Stress Divergence RZ Tensors

Calculate stress divergence for an axisymmetric problem in cylindrical coordinates.

Description

The kernel StressDivergenceRZTensors solves the stress divergence equation for an Axisymmetric problem in the cylindrical coordinate system on a 2D mesh.

warningwarning:Symmetry Assumed About the -axis

The axis of symmetry must lie along the -axis in a or cylindrical coordinate system. This symmetry orientation is required for the calculation of the residual and of the jacobian, as defined in Eq. (1).

The StressDivergenceRZTensors kernel can be automatically created with the Solid Mechanics Physics. Use of the tensor mechanics quasi-static physics is recommended to ensure the consistent setting of the use_displaced_mesh parameter for the strain formulation selected. For a detailed explanation of the settings for _use_displaced_mesh_ in mechanics problems and the Solid Mechanics Physics usage, see the Introduction/Stress Divergence page.

Residual Calculation

The stress divergence kernel handles the calculation of the residual, , from the governing equation and the calculation of the Jacobian. From the strong form of the governing equation for mechanics, neglecting body forces, the weak form, using Galerkin's method and the Gauss divergence theorem, becomes in which is the test function. The second term of the weak form equation is the residual contribution calculated by the stress divergence kernel.

The calculation of the Jacobian can be approximated with the elasticity tensor if the simulation solve type is JFNK:

which is nonzero for .

If the solve type for the simulation is set to NEWTON the finite deformation Jacobian will need to be calculated. Set the parameter use_finite_deform_jacobian = true in this case.

commentnote:Use of the Solid Mechanics QuasiStatic Physics Recommended

The use_displaced_mesh parameter must be set correcting to ensure consistency in the equilibrium equation: if the stress is calculated with respect to the deformed mesh, the test function gradients must also be calculated with respect to the deformed mesh. The Solid Mechanics QuasiStatic Physics is designed to automatically determine and set the parameter correctly for the selected strain formulation. We recommend that users employ the Solid Mechanics QuasiStatic Physics whenever possible to ensure consistency between the test function gradients and the strain formulation selected.

In cylindrical coordinates, the divergence of a rank-2 tensor includes mixed term contributions. In the axisymmetric model we assume symmetric loading conditions, in addition to the zero out-of-plane shear strains, so that the residual computation is simplified.

(1)

The calculation of the Jacobian is similarly complex, requiring up to four terms in the calculation of the diagonal entries.

commentnote:Notation Order Change

The axisymmetric system changes the order of the displacement vector from , usually seen in textbooks, to . Take care to follow this convention in your input files and when adding extra stresses.

Example Input File

commentnote:Use RZ Coordinate Type

The coordinate type in the Problem block of the input file must be set to COORD_TYPE = RZ.

Using the solid mechanics quasi-static physics, as shown

[Physics]
  [SolidMechanics]
    [QuasiStatic]
      [./all]
        strain = FINITE
        add_variables = true
        block = 1
      [../]
    []
  []
[]
(moose/modules/solid_mechanics/test/tests/2D_geometries/2D-RZ_finiteStrain_test.i)

the StressDivergenceRZTensors kernel will be automatically built when the coordinate system in the Problem block is specified for the axisymmetric RZ system,

[Problem]
  coord_type = RZ
[]
(moose/modules/solid_mechanics/test/tests/2D_geometries/2D-RZ_finiteStrain_test.i)

and only two displacement variables are provided:

[GlobalParams]
  displacements = 'disp_r disp_z'
[]
(moose/modules/solid_mechanics/test/tests/2D_geometries/2D-RZ_finiteStrain_test.i)

Input Parameters

  • componentAn integer corresponding to the direction the variable this kernel acts in. (0 refers to the radial and 1 to the axial displacement.)

    C++ Type:unsigned int

    Unit:(no unit assumed)

    Controllable:No

    Description:An integer corresponding to the direction the variable this kernel acts in. (0 refers to the radial and 1 to the axial displacement.)

  • displacementsThe string of displacements suitable for the problem statement

    C++ Type:std::vector<VariableName>

    Unit:(no unit assumed)

    Controllable:No

    Description:The string of displacements suitable for the problem statement

  • variableThe name of the variable that this residual object operates on

    C++ Type:NonlinearVariableName

    Unit:(no unit assumed)

    Controllable:No

    Description:The name of the variable that this residual object operates on

Required Parameters

  • base_nameMaterial property base name

    C++ Type:std::string

    Unit:(no unit assumed)

    Controllable:No

    Description:Material property base name

  • blockThe list of blocks (ids or names) that this object will be applied

    C++ Type:std::vector<SubdomainName>

    Unit:(no unit assumed)

    Controllable:No

    Description:The list of blocks (ids or names) that this object will be applied

  • coupled_variablesVector of nonlinear variable arguments this object depends on

    C++ Type:std::vector<VariableName>

    Unit:(no unit assumed)

    Controllable:No

    Description:Vector of nonlinear variable arguments this object depends on

  • eigenstrain_namesList of eigenstrains used in the strain calculation. Used for computing their derivatives for off-diagonal Jacobian terms.

