HT9PlasticityUpdate

Computes the plastic strain as a function of strain rate for HT9 cladding. Note: This material must be run in conjunction with both ComputeMultipleInelasticStress and HT9ElasticityTensor.

Description

HT9PlasticityUpdate calculates the plastic strain for tempered martensitic steel HT9, which has been used as sodium-cooled fast reactor (SFR) fuel cladding materials, as a function of straining temperature, strain rate, and radiation conditions (temperature and dose). This material must be run in conjunction with ComputeMultipleInelasticStress. The material model inherits from IsotropicPlasticityStressUpdate. The correlation is based on the yield strength, ultimate tensile strength, and elongation as described in Metallic Fuel Handbook (Hofman et al., 2019).

Metallic Fuel Handbook Model

The correlation that describes the plastic behavior of HT9 is adopted from Chapter E-2 of the Metallic Fuel Handbook. It covers the yield strength, ultimate tensile strength, and elongation of HT9.

Yield Strength

The 0.2% off yield strength ( $var element = document.getElementById("moose-equation-ac424b00-d94a-4de0-b50d-d8c3081d7d82");katex.render("\\sigma_y", element, {displayMode:false,throwOnError:false});$ in MPa) has the following form:

$var element = document.getElementById("moose-equation-988c22e7-e141-4ca2-b3b2-dd6ad5be5498");katex.render(" ln\\left(\\frac{\\sigma^{\\ast} F}{\\sigma_y}\\right)=A \\left[ \\frac{\\left({\\sigma^{\\ast}}/{G}\\right)^M}{\\dot{\\varepsilon}~exp\\left({Q}/{RT_k}\\right)} \\right]^{\\lambda}", element, {displayMode:true,throwOnError:false});$

where,

$var element = document.getElementById("moose-equation-68848c49-3874-4d82-90ac-daca4284cd7e");katex.render(" F = B \\left[ 1.0 - 0.5 tanh \\left( \\frac{T_i - D}{90.0} \\right) \\right]^{\\frac12} + C,", element, {displayMode:true,throwOnError:false});$

$var element = document.getElementById("moose-equation-13fa51b9-a8d4-44e0-a16f-fd2e2a1dfefb");katex.render(" \\begin{cases} B=1-0.02~\\phi t\\\\ C=0.02~\\phi t\\\\ D=425+10~\\phi t \\end{cases},", element, {displayMode:true,throwOnError:false});$

$var element = document.getElementById("moose-equation-8f21395a-6766-4182-add7-8da2cde3ac89");katex.render(" \\sigma^{\\ast} = 430.0 - 190.0~tanh \\left( \\frac{T_t-640.0}{225.0} \\right),", element, {displayMode:true,throwOnError:false});$

and the shear modulus ( $var element = document.getElementById("moose-equation-fe24fb8c-5d3a-4f79-97e9-420ba12dc72d");katex.render("G", element, {displayMode:false,throwOnError:false});$ in MPa) is

$var element = document.getElementById("moose-equation-1d0808ca-51c3-4104-a9f4-414f9a72cda5");katex.render(" G = 89,640 - 53.78~T_t.", element, {displayMode:true,throwOnError:false});$

