FeCrAlVolumetricSwellingEigenstrain

Computes the change in cladding volume due to irradiation by fast neutrons. This class applies a volumetric strain correction before adding the strain from this class to the diagonal entries of the eigenstrain tensor.

Description

It is expected that FeCrAl alloys will be subjected to irradiation induced swelling due to their cubic crystal structure. As an approximation for the swelling of FeCrAl alloys a simplistic model provided in Terrani et al. (2016) has been implemented in BISON. The estimated swelling rate is 0.05% per dpa. Using a conversion factor of (1 $var element = document.getElementById("moose-equation-ffc186b2-6cd9-45bf-a485-b51c96bc43f5");katex.render("\\times", element, {displayMode:false,throwOnError:false});$ 10 $var element = document.getElementById("moose-equation-39cb7e5f-0a95-4629-883a-45feb5d5243d");katex.render("^{25}", element, {displayMode:false,throwOnError:false});$ n/m $var element = document.getElementById("moose-equation-52331ea8-c992-4b01-8293-3f2339117b7b");katex.render("^2", element, {displayMode:false,throwOnError:false});$ = 0.9 dpa) as given by Field et al. (2015) the volumetric swelling strain rate is given by: $var element = document.getElementById("moose-equation-b8e27bd4-ca68-449b-acae-bd9255ed8d22");katex.render(" \\dot{\\epsilon} = 4.5\\times 10^{-29} \\phi", element, {displayMode:true,throwOnError:false});$ Integrating over time the volumetric swelling is given by $var element = document.getElementById("moose-equation-ec463fd6-4447-4665-930b-3f8f1ac12e83");katex.render(" \\epsilon = 4.5\\times 10^{-29} \\Phi", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-5a5b257f-b7ee-4e27-bda4-1250a4d58ae9");katex.render("\\Phi", element, {displayMode:false,throwOnError:false});$ is the fast neutron fluence given in n/m $var element = document.getElementById("moose-equation-a7ff0489-fef8-41fb-937c-452ef773100e");katex.render("^2", element, {displayMode:false,throwOnError:false});$ .

Example Input Syntax

[Materials<<<{"href": "../../../syntax/Materials/index.html"}>>>]
  [clad_swelling]
    type = FeCrAlVolumetricSwellingEigenstrain<<<{"description": "Computes the change in cladding volume due to irradiation by fast neutrons. This class applies a volumetric strain correction before adding the strain from this class to the diagonal entries of the eigenstrain tensor.", "href": "FeCrAlVolumetricSwellingEigenstrain.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = '1 2 3 4 5 6 7'
    temperature<<<{"description": "Coupled temperature in Kelvin"}>>> = temp
    fast_neutron_fluence<<<{"description": "Fast neutron fluence in neutrons/m^2"}>>> = fluence
    eigenstrain_name<<<{"description": "Material property name for the eigenstrain tensor computed by this model. IMPORTANT: The name of this property must also be provided to the strain calculator."}>>> = swell
  []
[]

The eigenstrain name must also be passed to the strain calculator as shown below:

[Physics<<<{"href": "../../../syntax/Physics/index.html"}>>>]
  [SolidMechanics<<<{"href": "../../../syntax/Physics/SolidMechanics/index.html"}>>>]
    [QuasiStatic<<<{"href": "../../../syntax/Physics/SolidMechanics/QuasiStatic/index.html"}>>>]
      [all]
        strain<<<{"description": "Strain formulation"}>>> = finite
        eigenstrain_names<<<{"description": "List of eigenstrains to be applied in this strain calculation"}>>> = 'fuelthermal_strain swell'
      []
    []
  []
[]

Input Parameters

eigenstrain_nameMaterial property name for the eigenstrain tensor computed by this model. IMPORTANT: The name of this property must also be provided to the strain calculator.
C++ Type:std::string
Controllable:No
Description:Material property name for the eigenstrain tensor computed by this model. IMPORTANT: The name of this property must also be provided to the strain calculator.
fast_neutron_fluenceFast neutron fluence in neutrons/m^2
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Fast neutron fluence in neutrons/m^2
temperatureCoupled temperature in Kelvin
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Coupled temperature in Kelvin

Required Parameters

base_nameOptional parameter that allows the user to define multiple mechanics material systems on the same block, i.e. for multiple phases
C++ Type:std::string
Controllable:No
Description:Optional parameter that allows the user to define multiple mechanics material systems on the same block, i.e. for multiple phases
blockThe list of blocks (ids or names) that this object will be applied
C++ Type:std::vector<SubdomainName>
Controllable:No
Description:The list of blocks (ids or names) that this object will be applied
boundaryThe list of boundaries (ids or names) from the mesh where this object applies
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:The list of boundaries (ids or names) from the mesh where this object applies
computeTrueWhen false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
Default:True
C++ Type:bool
Controllable:No
Description:When false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
constant_onNONEWhen ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
Default:NONE
C++ Type:MooseEnum
Options:NONE, ELEMENT, SUBDOMAIN
Controllable:No
Description:When ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
declare_suffixAn optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:An optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.

