.render("P_g^{cr}", element, {displayMode:false,throwOnError:false});$ to account for uncertainties.

In all these cases, it is assumed that the local volume fraction of HBS formation must be greater than a threshold value (user-definable with a default of 0.17 (Biswas et al., 2023)) for pulverization to occur.

Bubble pressure calculation

The gas pressure in the statistically most likely bubble is determined starting from previous experimental observations of the HBS region (Nogita and Une, 1995). The pressure in a bubble with $var element = document.getElementById("moose-equation-260a0a6d-7ee5-4938-91c8-b6198b9f73c5");katex.render("r = 0.5", element, {displayMode:false,throwOnError:false});$ $var element = document.getElementById("moose-equation-1b31d576-dd8c-43dd-8c2b-97f6fec0137f");katex.render("\\mu", element, {displayMode:false,throwOnError:false});$ m was estimated to have an upper bound limit of 100 MPa in fuel that was operated at a temperature of 673 K. The default values for initial pressure and reference temperature are set based on this estimate. The current bubble pressure and size are evolved based on the following set of equations. The gas concentration in the solid matrix surrounding the bubbles is assumed to be in quasi-steady state conditions. In this case, the number of gas atoms transported to each existing bubble is equal to the production rate per unit volume, divided by the number of bubbles per unit volume: $var element = document.getElementById("moose-equation-33205ffc-5469-4584-8735-dad32b654fc2");katex.render(" \\frac{d\\bar{n}}{dt} = \\frac{Y \\dot{F}}{N},", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-da77e2d4-6cd6-491a-b290-a4d0a866554c");katex.render("\\bar{n}", element, {displayMode:false,throwOnError:false});$ is the number of gas atoms per bubble, $var element = document.getElementById("moose-equation-db69abaf-03fd-472c-b726-13fe6d728508");katex.render("Y", element, {displayMode:false,throwOnError:false});$ is the fission gas yield, $var element = document.getElementById("moose-equation-ab983b6d-8c22-4477-93bd-05e3c0af5551");katex.render("\\dot{F}", element, {displayMode:false,throwOnError:false});$ is the fission rate density, and $var element = document.getElementById("moose-equation-c020ce09-9854-48ee-9057-b936dd8d664c");katex.render("N", element, {displayMode:false,throwOnError:false});$ is the number of bubbles per unit volume. The number of vacancies per bubble, $var element = document.getElementById("moose-equation-bbda5621-8c29-49d1-aca7-4f0ba371e30e");katex.render("n_{iv}", element, {displayMode:false,throwOnError:false});$ , was calculated as (Barani et al., 2019): $(4)var element = document.getElementById("moose-equation-eebbce58-f1d6-4a8f-966e-36ccfe1c1720");katex.render(" \\frac{dn_{iv}}{dt} = \\frac{2\\pi D_{ig}^v \\rho}{kT \\zeta} \\left( P - P_{eq}\\right), ", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-56658cc2-7ad3-42cb-9810-0e891d816e34");katex.render("D_{ig}^v", element, {displayMode:false,throwOnError:false});$ is the intra-granular vacancy diffusion coefficient, $var element = document.getElementById("moose-equation-de292531-f3d7-4491-aa17-1832991d7b72");katex.render("\\rho", element, {displayMode:false,throwOnError:false});$ is the radius of the equivalent Wigner-Seitz cell surrounding a bubble, and $var element = document.getElementById("moose-equation-40b0145d-48e1-4fb8-aa9e-68d0a574e6de");katex.render("\\zeta", element, {displayMode:false,throwOnError:false});$ is a dimensionless factor defined as: $(5)var element = document.getElementById("moose-equation-f58089b8-8d72-4ffb-828d-0ec1e7ed6985");katex.render(" \\zeta = \\frac{10\\psi(1+\\psi^3)}{-\\psi^6 + 5\\psi^2 - 9\\psi + 5}, ", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-3413f750-0647-49e0-88f0-059efc131f46");katex.render("\\psi = r / \\rho", element, {displayMode:false,throwOnError:false});$ . $var element = document.getElementById("moose-equation-85ede955-57d6-4d81-a767-15ccd7ef4032");katex.render("P_{eq}", element, {displayMode:false,throwOnError:false});$ is the equilibrium pressure for a bubble of radius $var element = document.getElementById("moose-equation-ee33a413-24ed-434f-889c-4022a06713ae");katex.render("r", element, {displayMode:false,throwOnError:false});$ , as calculated using the Laplace-Young equation: $(6)var element = document.getElementById("moose-equation-ccfab3c2-8bbd-4539-bc69-c775a819020b");katex.render(" P_{eq} = \\frac{2\\gamma}{r} - \\sigma_h ,", element, {displayMode:true,throwOnError:false});$ After updated values of $var element = document.getElementById("moose-equation-2c695878-5dcb-443e-a2d4-68e16d039401");katex.render("\\bar{n}", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-7f747c33-4fb1-4482-b4f5-511f7f4514f2");katex.render("n_{iv}", element, {displayMode:false,throwOnError:false});$ are calculated, the bubble pressure is calculated using a rearranged formulation of the van der Waals equation of state (Barani et al., 2019): $(7)var element = document.getElementById("moose-equation-0db30ee4-69b9-42a2-ba11-a8e17e5d1ace");katex.render(" P_g = \\frac{kT}{\\Omega} \\frac{\\bar{n}}{n_{iv}} ", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-5a66d37e-7c63-45c4-b924-045b221ab962");katex.render("\\Omega = 4.09 \\times 10^{-29}", element, {displayMode:false,throwOnError:false});$ m $var element = document.getElementById("moose-equation-5f72d4ea-cbc5-478e-86e1-17a9f13f80c7");katex.render("^3", element, {displayMode:false,throwOnError:false});$ is the volume of a vacancy on a U lattice site in UO $var element = document.getElementById("moose-equation-36bffe18-50b9-40ff-b6c2-c9538da93906");katex.render("_2", element, {displayMode:false,throwOnError:false});$ . The updated bubble volume is calculated using $var element = document.getElementById("moose-equation-886384da-6118-4f8e-ad0d-d45d364e63ab");katex.render(" V_b = \\omega \\bar{n} + \\Omega n_{iv}", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-793bde03-b51b-4e33-90b1-82795178dc45");katex.render("\\omega = 8.5 \\times 10^{-29}", element, {displayMode:false,throwOnError:false});$ m $var element = document.getElementById("moose-equation-5d5eb4f7-c1c7-4f24-9040-8dcf5918aba0");katex.render("^3", element, {displayMode:false,throwOnError:false});$ is the van der Waals atomic volume for Xe (Olander, 1976). The current bubble radius is calculated from the volume as $var element = document.getElementById("moose-equation-67cec203-a9f1-43c7-b75c-af5630ff75d4");katex.render(" r = \\sqrt[3]{\\frac{3 V_b}{4 \\pi}}", element, {displayMode:true,throwOnError:false});$

The values of $var element = document.getElementById("moose-equation-2299cf3d-facd-4527-a943-70eb0dd31962");katex.render("P_g", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-1e79754b-b4dc-4629-b233-4f0c7538c4b3");katex.render("P_g^{cr}", element, {displayMode:false,throwOnError:false});$ are compared, and when $var element = document.getElementById("moose-equation-7c9ce667-a8bb-4756-819a-564f6e755ecd");katex.render("P_g > P_g^{cr}", element, {displayMode:false,throwOnError:false});$ and the local volume fraction of HBS is greater than the threshold (user-definable with a default of 0.17 (Biswas et al., 2023)), pulverization is determined to occur at the local quadrature point.

Example Input Syntax

[Materials<<<{"href": "../../syntax/Materials/index.html"}>>>]
  [uo2pulverizationmesoscale]
    type = UO2PulverizationMesoscale<<<{"description": "Determines whether or not the fuel has pulverized into small fragments during a Loss of Coolant Accident using a mesoscale-informed pulverization criterion.", "href": "UO2PulverizationMesoscale.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = fuel
    temperature<<<{"description": "Coupled temperature"}>>> = temperature
    output_properties<<<{"description": "List of material properties, from this material, to output (outputs must also be defined to an output type)"}>>> = pulverized
    outputs<<<{"description": "Vector of output names where you would like to restrict the output of variables(s) associated with this object"}>>> = exodus
  []
[]

Input Parameters

temperatureCoupled temperature
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Coupled temperature

Required Parameters

blockThe list of blocks (ids or names) that this object will be applied
C++ Type:std::vector<SubdomainName>
Controllable:No
Description:The list of blocks (ids or names) that this object will be applied
boundaryThe list of boundaries (ids or names) from the mesh where this object applies
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:The list of boundaries (ids or names) from the mesh where this object applies
computeTrueWhen false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
Default:True
C++ Type:bool
Controllable:No
Description:When false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
constant_onNONEWhen ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
Default:NONE
C++ Type:MooseEnum
Options:NONE, ELEMENT, SUBDOMAIN
Controllable:No
Description:When ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
critical_gb_stress1.3e+08Critical stress at which a grain boundary fractures
Default:1.3e+08
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Critical stress at which a grain boundary fractures
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.
hbs_volume_fraction_threshold0.17Minimum local volume fraction of HBS for pulverization to occur
Default:0.17
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Minimum local volume fraction of HBS for pulverization to occur
pulverization_criterion_typeAnalyticalWhich pulverization criterion to use
Default:Analytical
C++ Type:MooseEnum
Options:Analytical, Phase_field_2D, Phase_field_3D, Phase_field_2D_multiscale
Controllable:No
Description:Which pulverization criterion to use
scalar_critical_pressure1Multiplicative scalar to adjust the value of the critical fragmentation pressure
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Multiplicative scalar to adjust the value of the critical fragmentation pressure

Optional Parameters

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

Advanced Parameters

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

Outputs Parameters

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

Material Property Retrieval Parameters

Input Files

(test/tests/axial_relocation/uo2_pulverization_mesoscale.i)
(test/tests/uo2_transient_fission_gas_release/ad_uo2_pulverization_phasefield2_transient_FGR.i)
(test/tests/axial_relocation/uo2_pulverization_phasefield.i)
(test/tests/axial_relocation/ad_uo2_pulverization_phasefield2.i)
(test/tests/uo2_transient_fission_gas_release/uo2_pulverization_phasefield2_transient_FGR.i)
(test/tests/axial_relocation/ad_uo2_pulverization_phasefield.i)
(test/tests/uo2_transient_fission_gas_release/uo2_pulverization_transient_FGR_1D.i)
(test/tests/axial_relocation/ad_uo2_pulverization_mesoscale.i)
(test/tests/axial_relocation/uo2_pulverization_phasefield2.i)

References

Larry K Aagesen, Sudipta Biswas, Kyle Gamble, Wen Jiang, Pierre-Clément Simon, and Benjamin Spencer. Implementation and testing of physics-based pulverization model in BISON. Technical Report INL/RPT-22-67941 Rev. 0, Idaho National Laboratory, 2022.