The definitions of other symbols are list in the following table,

Symbol	Value	Unit	Description
$var element = document.getElementById("moose-equation-8de45823-eff5-460b-9fdb-85f60cd239f6");katex.render("A", element, {displayMode:false,throwOnError:false});$	20,000	n.a.	fitting parameter
$var element = document.getElementById("moose-equation-8fed8082-59fa-491c-9b3c-9971a0aaae85");katex.render("M", element, {displayMode:false,throwOnError:false});$	5.0	n.a.	fitting parameter
$var element = document.getElementById("moose-equation-a0edc480-df90-4fe0-b888-a0956b2e7004");katex.render("\\lambda", element, {displayMode:false,throwOnError:false});$	0.172	n.a.	fitting parameter
$var element = document.getElementById("moose-equation-1ea6c355-ce8a-4d7d-9f79-b59319b7ee3a");katex.render("Q", element, {displayMode:false,throwOnError:false});$	82,000	$var element = document.getElementById("moose-equation-09eee672-4f34-4a78-a5f8-a6bb63813c09");katex.render("cal", element, {displayMode:false,throwOnError:false});$	activation energy
$var element = document.getElementById("moose-equation-5524343f-fb77-4a2c-acce-768522d6c906");katex.render("R", element, {displayMode:false,throwOnError:false});$	1.98726	$var element = document.getElementById("moose-equation-b51440d0-997c-4509-bd4c-ef8ed66f30da");katex.render("cal \\cdot mol^{-1} \\cdot K^{-1}", element, {displayMode:false,throwOnError:false});$	gas constant
$var element = document.getElementById("moose-equation-91eb574a-8383-4971-a42a-93bd84fe56c7");katex.render("\\dot{\\varepsilon}", element, {displayMode:false,throwOnError:false});$	$var element = document.getElementById("moose-equation-8c02e0ff-4f7e-448a-9541-02e2a370fde7");katex.render("10^{-5} \\leq \\dot{\\varepsilon} \\leq 10^{-2}", element, {displayMode:false,throwOnError:false});$	$var element = document.getElementById("moose-equation-73c377a4-f376-4f81-937f-79863c1b0b27");katex.render("s^{-1}", element, {displayMode:false,throwOnError:false});$	strain rate
$var element = document.getElementById("moose-equation-7a39f3e4-8709-4cc9-8665-3a79266e2647");katex.render("T_k", element, {displayMode:false,throwOnError:false});$	–	K	instantaneous temperature
$var element = document.getElementById("moose-equation-db361c00-b49c-406b-9254-fe5f7d6b99f2");katex.render("T_l", element, {displayMode:false,throwOnError:false});$	723< $var element = document.getElementById("moose-equation-57a1303a-7f48-4e83-bff9-7c51baa912db");katex.render("T_k", element, {displayMode:false,throwOnError:false});$ <933	K	irradiation temperature
$var element = document.getElementById("moose-equation-a34a12d2-aead-488f-8b2f-47eafb490d63");katex.render("T_t", element, {displayMode:false,throwOnError:false});$	$var element = document.getElementById("moose-equation-cedc6643-dab6-494c-8717-f991db68f488");katex.render("T_k", element, {displayMode:false,throwOnError:false});$ -273.15	$var element = document.getElementById("moose-equation-7b021e0b-7a00-4281-8667-0aa404f8dc0c");katex.render("^{\\circ}", element, {displayMode:false,throwOnError:false});$ C	instantaneous temperature
$var element = document.getElementById("moose-equation-01d82826-e9e5-4726-b544-80d02160137e");katex.render("T_i", element, {displayMode:false,throwOnError:false});$	$var element = document.getElementById("moose-equation-bfbd4568-6638-4b76-950c-13cffa8b8398");katex.render("T_l", element, {displayMode:false,throwOnError:false});$ -273.15	$var element = document.getElementById("moose-equation-9f213738-4de7-451f-9923-0d680eb00c63");katex.render("^{\\circ}", element, {displayMode:false,throwOnError:false});$ C	irradiation temperature
$var element = document.getElementById("moose-equation-a55e661e-cce1-461b-9c79-985887977a0e");katex.render("\\phi t", element, {displayMode:false,throwOnError:false});$	0 $var element = document.getElementById("moose-equation-d11d5c12-d6fc-49b9-b5d8-5cfb1d4c34a5");katex.render("\\leq \\phi t \\leq", element, {displayMode:false,throwOnError:false});$ 11	10 $var element = document.getElementById("moose-equation-5e7ec449-833e-4ed4-9d33-267e97ef01f8");katex.render("^{22}~n \\cdot cm^{-2}", element, {displayMode:false,throwOnError:false});$	fast neutron fluence

Ultimate Tensile Strength and Elongation

The ultimate tensile strength ( $var element = document.getElementById("moose-equation-8a748714-d6ed-4ec6-80ca-2efd063f59f1");katex.render("\\sigma_{uts}", element, {displayMode:false,throwOnError:false});$ in MPa) is calculated by scaling the yield strength, which has the following form:

$var element = document.getElementById("moose-equation-763e684b-f69b-49c8-8d03-e560ce28ac4d");katex.render(" \\sigma_{uts} = \\sigma_y \\left[ 1.1 - 0.1 tanh\\left( \\frac{T_t - T_i - 200.0}{200.0} \\right) \\right]", element, {displayMode:true,throwOnError:false});$

