Al6061ThermalExpansionEigenstrain

Computes eigenstrain due to thermal expansion for Al6061 using a function that describes the mean thermal expansion as a function of temperature.

Description

The mean thermal expansion data for this model was obtained from tabular data in the Committee (1990). This model is the recommended model in Rabin et al. (2020).

Table 1: Temperature dependent value of the coefficient of thermal expansion (CTE) for Al6061 (Rabin et al., 2020; Committee, 1990).

T ( $var element = document.getElementById("moose-equation-25496b85-bdd0-4255-a972-8c42b5b277b6");katex.render("\\degree{C}", element, {displayMode:false,throwOnError:false});$ )	CTE (1/ $var element = document.getElementById("moose-equation-199a61e6-47a7-4f91-a7d3-15c1459cac94");katex.render("\\degree{C}", element, {displayMode:false,throwOnError:false});$ )
20 – 100	23.2 $var element = document.getElementById("moose-equation-0118cf4f-9bdd-4545-9654-a8acf7b3f25c");katex.render("\\times 10^{-6}", element, {displayMode:false,throwOnError:false});$
20 – 200	24.1 $var element = document.getElementById("moose-equation-97e046eb-66a4-48ab-a4c6-e0581e12dc10");katex.render("\\times 10^{-6}", element, {displayMode:false,throwOnError:false});$
20 – 300	25.1 $var element = document.getElementById("moose-equation-774c5047-dc58-44be-95f6-d639b9104ab1");katex.render("\\times 10^{-6}", element, {displayMode:false,throwOnError:false});$

Example Input syntax

[Materials<<<{"href": "../../../syntax/Materials/index.html"}>>>]
  [thermal_expansion]
    type = Al6061ThermalExpansionEigenstrain<<<{"description": "Computes eigenstrain due to thermal expansion for Al6061 using a function that describes the mean thermal expansion as a function of temperature.", "href": "Al6061ThermalExpansionEigenstrain.html"}>>>
    stress_free_temperature<<<{"description": "Reference temperature at which there is no thermal expansion for thermal eigenstrain calculation"}>>> = 293.15
    temperature<<<{"description": "Coupled temperature"}>>> = temperature
    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."}>>> = thermal_expansion
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = 0
  []
[]

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.
stress_free_temperatureReference temperature at which there is no thermal expansion for thermal eigenstrain calculation
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Reference temperature at which there is no thermal expansion for thermal eigenstrain calculation

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.
mean_thermal_expansion_coefficient_nameName of the mean coefficient of thermal expansion.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:Name of the mean coefficient of thermal expansion.
temperatureCoupled temperature
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Coupled temperature
use_old_temperatureFalseFlag to optionally use the temperature value from the previous timestep.
Default:False
C++ Type:bool
Controllable:No
Description:Flag to optionally use the temperature value from the previous timestep.

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
thermal_expansion_scale_factor1Scalar multiplier to apply to thermal expansion.
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Scalar multiplier to apply to thermal expansion.
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/solid_mechanics/al6061_thermal_expansion/points.i)
(examples/plate_fuel/plate_fuel_hypre.i)
(test/tests/solid_mechanics/al6061_thermal_expansion/test.i)

References

ASM Handbook Committee. Properties and Selection: Nonferrous Alloys and Special-Purpose Materials. Volume 2. ASM International, 1 1990. ISBN 978-1-62708-162-7. URL: https://doi.org/10.31399/asm.hb.v02.9781627081627, doi:10.31399/asm.hb.v02.9781627081627.

@book{ASMHandbook,
    author = "Committee, ASM Handbook",
    title = "{Properties and Selection: Nonferrous Alloys and Special-Purpose Materials}",
    publisher = "ASM International",
    isbn = "978-1-62708-162-7",
    doi = "10.31399/asm.hb.v02.9781627081627",
    url = "https://doi.org/10.31399/asm.hb.v02.9781627081627",
    volume = "2",
    month = "1",
    year = "1990"
}

B. Rabin, M. Meyer, J. Cole, I. Glagolenko, W. Jones, J-F. Jue, D. Keiser Jr, C. Miller, G. Moore, H. Ozaltun, F. Rice, A. Robinson, J. Smith, D. Wachs, W. Williams, N. Woolstenhulme, G. Hofman, and Y. Kim. Preliminary report on U-Mo monolithic fuel for research reactors. Technical Report INL EXT-17-40975, Idaho National Laboratory, 4 2020.

