DamagedSiCElasticityTensor

Calculates and updates a damaged elastic modulus for CVI SiC based on stress threshold stress microcracking data

Description

The DamagedSiCElasticityTensor material model determines the Young's modulus and Poisson's ratio of composite CVI SiC using an initial isotropic Young's modulus that is successively damaged according to a user provided damage coefficient.

The Young's modulus is given by: $var element = document.getElementById("moose-equation-2defbf03-c371-42f0-8384-a76c6a06d495");katex.render(" E = E_o D_F", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-8257c95b-30a6-43a7-b84b-d1f227821bcd");katex.render("E", element, {displayMode:false,throwOnError:false});$ is the Young's modulus (Pa) and $var element = document.getElementById("moose-equation-bf8c4eca-52b0-4ef4-a421-b4f7df81b7dc");katex.render("D_F", element, {displayMode:false,throwOnError:false});$ is the damage factor as determined by a user defined function.

Poisson's ratio is calculated from an approximate relationship for brittle ceramics (Zimmerman, 1985): $var element = document.getElementById("moose-equation-181b3f67-983b-41da-9f09-53d446532fc8");katex.render(" \\nu = \\nu_o D_F^{0.9}", element, {displayMode:true,throwOnError:false});$

Example Input Syntax

[Materials<<<{"href": "../../../syntax/Materials/index.html"}>>>]
  [elasticity_tensor]
    type = U3Si2ElasticityTensor<<<{"description": "Computes the Young's modulus and Poisson's ratio for U3Si2 as a function of porosity.", "href": "U3Si2ElasticityTensor.html"}>>>
    block<<<{"description": "The list of blocks (ids or names) that this object will be applied"}>>> = 0
  []
[]

Input 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.
elasticity_tensor_prefactorOptional function to use as a scalar prefactor on the elasticity tensor.
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:Optional function to use as a scalar prefactor on the elasticity tensor.

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

shear_modulus_scale_factor1The scaling factor on the shear modulus.
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The scaling factor on the shear modulus.
youngs_modulus_scale_factor1The scaling factor on the Young's modulus.
Default:1
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:The scaling factor on the Young's modulus.

Advanced: Scaling Factor Parameters

Input Files

(examples/accident_tolerant_fuel/u3si2_sic/u3si2_outer_monolith_1.5D.i)
(examples/accident_tolerant_fuel/u3si2_zircaloy/u3si2_zircaloy.i)
(test/tests/solid_mechanics/u3si2_elasticity_tensor/elasticity.i)

References

R. W. Zimmerman. The effect of microcracks on the elastic moduli of brittle materials. Journal of Materials Science Letters, 4:1457–1460, 1985.

@ARTICLE{zimmerman1985,
    author = "Zimmerman, R. W.",
    title = "The effect of microcracks on the elastic moduli of brittle materials",
    journal = "Journal of Materials Science Letters",
    year = "1985",
    volume = "4",
    pages = "1457-1460"
}

(test/tests/solid_mechanics/u3si2_elasticity_tensor/elasticity.i)

#--------------------------------------------------------------------------------
#
#   This test case is prepared to test the elastic behavior of U3Si2. A simple
#   3D cube (1x1x1 m) is subjected to a linearly increasing temperature from
#   300 K to 800 K over 1 second. The temperature change induces a thermal
#   strain caused by thermal expansion. The thermal expansion causes a change
#   in volume, which subsequently causes a change in density of the block and
#   thus porosity.
#
#   The change in porosity causes a change in the Poisson's ratio and Young's
#   modulus of the U3Si2 block. For this material the Young's modulus and
#   Poisson's ratio can be output as a material property.  The averages are
#   reported in two postprocessors.
#
#   The initial density is taken as 95.0% theoretical resulting in an initial
#   porosity of 5.0%.
#
#   The values reported by BISON in the two postprocessors are compared to the
#   analytical values for the initial, mid, and final densities respectively.
#
#   Initial density:
#
#   Porosity = 5.0%
#   Young's modulus = -6.425 * 5.0 + 142.68 = 110.555 GPa
#   Shear modulus = -2.901 * 5.0 + 61.27 = 46.765 GPa
#   Poisson's ratio = 110.555 / (2.0 * 46.765) - 1.0 = 0.1820
#
#   Mid density (thermal strain = 0.0025):
#
#   New volume = 1.0025 * 1.0025 * 1.0025 = 1.007519 m^3
#   New density = (1.0 / 1.007519) * 95% = 94.291%
#   Porosity = 100 - 94.291 = 5.709%
#   Young's modulus = -6.425 * 5.709 + 142.68 = 106.0 GPa
#   Shear modulus = -2.901 * 5.709 + 61.27 = 44.708 GPa
#   Poisson's ratio = 106.0 / (2.0 * 44.708) - 1.0 = 0.1855
#
#   Final density (thermal strain = 0.005):
#
#   New volume = 1.005 * 1.005 * 1.005 = 1.015075 m^3
#   New density = (1.0 / 1.015075) * 95% = 93.589%
#   Porosity = 100.0 - 93.589 = 6.411%
#   Young's modulus = -6.425 * 6.411 + 142.68 = 101.489 GPa
#   Shear modulus = -2.901 * 6.411 + 61.27 = 42.672 GPa
#   Poisson's ratio = 101.489 / (2.0 * 42.672) - 1.0 = 0.1892
#
#   These analytical answers above are consistent with the BISON reported
#   values from the postprocessors.
#--------------------------------------------------------------------------------
[GlobalParams]
  order = FIRST
  family = LAGRANGE
  displacements = 'disp_x disp_y disp_z'
  volumetric_locking_correction = true
[]