@techreport{aagesen2022_67941,
    author = "Aagesen, Larry K and Biswas, Sudipta and Gamble, Kyle and Jiang, Wen and Simon, Pierre-Cl\'{e}ment and Spencer, Benjamin",
    institution = "Idaho National Laboratory",
    number = "INL/RPT-22-67941 Rev. 0",
    title = "Implementation and testing of physics-based pulverization model in {BISON}",
    year = "2022"
}

Larry K Aagesen, Sudipta Biswas, Wen Jiang, David Andersson, Michael Cooper, and Christopher Matthews. Mesoscale simulations to inform microstructure-based pulverization criterion in high-burnup UO$_2$. Technical Report INL/EXT-21-64275 Rev. 0, Idaho National Laboratory, 2021.

@techreport{aagesen2021_64275,
    author = "Aagesen, Larry K and Biswas, Sudipta and Jiang, Wen and Andersson, David and Cooper, Michael and Matthews, Christopher",
    institution = "Idaho National Laboratory",
    number = "INL/EXT-21-64275 Rev. 0",
    title = "Mesoscale simulations to inform microstructure-based pulverization criterion in high-burnup {UO}$\_2$",
    year = "2021"
}

T. Barani, G. Pastore, D. Pizzocri, D.A. Andersson, C. Matthews, A. Alfonsi, K.A. Gamble, P. Van Uffelen, L. Luzzi, and J.D. Hales. Multiscale modeling of fission gas behavior in U3Si2 under LWR conditions. Journal of Nuclear Materials, 522:97 – 110, 2019. doi:10.1016/j.jnucmat.2019.04.037.

@article{BARANI201997,
    author = "Barani, T. and Pastore, G. and Pizzocri, D. and Andersson, D.A. and Matthews, C. and Alfonsi, A. and Gamble, K.A. and Uffelen, P. Van and Luzzi, L. and Hales, J.D.",
    title = "Multiscale modeling of fission gas behavior in {U3Si2} under {LWR} conditions",
    journal = "Journal of Nuclear Materials",
    volume = "522",
    pages = "97 - 110",
    year = "2019",
    issn = "0022-3115",
    doi = "10.1016/j.jnucmat.2019.04.037"
}

Sudipta Biswas, Larry K Aagesen, Wen Jiang, Conor O Galvin, and Michael Cooper. Multiscale modeling for high burnup structure formation and associated pulverization. Technical Report INL/RPT-23-74953 Rev. 0, Idaho National Laboratory, 2023.

@techreport{biswas2023_74953,
    author = "Biswas, Sudipta and Aagesen, Larry K and Jiang, Wen and Galvin, Conor O and Cooper, Michael",
    institution = "Idaho National Laboratory",
    number = "INL/RPT-23-74953 Rev. 0",
    title = "Multiscale modeling for high burnup structure formation and associated pulverization",
    year = "2023"
}

K. Kulacsy. Mechanistic model for the fragmentation of the high-burnup structure during LOCA. Journal of Nuclear Materials, 466:409–416, 2015.

@ARTICLE{kulacsy2015,
    author = "Kulacsy, K.",
    title = "Mechanistic model for the fragmentation of the high-burnup structure during {LOCA}",
    journal = "Journal of Nuclear Materials",
    volume = "466",
    pages = "409-416",
    year = "2015",
    publisher = "Elsevier"
}

Kazuhiro Nogita and Katsumi Une. Irradiation-induced recrystallization in high burnup UO$_2$ fuel. Journal of Nuclear Materials, 226:302–310, 1995.

@article{nogita1995,
    author = "Nogita, Kazuhiro and Une, Katsumi",
    title = "Irradiation-induced recrystallization in high burnup {UO}$\_2$ fuel",
    journal = "Journal of Nuclear Materials",
    volume = "226",
    pages = "302-310",
    year = "1995",
    publisher = "Elsevier"
}

D. R. Olander. Fundamental aspects of nuclear reactor fuel elements. Technical Information Center, Energy Research and Development Administration, 1976.

@BOOK{olander76,
    author = "Olander, D. R.",
    title = "Fundamental aspects of nuclear reactor fuel elements",
    publisher = "Technical Information Center, Energy Research and Development Administration",
    year = "1976"
}

D. R. Olander. RIA-related issues concerning fission gas in irradiated PWR fuel. Technical Report, Institut de Protection et de Surete Nucleaire, Cadarache, France, 1997.

@TECHREPORT{olander1997,
    author = "Olander, D. R.",
    title = "{RIA}-related issues concerning fission gas in irradiated {PWR} fuel",
    institution = "Institut de Protection et de Surete Nucleaire, Cadarache, France",
    year = "1997"
}

(test/tests/axial_relocation/uo2_pulverization_mesoscale.i)

# This file is to test the mesoscale-informed pulverization criterion for UO2 fuel.
# In the test 5 axial fuel slices are modeled without cladding with an outer fuel
# radius of 4.5 mm and slice height of 0.1 m. Ten radial finite elements are used.
# The burnup increases linearly from the fuel centerline to the fuel surface.
# Temperature is held at constant T = 900 K from t = 0 to t = 100, followed
# by a ramp in temperature from t = 100 to t = 110. Pulverization will occur
# during the ramp only, in the rim region where a significant amount of high burnup
# structure formation has begun. Local pulverization is tracked with the material
# property pulverized, which is 0 where pulverization has not occured and 1 where
# it has occurred. This material property is output to the exodus file for this test.

# At each time step, the porosity in the HBS region is calculated at each radial
# position using the correlation due to Kampf in the UO2Thermal material.
# The porosity, along with the grain boundary strength and hydrostatic stress, are
# used to calculate the critical pressure for grain boundary fracture by the
# UO2PulverizationMesoscale material. The current pressure of the most likely bubble
# size is compared to the critical pressure to determine whether pulverization has
# occurred at each quadrature point.

# Based upon the conditions and threshold given above at t = 110 s the outer three
# elements should be completely pulverized.  The inner radius of the third element
# is at a radius of 3.150 mm. Therefore the layered averaged pulverized fuel volume
# (in each layer in this case) is analytically determined by:
#
# V_p = pi * L * (R_o^2 - R_p^2)
#
# where L is the slice height (0.1 m), R_o is the outer fuel radius, and R_p is the
# radius into the fuel at which pulverization ends. Therefore:
#
# V_p = pi * (0.1) * (4.5e-3^2 - 3.150e-3^2)
# V_p = 3.24448e-6 m^3  in each layer.
#
# The layered_pulverized_fuel_volume AuxVariable computed by BISON gives
# a layered volume of pulverized fuel as 3.24448e-6 m^3.

[Mesh]
  coord_type = RZ
  [layered1D_mesh]
    type = Layered1DMeshGenerator
    elem_type = EDGE2
    slices_per_block = 5
    pellet_outer_radius = 4.5e-3
    include_clad = false
    fuel_height = 0.5
    include_plenum = false
    nx_p = 10
    pellet_mesh_density = customize
    pellet_bottom_coor = 0.0
  []
  patch_update_strategy = auto
  partitioner = centroid
  centroid_partitioner_direction = y
[]

[Variables]
  [temperature]
    order = FIRST
    family = LAGRANGE
    initial_condition = 600
  []
[]

[AuxVariables]
  [burnup]
    order = FIRST
    family = LAGRANGE
  []
  [fission_rate]
    order = FIRST
    family = LAGRANGE
  []
  [pulverized_aux]
    order = CONSTANT
    family = MONOMIAL
  []
  [layered_pulverized_fuel_volume]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [burnup_function]
    type = ParsedFunction
    expression = 'x*1.6*t/4.275'
  []
  [temperature_function]
    type = ParsedFunction
    expression = 'if(t < 100, 900, 900+(t-100)*200)'
  []
  [Fiss_func]
    type = ParsedFunction
    expression = '1.e19'
  []
[]

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

[AuxKernels]
  [burnup]
    type = FunctionAux
    variable = burnup
    function = burnup_function
    execute_on = 'initial linear'
  []
  [fissionrate]
    type = FissionRateGeneral
    fission_rate_formulation = GENERIC
    variable = fission_rate
    value = 1
    fission_rate_function = Fiss_func
    execute_on = 'initial timestep_begin'
  []
  [pulverized]
    type = MaterialRealAux
    block = fuel
    variable = pulverized_aux
    property = pulverized
    execute_on = 'initial nonlinear'
  []
  [layered_pulverized_fuel_volume]
    type = SpatialUserObjectAux
    variable = layered_pulverized_fuel_volume
    execute_on = timestep_end
    block = fuel
    user_object = layered_pulverized_fuel_volume
  []
[]

[BCs]
  [temperature]
    type = FunctionDirichletBC
    boundary = '10 12'
    variable = temperature
    function = temperature_function
  []
[]

[Materials]
  [fission_gas_behavior]
    type = UO2Sifgrs
    block = fuel
    temperature = temperature
    fission_rate = fission_rate
    burnup = burnup
    skip_bdr_model = true
    hbs_model = true
    hbs_material = hbs_formation
  []
  [uo2pulverizationmesoscale]
    type = UO2PulverizationMesoscale
    block = fuel
    temperature = temperature
    output_properties = pulverized
    outputs = exodus
  []
  [dummy_stress]
    type = GenericConstantRankTwoTensor
    tensor_name = 'stress'
    tensor_values = '-1e7 -1e7 -1e7 0 0 0'
  []
  [fuel_thermal]
    type = UO2Thermal
    block = fuel
    thermal_conductivity_model = STAICU
    hbs_porosity_correction = KAMPF
    model_hbs_formation = true
    temperature = temperature
    burnup_function = burnup_function
    output_properties = hbs_porosity
    outputs = exodus
  []
  [hbs_formation]
    type = HighBurnupStructureFormation
    block = fuel
    temperature = temperature
    burnup = burnup
    threshold_temperature = 1273.15 # default
    output_properties = hbs_volume_fraction
    outputs = exodus
  []
[]

[UserObjects]
  [fuel_pin_geometry]
    type = Layered1DFuelPinGeometry
    include_clad = false
    mesh_generator = layered1D_mesh
  []
  [layered_pulverized_fuel_volume]
    type = LayeredVariableIntegral
    variable = pulverized_aux
    fuel_pin_geometry = fuel_pin_geometry
    direction = y
    execute_on = 'initial timestep_end'
    block = fuel
    num_layers = 5
  []
[]

[Executioner]
  type = Transient

  solve_type = PJFNK

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'

  line_search = 'none'

  l_max_its = 100
  nl_max_its = 100
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-10
  l_tol = 1e-5
  start_time = 0.0
  num_steps = 110
  dt = 1
[]

[Outputs]
  exodus = true
[]

(test/tests/axial_relocation/uo2_pulverization_mesoscale.i)

# This file is to test the mesoscale-informed pulverization criterion for UO2 fuel.
# In the test 5 axial fuel slices are modeled without cladding with an outer fuel
# radius of 4.5 mm and slice height of 0.1 m. Ten radial finite elements are used.
# The burnup increases linearly from the fuel centerline to the fuel surface.
# Temperature is held at constant T = 900 K from t = 0 to t = 100, followed
# by a ramp in temperature from t = 100 to t = 110. Pulverization will occur
# during the ramp only, in the rim region where a significant amount of high burnup
# structure formation has begun. Local pulverization is tracked with the material
# property pulverized, which is 0 where pulverization has not occured and 1 where
# it has occurred. This material property is output to the exodus file for this test.