@techreport{EXT-17-40975R4,
    author = "Rabin, B. and Meyer, M. and Cole, J. and Glagolenko, I. and Jones, W. and Jue, J-F. and Jr, D. Keiser and Miller, C. and Moore, G. and Ozaltun, H. and Rice, F. and Robinson, A. and Smith, J. and Wachs, D. and Williams, W. and Woolstenhulme, N. and Hofman, G. and Kim, Y.",
    title = "Preliminary Report on {U-Mo} Monolithic Fuel for Research Reactors",
    institution = "Idaho National Laboratory",
    number = "INL EXT-17-40975",
    month = "4",
    year = "2020"
}

(test/tests/solid_mechanics/al6061_thermal_expansion/test.i)

#--------------------------------------------------------------------------------
#
#   This test case is prepared to test the thermal expansion behavior of Al6061.
#
#   - Geometry: Ri = 0.005 m, Ro = 0.0055 m, and H  = 0.01 m
#   - Single element
#   - Temperature = 294.26 - 1088.71 K
#   - BCs: T specified over entire domain as a function of time
#
# The thermal expansion data was obtained from EXT-17-40975R4,
# for the model of the ASM Handbook.
#
#--------------------------------------------------------------------------------
[GlobalParams]
  order = FIRST
  family = LAGRANGE
  displacements = 'disp_x disp_y'
  volumetric_locking_correction = true
[]

[Mesh]
  coord_type = RZ
  [mesh]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 1
    ny = 1
    xmin = 0.005
    xmax = 0.0055
    ymin = 0.0
    ymax = 0.01
    elem_type = QUAD4
  []
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [temperature]
    initial_condition = 294.26
  []
[]

[AuxVariables]
  [elastic_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []
  [elastic_strain_xx]
    order = CONSTANT
    family = MONOMIAL
  []
  [elastic_strain_zz]
    order = CONSTANT
    family = MONOMIAL
  []
  [total_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []
  [total_strain_xx]
    order = CONSTANT
    family = MONOMIAL
  []
  [total_strain_zz]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [temperature_function]
    type = PiecewiseLinear
    x = '0     1    2   3   4   5   6   7   8   9   10   11   12   13   14
    15   16   17   18   19   20   21   22   23   24   25   26   27   28   29'
    y = '294.26 310.93 338.71 366.48 394.26 422.04 449.82 477.59 505.37 533.15
    560.93 588.71 616.48 644.26 672.04 699.82 727.59 755.37 783.15 810.93
    838.71 866.48 894.26 922.04 949.82 977.59 1005.37 1033.15 1060.93 1088.71'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = finite
    eigenstrain_names = thermal_expansion
  []
[]

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

[AuxKernels]
  [elastic_strain_yy]
    type = RankTwoAux
    rank_two_tensor = elastic_strain
    variable = elastic_strain_yy
    index_i = 1
    index_j = 1
    execute_on = timestep_end
  []
  [elastic_strain_xx]
    type = RankTwoAux
    rank_two_tensor = elastic_strain
    variable = elastic_strain_xx
    index_i = 0
    index_j = 0
    execute_on = timestep_end
  []
  [elastic_strain_zz]
    type = RankTwoAux
    rank_two_tensor = elastic_strain
    variable = elastic_strain_zz
    index_i = 2
    index_j = 2
    execute_on = timestep_end
  []
  [total_strain_yy]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = total_strain_yy
    index_i = 1
    index_j = 1
    execute_on = timestep_end
  []
  [total_strain_xx]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = total_strain_xx
    index_i = 0
    index_j = 0
    execute_on = timestep_end
  []
  [total_strain_zz]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = total_strain_zz
    index_i = 2
    index_j = 2
    execute_on = timestep_end
  []
[]