The minimum elongation ( $var element = document.getElementById("moose-equation-61d92110-9b7e-44fe-b1ff-08df23e422a8");katex.render("\\varepsilon_t", element, {displayMode:false,throwOnError:false});$ ) has the following form:

$var element = document.getElementById("moose-equation-9b5e5eff-2fcd-4953-a5d0-b7d8510be3c8");katex.render(" \\varepsilon_t = 9.97 + 1.34\\times10^{-3}~exp\\left( \\frac{T_t}{100} \\right)", element, {displayMode:true,throwOnError:false});$

A linear hardening model is adopted here based on $var element = document.getElementById("moose-equation-16b40f75-1b9b-4e6f-ae65-a1a89f414b24");katex.render("\\sigma_{uts}", element, {displayMode:false,throwOnError:false});$ and $var element = document.getElementById("moose-equation-55420e83-0b66-42db-9afc-d2ab46df2ebf");katex.render("\\varepsilon_t", element, {displayMode:false,throwOnError:false});$ .

Example Input Syntax

[Materials<<<{"href": "../../../syntax/Materials/index.html"}>>>]
  [ht9_plasticity]
    type = ADHT9PlasticityUpdate<<<{"description": "Computes the plastic strain as a function of strain rate for HT9 cladding. Note: This material must be run in conjunction with both ComputeMultipleInelasticStress and HT9ElasticityTensor.", "href": "HT9PlasticityUpdate.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = '1 2 3 4'
    temperature<<<{"description": "Temperature of the cladding (K)"}>>> = temp
    fast_neutron_fluence<<<{"description": "Material property having the fast neutron fluence."}>>> = 0
    strain_rate<<<{"description": "Fixed strain rate value"}>>> = 1e-5
  []
[]

Input Parameters

fast_neutron_fluenceMaterial property having the fast neutron fluence.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:Material property having the fast neutron fluence.
temperatureTemperature of the cladding (K)
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Temperature of the cladding (K)

Required Parameters

absolute_tolerance1e-11Absolute convergence tolerance for Newton iteration
Default:1e-11
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Absolute convergence tolerance for Newton iteration
acceptable_multiplier10Factor applied to relative and absolute tolerance for acceptable convergence if iterations are no longer making progress
Default:10
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Factor applied to relative and absolute tolerance for acceptable convergence if iterations are no longer making progress
adaptive_substeppingFalseUse adaptive substepping, where the number of substeps is successively doubled until the return mapping model successfully converges or the maximum number of substeps is reached.
Default:False
C++ Type:bool
Controllable:No
Description:Use adaptive substepping, where the number of substeps is successively doubled until the return mapping model successfully converges or the maximum number of substeps is reached.
automatic_differentiation_return_mappingFalseWhether to use automatic differentiation to compute the derivative.
Default:False
C++ Type:bool
Controllable:No
Description:Whether to use automatic differentiation to compute the derivative.
base_nameOptional parameter that defines a prefix for all material properties related to this stress update model. This allows for multiple models of the same type to be used without naming conflicts.
C++ Type:std::string
Controllable:No
Description:Optional parameter that defines a prefix for all material properties related to this stress update model. This allows for multiple models of the same type to be used without naming conflicts.
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
consider_hardeningTrueWhether hardening effect is calculated.
Default:True
C++ Type:bool
Controllable:No
Description:Whether hardening effect is calculated.
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.
id_wastage_degradation_functionThe optional ID wastage degradation function that takes FCCI effect on cladding into consideration.
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:The optional ID wastage degradation function that takes FCCI effect on cladding into consideration.
initial_fast_fluence0Initial fast fluence to be used with the MATPRO model.
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Initial fast fluence to be used with the MATPRO model.
irradiation_temperature873.15The irradiation temperature
Default:873.15
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The irradiation temperature
max_inelastic_increment0.0001The maximum inelastic strain increment allowed in a time step
Default:0.0001
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The maximum inelastic strain increment allowed in a time step
maximum_number_substeps25The maximum number of substeps allowed before cutting the time step.
Default:25
C++ Type:unsigned int
Controllable:No
Description:The maximum number of substeps allowed before cutting the time step.
od_wastage_degradation_functionThe optional OD wastage degradation function that takes CCCI effect on cladding into consideration.
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:The optional OD wastage degradation function that takes CCCI effect on cladding into consideration.
relative_tolerance1e-08Relative convergence tolerance for Newton iteration
Default:1e-08
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Relative convergence tolerance for Newton iteration
strain_rateFixed strain rate value
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Fixed strain rate value
use_substep_integration_errorFalseIf true, it establishes a substep size that will yield, at most,the creep numerical integration error given by substep_strain_tolerance.
Default:False
C++ Type:bool
Controllable:No
Description:If true, it establishes a substep size that will yield, at most,the creep numerical integration error given by substep_strain_tolerance.
use_substeppingNONEWhether and how to use substepping
Default:NONE
C++ Type:MooseEnum
Options:NONE, ERROR_BASED, INCREMENT_BASED
Controllable:No
Description:Whether and how to use substepping