# At each time step, the porosity in the HBS region is calculated at each radial
# position using the correlation due to Kampf in the UO2Thermal material.
# The porosity, along with the grain boundary strength and hydrostatic stress, are
# used to calculate the critical pressure for grain boundary fracture by the
# UO2PulverizationMesoscale material. The current pressure of the most likely bubble
# size is compared to the critical pressure to determine whether pulverization has
# occurred at each quadrature point.

# Based upon the conditions and threshold given above at t = 110 s the outer three
# elements should be completely pulverized.  The inner radius of the third element
# is at a radius of 3.150 mm. Therefore the layered averaged pulverized fuel volume
# (in each layer in this case) is analytically determined by:
#
# V_p = pi * L * (R_o^2 - R_p^2)
#
# where L is the slice height (0.1 m), R_o is the outer fuel radius, and R_p is the
# radius into the fuel at which pulverization ends. Therefore:
#
# V_p = pi * (0.1) * (4.5e-3^2 - 3.150e-3^2)
# V_p = 3.24448e-6 m^3  in each layer.
#
# The layered_pulverized_fuel_volume AuxVariable computed by BISON gives
# a layered volume of pulverized fuel as 3.24448e-6 m^3.

[Mesh]
  coord_type = RZ
  [layered1D_mesh]
    type = Layered1DMeshGenerator
    elem_type = EDGE2
    slices_per_block = 5
    pellet_outer_radius = 4.5e-3
    include_clad = false
    fuel_height = 0.5
    include_plenum = false
    nx_p = 10
    pellet_mesh_density = customize
    pellet_bottom_coor = 0.0
  []
  patch_update_strategy = auto
  partitioner = centroid
  centroid_partitioner_direction = y
[]

[Variables]
  [temperature]
    order = FIRST
    family = LAGRANGE
    initial_condition = 600
  []
[]

[AuxVariables]
  [burnup]
    order = FIRST
    family = LAGRANGE
  []
  [fission_rate]
    order = FIRST
    family = LAGRANGE
  []
  [pulverized_aux]
    order = CONSTANT
    family = MONOMIAL
  []
  [layered_pulverized_fuel_volume]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [burnup_function]
    type = ParsedFunction
    expression = 'x*1.6*t/4.275'
  []
  [temperature_function]
    type = ParsedFunction
    expression = 'if(t < 100, 900, 900+(t-100)*200)'
  []
  [Fiss_func]
    type = ParsedFunction
    expression = '1.e19'
  []
[]

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

[AuxKernels]
  [burnup]
    type = FunctionAux
    variable = burnup
    function = burnup_function
    execute_on = 'initial linear'
  []
  [fissionrate]
    type = FissionRateGeneral
    fission_rate_formulation = GENERIC
    variable = fission_rate
    value = 1
    fission_rate_function = Fiss_func
    execute_on = 'initial timestep_begin'
  []
  [pulverized]
    type = MaterialRealAux
    block = fuel
    variable = pulverized_aux
    property = pulverized
    execute_on = 'initial nonlinear'
  []
  [layered_pulverized_fuel_volume]
    type = SpatialUserObjectAux
    variable = layered_pulverized_fuel_volume
    execute_on = timestep_end
    block = fuel
    user_object = layered_pulverized_fuel_volume
  []
[]

[BCs]
  [temperature]
    type = FunctionDirichletBC
    boundary = '10 12'
    variable = temperature
    function = temperature_function
  []
[]

[Materials]
  [fission_gas_behavior]
    type = UO2Sifgrs
    block = fuel
    temperature = temperature
    fission_rate = fission_rate
    burnup = burnup
    skip_bdr_model = true
    hbs_model = true
    hbs_material = hbs_formation
  []
  [uo2pulverizationmesoscale]
    type = UO2PulverizationMesoscale
    block = fuel
    temperature = temperature
    output_properties = pulverized
    outputs = exodus
  []
  [dummy_stress]
    type = GenericConstantRankTwoTensor
    tensor_name = 'stress'
    tensor_values = '-1e7 -1e7 -1e7 0 0 0'
  []
  [fuel_thermal]
    type = UO2Thermal
    block = fuel
    thermal_conductivity_model = STAICU
    hbs_porosity_correction = KAMPF
    model_hbs_formation = true
    temperature = temperature
    burnup_function = burnup_function
    output_properties = hbs_porosity
    outputs = exodus
  []
  [hbs_formation]
    type = HighBurnupStructureFormation
    block = fuel
    temperature = temperature
    burnup = burnup
    threshold_temperature = 1273.15 # default
    output_properties = hbs_volume_fraction
    outputs = exodus
  []
[]

[UserObjects]
  [fuel_pin_geometry]
    type = Layered1DFuelPinGeometry
    include_clad = false
    mesh_generator = layered1D_mesh
  []
  [layered_pulverized_fuel_volume]
    type = LayeredVariableIntegral
    variable = pulverized_aux
    fuel_pin_geometry = fuel_pin_geometry
    direction = y
    execute_on = 'initial timestep_end'
    block = fuel
    num_layers = 5
  []
[]

[Executioner]
  type = Transient

  solve_type = PJFNK

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'

  line_search = 'none'

  l_max_its = 100
  nl_max_its = 100
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-10
  l_tol = 1e-5
  start_time = 0.0
  num_steps = 110
  dt = 1
[]

[Outputs]
  exodus = true
[]

(test/tests/uo2_transient_fission_gas_release/ad_uo2_pulverization_phasefield2_transient_FGR.i)

# This file is to test the transient fission gas release model that accounts for
# the amount of fission gas released as a result of fuel pulverization. it is
# based on the input file called uo2_pulverization_mesoscale.i, which tests the
# pulverization criteria for UO2 fuel with evolve_bubble_pressure_hbs = true and
# using the 3D phase field criterion for pulverization.
# In the test 5 axial fuel slices are modeled without cladding with an outer fuel
# radius of 4.5 mm and slice height of 0.1 m. Ten radial finite elements are used.
# The burnup increases linearly from the fuel centerline to the fuel surface.
# Temperature is held at constant T = 673.15 K from t = 0 to t = 100, followed
# by a ramp in temperature from t = 100 to t = 125. Pulverization will occur
# during the ramp only, in the rim region where a significant amount of high burnup
# structure formation has begun. Local pulverization is tracked with the material
# property pulverized, which is 0 where pulverization has not occured and 1 where
# it has occurred. A material property uses the local pulverization to compute the
# amount of fission gas released as a results of fuel pulverization.
# This material property is output to the exodus file for this test.

# At each time step, the pulverized material property is computed, as well as
# the bubble radius and amount of fission gas in bubbles. These material property
# are then used to determine the amount of fission gas release due to pulverization.
# This amount predicted by the material block
# UO2PulverizationTransientFissionGasRelease is compared with analytical calculations
# made in the material block fission_gas_released_amount for verification.

# This input is the AD version.

hydrostatic_stress_constant = 1e7

[GlobalParams]
  value_range_behavior = WARN
[]

[Mesh]
  coord_type = RZ
  [layered1D_mesh]
    type = Layered1DMeshGenerator
    elem_type = EDGE2
    slices_per_block = 5
    pellet_outer_radius = 4.5e-3
    include_clad = false
    fuel_height = 0.5
    include_plenum = false
    nx_p = 10
    pellet_mesh_density = customize
    pellet_bottom_coor = 0.0
  []
  patch_update_strategy = auto
  partitioner = centroid
  centroid_partitioner_direction = y
[]

[Variables]
  [temperature]
    order = FIRST
    family = LAGRANGE
    initial_condition = 600
  []
[]

[AuxVariables]
  [burnup]
    order = FIRST
    family = LAGRANGE
  []
  [fission_rate]
    order = FIRST
    family = LAGRANGE
  []
  [pulverized_aux]
    order = CONSTANT
    family = MONOMIAL
  []
  [layered_pulverized_fuel_volume]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [burnup_function]
    type = ParsedFunction
    expression = 'x*1.6*t/4.275'
  []
  [temperature_function]
    type = ParsedFunction
    expression = 'if(t < 100, 900, 900+(t-100)*200)'
  []
  [Fiss_func]
    type = ParsedFunction
    expression = '1.e19'
  []
[]

[Kernels]
  [heat]
    type = ADHeatConduction
    variable = temperature
  []
[]

[AuxKernels]
  [burnup]
    type = FunctionAux
    variable = burnup
    function = burnup_function
    execute_on = 'initial linear'
  []
  [fissionrate]
    type = FissionRateGeneral
    fission_rate_formulation = GENERIC
    variable = fission_rate
    value = 1
    fission_rate_function = Fiss_func
    execute_on = 'initial timestep_begin'
  []
  [pulverized]
    type = ADMaterialRealAux
    block = fuel
    variable = pulverized_aux
    property = pulverized
    execute_on = 'initial nonlinear'
  []
  [layered_pulverized_fuel_volume]
    type = SpatialUserObjectAux
    variable = layered_pulverized_fuel_volume
    execute_on = timestep_end
    block = fuel
    user_object = layered_pulverized_fuel_volume
  []
[]

[BCs]
  [temperature]
    type = FunctionDirichletBC
    boundary = '10 12'
    variable = temperature
    function = temperature_function
  []
[]

[Materials]
  [UO2PulverizationTransientFissionGasRelease] # moles/m^3
    type = ADUO2PulverizationTransientFissionGasRelease
    block = fuel
    outputs = exodus
  []
  [fission_gas_behavior]
    type = ADUO2Sifgrs
    block = fuel
    temperature = temperature
    fission_rate = fission_rate
    burnup = burnup
    skip_bdr_model = true
    ig_bubble_model = MECHANISTIC_AAGESEN
    hbs_model = true
    hbs_material = hbs_formation
    pulverization_model = true
    pulverization_transient_fission_gas_release_material = UO2PulverizationTransientFissionGasRelease
    ig_diff_algorithm = FORMAS
    hydrostatic_stress_const = ${hydrostatic_stress_constant}
    igdiffcoeff_scalef_HBS = 1e24 # Ensures that all the generated fission gases diffuse from the HBS matrix to the HBS bubbles
  []
  [uo2pulverizationmesoscale]
    type = ADUO2PulverizationMesoscale
    block = fuel
    temperature = temperature
    output_properties = pulverized
    pulverization_criterion_type = phase_field_3D
    outputs = exodus
  []
  [dummy_stress]
    type = ADGenericConstantRankTwoTensor
    tensor_name = 'stress'
    tensor_values = '-${hydrostatic_stress_constant} -${hydrostatic_stress_constant} -${hydrostatic_stress_constant} 0 0 0'
  []
  [fuel_thermal]
    type = ADUO2Thermal
    block = fuel
    thermal_conductivity_model = STAICU
    hbs_porosity_correction = KAMPF
    model_hbs_formation = true
    temperature = temperature
    burnup_function = burnup_function
    output_properties = hbs_porosity
    outputs = exodus
  []
  [hbs_formation]
    type = ADHighBurnupStructureFormation
    block = fuel
    temperature = temperature
    burnup = burnup
    threshold_temperature = 1273.15 # default
    output_properties = hbs_volume_fraction
    outputs = exodus
  []
  [fission_gas_density_bubble_HBS] # moles/m^3
    type = ADParsedMaterial
    block = fuel
    property_name = 'rho_FG_hbs'
    material_property_names = 'atom_per_bubble_GB_HBS bubble_GB_volume_density_HBS'
    constant_names = 'Na'
    constant_expressions = '6.02214076e23'
    expression = 'atom_per_bubble_GB_HBS * bubble_GB_volume_density_HBS / Na'
    outputs = exodus
  []
  [opened_pore_volume_fraction] # -
    type = ADParsedMaterial
    block = fuel
    property_name = 'f_V_pul'
    material_property_names = 'hbs_porosity bubble_radius_GB_HBS'
    constant_names = 'fragment_size c_p  c_r  c_0'
    constant_expressions = '5e-5    0.03 5.17 0.02'
    expression = 'c_p * hbs_porosity + c_r * bubble_radius_GB_HBS/fragment_size + c_0'
    outputs = exodus
  []
  [fission_gas_released_amount_analytical] # moles/m^3
    type = ADParsedMaterial
    block = fuel
    property_name = 'fis_gas_rel'
    material_property_names = 'f_V_pul rho_FG_hbs pulverized'
    expression = 'pulverized * f_V_pul * rho_FG_hbs'
    outputs = exodus
  []
[]