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

total_swelling_scaling_factor1Scaling factor to be applied to the swelling strain. Used for sensitivity and calibration studies
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Scaling factor to be applied to the swelling strain. Used for sensitivity and calibration studies

Advanced: Scaling Factors Parameters

Input Files

(test/tests/solid_mechanics/fecral_eigenstrains/fecral_vswelling/swelling.i)
(examples/accident_tolerant_fuel/uo2_fecral/uo2_fecral.i)

References

K. G. Field, X. Hu, K. C. Littrell, Y. Yamamoto, and L. L. Snead. Radiation tolerance of neutron-irradiated model fe-cr-al alloys. Journal of Nuclear Materials, 465:746–755, 2015.

@article{field2015,
    author = "Field, K. G. and Hu, X. and Littrell, K. C. and Yamamoto, Y. and Snead, L. L.",
    title = "Radiation tolerance of neutron-irradiated model Fe-Cr-Al alloys",
    journal = "Journal of Nuclear Materials",
    volume = "465",
    pages = "746-755",
    year = "2015"
}

K. A. Terrani, T. M. Karlsen, and Y. Yamamoto. Input correlations for irradiation creep of FeCrAl and SiC based on in-pile Halden test results. Technical Report ORNL/TM-2016/191, ORNL, May 2016.

@techreport{terrani_et_al_2016,
    author = "Terrani, K. A. and Karlsen, T. M. and Yamamoto, Y.",
    title = "Input Correlations for Irradiation Creep of {FeCrAl} and {SiC} Based on In-Pile {Halden} Test Results",
    institution = "{ORNL}",
    year = "2016",
    month = "May",
    number = "ORNL/TM-2016/191"
}

(test/tests/solid_mechanics/fecral_eigenstrains/fecral_vswelling/swelling.i)

# Test of volumetric swelling of FeCrAl alloys (1000K).
#
# The model used is based upon the upper limit of swelling suggested by:
#
# K. A. Terrani, T. M. Karlsen, and Y. Yamamoto, "Input Correlations for
# Irradiation Creep of FeCrAl and SiC based on in-pile Halden test results,"
# Technical Report ORNL/TM-2016/191, Oak Ridge National Laboratory, May 2016
#
# The suggested upper limit is 0.05% per dpa.  Using a conversion factor of
# 1x10^25 neutrons/m^2-s = 0.9 dpa as proposed by:
#
# K. G. Field, X. Hu, K. C. Littrell, Y. Yamamoto, and L. L. Snead, "Radiation
# tolerance of neutroni-irradiated model Fe-Cr-Al alloys," Journal of Nuclear
# Materials, Vol. 465, pp. 746-755, 2015.
#
# A creep strain rate due to swelling is obtained and given by:
#
# e_dot_sw = 0.0005 per dpa
#
# e_dot_sw = 0.0005 * 0.9 / 1e25 [m^2-s/n]
#
# To get the correct units multiply the factor above by flux
#
# e_dot_sw = 4.5e-29 * fast_flux
#
# To get the volumteric strain the above equation must be integrated over time:
#
# e_sw = 4.5e-29 * fast_fluence
#
# With a fast fluence of 1e24, the volumetric strain should be 4.5e-5.
# This is easily checked with the 'volume' postprocessor value.

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

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

[Variables]
  [disp_x]
    order = FIRST
    family = LAGRANGE
  []
  [disp_y]
    order = FIRST
    family = LAGRANGE
  []
  [disp_z]
    order = FIRST
    family = LAGRANGE
  []
  [temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 1000.0
  []
[]

[AuxVariables]
  [flux]
    order = FIRST
    family = LAGRANGE
  []
  [fluence]
    order = FIRST
    family = LAGRANGE
  []
  [swelling]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = finite
    eigenstrain_names = 'fuelthermal_strain swell'
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = temp
  []
  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temp
  []
[]

[AuxKernels]
  [flux_neutron_flux]
    type = FastNeutronFluxAux
    variable = flux
    factor = 1e18
    execute_on = 'initial timestep_begin'
  []
  [fast_neutron_fluence]
    type = FastNeutronFluenceAux
    variable = fluence
    block = '1 2 3 4 5 6 7'
    fast_neutron_flux = flux
    execute_on = timestep_begin
  []
  [swelling]
    type = MaterialRealAux
    variable = swelling
    property = volumetric_swelling_strain
    execute_on = timestep_end
  []
[]