[Mesh]
  [mesh]
    type = GeneratedMeshGenerator
    dim = 3
    elem_type = HEX8
  []
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [disp_z]
  []
  [temperature]
    initial_condition = 300.0
  []
[]

[AuxVariables]
  [youngs_modulus]
    order = CONSTANT
    family = MONOMIAL
  []
  [poissons_ratio]
    order = CONSTANT
    family = MONOMIAL
  []
  [density]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [temperature_ramp]
    type = PiecewiseLinear
    x = '0 1'
    y = '300 800'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = small
    eigenstrain_names = thermal_eigenstrain
  []
[]

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

[AuxKernels]
  [youngs_modulus]
    type = MaterialRealAux
    property = youngs_modulus
    variable = youngs_modulus
    execute_on = 'initial timestep_end'
  []
  [poissons_ratio]
    type = MaterialRealAux
    property = poissons_ratio
    variable = poissons_ratio
    execute_on = 'initial timestep_end'
  []
  [density]
    type = MaterialRealAux
    property = density
    variable = density
    execute_on = 'initial timestep_end'
  []
[]

[BCs]
  [left_fix]
    type = DirichletBC
    variable = disp_x
    boundary = left
    value = 0.0
  []
  [bottom_fix]
    type = DirichletBC
    variable = disp_y
    boundary = bottom
    value = 0.0
  []
  [back_fix]
    type = DirichletBC
    variable = disp_z
    boundary = back
    value = 0.0
  []
  [temperature]
    type = FunctionDirichletBC
    variable = temperature
    boundary = 'front back top back left right'
    function = temperature_ramp
  []
[]

[Materials]
  [elasticity_tensor]
    type = U3Si2ElasticityTensor
    block = 0
  []
  [stress]
    type = ComputeLinearElasticStress
    block = 0
  []
  [density]
    type = StrainAdjustedDensity
    block = 0
    strain_free_density = 11590.0
  []
  [thermal_expansion]
    type = ComputeThermalExpansionEigenstrain
    block = 0
    temperature = temperature
    thermal_expansion_coeff = 10e-6
    eigenstrain_name = thermal_eigenstrain
    stress_free_temperature = 300.0
  []
  [conduction]
    type = GenericConstantMaterial
    block = 0
    prop_names = "thermal_conductivity specific_heat"
    prop_values = '10000 1'
  []
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'
  petsc_options       = '-snes_ksp_ew'
  petsc_options_iname = '-ksp_gmres_restart'
  petsc_options_value = '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   = 1.0
  dt         = 0.5
[]

[Postprocessors]
  [average_temperature]
    type = AverageNodalVariableValue
    variable = temperature
    execute_on = 'initial timestep_end'
  []
  [volume]
    type = InternalVolume
    boundary = 'bottom top left right front back'
    scale_factor = -1.0
    execute_on = 'initial timestep_end'
  []
  [youngs_avg]
    type = ElementAverageValue
    variable = youngs_modulus
    execute_on = 'initial timestep_end'
  []
  [poissons_avg]
    type = ElementAverageValue
    variable = poissons_ratio
    execute_on = 'initial timestep_end'
  []
  [density]
    type = ElementAverageValue
    variable = density
    execute_on = 'initial timestep_end'
  []
[]

[Outputs]
  exodus = true
[]

(examples/accident_tolerant_fuel/u3si2_sic/u3si2_outer_monolith_1.5D.i)

# Model is of a 10 pellet fuel rodlet modeled in 1.5D.  The rodlet contains
# U3Si2 fuel and a multilayer silicon carbide cladding (an inner composite
# winding layer) and an outer monolithic layer. The inner composite layer is
# 0.75 mm thick and the outer monolithic layer is 0.25 mm thick. The internal
# layered1D mesh generator can model a clad an arbitrary number of additional blocks.
# Therefore, to create the multilayer SiC clad the composite layer is assigned to the
# clad block and the monolithic_layer is assigned to the monolithic_layer block
# as specified in the additional_block_names parameter in the Mesh block.


initial_fuel_density = 11590.0

[GlobalParams]
  density = ${initial_fuel_density}
  initial_porosity = 0.05
  order = SECOND
  family = LAGRANGE
  energy_per_fission = 3.2e-11 # J/fission
  displacements = disp_x
  temperature = temperature
[]

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

[Mesh]
  coord_type = RZ
  [layered1D_mesh]
    type = Layered1DMeshGenerator
    slices_per_block = 10
    clad_gap_width = 8.0e-5
    clad_mesh_density = customize
    clad_thickness = 0.00075
    nx_c = 5
    additional_block_names = 'monolithic_layer'
    additional_elements_per_ring = '3'
    additional_ring_thicknesses = '0.00025'
    fuel_height = 0.1186
    plenum_height = 0.027
  []
  patch_update_strategy = auto
  partitioner = centroid
  centroid_partitioner_direction = y
[]