[UserObjects]
  [fuel_pin_geometry]
    type = Layered1DFuelPinGeometry
    include_clad = false
    mesh_generator = layered1D_mesh
  []
  [layered_pulverized_fuel_volume]
    type = LayeredVariableIntegral
    variable = pulverized_aux
    fuel_pin_geometry = fuel_pin_geometry
    direction = y
    execute_on = 'initial timestep_end'
    block = fuel
    num_layers = 5
  []
[]

[Postprocessors]
  [FG_amount_bubble_HBS]
    type = ADLayeredElementIntegralMaterialProperty
    mat_prop = rho_FG_hbs
    block = fuel
    fuel_pin_geometry = fuel_pin_geometry
  []
  [FGR_analytical]
    type = ADLayeredElementIntegralMaterialProperty
    mat_prop = fis_gas_rel
    block = fuel
    fuel_pin_geometry = fuel_pin_geometry
  []
  [FGR]
    type = ADLayeredElementIntegralMaterialProperty
    mat_prop = gas_concentration_release_pulverization
    block = fuel
    fuel_pin_geometry = fuel_pin_geometry
  []
  [FGR_pps_diff_bison_analytical]
    type = DifferencePostprocessor
    value1 = FGR_analytical
    value2 = FGR
  []
  [FG_pps_diff_total_released]
    type = DifferencePostprocessor
    value1 = FG_amount_bubble_HBS
    value2 = FGR
  []
  [volume_domain]
    type = ADLayeredElementIntegralMaterialProperty
    mat_prop = 1
    block = fuel
    execute_on = TIMESTEP_END
    fuel_pin_geometry = fuel_pin_geometry
  []
  [hbs_volume]
    type = ADLayeredElementIntegralMaterialProperty
    mat_prop = hbs_volume_fraction
    block = fuel
    execute_on = TIMESTEP_END
    fuel_pin_geometry = fuel_pin_geometry
  []
  [hbs_volume_fraction]
    type = ParsedPostprocessor
    pp_names = 'hbs_volume volume_domain'
    expression = 'hbs_volume / volume_domain'
    execute_on = TIMESTEP_END
  []
  [pulverized_volume]
    type = ADLayeredElementIntegralMaterialProperty
    mat_prop = pulverized
    block = fuel
    execute_on = TIMESTEP_END
    fuel_pin_geometry = fuel_pin_geometry
  []
[]

[Executioner]
  type = Transient

  solve_type = Newton

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'

  line_search = 'none'

  l_max_its = 100
  nl_max_its = 100
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-10
  l_tol = 1e-5
  start_time = 0.0
  num_steps = 125
  dt = 1
[]

[Outputs]
  exodus = true
  csv = true
  file_base = ad_uo2_pulverization_phasefield2_transient_FGR_out
[]

(test/tests/axial_relocation/uo2_pulverization_phasefield.i)

# This file is to test the phase-field based pulverization criterion for UO2 fuel
# with evolve_bubble_pressure_hbs = false and using the 2D phase field criterion
# for pulverization.
# In the test 5 axial fuel slices are modeled without cladding with an outer fuel
# radius of 4.5 mm and slice height of 0.1 m. Ten radial finite elements are used.
# The burnup increases linearly from the fuel centerline to the fuel surface.
# Temperature is held at constant T = 673.15 K from t = 0 to t = 100, followed
# by a ramp in temperature from t = 100 to t = 110. Pulverization will occur
# during the ramp only, in the rim region where a significant amount of high burnup
# structure formation has begun. Local pulverization is tracked with the material
# property pulverized, which is 0 where pulverization has not occured and 1 where
# it has occurred. This material property is output to the exodus file for this test.

# At each time step, the porosity in the HBS region is calculated at each radial
# position using the correlation due to Kampf in the UO2Thermal material.
# The porosity, along with the hydrostatic stress, are used to calculate the
# critical pressure for grain boundary fracture using data from fits to phase-field
# fracture simulations. The current pressure of the most likely bubble
# size is compared to the critical pressure to determine whether pulverization has
# occurred at each quadrature point.

# Based upon the conditions and threshold given above at t = 110 s the outer three
# elements should be completely pulverized.  The inner radius of the third element
# is at a radius of 3.150 mm. Therefore the layered averaged pulverized fuel volume
# (in each layer in this case) is analytically determined by:
#
# V_p = pi * L * (R_o^2 - R_p^2)
#
# where L is the slice height (0.1 m), R_o is the outer fuel radius, and R_p is the
# radius into the fuel at which pulverization ends. Therefore:
#
# V_p = pi * (0.1) * (4.5e-3^2 - 3.150e-3^2)
# V_p = 3.24448e-6 m^3  in each layer.
#
# The layered_pulverized_fuel_volume AuxVariable computed by BISON gives
# a layered volume of pulverized fuel as 3.24448e-6 m^3.

[Mesh]
  coord_type = RZ
  [layered1D_mesh]
    type = Layered1DMeshGenerator
    elem_type = EDGE2
    slices_per_block = 5
    pellet_outer_radius = 4.5e-3
    include_clad = false
    fuel_height = 0.5
    include_plenum = false
    nx_p = 10
    pellet_mesh_density = customize
    pellet_bottom_coor = 0.0
  []
  patch_update_strategy = auto
  partitioner = centroid
  centroid_partitioner_direction = y
[]

[Variables]
  [temperature]
    order = FIRST
    family = LAGRANGE
    initial_condition = 600
  []
[]

[AuxVariables]
  [burnup]
    order = FIRST
    family = LAGRANGE
  []
  [fission_rate]
    order = FIRST
    family = LAGRANGE
  []
  [pulverized_aux]
    order = CONSTANT
    family = MONOMIAL
  []
  [layered_pulverized_fuel_volume]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [burnup_function]
    type = ParsedFunction
    expression = 'x*1.6*t/4.275'
  []
  [temperature_function]
    type = ParsedFunction
    expression = 'if(t < 100, 673.15, 673.15+(t-100)*15.5)'
  []
  [Fiss_func]
    type = ParsedFunction
    expression = '1.e19'
  []
[]

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

[AuxKernels]
  [burnup]
    type = FunctionAux
    variable = burnup
    function = burnup_function
    execute_on = 'initial linear'
  []
  [fissionrate]
    type = FissionRateGeneral
    fission_rate_formulation = GENERIC
    variable = fission_rate
    value = 1
    fission_rate_function = Fiss_func
    execute_on = 'initial timestep_begin'
  []
  [pulverized]
    type = MaterialRealAux
    block = fuel
    variable = pulverized_aux
    property = pulverized
    execute_on = 'initial nonlinear'
  []
  [layered_pulverized_fuel_volume]
    type = SpatialUserObjectAux
    variable = layered_pulverized_fuel_volume
    execute_on = timestep_end
    block = fuel
    user_object = layered_pulverized_fuel_volume
  []
[]

[BCs]
  [temperature]
    type = FunctionDirichletBC
    boundary = '10 12'
    variable = temperature
    function = temperature_function
  []
[]

[Materials]
  [fission_gas_behavior]
    type = UO2Sifgrs
    block = fuel
    temperature = temperature
    fission_rate = fission_rate
    burnup = burnup
    skip_bdr_model = true
    hbs_model = true
    hbs_material = hbs_formation
    evolve_bubble_pressure_hbs = false
  []
  [uo2pulverizationmesoscale]
    type = UO2PulverizationMesoscale
    block = fuel
    temperature = temperature
    output_properties = pulverized
    pulverization_criterion_type = phase_field_2D
    outputs = exodus
  []
  [dummy_stress]
    type = GenericConstantRankTwoTensor
    tensor_name = 'stress'
    tensor_values = '-1e7 -1e7 -1e7 0 0 0'
  []
  [fuel_thermal]
    type = UO2Thermal
    block = fuel
    thermal_conductivity_model = STAICU
    hbs_porosity_correction = KAMPF
    model_hbs_formation = true
    temperature = temperature
    burnup_function = burnup_function
    output_properties = hbs_porosity
    outputs = exodus
  []
  [hbs_formation]
    type = HighBurnupStructureFormation
    temperature = temperature
    burnup = burnup
    threshold_temperature = 1273.15 # default
    output_properties = hbs_volume_fraction
    outputs = exodus
  []
[]

[UserObjects]
  [fuel_pin_geometry]
    type = Layered1DFuelPinGeometry
    include_clad = false
    mesh_generator = layered1D_mesh
  []
  [layered_pulverized_fuel_volume]
    type = LayeredVariableIntegral
    variable = pulverized_aux
    fuel_pin_geometry = fuel_pin_geometry
    direction = y
    execute_on = 'initial timestep_end'
    block = fuel
    num_layers = 5
  []
[]

[Executioner]
  type = Transient

  solve_type = PJFNK

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'

  line_search = 'none'

  l_max_its = 100
  nl_max_its = 100
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-10
  l_tol = 1e-5
  start_time = 0.0
  num_steps = 110
  dt = 1
[]

[Outputs]
  exodus = true
[]

(test/tests/axial_relocation/ad_uo2_pulverization_phasefield2.i)

# This file is to test the phase-field based pulverization criterion for UO2 fuel
# with evolve_bubble_pressure_hbs = true and using the 3D phase field criterion
# for pulverization.
# In the test 5 axial fuel slices are modeled without cladding with an outer fuel
# radius of 4.5 mm and slice height of 0.1 m. Ten radial finite elements are used.
# The burnup increases linearly from the fuel centerline to the fuel surface.
# Temperature is held at constant T = 673.15 K from t = 0 to t = 100, followed
# by a ramp in temperature from t = 100 to t = 125. Pulverization will occur
# during the ramp only, in the rim region where a significant amount of high burnup
# structure formation has begun. Local pulverization is tracked with the material
# property pulverized, which is 0 where pulverization has not occured and 1 where
# it has occurred. This material property is output to the exodus file for this test.