[BCs]
  [bottom_x]
    type = DirichletBC
    variable = disp_x
    boundary = 10
    value = 0.0
  []
  [bottom_y]
    type = DirichletBC
    variable = disp_y
    boundary = 9
    value = 0.0
  []
  [bottom_z]
    type = DirichletBC
    variable = disp_z
    boundary = 14
    value = 0.0
  []
  [bottom_temp]
    type = DirichletBC
    variable = temp
    boundary = 3
    value = 1000.0
  []
  [top_temp]
    type = DirichletBC
    variable = temp
    boundary = 5
    value = 1000.0
  []
[]

[Materials]
  [clad_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = '1 2 3 4 5 6 7'
    youngs_modulus = 1.0
    poissons_ratio = 0.3
  []
  [clad_swelling]
    type = FeCrAlVolumetricSwellingEigenstrain
    block = '1 2 3 4 5 6 7'
    temperature = temp
    fast_neutron_fluence = fluence
    eigenstrain_name = swell
  []
  [clad_thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    block = '1 2 3 4 5 6 7'
    thermal_expansion_coeff = 1.0e-5
    temperature = temp
    stress_free_temperature = 1000.0
    eigenstrain_name = fuelthermal_strain
  []
  [clad_stress]
    type = ComputeFiniteStrainElasticStress
    block = '1 2 3 4 5 6 7'
  []
  [thermal]
    type = FeCrAlThermal
    block = '1 2 3 4 5 6 7'
    material = APMT
    temperature = temp
  []
  [density]
    type = StrainAdjustedDensity
    block = '1 2 3 4 5 6 7'
    strain_free_density = 7225.0
  []
[]

[Executioner]
   type = Transient

  solve_type = 'PJFNK'


  petsc_options = '-snes_ksp_ew '
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'
  l_max_its = 60
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-10
  l_tol = 1e-6

  start_time = 0.0
  dt = 10000
  num_steps = 100
[]

[Postprocessors]
  [volume]
    type = InternalVolume
    boundary = 15
    execute_on = 'initial linear'
  []
  [ave_fluence]
    type = ElementAverageValue
    variable = fluence
    block = '1 2 3 4 5 6 7'
  []
[]

[Outputs]
  exodus = true
[]

(test/tests/solid_mechanics/fecral_eigenstrains/fecral_vswelling/swelling.i)

# Test of volumetric swelling of FeCrAl alloys (1000K).
#
# The model used is based upon the upper limit of swelling suggested by:
#
# K. A. Terrani, T. M. Karlsen, and Y. Yamamoto, "Input Correlations for
# Irradiation Creep of FeCrAl and SiC based on in-pile Halden test results,"
# Technical Report ORNL/TM-2016/191, Oak Ridge National Laboratory, May 2016
#
# The suggested upper limit is 0.05% per dpa.  Using a conversion factor of
# 1x10^25 neutrons/m^2-s = 0.9 dpa as proposed by:
#
# K. G. Field, X. Hu, K. C. Littrell, Y. Yamamoto, and L. L. Snead, "Radiation
# tolerance of neutroni-irradiated model Fe-Cr-Al alloys," Journal of Nuclear
# Materials, Vol. 465, pp. 746-755, 2015.
#
# A creep strain rate due to swelling is obtained and given by:
#
# e_dot_sw = 0.0005 per dpa
#
# e_dot_sw = 0.0005 * 0.9 / 1e25 [m^2-s/n]
#
# To get the correct units multiply the factor above by flux
#
# e_dot_sw = 4.5e-29 * fast_flux
#
# To get the volumteric strain the above equation must be integrated over time:
#
# e_sw = 4.5e-29 * fast_fluence
#
# With a fast fluence of 1e24, the volumetric strain should be 4.5e-5.
# This is easily checked with the 'volume' postprocessor value.