[UserObjects]
  [pin_geometry]
    type = Layered1DFuelPinGeometry
    mesh_generator = layered1D_mesh
  []
[]

[Variables]
  [temperature]
    initial_condition = 580.0 # set initial temperature to coolant inlet
  []
[]

[AuxVariables]
  [disp_y] ## Required for easier visualization in Paraview
  []
  [disp_z] ## Required for easier visualization in Paraview
  []
  [fast_neutron_flux]
    block = 'clad monolithic_layer'
    order = CONSTANT
    family = MONOMIAL
  []
  [fast_neutron_fluence]
    block = 'clad monolithic_layer'
    order = CONSTANT
    family = MONOMIAL
  []
  [grain_radius]
    block = fuel
    initial_condition = 10e-6
  []
  [solid_swell]
    order = CONSTANT
    family = MONOMIAL
    block = fuel
  []
  [gaseous_swelling]
    order = CONSTANT
    family = MONOMIAL
    block = fuel
  []
  [densification]
    order = CONSTANT
    family = MONOMIAL
    block = fuel
  []
  [volumetric_swelling_strain]
    order = CONSTANT
    family = MONOMIAL
    block = fuel
  []
  [relocation]
    order = CONSTANT
    family = MONOMIAL
    block = fuel
  []
[]

[Functions]
  [power_history]
    type = PiecewiseLinear
    x = '0 1e4 1e8'
    y = '0 25000 25000'
    scale_factor = 1
  []
  [axial_peaking_factors]
    type = ParsedFunction
    expression = 1
  []
  [pressure_ramp]
    type = PiecewiseLinear
    x = '-200 0 1e8'
    y = '6.537e-3 1 1'
  []
  [q]
    type = CompositeFunction
    functions = 'power_history axial_peaking_factors'
  []
  [clad_axial_pressure]
    type = CladdingAxialPressureFunction
    plenum_pressure = plenum_pressure
    coolant_pressure = pressure_ramp
    coolant_pressure_scaling_factor = 15.5e6
    fuel_pin_geometry = pin_geometry
  []
  [fuel_axial_pressure]
    type = ParsedFunction
    expression = plenum_pressure
    symbol_names = plenum_pressure
    symbol_values = plenum_pressure
  []
[]

[Kernels]
  [heat]
    type = HeatConduction
    variable = temperature
    extra_vector_tags = 'ref'
  []
  [heat_ie]
    type = HeatConductionTimeDerivative
    variable = temperature
    extra_vector_tags = 'ref'
  []
  [heat_source]
    type = NeutronHeatSource
    variable = temperature
    block = fuel
    burnup_function = burnup
    extra_vector_tags = 'ref'
  []
[]

[Physics]
  [SolidMechanics]
    [Layered1D]
      [fuel]
        block = fuel
        add_variables = true
        strain = SMALL
        incremental = true
        add_scalar_variables = true
        out_of_plane_strain_name = strain_yy
        fuel_pin_geometry = pin_geometry
        out_of_plane_pressure_function = fuel_axial_pressure
        eigenstrain_names = 'fuel_thermal_strain fuel_swelling_strain'
        generate_output = 'stress_xx stress_yy stress_zz vonmises_stress strain_xx'
        extra_vector_tags = 'ref'
        group_scalar_vars_in_reference_residual = true
        mesh_generator = layered1D_mesh
      []
      [composite]
        block = clad
        add_variables = true
        strain = SMALL
        incremental = true
        add_scalar_variables = true
        out_of_plane_strain_name = strain_yy
        fuel_pin_geometry = pin_geometry
        out_of_plane_pressure_function = clad_axial_pressure
        eigenstrain_names = 'composite_thermal_strain composite_swelling_strain'
        generate_output = 'stress_xx stress_yy stress_zz vonmises_stress strain_xx'
        extra_vector_tags = 'ref'
        group_scalar_vars_in_reference_residual = true
        mesh_generator = layered1D_mesh
      []
      [monolith]
        block = monolithic_layer
        add_variables = true
        strain = SMALL
        incremental = true
        add_scalar_variables = true
        out_of_plane_strain_name = strain_yy
        fuel_pin_geometry = pin_geometry
        out_of_plane_pressure_function = clad_axial_pressure
        eigenstrain_names = 'monolith_thermal_strain monolith_swelling_strain'
        generate_output = 'stress_xx stress_yy stress_zz vonmises_stress strain_xx'
        extra_vector_tags = 'ref'
        group_scalar_vars_in_reference_residual = true
        mesh_generator = layered1D_mesh
      []
    []
  []
[]

[Burnup]
  [burnup]
    block = fuel
    rod_ave_lin_pow = power_history
    axial_power_profile = axial_peaking_factors
    num_radial = 80
    num_axial = 11
    order = CONSTANT
    family = MONOMIAL
    fuel_pin_geometry = pin_geometry
    fuel_volume_ratio = 1.0
    RPF = RPF
    fuel_type = U3Si2
  []
[]