# At each time step, the porosity in the HBS region is calculated at each radial
# position using the correlation due to Kampf in the UO2Thermal material.
# The porosity, along with the hydrostatic stress, are used to calculate the
# critical pressure for grain boundary fracture using data from fits to phase-field
# fracture simulations. The current pressure of the most likely bubble
# size is compared to the critical pressure to determine whether pulverization has
# occurred at each quadrature point.

# Based upon the conditions and threshold given above at t = 110 s the outer three
# elements should be completely pulverized.  The inner radius of the third element
# is at a radius of 3.150 mm. Therefore the layered averaged pulverized fuel volume
# (in each layer in this case) is analytically determined by:
#
# V_p = pi * L * (R_o^2 - R_p^2)
#
# where L is the slice height (0.1 m), R_o is the outer fuel radius, and R_p is the
# radius into the fuel at which pulverization ends. Therefore:
#
# V_p = pi * (0.1) * (4.5e-3^2 - 3.150e-3^2)
# V_p = 3.24448e-6 m^3  in each layer.
#
# The layered_pulverized_fuel_volume AuxVariable computed by BISON gives
# a layered volume of pulverized fuel as 3.24448e-6 m^3.

[Mesh]
  coord_type = RZ
  [layered1D_mesh]
    type = Layered1DMeshGenerator
    elem_type = EDGE2
    slices_per_block = 5
    pellet_outer_radius = 4.5e-3
    include_clad = false
    fuel_height = 0.5
    include_plenum = false
    nx_p = 10
    pellet_mesh_density = customize
    pellet_bottom_coor = 0.0
  []
  patch_update_strategy = auto
  partitioner = centroid
  centroid_partitioner_direction = y
[]

[Variables]
  [temperature]
    order = FIRST
    family = LAGRANGE
    initial_condition = 600
  []
[]

[AuxVariables]
  [burnup]
    order = FIRST
    family = LAGRANGE
  []
  [fission_rate]
    order = FIRST
    family = LAGRANGE
  []
  [pulverized_aux]
    order = CONSTANT
    family = MONOMIAL
  []
  [layered_pulverized_fuel_volume]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [burnup_function]
    type = ParsedFunction
    expression = 'x*1.6*t/4.275'
  []
  [temperature_function]
    type = ParsedFunction
    expression = 'if(t < 100, 673.15, 673.15+(t-100)*15.5)'
  []
  [Fiss_func]
    type = ParsedFunction
    expression = '1.e19'
  []
[]

[Kernels]
  [heat]
    type = ADHeatConduction
    variable = temperature
  []
[]

[AuxKernels]
  [burnup]
    type = FunctionAux
    variable = burnup
    function = burnup_function
    execute_on = 'initial linear'
  []
  [fissionrate]
    type = FissionRateGeneral
    fission_rate_formulation = GENERIC
    variable = fission_rate
    value = 1
    fission_rate_function = Fiss_func
    execute_on = 'initial timestep_begin'
  []
  [pulverized]
    type = ADMaterialRealAux
    block = fuel
    variable = pulverized_aux
    property = pulverized
    execute_on = 'initial nonlinear'
  []
  [layered_pulverized_fuel_volume]
    type = SpatialUserObjectAux
    variable = layered_pulverized_fuel_volume
    execute_on = timestep_end
    block = fuel
    user_object = layered_pulverized_fuel_volume
  []
[]

[BCs]
  [temperature]
    type = FunctionDirichletBC
    boundary = '10 12'
    variable = temperature
    function = temperature_function
  []
[]

[Materials]
  [fission_gas_behavior]
    type = ADUO2Sifgrs
    block = fuel
    temperature = temperature
    fission_rate = fission_rate
    burnup = burnup
    skip_bdr_model = true
    hbs_model = true
    hbs_material = hbs_formation
  []
  [uo2pulverizationmesoscale]
    type = ADUO2PulverizationMesoscale
    block = fuel
    temperature = temperature
    output_properties = pulverized
    pulverization_criterion_type = phase_field_3D
    outputs = exodus
  []
  [dummy_stress]
    type = ADGenericConstantRankTwoTensor
    tensor_name = 'stress'
    tensor_values = '-1e7 -1e7 -1e7 0 0 0'
  []
  [fuel_thermal]
    type = ADUO2Thermal
    block = fuel
    thermal_conductivity_model = STAICU
    hbs_porosity_correction = KAMPF
    model_hbs_formation = true
    temperature = temperature
    burnup_function = burnup_function
    output_properties = hbs_porosity
    outputs = exodus
  []
  [hbs_formation]
    type = ADHighBurnupStructureFormation
    temperature = temperature
    burnup = burnup
    threshold_temperature = 1273.15 # default
    output_properties = hbs_volume_fraction
    outputs = exodus
  []
[]

[UserObjects]
  [fuel_pin_geometry]
    type = Layered1DFuelPinGeometry
    include_clad = false
    mesh_generator = layered1D_mesh
  []
  [layered_pulverized_fuel_volume]
    type = LayeredVariableIntegral
    variable = pulverized_aux
    fuel_pin_geometry = fuel_pin_geometry
    direction = y
    execute_on = 'initial timestep_end'
    block = fuel
    num_layers = 5
  []
[]

[Executioner]
  type = Transient

  solve_type = Newton

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'

  line_search = 'none'

  l_max_its = 100
  nl_max_its = 100
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-10
  l_tol = 1e-5
  start_time = 0.0
  num_steps = 125
  dt = 1
[]

[Outputs]
  exodus = true
[]

(test/tests/uo2_transient_fission_gas_release/uo2_pulverization_phasefield2_transient_FGR.i)

# This file is to test the transient fission gas release model that accounts for
# the amount of fission gas released as a result of fuel pulverization. it is
# based on the input file called uo2_pulverization_mesoscale.i, which tests the
# pulverization criteria for UO2 fuel with evolve_bubble_pressure_hbs = true and
# using the 3D phase field criterion for pulverization.
# In the test 5 axial fuel slices are modeled without cladding with an outer fuel
# radius of 4.5 mm and slice height of 0.1 m. Ten radial finite elements are used.
# The burnup increases linearly from the fuel centerline to the fuel surface.
# Temperature is held at constant T = 673.15 K from t = 0 to t = 100, followed
# by a ramp in temperature from t = 100 to t = 125. Pulverization will occur
# during the ramp only, in the rim region where a significant amount of high burnup
# structure formation has begun. Local pulverization is tracked with the material
# property pulverized, which is 0 where pulverization has not occured and 1 where
# it has occurred. A material property uses the local pulverization to compute the
# amount of fission gas released as a results of fuel pulverization.
# This material property is output to the exodus file for this test.

# At each time step, the pulverized material property is computed, as well as
# the bubble radius and amount of fission gas in bubbles. These material property
# are then used to determine the amount of fission gas release due to pulverization.
# This amount predicted by the material block
# UO2PulverizationTransientFissionGasRelease is compared with analytical calculations
# made in the material block fission_gas_released_amount for verification.

# This input is the non-AD version.

hydrostatic_stress_constant = 1e7

[GlobalParams]
  value_range_behavior = WARN
[]

[Mesh]
  coord_type = RZ
  [layered1D_mesh]
    type = Layered1DMeshGenerator
    elem_type = EDGE2
    slices_per_block = 5
    pellet_outer_radius = 4.5e-3
    include_clad = false
    fuel_height = 0.5
    include_plenum = false
    nx_p = 10
    pellet_mesh_density = customize
    pellet_bottom_coor = 0.0
  []
  patch_update_strategy = auto
  partitioner = centroid
  centroid_partitioner_direction = y
[]

[Variables]
  [temperature]
    order = FIRST
    family = LAGRANGE
    initial_condition = 600
  []
[]

[AuxVariables]
  [burnup]
    order = FIRST
    family = LAGRANGE
  []
  [fission_rate]
    order = FIRST
    family = LAGRANGE
  []
  [pulverized_aux]
    order = CONSTANT
    family = MONOMIAL
  []
  [layered_pulverized_fuel_volume]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [burnup_function]
    type = ParsedFunction
    expression = 'x*1.6*t/4.275'
  []
  [temperature_function]
    type = ParsedFunction
    expression = 'if(t < 100, 900, 900+(t-100)*200)'
  []
  [Fiss_func]
    type = ParsedFunction
    expression = '1.e19'
  []
[]

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

[AuxKernels]
  [burnup]
    type = FunctionAux
    variable = burnup
    function = burnup_function
    execute_on = 'initial linear'
  []
  [fissionrate]
    type = FissionRateGeneral
    fission_rate_formulation = GENERIC
    variable = fission_rate
    value = 1
    fission_rate_function = Fiss_func
    execute_on = 'initial timestep_begin'
  []
  [pulverized]
    type = MaterialRealAux
    block = fuel
    variable = pulverized_aux
    property = pulverized
    execute_on = 'initial nonlinear'
  []
  [layered_pulverized_fuel_volume]
    type = SpatialUserObjectAux
    variable = layered_pulverized_fuel_volume
    execute_on = timestep_end
    block = fuel
    user_object = layered_pulverized_fuel_volume
  []
[]

[BCs]
  [temperature]
    type = FunctionDirichletBC
    boundary = '10 12'
    variable = temperature
    function = temperature_function
  []
[]

[Materials]
  [fission_gas_behavior]
    type = UO2Sifgrs
    block = fuel
    temperature = temperature
    fission_rate = fission_rate
    burnup = burnup
    skip_bdr_model = true
    ig_bubble_model = MECHANISTIC_AAGESEN
    hbs_model = true
    hbs_material = hbs_formation
    pulverization_model = true
    pulverization_transient_fission_gas_release_material = UO2PulverizationTransientFissionGasRelease
    ig_diff_algorithm = FORMAS
    hydrostatic_stress_const = ${hydrostatic_stress_constant}
    igdiffcoeff_scalef_HBS = 1e24 # Ensures that all the generated fission gases diffuse from the HBS matrix to the HBS bubbles
  []
  [uo2pulverizationmesoscale]
    type = UO2PulverizationMesoscale
    block = fuel
    temperature = temperature
    output_properties = pulverized
    pulverization_criterion_type = phase_field_3D
    outputs = exodus
  []
  [dummy_stress]
    type = GenericConstantRankTwoTensor
    tensor_name = 'stress'
    tensor_values = '-${hydrostatic_stress_constant} -${hydrostatic_stress_constant} -${hydrostatic_stress_constant} 0 0 0'
  []
  [fuel_thermal]
    type = UO2Thermal
    block = fuel
    thermal_conductivity_model = STAICU
    hbs_porosity_correction = KAMPF
    model_hbs_formation = true
    temperature = temperature
    burnup_function = burnup_function
    output_properties = hbs_porosity
    outputs = exodus
  []
  [hbs_formation]
    type = HighBurnupStructureFormation
    block = fuel
    temperature = temperature
    burnup = burnup
    threshold_temperature = 1273.15 # default
    output_properties = hbs_volume_fraction
    outputs = exodus
  []
  [fission_gas_density_bubble_HBS] # moles/m^3
    type = ParsedMaterial
    block = fuel
    property_name = 'rho_FG_hbs'
    material_property_names = 'atom_per_bubble_GB_HBS bubble_GB_volume_density_HBS'
    constant_names = 'Na'
    constant_expressions = '6.02214076e23'
    expression = 'atom_per_bubble_GB_HBS * bubble_GB_volume_density_HBS / Na'
    outputs = exodus
  []
  [opened_pore_volume_fraction] # -
    type = ParsedMaterial
    block = fuel
    property_name = 'f_V_pul'
    material_property_names = 'hbs_porosity bubble_radius_GB_HBS'
    constant_names = 'fragment_size c_p  c_r  c_0'
    constant_expressions = '5e-5    0.03 5.17 0.02'
    expression = 'c_p * hbs_porosity + c_r * bubble_radius_GB_HBS/fragment_size + c_0'
    outputs = exodus
  []
  [fission_gas_released_amount_analytical] # moles/m^3
    type = ParsedMaterial
    block = fuel
    property_name = 'fis_gas_rel'
    material_property_names = 'f_V_pul rho_FG_hbs pulverized'
    expression = 'pulverized * f_V_pul * rho_FG_hbs'
    outputs = exodus
  []
  [UO2PulverizationTransientFissionGasRelease] # moles/m^3
    type = UO2PulverizationTransientFissionGasRelease
    block = fuel
    outputs = exodus
  []
[]

