Compute Elasticity Tensor CP

Compute an elasticity tensor for crystal plasticity.

Description

The material ComputeElasticityTensorCP is used to create an elasticity tensor for crystal plasticity simulations. This material builds an orthotropic elasticity tensor using the fill_method symmetric9 from ComputeElasticityTensor. ComputeElasticityTensorCP rotates the elasticity tensor both during the initial setup step, if Euler angles are provided, and at the start of each timestep.

warning:Crystal Plasticity Simulations use Active Rotation

The rotation matrix used in this class,ComputeElasticityTensorCP, is the transpose of the rotation matrix created from the Bunge Euler angles in the base class, ComputeElasticityTensor. This difference in the rotation matrix is because of the active rotation convention used in crystal plasticity simulations.

The fill method symmetric9 is appropriate for materials with three orthotropic planes of symmetry (Malvern, 1969), and is used for simulations of anistropic materials such as cubic crystals. The engineering elasticity tensor notation for an orthotropic material is given in Eq. (1): $(1)var element = document.getElementById("moose-equation-9d2edd95-f1b2-4d75-9732-e8dd31192521");katex.render(" C_{ijkl} = \\begin{bmatrix} C_{11} & C_{12} & C_{13} & 0 & 0 & 0 \\\\ C_{12} & C_{22} & C_{23} & 0 & 0 & 0 \\\\ C_{13} & C_{23} & C_{33} & 0 & 0 & 0 \\\\ 0 & 0 & 0 & C_{44} & 0 & 0 \\\\ 0 & 0 & 0 & 0 & C_{55} & 0 \\\\ 0 & 0 & 0 & 0 & 0 & C_{66} \\end{bmatrix}", element, {displayMode:true,throwOnError:false});$

Rotation Tensor Conventions

The Euler angle convention used in ComputeElasticityTensorCP is the $var element = document.getElementById("moose-equation-320cce67-b13d-4658-8938-85bf0e7eef7c");katex.render("z", element, {displayMode:false,throwOnError:false});$ - $var element = document.getElementById("moose-equation-285c7d34-fb91-4fb0-980c-765f7053331a");katex.render("x'", element, {displayMode:false,throwOnError:false});$ - $var element = document.getElementById("moose-equation-4b6a7bfb-6ea4-40c2-b9bc-1043d798c765");katex.render("z'", element, {displayMode:false,throwOnError:false});$ (3-1-3) convention. The Euler angles arguments are expected in degrees, not radians, and are denoted as $var element = document.getElementById("moose-equation-cb0a0f5a-791f-4551-9432-ef928ea10285");katex.render("\\phi_1", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-eb014488-504a-4f2f-b64d-67f33a7295dd");katex.render("\\Phi", element, {displayMode:false,throwOnError:false});$ , and $var element = document.getElementById("moose-equation-084954ee-f7d4-44b3-bce8-9188af5a00f1");katex.render("\\phi_2", element, {displayMode:false,throwOnError:false});$ , corresponding to the axis rotations. The rotation tensor, $var element = document.getElementById("moose-equation-440b440a-e724-44a9-9441-c5a7056a09ec");katex.render("R", element, {displayMode:false,throwOnError:false});$ , is calculated from the current Euler angles at each timestep as shown in Eq. (2). $(2)var element = document.getElementById("moose-equation-5c68f1bf-e52f-4275-9fd7-a21ae2121757");katex.render(" \\begin{aligned} R_{11} & = cos(\\phi_1)cos(\\phi_2) - cos(\\Phi)sin(\\phi_1)sin(\\phi_2) \\\\ R_{12} & = -cos(\\phi_1)sin(\\phi_2) - cos(\\Phi)cos(\\phi_2)sin(\\phi_1) \\\\ R_{13} & = sin(\\phi_1)sin(\\Phi) \\\\ R_{21} & = cos(\\phi_2)sin(\\phi_1) + cos(\\phi_1)cos(\\Phi)sin(\\phi_2) \\\\ R_{22} & = -sin(\\phi_1)sin(\\phi_2) + cos(\\phi_1)cos(\\Phi)cos(\\phi_2) \\\\ R_{23} & = -cos(\\phi_1)sin(\\Phi) \\\\ R_{31} & = sin(\\Phi) sin(\\phi_2) \\\\ R_{32} & = cos(\\phi_2) sin(\\Phi) \\\\ R_{33} & = cos(\\Phi) \\end{aligned}", element, {displayMode:true,throwOnError:false});$ The elasticity tensor is then rotated with Eq. (3) $(3)var element = document.getElementById("moose-equation-15c63c68-dcdc-475d-9111-ade114d4f5cd");katex.render(" C'_{ijkl} = R^T_{im} R^T_{jn} R^T_{ko} R^T_{lp} C_{mnop}", element, {displayMode:true,throwOnError:false});$ at the beginning of each material timestep calculation.

The crystal plasticity materials, including ComputeElasticityTensorCP employ an active rotation: the crystal system is rotated into the sample (loading) coordinate system. Generally the Bunge Euler angles are used to describe a passive rotation: rotating the sample coordinate system into the crystal coordinate system. As a result, the rotation tensor applied is the transpose of the rotation tensor given in Eq. (2) as noted in Eq. (3).

As in the base class ComputeElasticityTensor, ComputeElasticityTensorCP can also accept the rotation matrix, given as a series of nine entries. As with the Euler angle input parameter values, note that this crystal plasticity class uses the "passive" rotation convention.

