Cylindrical Rank Two Aux

Takes RankTwoTensor material and outputs component in cylindrical coordinates

Description

The AuxKernel CylindricalRankTwoAux transforms a Rank-2 tensor, $var element = document.getElementById("moose-equation-a803cd21-7798-42b7-bc72-2895b88a903b");katex.render("T", element, {displayMode:false,throwOnError:false});$ , into cylinderical coordinates, where the cylindrical rotation axis is along the Cartesian $var element = document.getElementById("moose-equation-b9f655c0-f41b-4703-a248-49afc882a41d");katex.render("\\hat{z}", element, {displayMode:false,throwOnError:false});$ axis and the user-defined center point lies within the Cartesian $var element = document.getElementById("moose-equation-c4a1e5b2-4ccc-4727-90c4-8ea26c301178");katex.render("\\hat{x}", element, {displayMode:false,throwOnError:false});$ - $var element = document.getElementById("moose-equation-3c8156a2-a271-42a0-bca3-c349078fd03e");katex.render("\\hat{y}", element, {displayMode:false,throwOnError:false});$ plane, as shown in Eq. (1). The AuxKernel will save the component of the tranformed Rank-2 tensor, $var element = document.getElementById("moose-equation-8c327df4-7167-4c2f-a940-1afb263f67ac");katex.render("T^R", element, {displayMode:false,throwOnError:false});$ , as defined by the arguments for the index_i and index_j parameters. $(1)var element = document.getElementById("moose-equation-237f3598-c462-4022-8fda-81564bedaf09");katex.render(" T^R_{ij} = \\boldsymbol{R} \\cdot \\boldsymbol{T} \\cdot \\boldsymbol{R}^T", element, {displayMode:true,throwOnError:false});$ The rotation tensor $var element = document.getElementById("moose-equation-92d66bdc-dede-48bd-837e-bb6e79a97000");katex.render("R", element, {displayMode:false,throwOnError:false});$ is defined as $(2)var element = document.getElementById("moose-equation-a8110915-f1be-441b-b8a0-6c47ad38e9c3");katex.render(" R = \\begin{bmatrix} cos(\\theta) & sin(\\theta) \\\\ -sin(\\theta) & cos(\\theta) \\end{bmatrix} \\quad \\text{ where } \\quad \\theta = atan2 \\left( \\frac{P^{qp}_y - P^c_y}{P^{qp}_x - P^c_x} \\right)", element, {displayMode:true,throwOnError:false});$ where $var element = document.getElementById("moose-equation-19062fb9-f060-4322-a584-a84dcad12150");katex.render("P^{qp}", element, {displayMode:false,throwOnError:false});$ is the location of the current quadrature point being evaluated and $var element = document.getElementById("moose-equation-f0ad29b9-62c5-40af-b150-7107ef778a39");katex.render("P^c", element, {displayMode:false,throwOnError:false});$ is the center point defined by the user with the parameter center_point in the input file.

Example Input File Syntax

[./stress_tt]
  type = CylindricalRankTwoAux
  variable = stress_tt
  rank_two_tensor = stress
  index_j = 1
  index_i = 1
  center_point = '0 0 0'
[../]

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

[./stress_tt]
  order = CONSTANT
  family = MONOMIAL
[../]

Input Parameters

center_pointLocation of the center point of the cylindrical coordinates
C++ Type:libMesh::Point
Controllable:No
Description:Location of the center point of the cylindrical coordinates
index_iThe index i of ij for the tensor to output (0, 1, 2)
C++ Type:unsigned int
Controllable:No
Description:The index i of ij for the tensor to output (0, 1, 2)
index_jThe index j of ij for the tensor to output (0, 1, 2)
C++ Type:unsigned int
Controllable:No
Description:The index j of ij for the tensor to output (0, 1, 2)
rank_two_tensorThe rank two material tensor name
C++ Type:MaterialPropertyName
Controllable:No
Description:The rank two material tensor name
variableThe name of the variable that this object applies to
C++ Type:AuxVariableName
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, the available options include NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM, ALWAYS, PRE_DISPLACE.
Default:LINEAR TIMESTEP_END
C++ Type:ExecFlagEnum
Options:NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM, ALWAYS, PRE_DISPLACE
Controllable:No
Description:The list of flag(s) indicating when this object should be executed, the available options include NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, MULTIAPP_FIXED_POINT_END, MULTIAPP_FIXED_POINT_BEGIN, FINAL, CUSTOM, ALWAYS, PRE_DISPLACE.
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.
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

(moose/modules/tensor_mechanics/test/tests/CylindricalRankTwoAux/test.i)

[Mesh]
  [file_mesh]
    type = FileMeshGenerator
    file = circle.e
  []
  [cnode]
    type = ExtraNodesetGenerator
    coord = '1000.0 0.0'
    new_boundary = 10
    input = file_mesh
  []
[]