[UserObjects]
  [fuel_pin_geometry]
    type = Layered1DFuelPinGeometry
    include_clad = false
    mesh_generator = layered1D_mesh
  []
  [layered_pulverized_fuel_volume]
    type = LayeredVariableIntegral
    variable = pulverized_aux
    fuel_pin_geometry = fuel_pin_geometry
    direction = y
    execute_on = 'initial timestep_end'
    block = fuel
    num_layers = 5
  []
[]

[Postprocessors]
  [FG_amount_bubble_HBS]
    type = LayeredElementIntegralMaterialProperty
    mat_prop = rho_FG_hbs
    block = fuel
    fuel_pin_geometry = fuel_pin_geometry
  []
  [FGR_analytical]
    type = LayeredElementIntegralMaterialProperty
    mat_prop = fis_gas_rel
    block = fuel
    fuel_pin_geometry = fuel_pin_geometry
  []
  [FGR]
    type = LayeredElementIntegralMaterialProperty
    mat_prop = gas_concentration_release_pulverization
    block = fuel
    fuel_pin_geometry = fuel_pin_geometry
  []
  [FGR_pps_diff_bison_analytical]
    type = DifferencePostprocessor
    value1 = FGR_analytical
    value2 = FGR
  []
  [FG_pps_diff_total_released]
    type = DifferencePostprocessor
    value1 = FG_amount_bubble_HBS
    value2 = FGR
  []
  [volume_domain]
    type = LayeredElementIntegralMaterialProperty
    mat_prop = 1
    block = fuel
    execute_on = TIMESTEP_END
    fuel_pin_geometry = fuel_pin_geometry
  []
  [hbs_volume]
    type = LayeredElementIntegralMaterialProperty
    mat_prop = hbs_volume_fraction
    block = fuel
    execute_on = TIMESTEP_END
    fuel_pin_geometry = fuel_pin_geometry
  []
  [hbs_volume_fraction]
    type = ParsedPostprocessor
    pp_names = 'hbs_volume volume_domain'
    expression = 'hbs_volume / volume_domain'
    execute_on = TIMESTEP_END
  []
  [pulverized_volume]
    type = LayeredElementIntegralMaterialProperty
    mat_prop = pulverized
    block = fuel
    execute_on = TIMESTEP_END
    fuel_pin_geometry = fuel_pin_geometry
  []
[]

[Executioner]
  type = Transient

  solve_type = PJFNK

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'

  line_search = 'none'

  l_max_its = 100
  nl_max_its = 100
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-10
  l_tol = 1e-5
  start_time = 0.0
  num_steps = 125
  dt = 1
[]

[Outputs]
  exodus = true
  csv = true
  file_base = uo2_pulverization_phasefield2_transient_FGR_out
[]

(test/tests/axial_relocation/ad_uo2_pulverization_phasefield.i)

# This file is to test the phase-field based pulverization criterion for UO2 fuel
# with evolve_bubble_pressure_hbs = false and using the 2D phase field criterion
# for pulverization.
# In the test 5 axial fuel slices are modeled without cladding with an outer fuel
# radius of 4.5 mm and slice height of 0.1 m. Ten radial finite elements are used.
# The burnup increases linearly from the fuel centerline to the fuel surface.
# Temperature is held at constant T = 673.15 K from t = 0 to t = 100, followed
# by a ramp in temperature from t = 100 to t = 110. Pulverization will occur
# during the ramp only, in the rim region where a significant amount of high burnup
# structure formation has begun. Local pulverization is tracked with the material
# property pulverized, which is 0 where pulverization has not occured and 1 where
# it has occurred. This material property is output to the exodus file for this test.

# At each time step, the porosity in the HBS region is calculated at each radial
# position using the correlation due to Kampf in the UO2Thermal material.
# The porosity, along with the hydrostatic stress, are used to calculate the
# critical pressure for grain boundary fracture using data from fits to phase-field
# fracture simulations. The current pressure of the most likely bubble
# size is compared to the critical pressure to determine whether pulverization has
# occurred at each quadrature point.

# Based upon the conditions and threshold given above at t = 110 s the outer three
# elements should be completely pulverized.  The inner radius of the third element
# is at a radius of 3.150 mm. Therefore the layered averaged pulverized fuel volume
# (in each layer in this case) is analytically determined by:
#
# V_p = pi * L * (R_o^2 - R_p^2)
#
# where L is the slice height (0.1 m), R_o is the outer fuel radius, and R_p is the
# radius into the fuel at which pulverization ends. Therefore:
#
# V_p = pi * (0.1) * (4.5e-3^2 - 3.150e-3^2)
# V_p = 3.24448e-6 m^3  in each layer.
#
# The layered_pulverized_fuel_volume AuxVariable computed by BISON gives
# a layered volume of pulverized fuel as 3.24448e-6 m^3.

[Mesh]
  coord_type = RZ
  [layered1D_mesh]
    type = Layered1DMeshGenerator
    elem_type = EDGE2
    slices_per_block = 5
    pellet_outer_radius = 4.5e-3
    include_clad = false
    fuel_height = 0.5
    include_plenum = false
    nx_p = 10
    pellet_mesh_density = customize
    pellet_bottom_coor = 0.0
  []
  patch_update_strategy = auto
  partitioner = centroid
  centroid_partitioner_direction = y
[]

[Variables]
  [temperature]
    order = FIRST
    family = LAGRANGE
    initial_condition = 600
  []
[]

[AuxVariables]
  [burnup]
    order = FIRST
    family = LAGRANGE
  []
  [fission_rate]
    order = FIRST
    family = LAGRANGE
  []
  [pulverized_aux]
    order = CONSTANT
    family = MONOMIAL
  []
  [layered_pulverized_fuel_volume]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [burnup_function]
    type = ParsedFunction
    expression = 'x*1.6*t/4.275'
  []
  [temperature_function]
    type = ParsedFunction
    expression = 'if(t < 100, 673.15, 673.15+(t-100)*15.5)'
  []
  [Fiss_func]
    type = ParsedFunction
    expression = '1.e19'
  []
[]

[Kernels]
  [heat]
    type = ADHeatConduction
    variable = temperature
  []
[]

[AuxKernels]
  [burnup]
    type = FunctionAux
    variable = burnup
    function = burnup_function
    execute_on = 'initial linear'
  []
  [fissionrate]
    type = FissionRateGeneral
    fission_rate_formulation = GENERIC
    variable = fission_rate
    value = 1
    fission_rate_function = Fiss_func
    execute_on = 'initial timestep_begin'
  []
  [pulverized]
    type = ADMaterialRealAux
    block = fuel
    variable = pulverized_aux
    property = pulverized
    execute_on = 'initial nonlinear'
  []
  [layered_pulverized_fuel_volume]
    type = SpatialUserObjectAux
    variable = layered_pulverized_fuel_volume
    execute_on = timestep_end
    block = fuel
    user_object = layered_pulverized_fuel_volume
  []
[]

[BCs]
  [temperature]
    type = FunctionDirichletBC
    boundary = '10 12'
    variable = temperature
    function = temperature_function
  []
[]

[Materials]
  [fission_gas_behavior]
    type = ADUO2Sifgrs
    block = fuel
    temperature = temperature
    fission_rate = fission_rate
    burnup = burnup
    skip_bdr_model = true
    hbs_model = true
    hbs_material = hbs_formation
    evolve_bubble_pressure_hbs = false
  []
  [uo2pulverizationmesoscale]
    type = ADUO2PulverizationMesoscale
    block = fuel
    temperature = temperature
    output_properties = pulverized
    pulverization_criterion_type = phase_field_2D
    outputs = exodus
  []
  [dummy_stress]
    type = ADGenericConstantRankTwoTensor
    tensor_name = 'stress'
    tensor_values = '-1e7 -1e7 -1e7 0 0 0'
  []
  [fuel_thermal]
    type = ADUO2Thermal
    block = fuel
    thermal_conductivity_model = STAICU
    hbs_porosity_correction = KAMPF
    model_hbs_formation = true
    temperature = temperature
    burnup_function = burnup_function
    output_properties = hbs_porosity
    outputs = exodus
  []
  [hbs_formation]
    type = ADHighBurnupStructureFormation
    block = fuel
    temperature = temperature
    burnup = burnup
    threshold_temperature = 1273.15 # default
    output_properties = hbs_volume_fraction
    outputs = exodus
  []
[]

[UserObjects]
  [fuel_pin_geometry]
    type = Layered1DFuelPinGeometry
    include_clad = false
    mesh_generator = layered1D_mesh
  []
  [layered_pulverized_fuel_volume]
    type = LayeredVariableIntegral
    variable = pulverized_aux
    fuel_pin_geometry = fuel_pin_geometry
    direction = y
    execute_on = 'initial timestep_end'
    block = fuel
    num_layers = 5
  []
[]

[Executioner]
  type = Transient

  solve_type = Newton

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'

  line_search = 'none'

  l_max_its = 100
  nl_max_its = 100
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-10
  l_tol = 1e-5
  start_time = 0.0
  num_steps = 110
  dt = 1
[]

[Outputs]
  exodus = true
[]

(test/tests/uo2_transient_fission_gas_release/uo2_pulverization_transient_FGR_1D.i)

# This file is to test the transient fission gas release model that accounts for
# the amount of fission gas released as a result of fuel pulverization.
# It uses evolve_bubble_pressure_hbs = true and the 3D phase field criterion for
# pulverization.
# Local pulverization is tracked with the material property pulverized, which is
# 0 where pulverization has not occured and 1 where it has occurred.
# A material property uses the local pulverization to compute the
# amount of fission gas released as a results of fuel pulverization.
# This material property is output to the exodus file for this test.

