Compute Eigenstrain

Computes a constant Eigenstrain

Description

The class ComputeEigenstrain allows the user to specify a constant value of an eigenstrain for a simulation. The eigenstrain is added to the mechanical strain, which can be elastic or inelastic, before computing the corresponding stress measure: $var element = document.getElementById("moose-equation-b24339fd-c636-419d-bc2d-f4f5cbb8b011");katex.render(" \\epsilon_{ij}^{total} = \\epsilon_{ij}^{mechanical} + \\epsilon_{ij}^{eigenstrain}", element, {displayMode:true,throwOnError:false,macros:{"\\bs":"\\boldsymbol{#1}","\\normal":"\\bs{n}","\\grad":"\\bs{\\nabla}","\\divergence":"\\grad \\cdot","\\norm":"\\left\\lVert#1\\right\\rVert","\\abs":"\\left\\lvert#1\\right\\rvert","\\tr":"\\text{tr}","\\dev":"\\text{dev}","\\sym":"\\text{sym}","\\diff":"\\text{ d}#1","\\activepart":"{\\left< A \\right>}","\\inactivepart":"{\\left< I \\right>}","\\Gc":"{\\mathcal{G}_c}","\\strain":"\\bs{\\varepsilon}","\\stress":"\\bs{\\sigma}","\\macaulay":"\\left<#1\\right>","\\body":"\\Omega","\\bodyboundary":"{\\partial\\body}","\\ep":"{\\varepsilon^p}","\\ep0":"{\\varepsilon_0^p}","\\epdot":"{\\dot{\\varepsilon}}^p","\\epdot0":"{\\dot{\\varepsilon}}_0^p","\\bfa":"\\boldsymbol{a}","\\bfb":"\\boldsymbol{b}","\\bfc":"\\boldsymbol{c}","\\bfd":"\\boldsymbol{d}","\\bfe":"\\boldsymbol{e}","\\bff":"\\boldsymbol{f}","\\bfg":"\\boldsymbol{g}","\\bfh":"\\boldsymbol{h}","\\bfi":"\\boldsymbol{i}","\\bfj":"\\boldsymbol{j}","\\bfk":"\\boldsymbol{k}","\\bfl":"\\boldsymbol{l}","\\bfm":"\\boldsymbol{m}","\\bfn":"\\boldsymbol{n}","\\bfo":"\\boldsymbol{o}","\\bfp":"\\boldsymbol{p}","\\bfq":"\\boldsymbol{q}","\\bfr":"\\boldsymbol{r}","\\bfs":"\\boldsymbol{s}","\\bft":"\\boldsymbol{t}","\\bfu":"\\boldsymbol{u}","\\bfv":"\\boldsymbol{v}","\\bfw":"\\boldsymbol{w}","\\bfx":"\\boldsymbol{x}","\\bfy":"\\boldsymbol{y}","\\bfz":"\\boldsymbol{z}","\\bfA":"\\boldsymbol{A}","\\bfB":"\\boldsymbol{B}","\\bfC":"\\boldsymbol{C}","\\bfD":"\\boldsymbol{D}","\\bfE":"\\boldsymbol{E}","\\bfF":"\\boldsymbol{F}","\\bfG":"\\boldsymbol{G}","\\bfH":"\\boldsymbol{H}","\\bfI":"\\boldsymbol{I}","\\bfJ":"\\boldsymbol{J}","\\bfK":"\\boldsymbol{K}","\\bfL":"\\boldsymbol{L}","\\bfM":"\\boldsymbol{M}","\\bfN":"\\boldsymbol{N}","\\bfO":"\\boldsymbol{O}","\\bfP":"\\boldsymbol{P}","\\bfQ":"\\boldsymbol{Q}","\\bfR":"\\boldsymbol{R}","\\bfS":"\\boldsymbol{S}","\\bfT":"\\boldsymbol{T}","\\bfU":"\\boldsymbol{U}","\\bfV":"\\boldsymbol{V}","\\bfW":"\\boldsymbol{W}","\\bfX":"\\boldsymbol{X}","\\bfY":"\\boldsymbol{Y}","\\bfZ":"\\boldsymbol{Z}"}});$

Eigenstrain is the term given to a strain which does not result directly from an applied force. Chapter 3 of Qu and Cherkaoui (2006) describes the relationship between total, elastic, and eigen- strains and provides examples using thermal expansion and dislocations. Eigenstrains are also referred to as residual strains, stress-free strains, or intrinsic strains; translated from German, Eigen means own or intrinsic in English. The term eigenstrain was introduced by Mura (1982).

Based on the number and values of constants provided as the argument to the eigen_base parameter, ComputeEigenstrain will build an isotropic, symmetric, or skew-symmetric Rank-2 eigenstrain tensor.

Example Input File Syntax

[./eigen]
  type = ComputeEigenstrain
  eigenstrain_name = eigen_true
  eigen_base = '1e-3 1e-3 1e-3 0 0 0'
[../]

Input Parameters

eigen_baseVector of values defining the constant base tensor for the Eigenstrain
C++ Type:std::vector<double>
Controllable:No
Description:Vector of values defining the constant base tensor for the Eigenstrain
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.