[AuxKernels]
  [fast_neutron_flux]
    type = MaterialRealAux
    variable = fast_neutron_flux
    property = fast_neutron_flux
    block = 'clad monolithic_layer'
    execute_on = timestep_begin
  []
  [fast_neutron_fluence]
    type = MaterialRealAux
    variable = fast_neutron_fluence
    property = fast_neutron_fluence
    block = 'clad monolithic_layer'
    execute_on = timestep_begin
  []
  [grain_radius]
    type = GrainRadiusAux
    block = fuel
    variable = grain_radius
    temperature = temperature
    execute_on = linear
  []
  [solid_swell]
    type = MaterialRealAux
    variable = solid_swell
    property = solid_swelling
    execute_on = timestep_end
    block = fuel
  []
  [gas_swell]
    type = MaterialRealAux
    variable = gaseous_swelling
    property = gaseous_swelling
    execute_on = timestep_end
    block = fuel
  []
  [densification]
    type = MaterialRealAux
    variable = densification
    property = densification
    execute_on = timestep_end
    block = fuel
  []
  [volumetric_swelling_strain]
    type = MaterialRealAux
    variable = volumetric_swelling_strain
    property = volumetric_swelling_strain
    execute_on = timestep_end
    block = fuel
  []
[]

[Contact]
  [pellet_clad_mechanical]
    primary = 5
    secondary = 10
    formulation = kinematic
    model = frictionless
    penalty = 1e7
  []
[]

[ThermalContact]
  [thermal_contact]
    type = GasGapHeatTransfer
    variable = temperature
    primary = 5
    secondary = 10
    initial_moles = initial_moles # coupling to a postprocessor which supplies the initial plenum/gap gas mass
    gas_released = fis_gas_released # coupling to a postprocessor which supplies the fission gas addition
    contact_pressure = contact_pressure
  []
[]

[BCs]
  [no_x_all] # pin pellets and clad along axis of symmetry (y)
    type = DirichletBC
    variable = disp_x
    boundary = 12
    value = 0.0
  []
  [Pressure] # apply coolant pressure on clad outer walls
    [coolantPressure]
      use_displaced_mesh = false
      boundary = 2
      function = pressure_ramp # use the pressure_ramp function defined above
      factor = 15.5e6
    []
  []
  [PlenumPressure] # apply plenum pressure on clad inner walls and pellet surfaces
    [plenumPressure]
      use_displaced_mesh = false
      boundary = 9
      initial_pressure = 2.0e6
      startup_time = 0
      R = 8.314
      output_initial_moles = initial_moles # coupling to post processor to get initial fill gas mass
      temperature = ave_temp_interior # coupling to post processor to get gas temperature approximation
      volume = gas_volume # coupling to post processor to get gas volume
      material_input = fis_gas_released # coupling to post processor to get fission gas added
      output = plenum_pressure # coupling to post processor to output plenum/gap pressure
    []
  []
[]

[CoolantChannel]
  [convective_clad_surface] # apply convective boundary to clad outer surface
    variable = temperature
    boundary = 2
    inlet_temperature = 580 # K
    inlet_pressure = 15.5e6 # Pa
    inlet_massflux = 3800 # kg/m^2-sec
    rod_diameter = 10.368e-3 # m
    rod_pitch = 1.26e-2 # m
    linear_heat_rate = power_history
    axial_power_profile = axial_peaking_factors
  []
[]

[Materials]
  [flux]
    type = FastNeutronFlux
    calculate_fluence = true
    block = 'clad monolithic_layer'
    rod_ave_lin_pow = power_history
    axial_power_profile = axial_peaking_factors
    factor = 3e13
  []
  ### U3Si2 Fuel
  [fuel_thermal]
    type = SilicideFuelThermal
    block = fuel
    thermal_conductivity_model = WHITE
    temperature = temperature
  []
  [fuel_elasticity_tensor]
    type = U3Si2ElasticityTensor
    block = fuel
  []
  [fuel_stress]
    type = ComputeMultipleInelasticStress
    block = fuel
    tangent_operator = elastic
    inelastic_models = 'fuel_creep'
  []
  [fuel_creep]
    type = U3Si2CreepUpdate
    block = fuel
    temperature = temperature
  []
  [fuel_thermal_expansion]
    type = U3Si2ThermalExpansionEigenstrain
    block = fuel
    temperature = temperature
    stress_free_temperature = 295.0
    eigenstrain_name = fuel_thermal_strain
  []
  [fuel_volumetric_swelling]
    type = U3Si2VolumetricSwellingEigenstrain
    block = fuel
    gaseous_swelling_type = FINLAY
    temperature = temperature
    burnup_function = burnup
    eigenstrain_name = fuel_swelling_strain
  []
  [fission_gas_release]
    type = U3Si2Sifgrs
    block = fuel
    temperature = temperature
    burnup_function = burnup
    grain_radius_const = 2.5e-05
  []

  [fuel_density]
    type = StrainAdjustedDensity
    block = fuel
    strain_free_density = ${initial_fuel_density}
  []

  ### Composite SiC
  [composite_thermal]
    type = CompositeSiCThermal
    thermal_conductivity_model = STONE
    temperature = temperature
    block = clad
  []
  [composite_density]
    type = StrainAdjustedDensity
    block = clad
    strain_free_density = 2700.0
  []
  [composite_elasticity_tensor]
    type = CompositeSiCElasticityTensor
    block = clad
  []
  [composite_stress]
    type = ComputeStrainIncrementBasedStress
    block = clad
  []
  [composite_thermal_expansion]
    type = CompositeSiCThermalExpansionEigenstrain
    block = clad
    stress_free_temperature = 295.0
    temperature = temperature
    eigenstrain_name = composite_thermal_strain
  []
  [composite_irradiation_swelling]
    type = CompositeSiCVolumetricSwellingEigenstrain
    block = clad
    temperature = temperature
    fast_neutron_fluence = fast_neutron_fluence
    swelling_model = KATOH
    number_of_substeps = 1000
    eigenstrain_name = composite_swelling_strain
  []