# At each time step, the pulverized material property is computed, as well as
# the bubble radius and amount of fission gas in bubbles. These material property
# are then used to determine the amount of fission gas release due to pulverization.
# This amount predicted by the material block
# UO2PulverizationTransientFissionGasRelease is compared with analytical calculations
# made in the material block fission_gas_released_amount for verification.

# This input is the non-AD version.

hydrostatic_stress_constant = 1e7

[GlobalParams]
  value_range_behavior = WARN
[]

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 10
  xmax = 4.5e-3 # m pellet outer radius
[]

[Variables]
  [temperature]
    order = FIRST
    family = LAGRANGE
    initial_condition = 600
  []
[]

[AuxVariables]
  [burnup]
    order = FIRST
    family = LAGRANGE
  []
  [fission_rate]
    order = FIRST
    family = LAGRANGE
  []
  [pulverized_aux]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [burnup_function]
    type = ParsedFunction
    expression = 'x*1.6*t/4.275'
  []
  [temperature_function]
    type = ParsedFunction
    expression = 'if(t < 100, 900, 900+(t-100)*200)'
  []
  [Fiss_func]
    type = ParsedFunction
    expression = '1.e19'
  []
[]

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

[AuxKernels]
  [burnup]
    type = FunctionAux
    variable = burnup
    function = burnup_function
    execute_on = 'initial linear'
  []
  [fissionrate]
    type = FissionRateGeneral
    fission_rate_formulation = GENERIC
    variable = fission_rate
    value = 1
    fission_rate_function = Fiss_func
    execute_on = 'initial timestep_begin'
  []
  [pulverized]
    type = MaterialRealAux
    variable = pulverized_aux
    property = pulverized
    execute_on = 'initial nonlinear'
  []
[]

[BCs]
  [temperature]
    type = FunctionDirichletBC
    boundary = 'left right'
    variable = temperature
    function = temperature_function
  []
[]

[Materials]
  [fission_gas_behavior]
    type = UO2Sifgrs
    temperature = temperature
    fission_rate = fission_rate
    burnup = burnup
    skip_bdr_model = true
    ig_bubble_model = MECHANISTIC_AAGESEN
    hbs_model = true
    hbs_material = hbs_formation
    pulverization_model = true
    pulverization_transient_fission_gas_release_material = UO2PulverizationTransientFissionGasRelease
    ig_diff_algorithm = FORMAS
    hydrostatic_stress_const = ${hydrostatic_stress_constant}
    igdiffcoeff_scalef_HBS = 1e24 # Ensures that all the generated fission gases diffuse from the HBS matrix to the HBS bubbles
    output_properties = 'bubble_concentration_intra_non_restructured bubble_radius_intra_non_restructured gas_concentration_bubble_intra_non_restructured gas_concentration_matrix_intra_non_restructured bubble_GB_volume_density_non_restructured bubble_radius_GB_non_restructured gas_concentration_GB_bubble_volume_non_restructured deltav_v0_intra_total bubble_concentration_intra_HBS bubble_radius_intra_HBS gas_concentration_bubble_intra_HBS gas_concentration_matrix_intra_HBS bubble_GB_volume_density_HBS bubble_radius_GB_HBS gas_concentration_GB_bubble_volume_HBS atom_per_bubble_GB_HBS gas_concentration_release_total'
    outputs = 'exodus'
  []
  [uo2pulverizationmesoscale]
    type = UO2PulverizationMesoscale
    temperature = temperature
    output_properties = pulverized
    pulverization_criterion_type = phase_field_3D
    outputs = exodus
  []
  [dummy_stress]
    type = GenericConstantRankTwoTensor
    tensor_name = 'stress'
    tensor_values = '-${hydrostatic_stress_constant} -${hydrostatic_stress_constant} -${hydrostatic_stress_constant} 0 0 0'
  []
  [fuel_thermal]
    type = UO2Thermal
    thermal_conductivity_model = STAICU
    hbs_porosity_correction = KAMPF
    model_hbs_formation = true
    temperature = temperature
    burnup_function = burnup_function
    output_properties = hbs_porosity
    outputs = exodus
  []
  [hbs_formation]
    type = HighBurnupStructureFormation
    temperature = temperature
    burnup = burnup
    threshold_temperature = 1273.15 # default
    output_properties = hbs_volume_fraction
    outputs = exodus
  []
  [fission_gas_density_bubble_HBS] # moles/m^3
    type = ParsedMaterial
    property_name = 'rho_FG_hbs'
    material_property_names = 'atom_per_bubble_GB_HBS bubble_GB_volume_density_HBS'
    constant_names = 'Na'
    constant_expressions = '6.02214076e23'
    expression = 'atom_per_bubble_GB_HBS * bubble_GB_volume_density_HBS / Na'
    outputs = exodus
  []
  [opened_pore_volume_fraction] # -
    type = ParsedMaterial
    property_name = 'f_V_pul'
    material_property_names = 'hbs_porosity bubble_radius_GB_HBS'
    constant_names = 'fragment_size c_p  c_r  c_0'
    constant_expressions = '5e-5    0.03 5.17 0.02'
    expression = 'c_p * hbs_porosity + c_r * bubble_radius_GB_HBS/fragment_size + c_0'
    outputs = exodus
  []
  [fission_gas_released_amount_analytical] # moles/m^3
    type = ParsedMaterial
    property_name = 'fis_gas_rel'
    material_property_names = 'f_V_pul rho_FG_hbs pulverized'
    expression = 'pulverized * f_V_pul * rho_FG_hbs'
    outputs = exodus
  []
  [UO2PulverizationTransientFissionGasRelease] # moles/m^3
    type = UO2PulverizationTransientFissionGasRelease
    output_properties = 'gas_concentration_release_pulverization'
    outputs = exodus
  []
[]

[Postprocessors]
  [FG_amount_bubble_HBS]
    type = ElementIntegralMaterialProperty
    mat_prop = rho_FG_hbs
  []
  [FGR_transient_pulverization_analytical]
    type = ElementIntegralMaterialProperty
    mat_prop = fis_gas_rel
  []
  [FGR_transient_pulverization]
    type = ElementIntegralMaterialProperty
    mat_prop = gas_concentration_release_pulverization
  []
  [FGR_pps_diff_bison_analytical]
    type = DifferencePostprocessor
    value1 = FGR_transient_pulverization_analytical
    value2 = FGR_transient_pulverization
  []
  [FG_pps_diff_total_released]
    type = DifferencePostprocessor
    value1 = FG_amount_bubble_HBS
    value2 = FGR_transient_pulverization
  []
  [fis_gas_generated]
    type = ElementIntegralMaterialProperty
    mat_prop = gas_concentration_generated_total
  []
  [fis_gas_released_total]
    type = ElementIntegralMaterialProperty
    mat_prop = gas_concentration_release_total
  []
  [fgr_percent]
    type = FGRPercent
    fission_gas_released = fis_gas_released_total
    fission_gas_generated = fis_gas_generated
  []
  [gas_amount_bubble_intra_non_restructured]
    type = ElementIntegralMaterialProperty
    mat_prop = gas_concentration_bubble_intra_non_restructured
  []
  [gas_amount_matrix_intra_non_restructured]
    type = ElementIntegralMaterialProperty
    mat_prop = gas_concentration_matrix_intra_non_restructured
  []
  [bubble_amount_intra_non_restructured]
    type = ElementIntegralMaterialProperty
    mat_prop = bubble_concentration_intra_non_restructured
  []
  [bubble_radius_intra_average_non_restructured]
    type = ElementAverageMaterialProperty
    mat_prop = bubble_radius_intra_non_restructured
  []
  [temperature]
    type = ElementAverageValue
    variable = temperature
  []
  [fission_rate]
    type = ElementAverageValue
    variable = fission_rate
  []
  [gas_amount_hbs_GB_bubbles]
    type = ElementIntegralMaterialProperty
    mat_prop = gas_concentration_GB_bubble_volume_HBS
  []
  [gas_amount_hbs_matrix]
    type = ElementIntegralMaterialProperty
    mat_prop = gas_concentration_matrix_intra_HBS
  []
  [gas_amount_hbs_intra_bubbles]
    type = ElementIntegralMaterialProperty
    mat_prop = gas_concentration_bubble_intra_HBS
  []
  [gas_amount_hbs_intra_total]
    type = ElementIntegralMaterialProperty
    mat_prop = gas_concentration_intra_total_HBS
  []
  [bubble_amount_GB_hbs]
    type = ElementIntegralMaterialProperty
    mat_prop = bubble_GB_volume_density_HBS
  []
  [bubble_radius_GB_average_hbs]
    type = ElementAverageMaterialProperty
    mat_prop = bubble_radius_GB_HBS
  []
  [volume_domain]
    type = ElementIntegralMaterialProperty
    mat_prop = 1
    execute_on = TIMESTEP_END
  []
  [hbs_volume]
    type = ElementIntegralMaterialProperty
    mat_prop = hbs_volume_fraction
    execute_on = TIMESTEP_END
  []
  [hbs_volume_fraction]
    type = ParsedPostprocessor
    pp_names = 'hbs_volume volume_domain'
    expression = 'hbs_volume / volume_domain'
    execute_on = TIMESTEP_END
  []
  [pulverized_volume]
    type = ElementIntegralMaterialProperty
    mat_prop = pulverized
    execute_on = TIMESTEP_END
  []
[]

[Executioner]
  type = Transient

  solve_type = PJFNK

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'

  line_search = 'none'

  l_max_its = 100
  nl_max_its = 100
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-8
  l_tol = 1e-5
  start_time = 0.0
  num_steps = 125
  dt = 1
[]

[Outputs]
  exodus = true
  csv = true
[]

(test/tests/axial_relocation/ad_uo2_pulverization_mesoscale.i)

# This file is to test the mesoscale-informed pulverization criterion for UO2 fuel.
# In the test 5 axial fuel slices are modeled without cladding with an outer fuel
# radius of 4.5 mm and slice height of 0.1 m. Ten radial finite elements are used.
# The burnup increases linearly from the fuel centerline to the fuel surface.
# Temperature is held at constant T = 900 K from t = 0 to t = 100, followed
# by a ramp in temperature from t = 100 to t = 110. Pulverization will occur
# during the ramp only, in the rim region where a significant amount of high burnup
# structure formation has begun. Local pulverization is tracked with the material
# property pulverized, which is 0 where pulverization has not occured and 1 where
# it has occurred. This material property is output to the exodus file for this test.

# At each time step, the porosity in the HBS region is calculated at each radial
# position using the correlation due to Kampf in the UO2Thermal material.
# The porosity, along with the grain boundary strength and hydrostatic stress, are
# used to calculate the critical pressure for grain boundary fracture by the
# UO2PulverizationMesoscale material. The current pressure of the most likely bubble
# size is compared to the critical pressure to determine whether pulverization has
# occurred at each quadrature point.

