Rank Four Aux

Access a component of a RankFourTensor

Description

The AuxKernel RankFourAux is used to save single components of Rank-4 tensors into an AuxVariable for visualization and/or post-processing purposes, similar to the functionality provided by RankTwoAux for Rank-2 tensors RankFourAux is commonly used to output components of the elasticity (or stiffness) tensor, CijklC_{ijkl}, in mechanics simulations.

The RankFourAux takes as arguments the values of the index_i, index_j, index_k, and index_l for the single Rank-4 tensor component to save into an AuxVariable. Cijkl  ⟹  [C11C12C13C14C15C16C21C22C23C24C25C26C31C32C33C34C35C36C41C42C43C44C45C46C51C52C53C54C55C56C61C62C63C64C65C66]undefinedtextbook notation  ⟹  [C0000C0011C0022C0012C0020C0001C1100C1111C1122C1112C1120C1101C2200C2211C2222C2212C2220C2201C1200C1211C1222C1212C1220C1201C2000C2011C2022C2012C2020C2001C0100C0111C0122C0112C0120C0101]undefinedRank Four Aux indices \begin{aligned} C_{ijkl} \implies & \underbrace{\begin{bmatrix} C_{11} & C_{12} & C_{13} & C_{14} & C_{15} & C_{16} \\ C_{21} & C_{22} & C_{23} & C_{24} & C_{25} & C_{26} \\ C_{31} & C_{32} & C_{33} & C_{34} & C_{35} & C_{36} \\ C_{41} & C_{42} & C_{43} & C_{44} & C_{45} & C_{46} \\ C_{51} & C_{52} & C_{53} & C_{54} & C_{55} & C_{56} \\ C_{61} & C_{62} & C_{63} & C_{64} & C_{65} & C_{66} \end{bmatrix}}_{\text{textbook notation}} \\[5.0em] \implies & \underbrace{\begin{bmatrix} C_{0000} & C_{0011} & C_{0022} & C_{0012} & C_{0020} & C_{0001} \\ C_{1100} & C_{1111} & C_{1122} & C_{1112} & C_{1120} & C_{1101} \\ C_{2200} & C_{2211} & C_{2222} & C_{2212} & C_{2220} & C_{2201} \\ C_{1200} & C_{1211} & C_{1222} & C_{1212} & C_{1220} & C_{1201} \\ C_{2000} & C_{2011} & C_{2022} & C_{2012} & C_{2020} & C_{2001} \\ C_{0100} & C_{0111} & C_{0122} & C_{0112} & C_{0120} & C_{0101} \end{bmatrix}}_{\text{Rank Four Aux indices}} \end{aligned}(1) Eq. (1) shows the index values for a linear hyperelastic stiffness tensor with 21 independent material parameters; the various available elasticity tensor symmetry options is discussed in the material ComputeElasticityTensor documentation.

Example Input File Syntax

[./matl_C25]
  type = RankFourAux
  rank_four_tensor = elasticity_tensor
  index_i = 1
  index_j = 1
  index_k = 0
  index_l = 2
  variable = C25
[../]
(modules/combined/test/tests/linear_elasticity/tensor.i)

An AuxVariable is required to store the RankFourAux AuxKernel information. Note that the name of the AuxVariable is used as the argument for the variable input parameter in the RankFourAux block.

[./C25]
  order = CONSTANT
  family = MONOMIAL
[../]
(modules/combined/test/tests/linear_elasticity/tensor.i)

Input Parameters

  • index_iThe index i of ijkl for the tensor to output (0, 1, 2)

    C++ Type:unsigned int

    Controllable:No

    Description:The index i of ijkl for the tensor to output (0, 1, 2)

  • index_jThe index j of ijkl for the tensor to output (0, 1, 2)

    C++ Type:unsigned int

    Controllable:No

    Description:The index j of ijkl for the tensor to output (0, 1, 2)

  • index_kThe index k of ijkl for the tensor to output (0, 1, 2)

    C++ Type:unsigned int

    Controllable:No

    Description:The index k of ijkl for the tensor to output (0, 1, 2)

  • index_lThe index l of ijkl for the tensor to output (0, 1, 2)

    C++ Type:unsigned int

    Controllable:No

    Description:The index l of ijkl for the tensor to output (0, 1, 2)

  • rank_four_tensorThe rank four material tensor name

    C++ Type:MaterialPropertyName

    Unit:(no unit assumed)

    Controllable:No

    Description:The rank four material tensor name

  • variableThe name of the variable that this object applies to

    C++ Type:AuxVariableName

    Unit:(no unit assumed)

    Controllable:No

    Description:The name of the variable that this object applies to

Required Parameters

  • 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

  • check_boundary_restrictedTrueWhether to check for multiple element sides on the boundary in the case of a boundary restricted, element aux variable. Setting this to false will allow contribution to a single element's elemental value(s) from multiple boundary sides on the same element (example: when the restricted boundary exists on two or more sides of an element, such as at a corner of a mesh

    Default:True

    C++ Type:bool

    Controllable:No

    Description:Whether to check for multiple element sides on the boundary in the case of a boundary restricted, element aux variable. Setting this to false will allow contribution to a single element's elemental value(s) from multiple boundary sides on the same element (example: when the restricted boundary exists on two or more sides of an element, such as at a corner of a mesh

  • execute_onLINEAR TIMESTEP_ENDThe list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.

    Default:LINEAR TIMESTEP_END

    C++ Type:ExecFlagEnum

    Options:XFEM_MARK, FORWARD, ADJOINT, HOMOGENEOUS_FORWARD, ADJOINT_TIMESTEP_BEGIN, ADJOINT_TIMESTEP_END, NONE, INITIAL, LINEAR, NONLINEAR_CONVERGENCE, NONLINEAR, POSTCHECK, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM, PRE_DISPLACE

    Controllable:No

    Description:The list of flag(s) indicating when this object should be executed. For a description of each flag, see https://mooseframework.inl.gov/source/interfaces/SetupInterface.html.

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.

  • 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

  • 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