  ### Monolithic SiC
  [monolith_thermal]
    type = MonolithicSiCThermal
    temperature = temperature
    thermal_conductivity_model = STONE
    block = monolithic_layer
  []
  [monolith_density]
    type = StrainAdjustedDensity
    block = monolithic_layer
    strain_free_density = 3120.0
  []
  [monolith_elasticity_tensor]
    type = MonolithicSiCElasticityTensor
    block = monolithic_layer
  []
  [monolith_stress]
    type = ComputeMultipleInelasticStress
    block = monolithic_layer
    tangent_operator = elastic
    inelastic_models = 'monolith_creep'
  []
  [monolith_creep]
    type = MonolithicSiCCreepUpdate
    block = monolithic_layer
    fast_neutron_flux = fast_neutron_flux
    temperature = temperature
    k_function = 2e-37
  []
  [monolith_thermal_expansion]
    type = MonolithicSiCThermalExpansionEigenstrain
    block = monolithic_layer
    stress_free_temperature = 295.0
    temperature = temperature
    eigenstrain_name = monolith_thermal_strain
  []
  [monolith_irradiation_swelling]
    type = CompositeSiCVolumetricSwellingEigenstrain
    block = monolithic_layer
    temperature = temperature
    fast_neutron_fluence = fast_neutron_fluence
    swelling_model = KATOH
    number_of_substeps = 1000
    eigenstrain_name = monolith_swelling_strain
  []
[]

[Dampers]
  [limitT]
    type = MaxIncrement
    max_increment = 100.0
    variable = temperature
  []
  [limitX]
    type = MaxIncrement
    max_increment = 1e-5
    variable = disp_x
  []
[]

[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'

  line_search = 'none'

  l_max_its = 50
  l_tol = 8e-3
  nl_max_its = 50
  nl_rel_tol = 1e-4
  nl_abs_tol = 1e-7

  start_time = -200
  n_startup_steps = 1
  end_time = 8.0e7
  dtmax = 1e6
  dtmin = 1

  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 2e2
    optimal_iterations = 25
    iteration_window = 5
    growth_factor = 2
    cutback_factor = .5
  []
[]

[Postprocessors]
  [ave_temp_interior] # average temperature of the cladding interior and all pellet exteriors
    type = LayeredSideAverageValuePostprocessor
    boundary = 9
    variable = temperature
    execute_on = 'initial linear'
    fuel_pin_geometry = pin_geometry
  []
  [clad_inner_vol] # volume inside of cladding
    type = LayeredInternalVolumePostprocessor
    boundary = 7
    component = 0
    fuel_pin_geometry = pin_geometry
    out_of_plane_strain = strain_yy
    execute_on = 'initial linear'
  []
  [pellet_volume] # fuel pellet total volume
    type = LayeredInternalVolumePostprocessor
    boundary = 8
    component = 0
    fuel_pin_geometry = pin_geometry
    out_of_plane_strain = strain_yy
    execute_on = 'initial linear'
  []
  [avg_clad_temp] # average temperature of cladding interior
    type = LayeredSideAverageValuePostprocessor
    boundary = 7
    variable = temperature
    fuel_pin_geometry = pin_geometry
    execute_on = 'initial linear'
  []
  [fis_gas_produced] # fission gas produced (moles)
    type = LayeredElementIntegralFisGasGeneratedSifgrsPostprocessor
    block = fuel
    fuel_pin_geometry = pin_geometry
  []
  [fis_gas_released] # fission gas released to plenum (moles)
    type = LayeredElementIntegralFisGasReleasedSifgrsPostprocessor
    block = fuel
    fuel_pin_geometry = pin_geometry
  []
  [fis_gas_grain]
    type = LayeredElementIntegralFisGasGrainSifgrsPostprocessor
    block = fuel
    outputs = exodus
    fuel_pin_geometry = pin_geometry
  []
  [fis_gas_boundary]
    type = LayeredElementIntegralFisGasBoundarySifgrsPostprocessor
    block = fuel
    outputs = exodus
    fuel_pin_geometry = pin_geometry
  []
  [fission_gas_release]
    type = FGRPercent
    fission_gas_released = fis_gas_released
    fission_gas_generated = fis_gas_produced
  []

  [gas_volume]
    type = LayeredInternalVolumePostprocessor
    boundary = 9
    execute_on = 'initial linear'
    component = 0
    out_of_plane_strain = strain_yy
    fuel_pin_geometry = pin_geometry
  []
  [flux_from_clad] # area integrated heat flux from the cladding
    type = LayeredSideFluxIntegralPostprocessor
    variable = temperature
    boundary = 5
    diffusivity = thermal_conductivity
    fuel_pin_geometry = pin_geometry
  []
  [flux_from_fuel] # area integrated heat flux from the fuel
    type = LayeredSideFluxIntegralPostprocessor
    variable = temperature
    boundary = 10
    diffusivity = thermal_conductivity
    fuel_pin_geometry = pin_geometry
  []
  [_dt] # time step
    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 = LayeredElementIntegralPowerPostprocessor
    variable = temperature
    burnup_function = burnup
    block = fuel
    fuel_pin_geometry = pin_geometry
  []
  [rod_input_power]
    type = FunctionValuePostprocessor
    function = power_history
    scale_factor = 0.1186 # rod height
  []