# Based upon the conditions and threshold given above at t = 110 s the outer three
# elements should be completely pulverized.  The inner radius of the third element
# is at a radius of 3.150 mm. Therefore the layered averaged pulverized fuel volume
# (in each layer in this case) is analytically determined by:
#
# V_p = pi * L * (R_o^2 - R_p^2)
#
# where L is the slice height (0.1 m), R_o is the outer fuel radius, and R_p is the
# radius into the fuel at which pulverization ends. Therefore:
#
# V_p = pi * (0.1) * (4.5e-3^2 - 3.150e-3^2)
# V_p = 3.24448e-6 m^3  in each layer.
#
# The layered_pulverized_fuel_volume AuxVariable computed by BISON gives
# a layered volume of pulverized fuel as 3.24448e-6 m^3.

[Mesh]
  coord_type = RZ
  [layered1D_mesh]
    type = Layered1DMeshGenerator
    elem_type = EDGE2
    slices_per_block = 5
    pellet_outer_radius = 4.5e-3
    include_clad = false
    fuel_height = 0.5
    include_plenum = false
    nx_p = 10
    pellet_mesh_density = customize
    pellet_bottom_coor = 0.0
  []
  patch_update_strategy = auto
  partitioner = centroid
  centroid_partitioner_direction = y
[]

[Variables]
  [temperature]
    order = FIRST
    family = LAGRANGE
    initial_condition = 600
  []
[]

[AuxVariables]
  [burnup]
    order = FIRST
    family = LAGRANGE
  []
  [fission_rate]
    order = FIRST
    family = LAGRANGE
  []
  [pulverized_aux]
    order = CONSTANT
    family = MONOMIAL
  []
  [layered_pulverized_fuel_volume]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [burnup_function]
    type = ParsedFunction
    expression = 'x*1.6*t/4.275'
  []
  [temperature_function]
    type = ParsedFunction
    expression = 'if(t < 100, 900, 900+(t-100)*200)'
  []
  [Fiss_func]
    type = ParsedFunction
    expression = '1.e19'
  []
[]

[Kernels]
  [heat]
    type = ADHeatConduction
    variable = temperature
  []
[]

[AuxKernels]
  [burnup]
    type = FunctionAux
    variable = burnup
    function = burnup_function
    execute_on = 'initial linear'
  []
  [fissionrate]
    type = FissionRateGeneral
    fission_rate_formulation = GENERIC
    variable = fission_rate
    value = 1
    fission_rate_function = Fiss_func
    execute_on = 'initial timestep_begin'
  []
  [pulverized]
    type = ADMaterialRealAux
    block = fuel
    variable = pulverized_aux
    property = pulverized
    execute_on = 'initial nonlinear'
  []
  [layered_pulverized_fuel_volume]
    type = SpatialUserObjectAux
    variable = layered_pulverized_fuel_volume
    execute_on = timestep_end
    block = fuel
    user_object = layered_pulverized_fuel_volume
  []
[]

[BCs]
  [temperature]
    type = FunctionDirichletBC
    boundary = '10 12'
    variable = temperature
    function = temperature_function
  []
[]

[Materials]
  [fission_gas_behavior]
    type = ADUO2Sifgrs
    block = fuel
    temperature = temperature
    fission_rate = fission_rate
    burnup = burnup
    skip_bdr_model = true
    hbs_model = true
    hbs_material = hbs_formation
  []
  [uo2pulverizationmesoscale]
    type = ADUO2PulverizationMesoscale
    block = fuel
    temperature = temperature
    output_properties = pulverized
    outputs = exodus
  []
  [dummy_stress]
    type = ADGenericConstantRankTwoTensor
    tensor_name = 'stress'
    tensor_values = '-1e7 -1e7 -1e7 0 0 0'
  []
  [fuel_thermal]
    type = ADUO2Thermal
    block = fuel
    thermal_conductivity_model = STAICU
    hbs_porosity_correction = KAMPF
    model_hbs_formation = true
    temperature = temperature
    burnup_function = burnup_function
    output_properties = hbs_porosity
    outputs = exodus
  []
  [hbs_formation]
    type = ADHighBurnupStructureFormation
    block = fuel
    temperature = temperature
    burnup = burnup
    threshold_temperature = 1273.15 # default
    output_properties = hbs_volume_fraction
    outputs = exodus
  []
[]

[UserObjects]
  [fuel_pin_geometry]
    type = Layered1DFuelPinGeometry
    include_clad = false
    mesh_generator = layered1D_mesh
  []
  [layered_pulverized_fuel_volume]
    type = LayeredVariableIntegral
    variable = pulverized_aux
    fuel_pin_geometry = fuel_pin_geometry
    direction = y
    execute_on = 'initial timestep_end'
    block = fuel
    num_layers = 5
  []
[]

[Executioner]
  type = Transient

  solve_type = Newton

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'

  line_search = 'none'

  l_max_its = 100
  nl_max_its = 100
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-10
  l_tol = 1e-5
  start_time = 0.0
  num_steps = 110
  dt = 1
[]

[Outputs]
  exodus = true
[]

(test/tests/axial_relocation/uo2_pulverization_phasefield2.i)

# This file is to test the phase-field based pulverization criterion for UO2 fuel
# with evolve_bubble_pressure_hbs = true and using the 3D phase field criterion
# for pulverization.
# In the test 5 axial fuel slices are modeled without cladding with an outer fuel
# radius of 4.5 mm and slice height of 0.1 m. Ten radial finite elements are used.
# The burnup increases linearly from the fuel centerline to the fuel surface.
# Temperature is held at constant T = 673.15 K from t = 0 to t = 100, followed
# by a ramp in temperature from t = 100 to t = 125. Pulverization will occur
# during the ramp only, in the rim region where a significant amount of high burnup
# structure formation has begun. Local pulverization is tracked with the material
# property pulverized, which is 0 where pulverization has not occured and 1 where
# it has occurred. This material property is output to the exodus file for this test.

# At each time step, the porosity in the HBS region is calculated at each radial
# position using the correlation due to Kampf in the UO2Thermal material.
# The porosity, along with the hydrostatic stress, are used to calculate the
# critical pressure for grain boundary fracture using data from fits to phase-field
# fracture simulations. The current pressure of the most likely bubble
# size is compared to the critical pressure to determine whether pulverization has
# occurred at each quadrature point.

# Based upon the conditions and threshold given above at t = 110 s the outer three
# elements should be completely pulverized.  The inner radius of the third element
# is at a radius of 3.150 mm. Therefore the layered averaged pulverized fuel volume
# (in each layer in this case) is analytically determined by:
#
# V_p = pi * L * (R_o^2 - R_p^2)
#
# where L is the slice height (0.1 m), R_o is the outer fuel radius, and R_p is the
# radius into the fuel at which pulverization ends. Therefore:
#
# V_p = pi * (0.1) * (4.5e-3^2 - 3.150e-3^2)
# V_p = 3.24448e-6 m^3  in each layer.
#
# The layered_pulverized_fuel_volume AuxVariable computed by BISON gives
# a layered volume of pulverized fuel as 3.24448e-6 m^3.

[Mesh]
  coord_type = RZ
  [layered1D_mesh]
    type = Layered1DMeshGenerator
    elem_type = EDGE2
    slices_per_block = 5
    pellet_outer_radius = 4.5e-3
    include_clad = false
    fuel_height = 0.5
    include_plenum = false
    nx_p = 10
    pellet_mesh_density = customize
    pellet_bottom_coor = 0.0
  []
  patch_update_strategy = auto
  partitioner = centroid
  centroid_partitioner_direction = y
[]

[Variables]
  [temperature]
    order = FIRST
    family = LAGRANGE
    initial_condition = 600
  []
[]

[AuxVariables]
  [burnup]
    order = FIRST
    family = LAGRANGE
  []
  [fission_rate]
    order = FIRST
    family = LAGRANGE
  []
  [pulverized_aux]
    order = CONSTANT
    family = MONOMIAL
  []
  [layered_pulverized_fuel_volume]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [burnup_function]
    type = ParsedFunction
    expression = 'x*1.6*t/4.275'
  []
  [temperature_function]
    type = ParsedFunction
    expression = 'if(t < 100, 673.15, 673.15+(t-100)*15.5)'
  []
  [Fiss_func]
    type = ParsedFunction
    expression = '1.e19'
  []
[]

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

[AuxKernels]
  [burnup]
    type = FunctionAux
    variable = burnup
    function = burnup_function
    execute_on = 'initial linear'
  []
  [fissionrate]
    type = FissionRateGeneral
    fission_rate_formulation = GENERIC
    variable = fission_rate
    value = 1
    fission_rate_function = Fiss_func
    execute_on = 'initial timestep_begin'
  []
  [pulverized]
    type = MaterialRealAux
    block = fuel
    variable = pulverized_aux
    property = pulverized
    execute_on = 'initial nonlinear'
  []
  [layered_pulverized_fuel_volume]
    type = SpatialUserObjectAux
    variable = layered_pulverized_fuel_volume
    execute_on = timestep_end
    block = fuel
    user_object = layered_pulverized_fuel_volume
  []
[]

[BCs]
  [temperature]
    type = FunctionDirichletBC
    boundary = '10 12'
    variable = temperature
    function = temperature_function
  []
[]

[Materials]
  [fission_gas_behavior]
    type = UO2Sifgrs
    block = fuel
    temperature = temperature
    fission_rate = fission_rate
    burnup = burnup
    skip_bdr_model = true
    hbs_model = true
    hbs_material = hbs_formation
  []
  [uo2pulverizationmesoscale]
    type = UO2PulverizationMesoscale
    block = fuel
    temperature = temperature
    output_properties = pulverized
    pulverization_criterion_type = phase_field_3D
    outputs = exodus
  []
  [dummy_stress]
    type = GenericConstantRankTwoTensor
    tensor_name = 'stress'
    tensor_values = '-1e7 -1e7 -1e7 0 0 0'
  []
  [fuel_thermal]
    type = UO2Thermal
    block = fuel
    thermal_conductivity_model = STAICU
    hbs_porosity_correction = KAMPF
    model_hbs_formation = true
    temperature = temperature
    burnup_function = burnup_function
    output_properties = hbs_porosity
    outputs = exodus
  []
  [hbs_formation]
    type = HighBurnupStructureFormation
    block = fuel
    temperature = temperature
    burnup = burnup
    threshold_temperature = 1273.15 # default
    output_properties = hbs_volume_fraction
    outputs = exodus
  []
[]

[UserObjects]
  [fuel_pin_geometry]
    type = Layered1DFuelPinGeometry
    include_clad = false
    mesh_generator = layered1D_mesh
  []
  [layered_pulverized_fuel_volume]
    type = LayeredVariableIntegral
    variable = pulverized_aux
    fuel_pin_geometry = fuel_pin_geometry
    direction = y
    execute_on = 'initial timestep_end'
    block = fuel
    num_layers = 5
  []
[]

[Executioner]
  type = Transient

  solve_type = PJFNK

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'

  line_search = 'none'

  l_max_its = 100
  nl_max_its = 100
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-10
  l_tol = 1e-5
  start_time = 0.0
  num_steps = 125
  dt = 1
[]

[Outputs]
  exodus = true
[]

Description
Example Input Syntax
Input Parameters
Input Files
References