[BCs]
  [u_bottom_fix]
    type = DirichletBC
    variable = disp_y
    boundary = 'bottom'
    value = 0.0
  []
  [temp_bc]
    type = FunctionDirichletBC
    variable = temperature
    boundary = 'left right top bottom'
    function = temperature_function
  []
[]

[Materials]
  [elasticity_tensor]
    type = Al6061ElasticityTensor
    temperature = temperature
    fast_neutron_fluence = 0
    block = 0
  []
  [stress]
    type = ComputeFiniteStrainElasticStress
    block = 0
  []
  [thermal_expansion]
    type = Al6061ThermalExpansionEigenstrain
    stress_free_temperature = 293.15
    temperature = temperature
    eigenstrain_name = thermal_expansion
    block = 0
  []
  [clad_density]
    type = StrainAdjustedDensity
    block = 0
    strain_free_density = 7874
  []
  [thermal]
    type = Al6061Thermal
    block = 0
    temperature = temperature
  []
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'
  petsc_options       = '-snes_ksp_ew'
  petsc_options_iname = '-pc_type -ksp_gmres_restart'
  petsc_options_value = 'lu 101'

  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
  end_time   = 29.0
  dt         = 1.0
[]

[Postprocessors]
  [elastic_strain_xx]
    type = ElementAverageValue
    variable = elastic_strain_xx
  []
  [elastic_strain_yy]
    type = ElementAverageValue
    variable = elastic_strain_yy
  []
  [elastic_strain_zz]
    type = ElementAverageValue
    variable = elastic_strain_zz
  []
  [total_strain_xx]
    type = ElementAverageValue
    variable = total_strain_xx
  []
  [total_strain_yy]
    type = ElementAverageValue
    variable = total_strain_yy
  []
  [total_strain_zz]
    type = ElementAverageValue
    variable = total_strain_zz
  []
  [thermal_strain_xx]
    type = DifferencePostprocessor
    value1 = total_strain_xx
    value2 = elastic_strain_xx
  []
  [thermal_strain_yy]
    type = DifferencePostprocessor
    value1 = total_strain_yy
    value2 = elastic_strain_yy
  []
  [thermal_strain_zz]
    type = DifferencePostprocessor
    value1 = total_strain_zz
    value2 = elastic_strain_zz
  []
  [temperature]
    type = AverageNodalVariableValue
    variable = temperature
    execute_on = 'initial timestep_end'
  []
  [disp_x3]
    type = NodalVariableValue
    nodeid = 2
    variable = disp_x
  []
  [disp_y3]
    type = NodalVariableValue
    nodeid = 2
    variable = disp_y
  []
[]

[Outputs]
  csv = true
  exodus = false
[]

(test/tests/solid_mechanics/al6061_thermal_expansion/points.i)

#--------------------------------------------------------------------------------
#
#   This test case is prepared to test the thermal expansion behavior of Al6061.
#
#   - Geometry: Ri = 0.005 m, Ro = 0.0055 m, and H  = 0.01 m
#   - Single element
#   - Temperature = 294.26 - 1088.71 K
#   - BCs: T specified over entire domain as a function of time
#
#   Time 1:
#     delta T = 79, alpha = 23.2e-6 gives strain =  0.0018328
#   Time 2:
#     delta T = 179, alpha = 24.1e-6 gives strain = 0.0043139
#   Time 3:
#     delta T = 279, alpha = 25.1e-6 gives strain = 0.0070029
#
#--------------------------------------------------------------------------------
[GlobalParams]
  order = FIRST
  family = LAGRANGE
  displacements = 'disp_x disp_y'
  volumetric_locking_correction = true
[]

[Mesh]
  coord_type = RZ
  [mesh]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 1
    ny = 1
    xmin = 0.005
    xmax = 0.0055
    ymin = 0.0
    ymax = 0.01
    elem_type = QUAD4
  []
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [temperature]
    initial_condition = 294.15
  []
[]

[AuxVariables]
  [elastic_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []
  [elastic_strain_xx]
    order = CONSTANT
    family = MONOMIAL
  []
  [elastic_strain_zz]
    order = CONSTANT
    family = MONOMIAL
  []
  [total_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []
  [total_strain_xx]
    order = CONSTANT
    family = MONOMIAL
  []
  [total_strain_zz]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [temperature_function]
    type = PiecewiseLinear
    x = '  0      1      2      3'
    y = '294.15 373.15 473.15 573.15'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = finite
    eigenstrain_names = thermal_expansion
  []
[]