Optional Parameters

apply_strainTrueFlag to apply strain. Used for testing.
Default:True
C++ Type:bool
Controllable:No
Description:Flag to apply strain. Used for testing.
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.
effective_inelastic_strain_nameeffective_plastic_strainName of the material property that stores the effective inelastic strain
Default:effective_plastic_strain
C++ Type:std::string
Controllable:No
Description:Name of the material property that stores the effective inelastic strain
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
substep_strain_tolerance0.1Maximum ratio of the initial elastic strain increment at start of the return mapping solve to the maximum inelastic strain allowable in a single substep. Reduce this value to increase the number of substeps
Default:0.1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Maximum ratio of the initial elastic strain increment at start of the return mapping solve to the maximum inelastic strain allowable in a single substep. Reduce this value to increase the number of substeps
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

internal_solve_full_iteration_historyFalseSet true to output full internal Newton iteration history at times determined by `internal_solve_output_on`. If false, only a summary is output.
Default:False
C++ Type:bool
Controllable:No
Description:Set true to output full internal Newton iteration history at times determined by `internal_solve_output_on`. If false, only a summary is output.
internal_solve_output_onon_errorWhen to output internal Newton solve information
Default:on_error
C++ Type:MooseEnum
Options:never, on_error, always
Controllable:No
Description:When to output internal Newton solve information

Debug Parameters

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

Outputs Parameters

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

Material Property Retrieval Parameters

Input Files

(test/tests/solid_mechanics/ht9_plasticity/ht9_plasticity.i)
(test/tests/solid_mechanics/ht9_plasticity/ht9_unirradiated_plasticity_ad.i)

References

G. L. Hofman, M. C. Billone, J. F. Koenig, J. M. Kramer, J. D. B. Lambert, L. Leibowitz, Y. Orechwa, D. R. Pedersen, D. L. Porter, H. Tsai, and A. E. Wright. Metallic fuels handbook. Technical Report ANL-NSE-3, Argonne National Laboratory, 2019.

@TECHREPORT{mfh1988,
    author = "Hofman, G. L. and Billone, M. C. and Koenig, J. F. and Kramer, J. M. and Lambert, J. D. B. and Leibowitz, L. and Orechwa, Y. and Pedersen, D. R. and Porter, D. L. and Tsai, H. and Wright, A. E.",
    institution = "Argonne National Laboratory",
    number = "ANL-NSE-3",
    title = "Metallic Fuels Handbook",
    year = "2019"
}

(test/tests/solid_mechanics/ht9_plasticity/ht9_unirradiated_plasticity_ad.i)

[GlobalParams]
  displacements = 'disp_x disp_y'
  volumetric_locking_correction = true
[]

[Mesh]
  coord_type = RZ
  [mesh]
    type = FileMeshGenerator
    file = 'vertical_squares.e'
  []
[]

[Variables]
  [disp_x]
    order = FIRST
    family = LAGRANGE
  []

  [disp_y]
    order = FIRST
    family = LAGRANGE
  []
  [temp]
    order = FIRST
    family = LAGRANGE
  []
[]

[AuxVariables]
  [fast_neutron_fluence]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Physics/SolidMechanics/QuasiStatic/all]
  strain = FINITE
  generate_output = 'stress_yy strain_yy plastic_strain_xx plastic_strain_yy plastic_strain_zz'
  use_automatic_differentiation = true
[]

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

[AuxKernels]
  [fast_neutron_fluence]
    type = FunctionAux
    function = fast_neutron_fluence
    variable = fast_neutron_fluence
  []
[]