Example Input File Syntax

[./elasticity_tensor]
  type = ComputeElasticityTensorCP
  C_ijkl = '1.684e5 1.214e5 1.214e5 1.684e5 1.214e5 1.684e5 0.754e5 0.754e5 0.754e5'
  fill_method = symmetric9
[../]

Input Parameters

C_ijklStiffness tensor for material
C++ Type:std::vector<double>
Controllable:No
Description:Stiffness tensor for material

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.
elasticity_tensor_prefactorOptional function to use as a scalar prefactor on the elasticity tensor.
C++ Type:FunctionName
Controllable:No
Description:Optional function to use as a scalar prefactor on the elasticity tensor.
euler_angle_10Euler angle in direction 1
Default:0
C++ Type:double
Controllable:No
Description:Euler angle in direction 1
euler_angle_20Euler angle in direction 2
Default:0
C++ Type:double
Controllable:No
Description:Euler angle in direction 2
euler_angle_30Euler angle in direction 3
Default:0
C++ Type:double
Controllable:No
Description:Euler angle in direction 3
fill_methodsymmetric9The fill method
Default:symmetric9
C++ Type:MooseEnum
Options:antisymmetric, symmetric9, symmetric21, general_isotropic, symmetric_isotropic, symmetric_isotropic_E_nu, antisymmetric_isotropic, axisymmetric_rz, general, principal, orthotropic
Controllable:No
Description:The fill method
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.
read_prop_user_objectThe ElementReadPropertyFile GeneralUserObject to read element specific property values from file
C++ Type:UserObjectName
Controllable:No
Description:The ElementReadPropertyFile GeneralUserObject to read element specific property values from file
rotation_matrixRotation matrix to apply to elasticity tensor.
C++ Type:libMesh::TensorValue<double>
Controllable:No
Description:Rotation matrix to apply to 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

References

Lawrence E Malvern. Introduction to the Mechanics of a Continuous Medium. Prentice-Hall, 1969.

(moose/modules/tensor_mechanics/test/tests/crystal_plasticity/stress_update_material_based/update_method_test.i)

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

[Mesh]
  type = GeneratedMesh
  dim = 3
  elem_type = HEX8
[]

[AuxVariables]
  [./pk2]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./fp_zz]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./e_zz]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./gss]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./slip_increment]
   order = CONSTANT
   family = MONOMIAL
  [../]
[]

[Modules/TensorMechanics/Master/all]
  strain = FINITE
  add_variables = true
  generate_output = stress_zz
[]

[AuxKernels]
  [./pk2]
   type = RankTwoAux
   variable = pk2
   rank_two_tensor = second_piola_kirchhoff_stress
   index_j = 2
   index_i = 2
   execute_on = timestep_end
  [../]
  [./fp_zz]
    type = RankTwoAux
    variable = fp_zz
    rank_two_tensor = plastic_deformation_gradient
    index_j = 2
    index_i = 2
    execute_on = timestep_end
  [../]
  [./e_zz]
    type = RankTwoAux
    variable = e_zz
    rank_two_tensor = total_lagrangian_strain
    index_j = 2
    index_i = 2
    execute_on = timestep_end
  [../]
  [./gss]
   type = MaterialStdVectorAux
   variable = gss
   property = slip_resistance
   index = 0
   execute_on = timestep_end
  [../]
  [./slip_inc]
   type = MaterialStdVectorAux
   variable = slip_increment
   property = slip_increment
   index = 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
  [../]
  [./tdisp]
    type = FunctionDirichletBC
    variable = disp_z
    boundary = front
    function = '0.01*t'
  [../]
[]

[Materials]
  [./elasticity_tensor]
    type = ComputeElasticityTensorCP
    C_ijkl = '1.684e5 1.214e5 1.214e5 1.684e5 1.214e5 1.684e5 0.754e5 0.754e5 0.754e5'
    fill_method = symmetric9
  [../]
  [./stress]
    type = ComputeMultipleCrystalPlasticityStress
    crystal_plasticity_models = 'trial_xtalpl'
    tan_mod_type = exact
  [../]
  [./trial_xtalpl]
    type = CrystalPlasticityKalidindiUpdate
    number_slip_systems = 12
    slip_sys_file_name = input_slip_sys.txt
  [../]
[]

[Postprocessors]
  [./stress_zz]
    type = ElementAverageValue
    variable = stress_zz
  [../]
  [./pk2]
   type = ElementAverageValue
   variable = pk2
  [../]
  [./fp_zz]
    type = ElementAverageValue
    variable = fp_zz
  [../]
  [./e_zz]
    type = ElementAverageValue
    variable = e_zz
  [../]
  [./gss]
    type = ElementAverageValue
    variable = gss
  [../]
  [./slip_increment]
   type = ElementAverageValue
   variable = slip_increment
  [../]
[]

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

[Executioner]
  type = Transient
  solve_type = 'PJFNK'

  petsc_options_iname = '-pc_type -pc_asm_overlap -sub_pc_type -ksp_type -ksp_gmres_restart'
  petsc_options_value = ' asm      2              lu            gmres     200'
  nl_abs_tol = 1e-10
  nl_rel_tol = 1e-10
  nl_abs_step_tol = 1e-10

  dt = 0.05
  dtmin = 0.01
  dtmax = 10.0
  num_steps = 10
[]

[Outputs]
  exodus = true
[]