Compute Incremental Small Strain

Compute a strain increment and rotation increment for small strains.

Description

The material ComputeIncrementalSmallStrain is designed for linear elasticity problems formulated within an incremental framework. As with ComputeSmallStrain, this material is useful for verifying material models with hand calculations because of the simplified strain calculations. As in the small strain material, the incremental small strain class assumes the gradient of displacement with respect to position is much smaller than unity, and the squared displacement gradient term is neglected in the small strain definition to give: $var element = document.getElementById("moose-equation-645d36dd-ab82-4cb0-b26c-649b3f83d1a0");katex.render("\\epsilon = \\frac{1}{2} \\left( u \\nabla + \\nabla u \\right) \\quad when \\quad \\frac{\\partial u}{ \\partial x} << 1", 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}"}});$ As the class name suggests, ComputeIncrementalSmallStrain is an incremental formulation. The stress increment is calculated from the current strain increment at each time step. In this class, the rotation tensor is defined to be the rank-2 Identity tensor: no rotations are allowed in the model. Stateful properties, including strain_old and stress_old, are stored. This incremental small strain material is useful as a component of verifying more complex finite incremental strain-stress calculations.

Example Input File Syntax

The incremental small strain calculator can be activated in the input file through the use of the TensorMechanics Master Action, as shown below.

[./TensorMechanics]
  [./Master]
    [./all]
      strain = SMALL
      incremental = true
      add_variables = true
      eigenstrain_names = eigenstrain
      generate_output = 'strain_xx strain_yy strain_zz'
    [../]
  [../]
[../]

note:Use of the Tensor Mechanics Master Action Recommended

The TensorMechanics Master Action is designed to automatically determine and set the strain and stress divergence parameters correctly for the selected strain formulation. We recommend that users employ the TensorMechanics Master Action whenever possible to ensure consistency between the test function gradients and the strain formulation selected.

Although not recommended, it is possible to directly use the ComputeIncrementalSmallStrain material in the input file.

[./small_strain]
  type = ComputeIncrementalSmallStrain
  eigenstrain_names = 'eigenstrain1 eigenstrain2'
[../]

Input Parameters

displacementsThe displacements appropriate for the simulation geometry and coordinate system
C++ Type:std::vector<VariableName>
Controllable:No
Description:The displacements appropriate for the simulation geometry and coordinate system

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.
eigenstrain_namesList of eigenstrains to be applied in this strain calculation
C++ Type:std::vector<MaterialPropertyName>
Controllable:No
Description:List of eigenstrains to be applied in this strain calculation
global_strainOptional material property holding a global strain tensor applied to the mesh as a whole
C++ Type:MaterialPropertyName
Controllable:No
Description:Optional material property holding a global strain tensor applied to the mesh as a whole
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.
volumetric_locking_correctionFalseFlag to correct volumetric locking
Default:False
C++ Type:bool
Controllable:No
Description:Flag to correct volumetric locking

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

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

(../moose/modules/tensor_mechanics/test/tests/thermal_expansion/constant_expansion_coeff.i)

# This test involves only thermal expansion strains on a 2x2x2 cube of approximate
# steel material.  An initial temperature of 25 degrees C is given for the material,
# and an auxkernel is used to calculate the temperature in the entire cube to
# raise the temperature each time step.  After the first timestep,in which the
# temperature jumps, the temperature increases by 6.25C each timestep.
# The thermal strain increment should therefore be
#     6.25 C * 1.3e-5 1/C = 8.125e-5 m/m.

# This test is also designed to be used to identify problems with restart files

[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 2
  ny = 2
  nz = 2
[]

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
[]

[AuxVariables]
  [./temp]
  [../]
[]

[Functions]
  [./temperature_load]
    type = ParsedFunction
    expression = t*(500.0)+300.0
  [../]
[]

[Modules]
  [./TensorMechanics]
    [./Master]
      [./all]
        strain = SMALL
        incremental = true
        add_variables = true
        eigenstrain_names = eigenstrain
        generate_output = 'strain_xx strain_yy strain_zz'
      [../]
    [../]
  [../]
[]

[AuxKernels]
  [./tempfuncaux]
    type = FunctionAux
    variable = temp
    function = temperature_load
  [../]
[]

[BCs]
  [./x_bot]
    type = DirichletBC
    variable = disp_x
    boundary = left
    value = 0.0
  [../]
  [./y_bot]
    type = DirichletBC
    variable = disp_y
    boundary = bottom
    value = 0.0
  [../]
  [./z_bot]
    type = DirichletBC
    variable = disp_z
    boundary = back
    value = 0.0
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 2.1e5
    poissons_ratio = 0.3
  [../]
  [./small_stress]
    type = ComputeFiniteStrainElasticStress
  [../]
  [./thermal_expansion_strain]
    type = ComputeThermalExpansionEigenstrain
    stress_free_temperature = 298
    thermal_expansion_coeff = 1.3e-5
    temperature = temp
    eigenstrain_name = eigenstrain
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  l_max_its = 50
  nl_max_its = 50
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-10
  l_tol = 1e-9

  start_time = 0.0
  end_time = 0.075
  dt = 0.0125
  dtmin = 0.0001
[]

