Strain Energy Rate Density

Computes the strain energy density rate using a combination of the elastic and inelastic components of the strain increment, which is a valid assumption for monotonic behavior.

Description

This material computes the strain energy rate density, $var element = document.getElementById("moose-equation-7aa8d110-f890-470d-84c5-b6217d9cbe2d");katex.render("\\dot{u}", element, {displayMode:false,throwOnError:false});$ , which is defined as the time rate of the strain energy density (see StrainEnergyDensity): $(1)var element = document.getElementById("moose-equation-ec6684da-a1ad-4db1-acdb-60a9700c5d29");katex.render(" \\dot{u} = \\int \\boldsymbol{\\sigma} : \\textrm{d}\\dot{\\boldsymbol{\\epsilon}}", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-229b8341-5530-47fd-977d-ab69819867b6");katex.render("\\boldsymbol{\\sigma}", element, {displayMode:false,throwOnError:false});$ is the stress tensor and $var element = document.getElementById("moose-equation-c08288f9-7270-4e7d-aec5-f73673e1e2b9");katex.render("\\dot{\\boldsymbol{\\epsilon}}", element, {displayMode:false,throwOnError:false});$ is the strain rate. This expression is multiplied by $var element = document.getElementById("moose-equation-2a1f5749-145f-4a9f-99ca-64d965b30394");katex.render("\\frac{n}{n+1}", element, {displayMode:false,throwOnError:false});$ , where $var element = document.getElementById("moose-equation-410e062a-a124-4be8-8fde-b4ef6209c67d");katex.render("n", element, {displayMode:false,throwOnError:false});$ is the power law exponent of the material provided though the inelastic_models input parameter. This factor decreases the strain energy rate density to better capture the strain rate field around a crack under steady-state creep growth. This factor is primarily used to compute the C(t) integral, see FractureIntegrals.

The strain rate here is the sum of the elastic and inelastic (e.g. plastic, creep) strain rates.

This class is available both for manually coded Jacobian and automatic differentiation strategies.

Example Input File

[strain_energy_rate_density]
  type = ADStrainEnergyRateDensity
  inelastic_models = 'powerlawcrp'
[]

Input Parameters

inelastic_modelsThe material objects to use to calculate the strain energy rate density.
C++ Type:std::vector<MaterialName>
Controllable:No
Description:The material objects to use to calculate the strain energy rate density.

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
Controllable:No
Description:An optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.
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
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.

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

References

No citations exist within this document.

(moose/modules/tensor_mechanics/test/tests/strain_energy_density/ad_rate_model_weak_plane.i)

# Single element test to check the strain energy density calculation

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

[Mesh]
  type = GeneratedMesh
  dim = 2
  nx = 1
  ny = 1
  xmin = 0
  xmax = 1
  ymin = 0
  ymax = 2
[]

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

[Variables]
  [strain_zz]
  []
[]

[Functions]
  [rampConstantUp]
    type = PiecewiseLinear
    x = '0. 1.'
    y = '0. 1.'
    scale_factor = -100
  []
[]

[Modules/TensorMechanics/Master]
  [master]
    strain = FINITE
    add_variables = true
    incremental = true
    generate_output = 'stress_xx stress_yy stress_zz vonmises_stress strain_xx strain_yy'
    planar_formulation = WEAK_PLANE_STRESS
    use_automatic_differentiation = true
  []
[]

[AuxKernels]
  [SERD]
    type = MaterialRealAux
    variable = SERD
    property = strain_energy_rate_density
    execute_on = timestep_end
  []
[]

[BCs]
  [no_x]
    type = ADDirichletBC
    variable = disp_x
    boundary = 'left'
    value = 0.0
  []
  [no_y]
    type = ADDirichletBC
    variable = disp_y
    boundary = 'bottom'
    value = 0.0
  []
  [Pressure]
    [top]
      boundary = 'top'
      function = rampConstantUp
    []
  []
[]

[Materials]
  [elasticity_tensor]
    type = ADComputeIsotropicElasticityTensor
    youngs_modulus = 206800
    poissons_ratio = 0.0
  []
  [radial_return_stress]
    type = ADComputeMultipleInelasticStress
    inelastic_models = 'powerlawcrp'
  []
  [powerlawcrp]
    type = ADPowerLawCreepStressUpdate
    coefficient = 3.125e-21 # 7.04e-17 #
    n_exponent = 4.0
    m_exponent = 0.0
    activation_energy = 0.0
    # max_inelastic_increment = 0.01
  []
  [strain_energy_rate_density]
    type = ADStrainEnergyRateDensity
    inelastic_models = 'powerlawcrp'
  []
[]

[Executioner]
  type = Transient

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

  line_search = 'none'

  l_max_its = 50
  nl_max_its = 20
  nl_abs_tol = 3e-7
  nl_rel_tol = 1e-12
  l_tol = 1e-2

  start_time = 0.0
  dt = 1

  end_time = 1
  num_steps = 1
[]

[Postprocessors]
  [SERD]
    type = ElementAverageValue
    variable = SERD
  []
[]

[Outputs]
  csv = true
[]