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

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

[Variables]
  [disp_x]
    order = FIRST
    family = LAGRANGE
  []
  [disp_y]
    order = FIRST
    family = LAGRANGE
  []
  [disp_z]
    order = FIRST
    family = LAGRANGE
  []
  [temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 1000.0
  []
[]

[AuxVariables]
  [flux]
    order = FIRST
    family = LAGRANGE
  []
  [fluence]
    order = FIRST
    family = LAGRANGE
  []
  [swelling]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = finite
    eigenstrain_names = 'fuelthermal_strain swell'
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = temp
  []
  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temp
  []
[]

[AuxKernels]
  [flux_neutron_flux]
    type = FastNeutronFluxAux
    variable = flux
    factor = 1e18
    execute_on = 'initial timestep_begin'
  []
  [fast_neutron_fluence]
    type = FastNeutronFluenceAux
    variable = fluence
    block = '1 2 3 4 5 6 7'
    fast_neutron_flux = flux
    execute_on = timestep_begin
  []
  [swelling]
    type = MaterialRealAux
    variable = swelling
    property = volumetric_swelling_strain
    execute_on = timestep_end
  []
[]

[BCs]
  [bottom_x]
    type = DirichletBC
    variable = disp_x
    boundary = 10
    value = 0.0
  []
  [bottom_y]
    type = DirichletBC
    variable = disp_y
    boundary = 9
    value = 0.0
  []
  [bottom_z]
    type = DirichletBC
    variable = disp_z
    boundary = 14
    value = 0.0
  []
  [bottom_temp]
    type = DirichletBC
    variable = temp
    boundary = 3
    value = 1000.0
  []
  [top_temp]
    type = DirichletBC
    variable = temp
    boundary = 5
    value = 1000.0
  []
[]

[Materials]
  [clad_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = '1 2 3 4 5 6 7'
    youngs_modulus = 1.0
    poissons_ratio = 0.3
  []
  [clad_swelling]
    type = FeCrAlVolumetricSwellingEigenstrain
    block = '1 2 3 4 5 6 7'
    temperature = temp
    fast_neutron_fluence = fluence
    eigenstrain_name = swell
  []
  [clad_thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    block = '1 2 3 4 5 6 7'
    thermal_expansion_coeff = 1.0e-5
    temperature = temp
    stress_free_temperature = 1000.0
    eigenstrain_name = fuelthermal_strain
  []
  [clad_stress]
    type = ComputeFiniteStrainElasticStress
    block = '1 2 3 4 5 6 7'
  []
  [thermal]
    type = FeCrAlThermal
    block = '1 2 3 4 5 6 7'
    material = APMT
    temperature = temp
  []
  [density]
    type = StrainAdjustedDensity
    block = '1 2 3 4 5 6 7'
    strain_free_density = 7225.0
  []
[]

[Executioner]
   type = Transient

  solve_type = 'PJFNK'


  petsc_options = '-snes_ksp_ew '
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'
  l_max_its = 60
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-10
  l_tol = 1e-6

  start_time = 0.0
  dt = 10000
  num_steps = 100
[]

[Postprocessors]
  [volume]
    type = InternalVolume
    boundary = 15
    execute_on = 'initial linear'
  []
  [ave_fluence]
    type = ElementAverageValue
    variable = fluence
    block = '1 2 3 4 5 6 7'
  []
[]

[Outputs]
  exodus = true
[]

(test/tests/solid_mechanics/fecral_eigenstrains/fecral_vswelling/swelling.i)

# Test of volumetric swelling of FeCrAl alloys (1000K).
#
# The model used is based upon the upper limit of swelling suggested by:
#
# K. A. Terrani, T. M. Karlsen, and Y. Yamamoto, "Input Correlations for
# Irradiation Creep of FeCrAl and SiC based on in-pile Halden test results,"
# Technical Report ORNL/TM-2016/191, Oak Ridge National Laboratory, May 2016
#
# The suggested upper limit is 0.05% per dpa.  Using a conversion factor of
# 1x10^25 neutrons/m^2-s = 0.9 dpa as proposed by:
#
# K. G. Field, X. Hu, K. C. Littrell, Y. Yamamoto, and L. L. Snead, "Radiation
# tolerance of neutroni-irradiated model Fe-Cr-Al alloys," Journal of Nuclear
# Materials, Vol. 465, pp. 746-755, 2015.
#
# A creep strain rate due to swelling is obtained and given by:
#
# e_dot_sw = 0.0005 per dpa
#
# e_dot_sw = 0.0005 * 0.9 / 1e25 [m^2-s/n]
#
# To get the correct units multiply the factor above by flux
#
# e_dot_sw = 4.5e-29 * fast_flux
#
# To get the volumteric strain the above equation must be integrated over time:
#
# e_sw = 4.5e-29 * fast_fluence
#
# With a fast fluence of 1e24, the volumetric strain should be 4.5e-5.
# This is easily checked with the 'volume' postprocessor value.