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

[AuxVariables]
  [./T]
  [../]
  [./stress_rr]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./stress_tt]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[ICs]
  [./T_IC]
    type = FunctionIC
    variable = T
    function = '1000-0.7*sqrt(x^2+y^2)'
  [../]
[]

[Kernels]
  [./TensorMechanics]
    displacements = 'disp_x disp_y'
  [../]
[]

[AuxKernels]
  [./stress_rr]
    type = CylindricalRankTwoAux
    variable = stress_rr
    rank_two_tensor = stress
    index_j = 0
    index_i = 0
    center_point = '0 0 0'
  [../]
  [./stress_tt]
    type = CylindricalRankTwoAux
    variable = stress_tt
    rank_two_tensor = stress
    index_j = 1
    index_i = 1
    center_point = '0 0 0'
  [../]
[]

[BCs]
  [./outer_x]
    type = DirichletBC
    variable = disp_x
    boundary = 2
    value = 0
  [../]
  [./outer_y]
    type = DirichletBC
    variable = disp_y
    boundary = '2 10'
    value = 0
  [../]
[]

[Materials]
  [./iso_C]
    type = ComputeElasticityTensor
    fill_method = symmetric_isotropic
    C_ijkl = '2.15e5 0.74e5'
    block = 1
  [../]
  [./strain]
    type = ComputeSmallStrain
    displacements = 'disp_x disp_y'
    block = 1
    eigenstrain_names = eigenstrain
  [../]
  [./stress]
    type = ComputeLinearElasticStress
    block = 1
  [../]
  [./thermal_strain]
    type= ComputeThermalExpansionEigenstrain
    thermal_expansion_coeff = 1e-6
    temperature = T
    stress_free_temperature = 273
    block = 1
    eigenstrain_name = eigenstrain
  [../]
[]

[Executioner]
  type = Steady
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type -ksp_gmres_restart'
  petsc_options_value = 'hypre boomeramg 101'
  l_max_its = 30
  nl_max_its = 10
  nl_abs_tol = 1e-9
  nl_rel_tol = 1e-14
  l_tol = 1e-4
[]

[Outputs]
  exodus = true
  perf_graph = true
[]

(moose/modules/tensor_mechanics/test/tests/CylindricalRankTwoAux/test.i)

[Mesh]
  [file_mesh]
    type = FileMeshGenerator
    file = circle.e
  []
  [cnode]
    type = ExtraNodesetGenerator
    coord = '1000.0 0.0'
    new_boundary = 10
    input = file_mesh
  []
[]

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

[AuxVariables]
  [./T]
  [../]
  [./stress_rr]
    order = CONSTANT
    family = MONOMIAL
  [../]
  [./stress_tt]
    order = CONSTANT
    family = MONOMIAL
  [../]
[]

[ICs]
  [./T_IC]
    type = FunctionIC
    variable = T
    function = '1000-0.7*sqrt(x^2+y^2)'
  [../]
[]

[Kernels]
  [./TensorMechanics]
    displacements = 'disp_x disp_y'
  [../]
[]

[AuxKernels]
  [./stress_rr]
    type = CylindricalRankTwoAux
    variable = stress_rr
    rank_two_tensor = stress
    index_j = 0
    index_i = 0
    center_point = '0 0 0'
  [../]
  [./stress_tt]
    type = CylindricalRankTwoAux
    variable = stress_tt
    rank_two_tensor = stress
    index_j = 1
    index_i = 1
    center_point = '0 0 0'
  [../]
[]

[BCs]
  [./outer_x]
    type = DirichletBC
    variable = disp_x
    boundary = 2
    value = 0
  [../]
  [./outer_y]
    type = DirichletBC
    variable = disp_y
    boundary = '2 10'
    value = 0
  [../]
[]

[Materials]
  [./iso_C]
    type = ComputeElasticityTensor
    fill_method = symmetric_isotropic
    C_ijkl = '2.15e5 0.74e5'
    block = 1
  [../]
  [./strain]
    type = ComputeSmallStrain
    displacements = 'disp_x disp_y'
    block = 1
    eigenstrain_names = eigenstrain
  [../]
  [./stress]
    type = ComputeLinearElasticStress
    block = 1
  [../]
  [./thermal_strain]
    type= ComputeThermalExpansionEigenstrain
    thermal_expansion_coeff = 1e-6
    temperature = T
    stress_free_temperature = 273
    block = 1
    eigenstrain_name = eigenstrain
  [../]
[]

[Executioner]
  type = Steady
  solve_type = PJFNK
  petsc_options_iname = '-pc_type -pc_hypre_type -ksp_gmres_restart'
  petsc_options_value = 'hypre boomeramg 101'
  l_max_its = 30
  nl_max_its = 10
  nl_abs_tol = 1e-9
  nl_rel_tol = 1e-14
  l_tol = 1e-4
[]

[Outputs]
  exodus = true
  perf_graph = true
[]