  [solid_swelling]
    type = ElementAverageValue
    variable = solid_swell
    block = fuel
  []
  [gaseous_swelling]
    type = ElementAverageValue
    variable = gaseous_swelling
    block = fuel
  []
  [densification]
    type = ElementAverageValue
    variable = densification
    block = fuel
  []
  [volumetric_swelling]
    type = ElementAverageValue
    variable = volumetric_swelling_strain
    block = fuel
  []
[]

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

(examples/accident_tolerant_fuel/u3si2_zircaloy/u3si2_zircaloy.i)


initial_fuel_density = 11590.0

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

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

[Mesh]
  coord_type = RZ
  # Import mesh file
  patch_size = 10 # For contact algorithm
  patch_update_strategy = auto
  partitioner = centroid
  centroid_partitioner_direction = y
  [mesh]
    type = FileMeshGenerator
    file = u3si2_zircaloy_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]
  # Define auxilary variables
  [fast_neutron_flux]
    block = clad
  []
  [fast_neutron_fluence]
    block = clad
  []
  [gap_cond]
    order = CONSTANT
    family = MONOMIAL
  []
  [hoop_stress]
    order = CONSTANT
    family = MONOMIAL
  []
  [coolant_htc]
    order = CONSTANT
    family = MONOMIAL
  []
  [oxide_thickness]
    order = CONSTANT
    family = MONOMIAL
  []
  [total_hoop_strain]
    order = CONSTANT
    family = MONOMIAL
  []
  [creep_rate]
    order = CONSTANT
    family = MONOMIAL
  []
  [densification]
    order = CONSTANT
    family = MONOMIAL
  []
  [solid_swell]
    order = CONSTANT
    family = MONOMIAL
  []
  [gaseous_swell]
    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'
  []
  [q]
    type = CompositeFunction
    functions = 'power_history axial_peaking_factors'
  []
[]

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

[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
    fuel_type = U3Si2
  []
[]

[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
  []
  [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
  []
  [conductance]
    type = MaterialRealAux
    property = gap_conductance
    variable = gap_cond
    boundary = 10
  []
  [coolant_htc]
    type = MaterialRealAux
    property = coolant_channel_htc
    variable = coolant_htc
    boundary = 2
  []
  [oxide]
    type = MaterialRealAux
    variable = oxide_thickness
    property = oxide_scale_thickness
    boundary = 2
  []
  [creep_rate]
    type = MaterialRealAux
    variable = creep_rate
    property = creep_rate
    execute_on = timestep_end
    block = clad
  []
  [densfication]
    type = MaterialRealAux
    property = densification
    variable = densification
    block = pellet_type_1
  []
  [solid_swell]
    type = MaterialRealAux
    property = solid_swelling
    variable = solid_swell
    block = pellet_type_1
  []
  [gaseous_swell]
    type = MaterialRealAux
    property = gaseous_swelling
    variable = gaseous_swell
    block = pellet_type_1
  []
[]

[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] # pin pellets and clad along axis of symmetry (y)
    type = DirichletBC
    variable = disp_x
    boundary = 12
    value = 0.0
  []
  [no_y_clad_bottom] # pin clad bottom in the axial direction (y)
    type = DirichletBC
    variable = disp_y
    boundary = '1'
    value = 0.0
  []
  [no_y_fuel_bottom] # pin fuel bottom in the axial direction (y)
    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 = 9.4996e-3 # m
    rod_pitch = 1.26e-2 # m
    linear_heat_rate = power_history
    axial_power_profile = axial_peaking_factors
  []
[]

[Materials]
  [fuel_thermal]
    type = SilicideFuelThermal
    block = pellet_type_1
    thermal_conductivity_model = WHITE
    silicon_mole_fraction = 0.4
    temperature = temp
  []
  [fuel_elasticity_tensor]
    type = U3Si2ElasticityTensor
    block = pellet_type_1
  []
  [fuel_stress]
    type = ComputeMultipleInelasticStress
    block = pellet_type_1
    tangent_operator = elastic
    inelastic_models = 'fuel_creep'
  []
  [fuel_creep]
    type = U3Si2CreepUpdate
    block = pellet_type_1
    temperature = temp
  []
  [fuel_thermal_expansion]
    type = U3Si2ThermalExpansionEigenstrain
    block = pellet_type_1
    temperature = temp
    stress_free_temperature = 295.0
    eigenstrain_name = fuel_thermal_strain
  []
  [fuel_volumetric_swelling]
    type = U3Si2VolumetricSwellingEigenstrain
    block = pellet_type_1
    gaseous_swelling_type = U3SI2FG
    temperature = temp
    burnup_function = burnup
    eigenstrain_name = fuel_volumetric_strain
  []