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

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

[Variables]
  [disp_x]
    order = FIRST
    family = LAGRANGE
  []
  [disp_y]
    order = FIRST
    family = LAGRANGE
  []
  [disp_z]
    order = FIRST
    family = LAGRANGE
  []
  [temp]
    order = FIRST
    family = LAGRANGE
    initial_condition = 1000.0
  []
[]

[AuxVariables]
  [flux]
    order = FIRST
    family = LAGRANGE
  []
  [fluence]
    order = FIRST
    family = LAGRANGE
  []
  [swelling]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = finite
    eigenstrain_names = 'fuelthermal_strain swell'
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = temp
  []
  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temp
  []
[]

[AuxKernels]
  [flux_neutron_flux]
    type = FastNeutronFluxAux
    variable = flux
    factor = 1e18
    execute_on = 'initial timestep_begin'
  []
  [fast_neutron_fluence]
    type = FastNeutronFluenceAux
    variable = fluence
    block = '1 2 3 4 5 6 7'
    fast_neutron_flux = flux
    execute_on = timestep_begin
  []
  [swelling]
    type = MaterialRealAux
    variable = swelling
    property = volumetric_swelling_strain
    execute_on = timestep_end
  []
[]

[BCs]
  [bottom_x]
    type = DirichletBC
    variable = disp_x
    boundary = 10
    value = 0.0
  []
  [bottom_y]
    type = DirichletBC
    variable = disp_y
    boundary = 9
    value = 0.0
  []
  [bottom_z]
    type = DirichletBC
    variable = disp_z
    boundary = 14
    value = 0.0
  []
  [bottom_temp]
    type = DirichletBC
    variable = temp
    boundary = 3
    value = 1000.0
  []
  [top_temp]
    type = DirichletBC
    variable = temp
    boundary = 5
    value = 1000.0
  []
[]

[Materials]
  [clad_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = '1 2 3 4 5 6 7'
    youngs_modulus = 1.0
    poissons_ratio = 0.3
  []
  [clad_swelling]
    type = FeCrAlVolumetricSwellingEigenstrain
    block = '1 2 3 4 5 6 7'
    temperature = temp
    fast_neutron_fluence = fluence
    eigenstrain_name = swell
  []
  [clad_thermal_strain]
    type = ComputeThermalExpansionEigenstrain
    block = '1 2 3 4 5 6 7'
    thermal_expansion_coeff = 1.0e-5
    temperature = temp
    stress_free_temperature = 1000.0
    eigenstrain_name = fuelthermal_strain
  []
  [clad_stress]
    type = ComputeFiniteStrainElasticStress
    block = '1 2 3 4 5 6 7'
  []
  [thermal]
    type = FeCrAlThermal
    block = '1 2 3 4 5 6 7'
    material = APMT
    temperature = temp
  []
  [density]
    type = StrainAdjustedDensity
    block = '1 2 3 4 5 6 7'
    strain_free_density = 7225.0
  []
[]

[Executioner]
   type = Transient

  solve_type = 'PJFNK'


  petsc_options = '-snes_ksp_ew '
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  petsc_options_value = 'lu superlu_dist'
  l_max_its = 60
  nl_rel_tol = 1e-8
  nl_abs_tol = 1e-10
  l_tol = 1e-6

  start_time = 0.0
  dt = 10000
  num_steps = 100
[]

[Postprocessors]
  [volume]
    type = InternalVolume
    boundary = 15
    execute_on = 'initial linear'
  []
  [ave_fluence]
    type = ElementAverageValue
    variable = fluence
    block = '1 2 3 4 5 6 7'
  []
[]

[Outputs]
  exodus = true
[]

(examples/accident_tolerant_fuel/uo2_fecral/uo2_fecral.i)


initial_fuel_density = 10431.0

[GlobalParams]
  # Set initial fuel density, other global parameters
  density = ${initial_fuel_density}
  order = SECOND
  family = LAGRANGE
  energy_per_fission = 3.2e-11 # J/fission
  displacements = 'disp_x disp_y'
[]

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

[Mesh]
  coord_type = RZ
  displacements = 'disp_x disp_y'
  patch_size = 10 # For contact algorithm
  patch_update_strategy = auto
  partitioner = centroid
  centroid_partitioner_direction = y
  [mesh]
    type = FileMeshGenerator
    file = uo2_fecral_smeared.e
  []
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [temp]
    initial_condition = 293.0
  []
[]

[UserObjects]
  [pin_geometry]
    type = FuelPinGeometry
    clad_inner_wall = 5
    clad_outer_wall = 2
    clad_top = 3
    clad_bottom = 1
    pellet_exteriors = 8
  []
[]