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.
prefactor1Name of material property defining the variable dependence
Default:1
C++ Type:MaterialPropertyName
Controllable:No
Description:Name of material property defining the variable dependence
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

Toshio Mura. General theory of eigenstrains. In Micromechanics of Defects in Solids, pages 1–62. Springer, 1982.

@incollection{mura1982general,
    author = "Mura, Toshio",
    title = "General theory of eigenstrains",
    booktitle = "Micromechanics of Defects in Solids",
    pages = "1--62",
    year = "1982",
    publisher = "Springer"
}

Jianmin Qu and Mohammed Cherkaoui. Fundamentals of micromechanics of solids. Wiley Online Library, 2006.

(../moose/modules/tensor_mechanics/test/tests/visco/gen_kv_driving.i)

# Represents a unique Maxwell module with E = 10GPa and eta = 10 days with an imposed eigenstrain alpha = 0.001.
# The behavior is set up so that the creep strain is driven by both the elastic stress and the internal
# stress induced by the eigenstrain (E * alpha).
#
# In this test, the specimen is free of external stress (sigma = 0) so the creep deformation only derives from
# the eigenstrain. The total strain to be expected is:
#     epsilon = alpha * (1 + t / eta)
# Both the stress and the elastic strain are 0.
#
[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 1
  ny = 1
  nz = 1
  elem_type = HEX8
  displacements = 'disp_x disp_y disp_z'
[]

[Variables]
  [./disp_x]
    order = FIRST
    family = LAGRANGE
  [../]
  [./disp_y]
    order = FIRST
    family = LAGRANGE
  [../]
  [./disp_z]
    order = FIRST
    family = LAGRANGE
  [../]
[]

[AuxVariables]
  [./stress_xx]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./strain_xx]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./creep_strain_xx]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[Kernels]
  [./TensorMechanics]
    displacements = 'disp_x disp_y disp_z'
    use_displaced_mesh = true
  [../]
[]

[AuxKernels]
  [./stress_xx]
    type = RankTwoAux
    variable = stress_xx
    rank_two_tensor = stress
    index_j = 0
    index_i = 0
    execute_on = timestep_end
  [../]
  [./strain_xx]
    type = RankTwoAux
    variable = strain_xx
    rank_two_tensor = total_strain
    index_j = 0
    index_i = 0
    execute_on = timestep_end
  [../]
  [./creep_strain_xx]
    type = RankTwoAux
    variable = creep_strain_xx
    rank_two_tensor = creep_strain
    index_j = 0
    index_i = 0
    execute_on = timestep_end
  [../]
[]

[BCs]
  [./symmy]
    type = DirichletBC
    variable = disp_y
    boundary = bottom
    value = 0
  [../]
  [./symmx]
    type = DirichletBC
    variable = disp_x
    boundary = left
    value = 0
  [../]
  [./symmz]
    type = DirichletBC
    variable = disp_z
    boundary = back
    value = 0
  [../]
[]

[Materials]
  [./eigen]
    type = ComputeEigenstrain
    eigenstrain_name = eigen_true
    eigen_base = '1e-3 1e-3 1e-3 0 0 0'
  [../]
  [./kelvin_voigt]
    type = GeneralizedKelvinVoigtModel
    creep_modulus = ''
    creep_viscosity = '10'
    poisson_ratio = 0.2
    young_modulus = 10e9
    driving_eigenstrain = eigen_true
  [../]
  [./stress]
    type = ComputeMultipleInelasticStress
    inelastic_models = 'creep'
  [../]
  [./creep]
    type = LinearViscoelasticStressUpdate
  [../]
  [./strain]
    type = ComputeIncrementalSmallStrain
    displacements = 'disp_x disp_y disp_z'
    eigenstrain_names = 'eigen_true'
  [../]
[]

[UserObjects]
  [./update]
    type = LinearViscoelasticityManager
    viscoelastic_model = kelvin_voigt
  [../]
[]

[Postprocessors]
  [./stress_xx]
    type = ElementAverageValue
    variable = stress_xx
    block = 'ANY_BLOCK_ID 0'
  [../]
  [./strain_xx]
    type = ElementAverageValue
    variable = strain_xx
    block = 'ANY_BLOCK_ID 0'
  [../]
  [./creep_strain_xx]
    type = ElementAverageValue
    variable = creep_strain_xx
    block = 'ANY_BLOCK_ID 0'
  [../]
[]

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

[Executioner]
  type = Transient

  l_max_its  = 50
  l_tol      = 1e-8
  nl_max_its = 20
  nl_rel_tol = 1e-11
  nl_abs_tol = 1e-8

  dtmin = 0.01
  end_time = 100
  [./TimeStepper]
    type = LogConstantDT
    first_dt = 0.1
    log_dt = 0.1
  [../]

[]

[Outputs]
  file_base = gen_kv_driving_out
  exodus = true
[]