Stress Divergence RSpherical Tensors

Calculate stress divergence for a spherically symmetric 1D problem in polar coordinates.

Description

The kernel StressDivergenceRSphericalTensors solves the stress divergence equation for a spherically symmetric system on a 1D mesh.

commentnote

The COORD_TYPE in the Problem block of the input file must be set to RSPHERICAL.

The StressDivergenceRSphericalTensors 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/StressDivergence 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.

The stress divergence in spherical coordinates includes contributions from the normal polar and azimuthal stresses even in the 1D case. After simplifying for the 1D case, the spherical stress divergence reduces to (1)

In deriving the weak form of this equation, the second term in Eq. (1) goes to zero and the residual contribution in the StressDivergenceRSphericalTensors kernel becomes

Example Input File syntax

Using the solid mechanics quasi-static physics, as shown

[Physics]
  [SolidMechanics]
    [QuasiStatic]
      [all]
        strain = FINITE
        add_variables = true
        spherical_center_point = '4.0 0.0 0.0'
        generate_output = 'spherical_radial_stress'
      []
    []
  []
[]
(modules/solid_mechanics/test/tests/1D_spherical/finiteStrain_1DSphere_hollow.i)

the StressDivergenceRSphericalTensors kernel will be automatically built when the coordinate system in the Problem block is specified for the spherical system,

[Problem]
  coord_type = RSPHERICAL
[]
(modules/solid_mechanics/test/tests/1D_spherical/finiteStrain_1DSphere_hollow.i)

and only a single displacement variable is provided:

[GlobalParams]
  displacements = 'disp_r'
[]
(modules/solid_mechanics/test/tests/1D_spherical/finiteStrain_1DSphere_hollow.i)

Input Parameters

  • component0An integer corresponding to the direction the variable this kernel acts in. (0 for x, 1 for y, 2 for z)

    Default:0

    C++ Type:unsigned int

    Controllable:No

    Description:An integer corresponding to the direction the variable this kernel acts in. (0 for x, 1 for y, 2 for z)

  • displacementsThe string of displacements suitable for the problem statement

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

    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

    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

    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>

    Controllable:No

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

  • coupled_variables

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

    Controllable:No

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

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

    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

    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>

    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

    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>

    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

    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

    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

    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>

    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>

    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>

    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

    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

    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>

    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>

    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

    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

  • 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>

    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

    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

    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

Input Files