[AuxVariables]
  [fast_neutron_flux]
    block = clad
  []
  [fast_neutron_fluence]
    block = clad
  []
  [grain_radius]
    block = pellet_type_1
    initial_condition = 10e-6
  []
  [gap_cond]
    order = CONSTANT
    family = MONOMIAL
  []
  [coolant_htc]
    order = CONSTANT
    family = MONOMIAL
  []
  [oxide_thickness]
    order = CONSTANT
    family = MONOMIAL
  []
  [total_hoop_strain]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_strain_hoop]
    order = CONSTANT
    family = MONOMIAL
  []
  [hoop_stress]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_rate]
    order = CONSTANT
    family = MONOMIAL
  []
  [mass_gain]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [power_history]
    type = PiecewiseLinear
    x = '0 1e4 1e8'
    y = '0 2.5e4 2.5e4'
    scale_factor = 1
  []

  [axial_peaking_factors]
    type = ParsedFunction
    expression = 1
  []

  [pressure_ramp]
    type = PiecewiseLinear
    x = '-200 0 1e8'
    y = '6.537e-3 1 1'
    scale_factor = 15.5e6
  []

  [mass_flux_func]
    type = PiecewiseLinear
    x = '-200 0  1e8'
    y = '3800. 3800. 3800.'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [pellets]
    block = pellet_type_1
    strain = FINITE
    eigenstrain_names = 'fuel_relocation_strain fuel_thermal_strain fuel_volumetric_strain'
    generate_output = 'vonmises_stress stress_xx stress_yy stress_zz'
    extra_vector_tags = 'ref'
    temperature = temp
  []
  [clad]
    block = clad
    strain = FINITE
    eigenstrain_names = 'clad_thermal_eigenstrain clad_volumetric_strain'
    generate_output = 'vonmises_stress stress_xx stress_yy stress_zz'
    extra_vector_tags = 'ref'
    temperature = temp
  []
[]

[Kernels]
  [gravity]
    type = Gravity
    variable = disp_y
    value = -9.81
    extra_vector_tags = 'ref'
  []

  [heat]
    type = HeatConduction
    variable = temp
    extra_vector_tags = 'ref'
  []

  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temp
    extra_vector_tags = 'ref'
  []

  [heat_source]
    type = NeutronHeatSource
    variable = temp
    block = pellet_type_1
    burnup_function = burnup
    extra_vector_tags = 'ref'
  []
[]

[Burnup]
  [burnup]
    block = pellet_type_1
    rod_ave_lin_pow = power_history
    axial_power_profile = axial_peaking_factors
    num_radial = 81
    num_axial = 11
    fuel_pin_geometry = pin_geometry
    fuel_volume_ratio = 1.0
    RPF = RPF
  []
[]

[AuxKernels]
  [fast_neutron_flux]
    type = FastNeutronFluxAux
    variable = fast_neutron_flux
    block = clad
    rod_ave_lin_pow = power_history
    axial_power_profile = axial_peaking_factors
    factor = 3e13
    execute_on = timestep_begin
  []
  [fast_neutron_fluence]
    type = FastNeutronFluenceAux
    variable = fast_neutron_fluence
    block = clad
    fast_neutron_flux = fast_neutron_flux
    execute_on = timestep_begin
  []
  [grain_radius]
    type = GrainRadiusAux
    block = pellet_type_1
    variable = grain_radius
    temperature = temp
    execute_on = linear
  []
  [hoop_stress]
    type = RankTwoScalarAux
    rank_two_tensor = stress
    variable = hoop_stress
    scalar_type = HoopStress
    execute_on = timestep_end
  []
  [total_hoop_strain]
    type = RankTwoScalarAux
    rank_two_tensor = total_strain
    variable = total_hoop_strain
    scalar_type = HoopStress
    execute_on = timestep_end
  []
  [creep_strain_hoop]
    type = RankTwoScalarAux
    rank_two_tensor = creep_strain
    variable = creep_strain_hoop
    scalar_type = HoopStress
    block = clad
    execute_on = timestep_end
  []
  [conductance]
    type = MaterialRealAux
    property = gap_conductance
    variable = gap_cond
    boundary = 10
  []
  [coolant_htc]
    type = MaterialRealAux
    property = coolant_channel_htc
    variable = coolant_htc
    boundary = 2
  []
  [creep_rate]
    type = MaterialRealAux
    variable = creep_rate
    property = creep_rate
    execute_on = timestep_end
    block = clad
  []
  [oxide]
    type = MaterialRealAux
    variable = oxide_thickness
    property = scale_thickness
    boundary = 2
  []
  [mass_gain]
    type = MaterialRealAux
    variable = mass_gain
    property = oxide_mass_gain
    boundary = 2
  []
[]

[Contact]
  [pellet_clad_mechanical]
    primary = 5
    secondary = 10
    normal_smoothing_distance = 0.1
    penalty = 1e7
  []
[]