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

[AuxKernels]
  [elastic_strain_yy]
    type = RankTwoAux
    rank_two_tensor = elastic_strain
    variable = elastic_strain_yy
    index_i = 1
    index_j = 1
    execute_on = timestep_end
  []
  [elastic_strain_xx]
    type = RankTwoAux
    rank_two_tensor = elastic_strain
    variable = elastic_strain_xx
    index_i = 0
    index_j = 0
    execute_on = timestep_end
  []
  [elastic_strain_zz]
    type = RankTwoAux
    rank_two_tensor = elastic_strain
    variable = elastic_strain_zz
    index_i = 2
    index_j = 2
    execute_on = timestep_end
  []
  [total_strain_yy]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = total_strain_yy
    index_i = 1
    index_j = 1
    execute_on = timestep_end
  []
  [total_strain_xx]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = total_strain_xx
    index_i = 0
    index_j = 0
    execute_on = timestep_end
  []
  [total_strain_zz]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = total_strain_zz
    index_i = 2
    index_j = 2
    execute_on = timestep_end
  []
[]

[BCs]
  [u_bottom_fix]
    type = DirichletBC
    variable = disp_y
    boundary = 'bottom'
    value = 0.0
  []
  [temp_bc]
    type = FunctionDirichletBC
    variable = temperature
    boundary = 'left right top bottom'
    function = temperature_function
  []
[]

[Materials]
  [elasticity_tensor]
    type = Al6061ElasticityTensor
    temperature = temperature
    fast_neutron_fluence = 0
    block = 0
  []
  [stress]
    type = ComputeFiniteStrainElasticStress
    block = 0
  []
  [thermal_expansion]
    type = Al6061ThermalExpansionEigenstrain
    stress_free_temperature = 294.15
    temperature = temperature
    eigenstrain_name = thermal_expansion
    block = 0
  []
  [clad_density]
    type = StrainAdjustedDensity
    block = 0
    strain_free_density = 7874
  []
  [thermal]
    type = Al6061Thermal
    block = 0
    temperature = temperature
  []
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'
  petsc_options       = '-snes_ksp_ew'
  petsc_options_iname = '-pc_type -ksp_gmres_restart'
  petsc_options_value = 'lu 101'

  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
  end_time   = 3.0
  dt         = 1.0
[]

[Postprocessors]
  [elastic_strain_xx]
    type = ElementAverageValue
    variable = elastic_strain_xx
  []
  [elastic_strain_yy]
    type = ElementAverageValue
    variable = elastic_strain_yy
  []
  [elastic_strain_zz]
    type = ElementAverageValue
    variable = elastic_strain_zz
  []
  [total_strain_xx]
    type = ElementAverageValue
    variable = total_strain_xx
  []
  [total_strain_yy]
    type = ElementAverageValue
    variable = total_strain_yy
  []
  [total_strain_zz]
    type = ElementAverageValue
    variable = total_strain_zz
  []
  [thermal_strain_xx]
    type = DifferencePostprocessor
    value1 = total_strain_xx
    value2 = elastic_strain_xx
  []
  [thermal_strain_yy]
    type = DifferencePostprocessor
    value1 = total_strain_yy
    value2 = elastic_strain_yy
  []
  [thermal_strain_zz]
    type = DifferencePostprocessor
    value1 = total_strain_zz
    value2 = elastic_strain_zz
  []
  [temperature]
    type = AverageNodalVariableValue
    variable = temperature
    execute_on = 'initial timestep_end'
  []
  [disp_x3]
    type = NodalVariableValue
    nodeid = 2
    variable = disp_x
  []
  [disp_y3]
    type = NodalVariableValue
    nodeid = 2
    variable = disp_y
  []
[]

[Outputs]
  csv = true
  exodus = false
[]

(examples/plate_fuel/plate_fuel_hypre.i)