  [clad_thermal]
    type = ZryThermal
    temperature = temp
    block = clad
  []
  [clad_elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 7.5e10
    poissons_ratio = 0.3
    block = clad
  []
  [clad_stress]
    type = ComputeMultipleInelasticStress
    tangent_operator = elastic
    inelastic_models = 'clad_zrycreep clad_plasticity'
    relative_tolerance = 1e-5
    block = clad
  []
  [clad_zrycreep]
    type = ZryCreepLimbackHoppeUpdate
    block = clad
    temperature = temp
    fast_neutron_flux = fast_neutron_flux
    fast_neutron_fluence = fast_neutron_fluence
    model_irradiation_creep = true
    model_primary_creep = true
    model_thermal_creep = true
    relative_tolerance = 1e-5
    max_inelastic_increment = 1e-4
    zircaloy_material_type = stress_relief_annealed
  []
  [thermal_expansion]
    type = ZryThermalExpansionMATPROEigenstrain
    block = clad
    temperature = temp
    stress_free_temperature = 295.0
    eigenstrain_name = clad_thermal_eigenstrain
  []
  [irradiation_swelling]
    type = ZryIrradiationGrowthEigenstrain
    block = clad
    fast_neutron_fluence = fast_neutron_fluence
    zircaloy_material_type = stress_relief_annealed
    eigenstrain_name = clad_irradiation_strain
  []
  [clad_plasticity]
    type = ZryPlasticityUpdate
    block = clad
    temperature = temp
    fast_neutron_flux = fast_neutron_flux
    fast_neutron_fluence = fast_neutron_fluence
    relative_tolerance = 1e-5
    cold_work_factor = 0.5
    plasticity_model_type = MATPRO
    zircaloy_alloy_type = 4
  []
  [fission_gas_behavior]
    type = U3Si2Sifgrs
    block = pellet_type_1
    temperature = temp
    burnup_function = burnup
    saturation_coverage = 0.5
  []
  [clad_density]
    type = StrainAdjustedDensity
    block = clad
    strain_free_density = 6511.0
  []
  [fuel_density]
    type = StrainAdjustedDensity
    block = pellet_type_1
    strain_free_density = ${initial_fuel_density}
  []
  [ZryOxidation]
    type = ZryOxidation
    boundary = 2
    clad_inner_radius = 4.1783e-3
    clad_outer_radius = 4.7498e-3
    normal_operating_temperature_model = epri_kwu_ce
    temperature = temp
    fast_neutron_flux = fast_neutron_flux
    use_coolant_channel = true
    oxygen_weight_fraction_initial = 0.0012
  []
[]

[Dampers]
  [limitT]
    type = MaxIncrement
    max_increment = 100.0
    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 = 1e6
  dtmin = 1e-3

  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 2.0e2
    force_step_every_function_point = true
    timestep_limiting_function = power_history
    max_function_change = 3e20
    optimal_iterations = 10
    iteration_window = 2
    linear_iteration_ratio = 100
    timestep_limiting_postprocessor = material_timestep
  []
  [Quadrature]
    order = FIFTH
    side_order = SEVENTH
  []
[]

[Postprocessors]
  [avg_fuel_surface]
    type = SideAverageValue
    boundary = 10
    variable = temp
  []
  [ave_temp_interior]
    type = SideAverageValue
    boundary = 9
    variable = temp
    execute_on = 'initial linear'
  []
  [clad_inner_vol]
    type = InternalVolume
    boundary = 7
  []
  [pellet_volume]
    type = InternalVolume
    boundary = 8
  []
  [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'
  []
  [flux_from_clad]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 5
    diffusivity = thermal_conductivity
  []
  [flux_from_fuel]
    type = SideDiffusiveFluxIntegral
    variable = temp
    boundary = 10
    diffusivity = thermal_conductivity
  []
  [_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
  []
  [rod_input_power]
    type = FunctionValuePostprocessor
    function = power_history
    scale_factor = 0.1186
  []
  [average_burnup]
    type = ElementAverageValue
    block = pellet_type_1
    variable = burnup
  []
  [oxide_thickness]
    type = ElementExtremeValue
    block = clad
    variable = oxide_thickness
  []
  [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
  color = false
  csv = true
  print_linear_residuals = true
  [console]
    type = Console
    max_rows = 25
  []
[]

(test/tests/solid_mechanics/u3si2_elasticity_tensor/elasticity.i)