[ThermalContact]
  [thermal_contact]
    type = GasGapHeatTransfer
    variable = temp
    primary = 5
    secondary = 10
    initial_moles = initial_moles
    gas_released = fis_gas_released
    contact_pressure = contact_pressure
    quadrature = true
  []
[]

[BCs]
  [no_x_all]
    type = DirichletBC
    variable = disp_x
    boundary = 12
    value = 0.0
  []

  [no_y_clad_bottom]
    type = DirichletBC
    variable = disp_y
    boundary = 1
    value = 0.0
  []

  [no_y_fuel_bottom]
    type = DirichletBC
    variable = disp_y
    boundary = 1020
    value = 0.0
  []

  [Pressure]
    [coolantPressure]
      boundary = '1 2 3'
      function = pressure_ramp
    []
  []

  [PlenumPressure]
    [plenumPressure]
      boundary = 9
      initial_pressure = 2.0e6
      startup_time = 0
      R = 8.3143
      output_initial_moles = initial_moles
      temperature = ave_temp_interior
      volume = gas_volume
      material_input = fis_gas_released
      output = plenum_pressure
    []
  []

[]

[CoolantChannel]
  [convective_clad_surface]
    boundary = '1 2 3'
    variable = temp
    inlet_temperature = 580 # K
    inlet_pressure = pressure_ramp # Pa
    inlet_massflux = mass_flux_func # kg/m^2-sec
    rod_diameter = 9.5e-3 # m
    rod_pitch = 1.26e-2 # m
    linear_heat_rate = power_history
    axial_power_profile = axial_peaking_factors
    oxide_thickness = oxide_thickness
  []
[]

[Materials]
  [fuel_thermal]
    type = UO2Thermal
    block = pellet_type_1
    thermal_conductivity_model = NFIR
    temperature = temp
    burnup_function = burnup
  []
  [fuel_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = pellet_type_1
    youngs_modulus = 2.0e11
    poissons_ratio = 0.345
  []
  [elastic_stress]
    type = ComputeSmearedCrackingStress
    block = pellet_type_1
    cracking_stress = 1.68e8
    inelastic_models = 'fuel_creep'
    softening_models = exponential_softening
    shear_retention_factor = 0.1
    max_stress_correction = 0
    cracked_elasticity_type = DIAGONAL
    output_properties = crack_damage
    outputs = exodus
  []
  [exponential_softening]
    type = ExponentialSoftening
  []
  [fuel_creep]
    type = UO2CreepUpdate
    block = pellet_type_1
    burnup_function = burnup
    temperature = temp
  []
  [fuel_relocation]
    type = UO2RelocationEigenstrain
    block = pellet_type_1
    burnup_function = burnup
    rod_ave_lin_pow = power_history
    axial_power_profile = axial_peaking_factors
    fuel_pin_geometry = 'pin_geometry'
    relocation_activation1 = 5000
    relocation_model = ESCORE_modified
    eigenstrain_name = fuel_relocation_strain
  []
  [fuel_thermal_expansion]
    type = UO2ThermalExpansionMATPROEigenstrain
    block = pellet_type_1
    temperature = temp
    stress_free_temperature = 295.0
    eigenstrain_name = fuel_thermal_strain
  []
  [fuel_volumetric_swelling]
    type = UO2VolumetricSwellingEigenstrain
    gas_swelling_model_type = SIFGRS
    block = pellet_type_1
    temperature = temp
    burnup_function = burnup
    initial_fuel_density = 10431.0
    eigenstrain_name = fuel_volumetric_strain
  []
  [clad_thermal]
    type = FeCrAlThermal
    material = C35M
    block = clad
    temperature = temp
  []
  [clad_elasticity_tensor] # isotropic elasticity tensor for Zry cladding
    type = FeCrAlElasticityTensor
    temperature = temp
    fecral_material_type = C35M
    block = clad
  []
  [clad_stress] # stress update class to govern the return mapping algorithm for creep
    type = ComputeMultipleInelasticStress
    tangent_operator = elastic
    inelastic_models = 'clad_creep clad_plasticity'
    block = clad
  []
  [clad_creep]
    type = FeCrAlCreepUpdate
    block = clad
    temperature = temp
    fecral_material_type = C35M
    fast_neutron_flux = fast_neutron_flux
    model_irradiation_creep = true
    model_thermal_creep = true
    max_inelastic_increment = 1e-4
  []
  [thermal_expansion]
    type = FeCrAlThermalExpansionEigenstrain
    block = clad
    temperature = temp
    fecral_material_type = C35M
    stress_free_temperature = 295.0
    eigenstrain_name = clad_thermal_eigenstrain
  []
  [irradiation_swelling]
    type = FeCrAlVolumetricSwellingEigenstrain
    block = clad
    temperature = temp
    fast_neutron_fluence = fast_neutron_fluence
    eigenstrain_name = clad_volumetric_strain
  []
  [clad_plasticity]
    type = FeCrAlPlasticityUpdate
    block = clad
    hardening_constant = 2.5e9
    temperature = temp
    yield_stress = 500.0
  []
  [fission_gas_release]
    type = UO2Sifgrs
    block = pellet_type_1
    temperature = temp
    burnup_function = burnup
    grain_radius = grain_radius
    gbs_model = true
  []
  [clad_density]
    type = StrainAdjustedDensity
    block = clad
    strain_free_density = 7250.0
  []
  [fuel_density]
    type = StrainAdjustedDensity
    block = pellet_type_1
    strain_free_density = ${initial_fuel_density}
  []