#
# Plate fuel example problem.
#

[GlobalParams]
  order = FIRST
  family = LAGRANGE
  displacements = 'disp_x disp_y disp_z'
  volumetric_locking_correction = false
[]

[Mesh]
  coord_type = XYZ
  [plate]
    type = PlateMeshGenerator
    fuel_dimensions = '82.550e-3 19.050e-3 0.216e-3'
    liner_thickness = 0.025e-3
    cladding_thicknesses = '9.4615e-3 9.4615e-3 3.175e-3 3.175e-3 0.489e-3 0.489e-3'
    number_fuel_elements = '25 15 3'
    number_cladding_elements = '4 4 3 3 4 4'
    ### For a more refined mesh (40 processors):
    # number_fuel_elements = '108 30 5'
    # number_cladding_elements = '15 15 5 5 8 8'
    ###
    number_liner_elements = 1
  []
  [translate_to_origin]
    type = TransformGenerator
    input = plate
    transform = translate_min_origin
  []
  [add_nodesets]
    type = ExtraNodesetGenerator
    input = translate_to_origin
    coord = '0 0 0; 0.101473 0 0; 0.101473 0.0254 0'
    new_boundary = 'left_bottom_back right_bottom_back right_top_back'
  []
[]

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

[Functions]
  [fission_density_fcn] # fis/m3
    type = PiecewiseLinear
    data_file = 'average_fission_density.csv'
    scale_factor = 1e27
    format = columns
  []
  [fluence_fcn] # n/m2
    type = PiecewiseLinear
    data_file = 'FLUENCE.csv'
    scale_factor = 1
    format = columns
  []
  [power_density]
    type = PiecewiseLinear
    data_file = 'POWER_DENSITY.csv' # W/cm3 to W/m3
    scale_factor = 1e6
    format = columns
  []
  [L2AR]
    type = ParsedFunction
    # fissprof_l2ar is the distribution from the L2AR tab: L2AR_ABAQUS at cell R64
    symbol_names = 'x_offset y_offset'
    symbol_values = '9.4615e-3 3.175e-3'
    expression = 'x0 := x-x_offset;
             y0 := y-y_offset;
             (4.669e-10*x0^5 - 8.657e-8*x0^4 + 5.877e-6*x0^3 - 0.0001962*x0^2 + 0.004373*x0 + 0.9446) * (5.047e-7*y0^6 - 2.974e-05*y0^5 + 0.0006881*y0^4 - 0.007883*y0^3 + 0.04726*y0^2 - 0.1458*y0 + 1.152)'
  []
  [power_history]
    type = CompositeFunction
    functions = 'power_density L2AR'
  []
[]

[Variables]
  [temperature]
    initial_condition = 294
  []
  [disp_x]
  []
  [disp_y]
  []
  [disp_z]
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = temperature
  []
  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temperature
  []
  [heat_source]
    type = HeatSource
    block = fuel
    function = power_history
    variable = temperature
    extra_vector_tags = 'ref'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  strain = FINITE
  temperature = temperature
  generate_output = 'stress_xx stress_yy stress_zz vonmises_stress
                     hydrostatic_stress elastic_strain_xx elastic_strain_yy
                     elastic_strain_zz strain_xx strain_yy strain_zz'
  [fuel_mechanics]
    block = fuel
    eigenstrain_names = 'fuel_thermal_strain'
    extra_vector_tags = 'ref'
  []
  [clad_mechanics]
    block = cladding
    eigenstrain_names = 'clad_thermal_strain'
    extra_vector_tags = ref
  []
  [liner_mechanics]
    block = liner
    eigenstrain_names = 'liner_thermal_strain'
    extra_vector_tags = ref
  []
[]