    C++ Type:std::vector<MaterialPropertyName>

    Unit:(no unit assumed)

    Controllable:No

    Description:List of eigenstrains used in the strain calculation. Used for computing their derivatives for off-diagonal Jacobian terms.

  • out_of_plane_directionzThe direction of the out_of_plane_strain variable used in the WeakPlaneStress kernel.

    Default:z

    C++ Type:MooseEnum

    Unit:(no unit assumed)

    Options:x, y, z

    Controllable:No

    Description:The direction of the out_of_plane_strain variable used in the WeakPlaneStress kernel.

  • out_of_plane_strainThe name of the out_of_plane_strain variable used in the WeakPlaneStress kernel.

    C++ Type:std::vector<VariableName>

    Unit:(no unit assumed)

    Controllable:No

    Description:The name of the out_of_plane_strain variable used in the WeakPlaneStress kernel.

  • 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.

  • temperatureThe name of the temperature variable used in the ComputeThermalExpansionEigenstrain. (Not required for simulations without temperature coupling.)

    C++ Type:std::vector<VariableName>

    Unit:(no unit assumed)

    Controllable:No

    Description:The name of the temperature variable used in the ComputeThermalExpansionEigenstrain. (Not required for simulations without temperature coupling.)

  • use_finite_deform_jacobianFalseJacobian for corotational finite strain

    Default:False

    C++ Type:bool

    Unit:(no unit assumed)

    Controllable:No

    Description:Jacobian for corotational finite strain

  • 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

    Unit:(no unit assumed)

    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.

  • volumetric_locking_correctionFalseSet to false to turn off volumetric locking correction

    Default:False

    C++ Type:bool

    Unit:(no unit assumed)

    Controllable:No

    Description:Set to false to turn off volumetric locking correction

Optional Parameters

  • absolute_value_vector_tagsThe tags for the vectors this residual object should fill with the absolute value of the residual contribution

    C++ Type:std::vector<TagName>

    Unit:(no unit assumed)

    Controllable:No

    Description:The tags for the vectors this residual object should fill with the absolute value of the residual contribution

  • extra_matrix_tagsThe extra tags for the matrices this Kernel should fill

    C++ Type:std::vector<TagName>

    Unit:(no unit assumed)

    Controllable:No

    Description:The extra tags for the matrices this Kernel should fill

  • extra_vector_tagsThe extra tags for the vectors this Kernel should fill

    C++ Type:std::vector<TagName>

    Unit:(no unit assumed)

    Controllable:No

    Description:The extra tags for the vectors this Kernel should fill

  • matrix_tagssystemThe tag for the matrices this Kernel should fill

    Default:system

    C++ Type:MultiMooseEnum

    Unit:(no unit assumed)

    Options:nontime, system

    Controllable:No

    Description:The tag for the matrices this Kernel should fill

  • vector_tagsnontimeThe tag for the vectors this Kernel should fill

    Default:nontime

    C++ Type:MultiMooseEnum

    Unit:(no unit assumed)

    Options:nontime, time

    Controllable:No

    Description:The tag for the vectors this Kernel should fill

Tagging Parameters

  • control_tagsAdds user-defined labels for accessing object parameters via control logic.

    C++ Type:std::vector<std::string>

    Unit:(no unit assumed)

    Controllable:No

    Description:Adds user-defined labels for accessing object parameters via control logic.

  • diag_save_inThe name of auxiliary variables to save this Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)

    C++ Type:std::vector<AuxVariableName>

    Unit:(no unit assumed)

    Controllable:No

    Description:The name of auxiliary variables to save this Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)

  • enableTrueSet the enabled status of the MooseObject.

    Default:True

    C++ Type:bool

    Unit:(no unit assumed)

    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

    Unit:(no unit assumed)

    Controllable:No

    Description:Determines whether this object is calculated using an implicit or explicit form

  • save_inThe name of auxiliary variables to save this Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)

    C++ Type:std::vector<AuxVariableName>

    Unit:(no unit assumed)

    Controllable:No

    Description:The name of auxiliary variables to save this Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)

  • seed0The seed for the master random number generator

    Default:0

    C++ Type:unsigned int

    Unit:(no unit assumed)

    Controllable:No

    Description:The seed for the master random number generator

  • use_displaced_meshTrueWhether 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:True

    C++ Type:bool

    Unit:(no unit assumed)

    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

The stress divergence family of automatic differentiation kernels