[Functions]
  [top_pull]
    type = ParsedFunction
    expression = t*(0.02)
  []
  [fast_neutron_fluence]
    type = PiecewiseLinear
    x = '0 1 2'
    y = '0 1.0e25 1.0e26'
  []
[]

[BCs]
  [square1]
    type = ADDirichletBC
    variable = temp
    boundary = '1 2 3 4'
    value = 300
  []

  [square2]
    type = ADDirichletBC
    variable = temp
    boundary = '5 6 7 8'
    value = 700
  []

  [square3]
    type = ADDirichletBC
    variable = temp
    boundary = '9 10 11 12'
    value = 900
  []

  [square4]
    type = ADDirichletBC
    variable = temp
    boundary = '13 14 15 16'
    value = 1100
  []

  [top_pull]
    type = ADFunctionDirichletBC
    boundary = '1 5 9 13'
    variable = disp_y
    function = top_pull
  []

  [y_bot]
    type = ADDirichletBC
    boundary = '3 7 11 15'
    variable = disp_y
    value = 0.0
  []
  [x_bot]
    type = ADDirichletBC
    boundary = ' 2 6 10 14'
    variable = disp_x
    value = 0.0
  []
[]

[Materials]
  [elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    block = '1 2 3 4'
    youngs_modulus = 200e9
    poissons_ratio = 0.3
  []
  [stress]
    type = ADComputeMultipleInelasticStress
    inelastic_models = 'ht9_plasticity'
    block = '1 2 3 4'
  []
  [ht9_plasticity]
    type = ADHT9PlasticityUpdate
    block = '1 2 3 4'
    temperature = temp
    fast_neutron_fluence = 0
    strain_rate = 1e-5
  []
  [heat_conduction]
    type = ADHeatConductionMaterial
    block = '1 2 3 4'
    thermal_conductivity = 1
    specific_heat = 1
  []
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
  petsc_options_value = '201                hypre    boomeramg      4'

  line_search = 'none'

  l_max_its = 100
  nl_max_its = 100
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-10
  l_tol = 1e-10

  start_time = 0.0
  end_time = 2.0
  dt = 0.1
[]

[Outputs]
  exodus = true
[]

(test/tests/solid_mechanics/ht9_plasticity/ht9_plasticity.i)

[GlobalParams]
  displacements = 'disp_x disp_y'
  volumetric_locking_correction = true
[]

[Mesh]
  coord_type = RZ
  [mesh]
    type = FileMeshGenerator
    file = 'vertical_squares.e'
  []
[]

[Variables]
  [disp_x]
    order = FIRST
    family = LAGRANGE
  []

  [disp_y]
    order = FIRST
    family = LAGRANGE
  []
  [temp]
    order = FIRST
    family = LAGRANGE
  []
[]

[Physics/SolidMechanics/QuasiStatic/all]
  strain = FINITE
  generate_output = 'stress_yy strain_yy plastic_strain_xx plastic_strain_yy plastic_strain_zz'
[]

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

[Functions]
  [top_pull]
    type = ParsedFunction
    expression = t*(0.02)
  []
  [fast_neutron_fluence_func]
    type = PiecewiseLinear
    x = '0 1 2'
    y = '0 1.0e25 1.0e26'
  []
[]

[BCs]
  [square1]
    type = DirichletBC
    variable = temp
    boundary = '1 2 3 4'
    value = 300
  []

  [square2]
    type = DirichletBC
    variable = temp
    boundary = '5 6 7 8'
    value = 700
  []

  [square3]
    type = DirichletBC
    variable = temp
    boundary = '9 10 11 12'
    value = 900
  []

  [square4]
    type = DirichletBC
    variable = temp
    boundary = '13 14 15 16'
    value = 1100
  []

  [top_pull]
    type = FunctionDirichletBC
    boundary = '1 5 9 13'
    variable = disp_y
    function = top_pull
  []

  [y_bot]
    type = DirichletBC
    boundary = '3 7 11 15'
    variable = disp_y
    value = 0.0
  []
  [x_bot]
    type = DirichletBC
    boundary = ' 2 6 10 14'
    variable = disp_x
    value = 0.0
  []
[]