[BCs]
  [conv_BC_front]
    type = ConvectiveHeatFluxBC
    variable = temperature
    boundary = front
    T_infinity = 'tfilm_outer' # film temperature
    heat_transfer_coefficient = 'htc_outer'
    heat_transfer_coefficient_dT = 'dhtc_dT_outer'
  []
  [conv_BC_back]
    type = ConvectiveHeatFluxBC
    variable = temperature
    boundary = back
    T_infinity = 'tfilm_inner' # film temperature
    heat_transfer_coefficient = 'htc_inner'
    heat_transfer_coefficient_dT = 'dhtc_dT_inner'
  []
  [disp_x]
    type = DirichletBC
    variable = disp_x
    boundary = 'left_bottom_back'
    value = 0.0
  []
  [disp_y]
    type = DirichletBC
    variable = disp_y
    boundary = 'left_bottom_back right_bottom_back'
    value = 0.0
  []
  [disp_z]
    type = DirichletBC
    variable = disp_z
    boundary = 'left_bottom_back right_bottom_back right_top_back'
    value = 0.0
  []
[]

[Materials]
  [fission_density]
    type = GenericFunctionMaterial
    prop_names = fission_density
    prop_values = fission_density_fcn
  []
  [fluence]
    type = GenericFunctionMaterial
    prop_names = fast_neutron_fluence
    prop_values = fluence_fcn
    outputs = all
  []
  [tfilm_inner]
    type = ParsedMaterial
    property_name = tfilm_inner
    coupled_variables = temperature
    expression = '325.15'
  []
  [htc_inner]
    type = ParsedMaterial
    property_name = htc_inner
    coupled_variables = 'temperature'
    expression = '-3.3647*temperature^2 + 2744.5*temperature - 454016.0'
  []
  [dhtc_dT_inner]
    type = ParsedMaterial
    property_name = dhtc_dT_inner
    coupled_variables = 'temperature'
    expression = '-6.7294*temperature + 2744.5'
  []
  [tfilm_outer]
    type = ParsedMaterial
    property_name = tfilm_outer
    coupled_variables = temperature
    expression = '325.15'
  []
  [htc_outer]
    type = ParsedMaterial
    property_name = htc_outer
    coupled_variables = 'temperature'
    expression = '-2.8992*temperature^2 + 2354.8*temperature - 387945.0'
  []
  [dhtc_dT_outer]
    type = ParsedMaterial
    property_name = dhtc_dT_outer
    coupled_variables = 'temperature'
    expression = '-5.7984*temperature + 2354.8'
  []
  # fuel properties
  [fuel_thermal]
    type = U10MoThermal
    block = fuel
    temperature = temperature
    thermal_conductivity_model = USHPRR
    specific_heat_model = USHPRR
  []
  [fuel_elasticity]
    type = U10MoElasticityTensor
    block = fuel
    temperature = temperature
  []
  [fuel_thermal_expansion]
    type = U10MoThermalExpansionEigenstrain
    block = fuel
    temperature = temperature
    eigenstrain_name = fuel_thermal_strain
    stress_free_temperature = 298
    model_option = Rest
  []
  [fuel_stress]
    type = ComputeFiniteStrainElasticStress
    block = fuel
  []
  #  [fuel_swelling]
  #    type = U10MoVolumetricSwellingEigenstrain
  #    eigenstrain_name = fuel_swelling_strain
  #    fission_rate = 0
  #  []
  [fuel_density]
    type = ParsedMaterial
    block = fuel
    property_name = density
    coupled_variables = 'temperature'
    expression = '-0.884*temperature + 17391.0'
    outputs = exodus
  []
  # liner properties
  [liner_thermal]
    type = ZrThermal
    block = liner
    temperature = temperature
    thermal_conductivity_model = USHPRR
    specific_heat_model = USHPRR
  []
  [liner_elasticity]
    type = ZrElasticityTensor
    block = liner
    temperature = temperature
  []
  [liner_stress]
    type = ComputeFiniteStrainElasticStress
    block = liner
  []
  [liner_thermal_expansion]
    type = ZrThermalExpansionEigenstrain
    block = liner
    temperature = temperature
    eigenstrain_name = liner_thermal_strain
    stress_free_temperature = 293.0
    model_option = ASM
  []
  [liner_density]
    type = StrainAdjustedDensity
    block = liner
    strain_free_density = 6499.0 # 6.499e-9 ton/mm3
    outputs = exodus
  []
  # cladding properties
  [clad_thermal]
    type = Al6061Thermal
    temperature = temperature
    block = cladding
    thermal_conductivity_model = T6
    specific_heat_model = ASM
  []
  [clad_elasticity]
    type = Al6061ElasticityTensor
    block = cladding
    temperature = temperature
    fast_neutron_fluence = 0
    youngs_modulus_model = Kaufman
  []
  [clad_thermal_expansion]
    type = Al6061ThermalExpansionEigenstrain
    stress_free_temperature = 293.15
    temperature = temperature
    eigenstrain_name = clad_thermal_strain
    block = cladding
  []
  [clad_stress]
    type = ComputeFiniteStrainElasticStress
    block = cladding
  []
  [clad_density]
    type = ParsedMaterial
    block = cladding
    property_name = density
    coupled_variables = 'temperature'
    expression = '-0.0003*temperature^2 + 0.0966*temperature + 2690.4'
    outputs = exodus
  []
[]

