BeOElasticityTensor

Computes Young's modulus and Poisson's ratio for BeO as a function of temperature and formulates the elasticity tensor.

Description

This computes the elasticity tensor for BeO. The tensor is symmetric and populated using the Poisson's ratio and Young's modulus.

Version of AD version is also available by adding the prefix AD to the name for the "type" parameter.

Poisson's Ratio

The Poisson's ratio is a constant, but may be supplied. The default Poisson's ratio is 0.3 (Nash, 2005) for a temperature, $var element = document.getElementById("moose-equation-3141434e-fde9-42e0-9016-97a45f9b467d");katex.render("T", element, {displayMode:false,throwOnError:false});$ , range of $var element = document.getElementById("moose-equation-503c13b5-2b48-4f3f-bb2c-4ec8dce0dc9b");katex.render("298 \\leq T \\leq 1400", element, {displayMode:false,throwOnError:false});$ K. No warning is given if $var element = document.getElementById("moose-equation-6e60f653-cd87-45b2-8293-65711a02901b");katex.render("T", element, {displayMode:false,throwOnError:false});$ is outside this range, though. A temperature-dependent function may also be provided.

Young's Modulus

The Young's modulus (modulus of elasticity) is a function of porosity and temperature (Nash, 2005). The porosity must be $var element = document.getElementById("moose-equation-cf94613c-5b37-481a-bbff-4c373575e956");katex.render("p \\leq 0.3", element, {displayMode:false,throwOnError:false});$ . The Young's modulus, $var element = document.getElementById("moose-equation-652a79d8-2655-4f4b-b726-b590afa56acb");katex.render("E", element, {displayMode:false,throwOnError:false});$ , in GPa is

$var element = document.getElementById("moose-equation-b79fd29e-5ec5-4690-9f20-b8dacdf8ee14");katex.render(" E(P,T) = \\left(344.7 - 805.7 p\\right) \\times \\begin{cases} 1 & \\text{for } 298 < T \\leq 800, \\\\ \\left(1.31 - 1.75\\times 10^{-3} T + 2.82\\times 10^{-6} T^2 - 1.39\\times 10^{-9} T^3\\right) & \\text{for } 800 < T \\leq 1500, \\end{cases}", element, {displayMode:true,throwOnError:false});$

where $var element = document.getElementById("moose-equation-e6ba72d1-50f7-4873-afef-0e99e3acac53");katex.render("E", element, {displayMode:false,throwOnError:false});$ is converted from GPa to Pa for use in other areas of the code. Temperatures below 298 K are allowed as the lower equation does not depend on temperature. Temperatures above 1500 K yield the same $var element = document.getElementById("moose-equation-f648cdbd-978b-4bee-8984-9a5d5916dabc");katex.render("E", element, {displayMode:false,throwOnError:false});$ as $var element = document.getElementById("moose-equation-16218509-81b4-4b40-a5e0-2259b48b08e8");katex.render("E(P,1500)", element, {displayMode:false,throwOnError:false});$ to avoid extrapolation.

Example Input Syntax

[Materials<<<{"href": "../../../syntax/Materials/index.html"}>>>]
  [elasticity_tensor]
    type = ADBeOElasticityTensor<<<{"description": "Computes Young's modulus and Poisson's ratio for BeO as a function of temperature and formulates the elasticity tensor.", "href": "BeOElasticityTensor.html"}>>>
    temperature<<<{"description": "Coupled temperature variable."}>>> = temperature
    output_properties<<<{"description": "List of material properties, from this material, to output (outputs must also be defined to an output type)"}>>> = 'youngs_modulus'
    outputs<<<{"description": "Vector of output names where you would like to restrict the output of variables(s) associated with this object"}>>> = all
  []
[]

Input Parameters

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

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.
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.
poissons_functionPossion's ratio function of temperature.
C++ Type:FunctionName
Unit:(no unit assumed)
Controllable:No
Description:Possion's ratio function of temperature.
poissons_ratio0.3Possion's ratio.
Default:0.3
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Possion's ratio.
porosityporosityPorosity material property name.
Default:porosity
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:Porosity material property name.