[Materials]
  [fast_fluence_mat]
    type = GenericFunctionMaterial
    block = '1 2 3 4'
    prop_names = fast_neutron_fluence
    prop_values = fast_neutron_fluence_func
    outputs = all
  []
  [elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    block = '1 2 3 4'
    youngs_modulus = 200e9
    poissons_ratio = 0.3
  []
  [stress]
    type = ComputeMultipleInelasticStress
    tangent_operator = elastic
    inelastic_models = 'ht9_plasticity'
    block = '1 2 3 4'
  []
  [ht9_plasticity]
    type = HT9PlasticityUpdate
    block = '1 2 3 4'
    temperature = temp
    fast_neutron_fluence = fast_neutron_fluence
  []
  [heat_conduction]
    type = HeatConductionMaterial
    block = '1 2 3 4'
    thermal_conductivity = 1
    specific_heat = 1
  []
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
  petsc_options_value = '201                hypre    boomeramg      4'

  line_search = 'none'

  l_max_its = 100
  nl_max_its = 100
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-10
  l_tol = 1e-10

  start_time = 0.0
  end_time = 3.0
  dt = 0.2
[]

[Outputs]
  exodus = true
[]

(test/tests/solid_mechanics/ht9_plasticity/ht9_unirradiated_plasticity_ad.i)

[GlobalParams]
  displacements = 'disp_x disp_y'
  volumetric_locking_correction = true
[]

[Mesh]
  coord_type = RZ
  [mesh]
    type = FileMeshGenerator
    file = 'vertical_squares.e'
  []
[]

[Variables]
  [disp_x]
    order = FIRST
    family = LAGRANGE
  []

  [disp_y]
    order = FIRST
    family = LAGRANGE
  []
  [temp]
    order = FIRST
    family = LAGRANGE
  []
[]

[AuxVariables]
  [fast_neutron_fluence]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Physics/SolidMechanics/QuasiStatic/all]
  strain = FINITE
  generate_output = 'stress_yy strain_yy plastic_strain_xx plastic_strain_yy plastic_strain_zz'
  use_automatic_differentiation = true
[]

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

[AuxKernels]
  [fast_neutron_fluence]
    type = FunctionAux
    function = fast_neutron_fluence
    variable = fast_neutron_fluence
  []
[]

[Functions]
  [top_pull]
    type = ParsedFunction
    expression = t*(0.02)
  []
  [fast_neutron_fluence]
    type = PiecewiseLinear
    x = '0 1 2'
    y = '0 1.0e25 1.0e26'
  []
[]

[BCs]
  [square1]
    type = ADDirichletBC
    variable = temp
    boundary = '1 2 3 4'
    value = 300
  []

  [square2]
    type = ADDirichletBC
    variable = temp
    boundary = '5 6 7 8'
    value = 700
  []

  [square3]
    type = ADDirichletBC
    variable = temp
    boundary = '9 10 11 12'
    value = 900
  []

  [square4]
    type = ADDirichletBC
    variable = temp
    boundary = '13 14 15 16'
    value = 1100
  []

  [top_pull]
    type = ADFunctionDirichletBC
    boundary = '1 5 9 13'
    variable = disp_y
    function = top_pull
  []

  [y_bot]
    type = ADDirichletBC
    boundary = '3 7 11 15'
    variable = disp_y
    value = 0.0
  []
  [x_bot]
    type = ADDirichletBC
    boundary = ' 2 6 10 14'
    variable = disp_x
    value = 0.0
  []
[]

[Materials]
  [elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    block = '1 2 3 4'
    youngs_modulus = 200e9
    poissons_ratio = 0.3
  []
  [stress]
    type = ADComputeMultipleInelasticStress
    inelastic_models = 'ht9_plasticity'
    block = '1 2 3 4'
  []
  [ht9_plasticity]
    type = ADHT9PlasticityUpdate
    block = '1 2 3 4'
    temperature = temp
    fast_neutron_fluence = 0
    strain_rate = 1e-5
  []
  [heat_conduction]
    type = ADHeatConductionMaterial
    block = '1 2 3 4'
    thermal_conductivity = 1
    specific_heat = 1
  []
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
  petsc_options_value = '201                hypre    boomeramg      4'

  line_search = 'none'

  l_max_its = 100
  nl_max_its = 100
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-10
  l_tol = 1e-10

  start_time = 0.0
  end_time = 2.0
  dt = 0.1
[]

[Outputs]
  exodus = true
[]

Description
Example Input Syntax
Input Parameters
Input Files
References