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

[Executioner]
  type = Transient
  solve_type = 'Newton'

  petsc_options_iname = '-ksp_gmres_restart -pc_type -pc_hypre_type -pc_hypre_boomeramg_max_iter'
  petsc_options_value = '201                hypre    boomeramg      4'
  #petsc_options_iname = '-pc_type -pc_factor_mat_solver_package'
  #petsc_options_value = 'lu superlu_dist'

  line_search = 'none'

  nl_rel_tol = 1e-6
  nl_abs_tol = 1e-8
  nl_max_its = 50

  l_tol = 1e-4
  l_max_its = 50

  start_time = 0.0
  end_time = 4586400
  num_steps = 2500

  dtmax = 86400

  [Predictor]
    type = SimplePredictor
    scale = 1
  []

  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 1800
    optimal_iterations = 12
    iteration_window = 2
    growth_factor = 2
    cutback_factor = .5
    timestep_limiting_function = power_density
    force_step_every_function_point = true
  []
[]

[Postprocessors]
  [average_fuel_T]
    type = ElementAverageValue
    block = fuel
    variable = temperature
    execute_on = 'initial timestep_end'
  []
  [fuelVolume]
    type = InternalVolume
    boundary = fuel_all
  []
  [totalVolume]
    type = InternalVolume
    boundary = all
  []
  [power_history]
    type = FunctionValuePostprocessor
    function = power_history
    execute_on = 'initial timestep_end'
  []
[]

[Outputs]
  perf_graph = true
  csv = true
  exodus = true
[]

(test/tests/solid_mechanics/al6061_thermal_expansion/test.i)

#--------------------------------------------------------------------------------
#
#   This test case is prepared to test the thermal expansion behavior of Al6061.
#
#   - Geometry: Ri = 0.005 m, Ro = 0.0055 m, and H  = 0.01 m
#   - Single element
#   - Temperature = 294.26 - 1088.71 K
#   - BCs: T specified over entire domain as a function of time
#
# The thermal expansion data was obtained from EXT-17-40975R4,
# for the model of the ASM Handbook.
#
#--------------------------------------------------------------------------------
[GlobalParams]
  order = FIRST
  family = LAGRANGE
  displacements = 'disp_x disp_y'
  volumetric_locking_correction = true
[]

[Mesh]
  coord_type = RZ
  [mesh]
    type = GeneratedMeshGenerator
    dim = 2
    nx = 1
    ny = 1
    xmin = 0.005
    xmax = 0.0055
    ymin = 0.0
    ymax = 0.01
    elem_type = QUAD4
  []
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [temperature]
    initial_condition = 294.26
  []
[]

[AuxVariables]
  [elastic_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []
  [elastic_strain_xx]
    order = CONSTANT
    family = MONOMIAL
  []
  [elastic_strain_zz]
    order = CONSTANT
    family = MONOMIAL
  []
  [total_strain_yy]
    order = CONSTANT
    family = MONOMIAL
  []
  [total_strain_xx]
    order = CONSTANT
    family = MONOMIAL
  []
  [total_strain_zz]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [temperature_function]
    type = PiecewiseLinear
    x = '0     1    2   3   4   5   6   7   8   9   10   11   12   13   14
    15   16   17   18   19   20   21   22   23   24   25   26   27   28   29'
    y = '294.26 310.93 338.71 366.48 394.26 422.04 449.82 477.59 505.37 533.15
    560.93 588.71 616.48 644.26 672.04 699.82 727.59 755.37 783.15 810.93
    838.71 866.48 894.26 922.04 949.82 977.59 1005.37 1033.15 1060.93 1088.71'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = finite
    eigenstrain_names = thermal_expansion
  []
[]