[Outputs]
  exodus = true
  checkpoint = true
[]

[Postprocessors]
  [./strain_xx]
    type = ElementAverageValue
    variable = strain_xx
  [../]
  [./strain_yy]
    type = ElementAverageValue
    variable = strain_yy
  [../]
  [./strain_zz]
    type = ElementAverageValue
    variable = strain_zz
  [../]
  [./temperature]
    type = AverageNodalVariableValue
    variable = temp
  [../]
[]

(../moose/modules/tensor_mechanics/test/tests/thermal_expansion/multiple_thermal_eigenstrains.i)

# The primary purpose of this test is to verify that the ability to combine
# multiple eigenstrains works correctly.  It should behave identically to the
# constant_expansion_coeff.i model in this directory. Instead of applying the
# thermal expansion in one eigenstrain, it splits that into two eigenstrains
# that get added together.

# This test involves only thermal expansion strains on a 2x2x2 cube of approximate
# steel material.  An initial temperature of 25 degrees C is given for the material,
# and an auxkernel is used to calculate the temperature in the entire cube to
# raise the temperature each time step.  After the first timestep,in which the
# temperature jumps, the temperature increases by 6.25C each timestep.
# The thermal strain increment should therefore be
#     6.25 C * 1.3e-5 1/C = 8.125e-5 m/m.

[Mesh]
  type = GeneratedMesh
  dim = 3
  nx = 2
  ny = 2
  nz = 2
[]

[GlobalParams]
  displacements = 'disp_x disp_y disp_z'
[]

[Variables]
  [./disp_x]
  [../]
  [./disp_y]
  [../]
  [./disp_z]
  [../]
[]

[AuxVariables]
  [./temp]
  [../]

  [./strain_yy]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./strain_xx]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./strain_zz]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[Functions]
  [./temperature_load]
    type = ParsedFunction
    expression = t*(500.0)+300.0
  [../]
[]

[Kernels]
  [./TensorMechanics]
    use_displaced_mesh = true
  [../]
[]

[AuxKernels]
  [./tempfuncaux]
    type = FunctionAux
    variable = temp
    function = temperature_load
    use_displaced_mesh = false
  [../]

  [./strain_xx]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = strain_xx
    index_i = 0
    index_j = 0
  [../]
  [./strain_yy]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = strain_yy
    index_i = 1
    index_j = 1
  [../]
  [./strain_zz]
    type = RankTwoAux
    rank_two_tensor = total_strain
    variable = strain_zz
    index_i = 2
    index_j = 2
  [../]
[]

[BCs]
  [./x_bot]
    type = DirichletBC
    variable = disp_x
    boundary = left
    value = 0.0
  [../]
  [./y_bot]
    type = DirichletBC
    variable = disp_y
    boundary = bottom
    value = 0.0
  [../]
  [./z_bot]
    type = DirichletBC
    variable = disp_z
    boundary = back
    value = 0.0
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 2.1e5
    poissons_ratio = 0.3
  [../]
  [./small_strain]
    type = ComputeIncrementalSmallStrain
    eigenstrain_names = 'eigenstrain1 eigenstrain2'
  [../]
  [./small_stress]
    type = ComputeFiniteStrainElasticStress
  [../]
  [./thermal_expansion_strain1]
    type = ComputeThermalExpansionEigenstrain
    stress_free_temperature = 298
    thermal_expansion_coeff = 1.0e-5
    temperature = temp
    eigenstrain_name = eigenstrain1
    mean_thermal_expansion_coefficient_name = mean1
  [../]
  [./thermal_expansion_strain2]
    type = ComputeThermalExpansionEigenstrain
    stress_free_temperature = 298
    thermal_expansion_coeff = 0.3e-5
    temperature = temp
    eigenstrain_name = eigenstrain2
    mean_thermal_expansion_coefficient_name = mean2
  [../]
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  l_max_its = 50
  nl_max_its = 50
  nl_rel_tol = 1e-12
  nl_abs_tol = 1e-10
  l_tol = 1e-9

  start_time = 0.0
  end_time = 0.075
  dt = 0.0125
  dtmin = 0.0001
[]

[Outputs]
  exodus = true
  checkpoint = true
[]

[Postprocessors]
  [./strain_xx]
    type = ElementAverageValue
    variable = strain_xx
    block = 0
  [../]
  [./strain_yy]
    type = ElementAverageValue
    variable = strain_yy
    block = 0
  [../]
  [./strain_zz]
    type = ElementAverageValue
    variable = strain_zz
    block = 0
  [../]
  [./temperature]
    type = AverageNodalVariableValue
    variable = temp
    block = 0
  [../]
[]