Optional Parameters

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

Advanced Parameters

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

Outputs Parameters

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

Material Property Retrieval Parameters

Input Files

(test/tests/solid_mechanics/beo_elasticity_tensor/exact.i)
(test/tests/solid_mechanics/beo_elasticity_tensor/ad_beo_mech.i)

References

J. Nash. Reflector and Shield Material Properties for Project Prometheus. Technical Report MDO-723-0042, Knolls Atomic Power Laboratory, 2005. doi:10.2172/883658.

@techreport{nash05,
    author = "Nash, J.",
    title = "{Reflector and Shield Material Properties for Project Prometheus}",
    institution = "Knolls Atomic Power Laboratory",
    year = "2005",
    number = "MDO-723-0042",
    doi = "10.2172/883658"
}

(test/tests/solid_mechanics/beo_elasticity_tensor/ad_beo_mech.i)

# Test ADBeOElasticityTensor when coupled to a changing temperature and porosity.

[GlobalParams]
  displacements = 'disp_x'
[]

[Mesh]
  [geo]
    type = GeneratedMeshGenerator
    dim = 1
    nx = 5
  []
[]

[Variables]
  [temperature]
    initial_condition = 500
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = FINITE
    add_variables = true
    use_automatic_differentiation = true
  []
[]

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

[BCs]
  [left]
    type = ADDirichletBC
    boundary = 'left'
    variable = temperature
    value = 1000
  []
  [right]
    type = ADDirichletBC
    boundary = 'right'
    variable = temperature
    value = 1000
  []
  [fix_x]
    type = ADDirichletBC
    boundary = 'left'
    variable = disp_x
    value = 0
  []
  [pull_x]
    type = ADPressure
    variable = disp_x
    boundary = 'right'
    factor = -1e7
  []
[]

[Materials]
  [mat_density]
    type = ADGenericConstantMaterial
    prop_names = 'density thermal_conductivity specific_heat'
    prop_values = '3000 120 1600'
  []
  [mat_porosity]
    type = ADPiecewiseLinearInterpolationMaterial
    property = porosity
    variable = temperature
    x = '500 900 1500'
    y = '0.1 0.2 0.29'
  []
  [stress]
    type = ADComputeFiniteStrainElasticStress
  []
  [elasticity_tensor]
    type = ADBeOElasticityTensor
    temperature = temperature
    output_properties = 'youngs_modulus'
    outputs = all
  []
  [calc_young]
    type = ADParsedMaterial
    property_name = 'calc_young'
    material_property_names = 'porosity'
    coupled_variables = 'temperature'
    expression = 'T := if(temperature > 1500, 1500, temperature); 1e9 * if(temperature > 800, (344.7 - 805.7 * porosity) * (1.31 - 1.75e-3 * T + 2.82e-6 * pow(T, 2) - 1.39e-9 * pow(T, 3)), 344.7 - 805.7 * porosity)'
    outputs = all
  []
[]

[Postprocessors]
  [avg_T]
    type = ElementAverageValue
    variable = temperature
  []
  [avg_porosity]
    type = ADElementAverageMaterialProperty
    mat_prop = 'porosity'
  []
  [avg_youngs]
    type = ADElementAverageMaterialProperty
    mat_prop = 'youngs_modulus'
  []
  [calc_youngs]
    type = ADElementAverageMaterialProperty
    mat_prop = 'calc_young'
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  num_steps = 10
  dt = 600
[]

[Outputs]
  exodus = true
[]

(test/tests/solid_mechanics/beo_elasticity_tensor/exact.i)

# Compares BeOElasticityTensor to exact calculations of Young's modulus.

[Problem]
  solve = false
[]

[Mesh]
  [mesh]
    type = GeneratedMeshGenerator
    dim = 1
  []
[]

[AuxVariables]
  [temperature]
  []
[]

[Functions]
  [temp_ramp]
    type = PiecewiseLinear
    x = '0 10'
    y = '500 2000'
  []
  [por_ramp]
    type = PiecewiseLinear
    x = '0 10'
    y = '0.05 0.25'
  []
[]

[AuxKernels]
  [temp_aux]
    type = FunctionAux
    variable = temperature
    function = temp_ramp
  []
[]