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

[AuxKernels]
  [elastic_strain_yy]
    type = RankTwoAux
    rank_two_tensor = elastic_strain
    variable = elastic_strain_yy
    index_i = 1
    index_j = 1
    execute_on = timestep_end
  []
  [elastic_strain_xx]
    type = RankTwoAux
    rank_two_tensor = elastic_strain
    variable = elastic_strain_xx
    index_i = 0
    index_j = 0
    execute_on = timestep_end
  []
  [elastic_strain_zz]
    type = RankTwoAux
    rank_two_tensor = elastic_strain
    variable = elastic_strain_zz
    index_i = 2
    index_j = 2
    execute_on = timestep_end
  []
  [total_strain_yy]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = total_strain_yy
    index_i = 1
    index_j = 1
    execute_on = timestep_end
  []
  [total_strain_xx]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = total_strain_xx
    index_i = 0
    index_j = 0
    execute_on = timestep_end
  []
  [total_strain_zz]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = total_strain_zz
    index_i = 2
    index_j = 2
    execute_on = timestep_end
  []
[]

[BCs]
  [u_bottom_fix]
    type = DirichletBC
    variable = disp_y
    boundary = 'bottom'
    value = 0.0
  []
  [temp_bc]
    type = FunctionDirichletBC
    variable = temperature
    boundary = 'left right top bottom'
    function = temperature_function
  []
[]

[Materials]
  [elasticity_tensor]
    type = Al6061ElasticityTensor
    temperature = temperature
    fast_neutron_fluence = 0
    block = 0
  []
  [stress]
    type = ComputeFiniteStrainElasticStress
    block = 0
  []
  [thermal_expansion]
    type = Al6061ThermalExpansionEigenstrain
    stress_free_temperature = 293.15
    temperature = temperature
    eigenstrain_name = thermal_expansion
    block = 0
  []
  [clad_density]
    type = StrainAdjustedDensity
    block = 0
    strain_free_density = 7874
  []
  [thermal]
    type = Al6061Thermal
    block = 0
    temperature = temperature
  []
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'
  petsc_options       = '-snes_ksp_ew'
  petsc_options_iname = '-pc_type -ksp_gmres_restart'
  petsc_options_value = 'lu 101'

  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
  end_time   = 29.0
  dt         = 1.0
[]

[Postprocessors]
  [elastic_strain_xx]
    type = ElementAverageValue
    variable = elastic_strain_xx
  []
  [elastic_strain_yy]
    type = ElementAverageValue
    variable = elastic_strain_yy
  []
  [elastic_strain_zz]
    type = ElementAverageValue
    variable = elastic_strain_zz
  []
  [total_strain_xx]
    type = ElementAverageValue
    variable = total_strain_xx
  []
  [total_strain_yy]
    type = ElementAverageValue
    variable = total_strain_yy
  []
  [total_strain_zz]
    type = ElementAverageValue
    variable = total_strain_zz
  []
  [thermal_strain_xx]
    type = DifferencePostprocessor
    value1 = total_strain_xx
    value2 = elastic_strain_xx
  []
  [thermal_strain_yy]
    type = DifferencePostprocessor
    value1 = total_strain_yy
    value2 = elastic_strain_yy
  []
  [thermal_strain_zz]
    type = DifferencePostprocessor
    value1 = total_strain_zz
    value2 = elastic_strain_zz
  []
  [temperature]
    type = AverageNodalVariableValue
    variable = temperature
    execute_on = 'initial timestep_end'
  []
  [disp_x3]
    type = NodalVariableValue
    nodeid = 2
    variable = disp_x
  []
  [disp_y3]
    type = NodalVariableValue
    nodeid = 2
    variable = disp_y
  []
[]

[Outputs]
  csv = true
  exodus = false
[]

Description
Example Input syntax
Input Parameters
Input Files
References