#--------------------------------------------------------------------------------
#
#   This test case is prepared to test the elastic behavior of U3Si2. A simple
#   3D cube (1x1x1 m) is subjected to a linearly increasing temperature from
#   300 K to 800 K over 1 second. The temperature change induces a thermal
#   strain caused by thermal expansion. The thermal expansion causes a change
#   in volume, which subsequently causes a change in density of the block and
#   thus porosity.
#
#   The change in porosity causes a change in the Poisson's ratio and Young's
#   modulus of the U3Si2 block. For this material the Young's modulus and
#   Poisson's ratio can be output as a material property.  The averages are
#   reported in two postprocessors.
#
#   The initial density is taken as 95.0% theoretical resulting in an initial
#   porosity of 5.0%.
#
#   The values reported by BISON in the two postprocessors are compared to the
#   analytical values for the initial, mid, and final densities respectively.
#
#   Initial density:
#
#   Porosity = 5.0%
#   Young's modulus = -6.425 * 5.0 + 142.68 = 110.555 GPa
#   Shear modulus = -2.901 * 5.0 + 61.27 = 46.765 GPa
#   Poisson's ratio = 110.555 / (2.0 * 46.765) - 1.0 = 0.1820
#
#   Mid density (thermal strain = 0.0025):
#
#   New volume = 1.0025 * 1.0025 * 1.0025 = 1.007519 m^3
#   New density = (1.0 / 1.007519) * 95% = 94.291%
#   Porosity = 100 - 94.291 = 5.709%
#   Young's modulus = -6.425 * 5.709 + 142.68 = 106.0 GPa
#   Shear modulus = -2.901 * 5.709 + 61.27 = 44.708 GPa
#   Poisson's ratio = 106.0 / (2.0 * 44.708) - 1.0 = 0.1855
#
#   Final density (thermal strain = 0.005):
#
#   New volume = 1.005 * 1.005 * 1.005 = 1.015075 m^3
#   New density = (1.0 / 1.015075) * 95% = 93.589%
#   Porosity = 100.0 - 93.589 = 6.411%
#   Young's modulus = -6.425 * 6.411 + 142.68 = 101.489 GPa
#   Shear modulus = -2.901 * 6.411 + 61.27 = 42.672 GPa
#   Poisson's ratio = 101.489 / (2.0 * 42.672) - 1.0 = 0.1892
#
#   These analytical answers above are consistent with the BISON reported
#   values from the postprocessors.
#--------------------------------------------------------------------------------
[GlobalParams]
  order = FIRST
  family = LAGRANGE
  displacements = 'disp_x disp_y disp_z'
  volumetric_locking_correction = true
[]

[Mesh]
  [mesh]
    type = GeneratedMeshGenerator
    dim = 3
    elem_type = HEX8
  []
[]

[Variables]
  [disp_x]
  []
  [disp_y]
  []
  [disp_z]
  []
  [temperature]
    initial_condition = 300.0
  []
[]

[AuxVariables]
  [youngs_modulus]
    order = CONSTANT
    family = MONOMIAL
  []
  [poissons_ratio]
    order = CONSTANT
    family = MONOMIAL
  []
  [density]
    order = CONSTANT
    family = MONOMIAL
  []
[]

[Functions]
  [temperature_ramp]
    type = PiecewiseLinear
    x = '0 1'
    y = '300 800'
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = small
    eigenstrain_names = thermal_eigenstrain
  []
[]

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

[AuxKernels]
  [youngs_modulus]
    type = MaterialRealAux
    property = youngs_modulus
    variable = youngs_modulus
    execute_on = 'initial timestep_end'
  []
  [poissons_ratio]
    type = MaterialRealAux
    property = poissons_ratio
    variable = poissons_ratio
    execute_on = 'initial timestep_end'
  []
  [density]
    type = MaterialRealAux
    property = density
    variable = density
    execute_on = 'initial timestep_end'
  []
[]

[BCs]
  [left_fix]
    type = DirichletBC
    variable = disp_x
    boundary = left
    value = 0.0
  []
  [bottom_fix]
    type = DirichletBC
    variable = disp_y
    boundary = bottom
    value = 0.0
  []
  [back_fix]
    type = DirichletBC
    variable = disp_z
    boundary = back
    value = 0.0
  []
  [temperature]
    type = FunctionDirichletBC
    variable = temperature
    boundary = 'front back top back left right'
    function = temperature_ramp
  []
[]

[Materials]
  [elasticity_tensor]
    type = U3Si2ElasticityTensor
    block = 0
  []
  [stress]
    type = ComputeLinearElasticStress
    block = 0
  []
  [density]
    type = StrainAdjustedDensity
    block = 0
    strain_free_density = 11590.0
  []
  [thermal_expansion]
    type = ComputeThermalExpansionEigenstrain
    block = 0
    temperature = temperature
    thermal_expansion_coeff = 10e-6
    eigenstrain_name = thermal_eigenstrain
    stress_free_temperature = 300.0
  []
  [conduction]
    type = GenericConstantMaterial
    block = 0
    prop_names = "thermal_conductivity specific_heat"
    prop_values = '10000 1'
  []
[]

[Executioner]
  type = Transient

  solve_type = 'PJFNK'
  petsc_options       = '-snes_ksp_ew'
  petsc_options_iname = '-ksp_gmres_restart'
  petsc_options_value = '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   = 1.0
  dt         = 0.5
[]

[Postprocessors]
  [average_temperature]
    type = AverageNodalVariableValue
    variable = temperature
    execute_on = 'initial timestep_end'
  []
  [volume]
    type = InternalVolume
    boundary = 'bottom top left right front back'
    scale_factor = -1.0
    execute_on = 'initial timestep_end'
  []
  [youngs_avg]
    type = ElementAverageValue
    variable = youngs_modulus
    execute_on = 'initial timestep_end'
  []
  [poissons_avg]
    type = ElementAverageValue
    variable = poissons_ratio
    execute_on = 'initial timestep_end'
  []
  [density]
    type = ElementAverageValue
    variable = density
    execute_on = 'initial timestep_end'
  []
[]

[Outputs]
  exodus = true
[]

Description
Example Input Syntax
Input Parameters
Input Files
References