[Materials]
  [mat_porosity]
    type = GenericFunctionMaterial
    prop_names = porosity
    prop_values = por_ramp
  []
  [elasticity_tensor]
    type = BeOElasticityTensor
    temperature = temperature
    output_properties = 'youngs_modulus'
    outputs = all
  []
  [calc_young]
    type = ParsedMaterial
    property_name = 'calc_young'
    material_property_names = 'porosity'
    coupled_variables = 'temperature'
    expression = 'T := if(temperature > 1500, 1500, temperature); 1e9 * if(temperature > 800, (344.7 - 805.7 * porosity) * (1.31 - 1.75e-3 * T + 2.82e-6 * pow(T, 2) - 1.39e-9 * pow(T, 3)), 344.7 - 805.7 * porosity)'
    outputs = all
  []
[]

[Postprocessors]
  [avg_T]
    type = ElementAverageValue
    variable = temperature
  []
  [avg_porosity]
    type = ElementAverageMaterialProperty
    mat_prop = 'porosity'
  []
  [avg_youngs]
    type = ElementAverageMaterialProperty
    mat_prop = 'youngs_modulus'
  []
  [calc_youngs]
    type = ElementAverageMaterialProperty
    mat_prop = 'calc_young'
  []
  [diff_youngs]
    type = RelativeDifferencePostprocessor
    value1 = avg_youngs
    value2 = calc_youngs
  []
  [relative_young_diff_max]
    type = TimeExtremeValue
    postprocessor = diff_youngs
    value_type = abs_max
  []
[]

[Executioner]
  type = Transient
  num_steps = 10
[]

[Outputs]
  csv = true
[]

(test/tests/solid_mechanics/beo_elasticity_tensor/ad_beo_mech.i)

# Test ADBeOElasticityTensor when coupled to a changing temperature and porosity.

[GlobalParams]
  displacements = 'disp_x'
[]

[Mesh]
  [geo]
    type = GeneratedMeshGenerator
    dim = 1
    nx = 5
  []
[]

[Variables]
  [temperature]
    initial_condition = 500
  []
[]

[Physics/SolidMechanics/QuasiStatic]
  [all]
    strain = FINITE
    add_variables = true
    use_automatic_differentiation = true
  []
[]

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

[BCs]
  [left]
    type = ADDirichletBC
    boundary = 'left'
    variable = temperature
    value = 1000
  []
  [right]
    type = ADDirichletBC
    boundary = 'right'
    variable = temperature
    value = 1000
  []
  [fix_x]
    type = ADDirichletBC
    boundary = 'left'
    variable = disp_x
    value = 0
  []
  [pull_x]
    type = ADPressure
    variable = disp_x
    boundary = 'right'
    factor = -1e7
  []
[]

[Materials]
  [mat_density]
    type = ADGenericConstantMaterial
    prop_names = 'density thermal_conductivity specific_heat'
    prop_values = '3000 120 1600'
  []
  [mat_porosity]
    type = ADPiecewiseLinearInterpolationMaterial
    property = porosity
    variable = temperature
    x = '500 900 1500'
    y = '0.1 0.2 0.29'
  []
  [stress]
    type = ADComputeFiniteStrainElasticStress
  []
  [elasticity_tensor]
    type = ADBeOElasticityTensor
    temperature = temperature
    output_properties = 'youngs_modulus'
    outputs = all
  []
  [calc_young]
    type = ADParsedMaterial
    property_name = 'calc_young'
    material_property_names = 'porosity'
    coupled_variables = 'temperature'
    expression = 'T := if(temperature > 1500, 1500, temperature); 1e9 * if(temperature > 800, (344.7 - 805.7 * porosity) * (1.31 - 1.75e-3 * T + 2.82e-6 * pow(T, 2) - 1.39e-9 * pow(T, 3)), 344.7 - 805.7 * porosity)'
    outputs = all
  []
[]

[Postprocessors]
  [avg_T]
    type = ElementAverageValue
    variable = temperature
  []
  [avg_porosity]
    type = ADElementAverageMaterialProperty
    mat_prop = 'porosity'
  []
  [avg_youngs]
    type = ADElementAverageMaterialProperty
    mat_prop = 'youngs_modulus'
  []
  [calc_youngs]
    type = ADElementAverageMaterialProperty
    mat_prop = 'calc_young'
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  num_steps = 10
  dt = 600
[]

[Outputs]
  exodus = true
[]

Description
Example Input Syntax
Input Parameters
Input Files
References