  [failure_criterion]
    type = FeCrAlCladdingFailure
    boundary = '2 5'
    hoop_stress = hoop_stress
    failure_criterion = UTS
    temperature = temp
  []
  [oxidation]
    type = FeCrAlOxidation
    reactor_type = PWR
    boundary = 2
  []
[]

[Dampers]
  [limitT]
    type = BoundingValueNodalDamper
    max_value = 3200.0
    min_value = 293.0
    variable = temp
  []
  [limitX]
    type = MaxIncrement
    max_increment = 1e-5
    variable = disp_x
  []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package -ksp_gmres_restart'
  petsc_options_value = 'lu       superlu_dist                  51'

  line_search = 'none'

  l_max_its = 100
  l_tol = 8e-3

  nl_max_its = 25
  nl_rel_tol = 1e-5
  nl_abs_tol = 1e-10

  start_time = -200
  n_startup_steps = 1
  end_time = 1e8

  dtmax = 1e5
  dtmin = 1

  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 2.0e2
    force_step_every_function_point = true
    timestep_limiting_function = power_history
    max_function_change = 5e5
    optimal_iterations = 10
    iteration_window = 2
    linear_iteration_ratio = 100
    growth_factor = 2.0
    timestep_limiting_postprocessor = material_timestep
  []

  [Quadrature]
    order = FIFTH
    side_order = SEVENTH
  []
[]

[Postprocessors]
  [ave_temp_interior]
    type = SideAverageValue
    boundary = 9
    variable = temp
    execute_on = 'initial linear'
  []

  [avg_clad_temp]
    type = SideAverageValue
    boundary = 7
    variable = temp
  []

  [fis_gas_produced]
    type = ElementIntegralFisGasGeneratedSifgrs
    block = pellet_type_1
  []

  [fis_gas_released]
    type = ElementIntegralFisGasReleasedSifgrs
    block = pellet_type_1
  []
  [fis_gas_grain]
    type = ElementIntegralFisGasGrainSifgrs
    block = pellet_type_1
  []
  [fis_gas_boundary]
    type = ElementIntegralFisGasBoundarySifgrs
    block = pellet_type_1
  []

  [gas_volume]
    type = InternalVolume
    boundary = 9
    execute_on = 'initial linear'
  []

  [_dt]
    type = TimestepSize
  []

  [num_lin_it]
    type = NumLinearIterations
  []
  [num_nonlin_it]
    type = NumNonlinearIterations
  []
  [tot_lin_it]
    type = CumulativeValuePostprocessor
    postprocessor = num_lin_it
  []
  [tot_nonlin_it]
    type = CumulativeValuePostprocessor
    postprocessor = num_nonlin_it
  []
  [alive_time]
    type = PerfGraphData
    section_name = Root
    data_type = TOTAL
  []

  [rod_total_power]
    type = ElementIntegralPower
    variable = temp
    burnup_function = burnup
    block = pellet_type_1
  []

  [alhr_input]
    type = FunctionValuePostprocessor
    function = power_history
  []
  [average_burnup]
    type = ElementAverageValue
    block = pellet_type_1
    variable = burnup
  []
  [oxide_thickness]
    type = ElementExtremeValue
    block = clad
    variable = oxide_thickness
  []
  [mass_gain]
    type = ElementExtremeValue
    block = clad
    variable = mass_gain
  []
  [fis_gas_percent]
    type = FGRPercent
    fission_gas_released = fis_gas_released
    fission_gas_generated = fis_gas_produced
  []
  [material_timestep]
    type = MaterialTimeStepPostprocessor
    block = clad
  []
[]

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

  [console]
    type = Console
    max_rows = 25
  []
[]

Description
Example Input Syntax
Input Parameters
Input Files
References