TotalLagrangianStressDivergenceCentrosymmetricSpherical

Enforce equilibrium with a total Lagrangian formulation in centrosymmetric spherical coordinates.

Overview

This kernel functions the same way as TotalLagrangianStressDivergence. The only difference is that this kernel enforces equilibrium in the 1D centrosymmetric spherical coordinates. See this page for the definition of the gradient operator in the 1D centrosymmetric spherical coordinates.

Input Parameters

componentWhich direction this kernel acts in
C++ Type:unsigned int
Controllable:No
Description:Which direction this kernel acts in
displacementsThe displacement components
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The displacement components
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
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
compute_field_residualsTrueWhether to compute residuals for the field variable.
Default:True
C++ Type:bool
Controllable:No
Description:Whether to compute residuals for the field variable.
compute_scalar_residualsTrueWhether to compute scalar residuals
Default:True
C++ Type:bool
Controllable:No
Description:Whether to compute scalar residuals
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.
large_kinematicsFalseUse large displacement kinematics
Default:False
C++ Type:bool
Controllable:No
Description:Use large displacement kinematics
matrix_onlyFalseWhether this object is only doing assembly to matrices (no vectors)
Default:False
C++ Type:bool
Controllable:No
Description:Whether this object is only doing assembly to matrices (no vectors)
out_of_plane_strainThe out-of-plane strain variable for weak plane stress formulation.
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The out-of-plane strain variable for weak plane stress formulation.
scalar_variablePrimary coupled scalar variable
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Primary coupled scalar variable
stabilize_strainFalseAverage the volumetric strains
Default:False
C++ Type:bool
Controllable:No
Description:Average the volumetric strains
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.)

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

Contribution To Tagged Field Data 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>
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
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>
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.)
search_methodnearest_node_connected_sidesChoice of search algorithm. All options begin by finding the nearest node in the primary boundary to a query point in the secondary boundary. In the default nearest_node_connected_sides algorithm, primary boundary elements are searched iff that nearest node is one of their nodes. This is fast to determine via a pregenerated node-to-elem map and is robust on conforming meshes. In the optional all_proximate_sides algorithm, primary boundary elements are searched iff they touch that nearest node, even if they are not topologically connected to it. This is more CPU-intensive but is necessary for robustness on any boundary surfaces which has disconnections (such as Flex IGA meshes) or non-conformity (such as hanging nodes in adaptively h-refined meshes).
Default:nearest_node_connected_sides
C++ Type:MooseEnum
Options:nearest_node_connected_sides, all_proximate_sides
Controllable:No
Description:Choice of search algorithm. All options begin by finding the nearest node in the primary boundary to a query point in the secondary boundary. In the default nearest_node_connected_sides algorithm, primary boundary elements are searched iff that nearest node is one of their nodes. This is fast to determine via a pregenerated node-to-elem map and is robust on conforming meshes. In the optional all_proximate_sides algorithm, primary boundary elements are searched iff they touch that nearest node, even if they are not topologically connected to it. This is more CPU-intensive but is necessary for robustness on any boundary surfaces which has disconnections (such as Flex IGA meshes) or non-conformity (such as hanging nodes in adaptively h-refined meshes).
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

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

(modules/solid_mechanics/test/tests/lagrangian/centrosymmetric_spherical/total/analytical/small.i)
(modules/solid_mechanics/test/tests/lagrangian/centrosymmetric_spherical/total/jacobian/dirichlet.i)
(modules/solid_mechanics/test/tests/lagrangian/centrosymmetric_spherical/total/thermal_expansion/jactest.i)
(modules/solid_mechanics/test/tests/lagrangian/centrosymmetric_spherical/total/jacobian/neumann.i)

(modules/solid_mechanics/test/tests/lagrangian/centrosymmetric_spherical/total/analytical/small.i)

# This test aims to verify the implementation by comparing the numerical solution
# to the analytical solution. The analytical solution for a hollow sphere is used in
# this test. Given inner pressure p = 100, inner radius a = 2, outer radius b = 4,
# the stress and displacements at the middle of the cylinder
# (r = 3) should be
# sigma_rr = -19.57
# sigma_tt = sigma_pp = 31.22
# u_r = 0.08492

# The numerical approximation yields
# sigma_rr = -19.92
# sigma_tt = sigma_pp = 31.39
# u_r = 0.08492

[GlobalParams]
  displacements = 'disp_r'
  large_kinematics = false
[]

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 1
    xmin = 2
    xmax = 4
    nx = 100
  []
  coord_type = RSPHERICAL
[]

[Variables]
  [disp_r]
  []
[]

[Kernels]
  [sdr]
    type = TotalLagrangianStressDivergenceCentrosymmetricSpherical
    variable = disp_r
    component = 0
  []
[]

[BCs]
  [inner]
    type = NeumannBC
    variable = disp_r
    boundary = left
    value = 100
  []
[]

[Materials]
  [elastic_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 1000.0
    poissons_ratio = 0.25
  []
  [compute_stress]
    type = ComputeLagrangianLinearElasticStress
    output_properties = 'cauchy_stress'
    outputs = 'exodus'
  []
  [compute_strain]
    type = ComputeLagrangianStrainCentrosymmetricSpherical
  []
[]

[Postprocessors]
  [u_r]
    type = PointValue
    variable = disp_r
    point = '3 0 0'
  []
  [sigma_rr]
    type = PointValue
    variable = cauchy_stress_00
    point = '3 0 0'
  []
  [sigma_tt]
    type = PointValue
    variable = cauchy_stress_11
    point = '3 0 0'
  []
[]

[Executioner]
  type = Transient

  solve_type = NEWTON

  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  automatic_scaling = true

  nl_abs_tol = 1e-10
  nl_rel_tol = 1e-10

  num_steps = 1
[]

[Outputs]
  exodus = true
[]

(modules/solid_mechanics/test/tests/lagrangian/centrosymmetric_spherical/total/jacobian/dirichlet.i)

[GlobalParams]
  displacements = 'disp_r'
  large_kinematics = true
  stabilize_strain = true
[]

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 1
    nx = 5
  []
  coord_type = RSPHERICAL
[]

[Variables]
  [disp_r]
  []
[]

[Kernels]
  [sdr]
    type = TotalLagrangianStressDivergenceCentrosymmetricSpherical
    variable = disp_r
    component = 0
  []
[]

[BCs]
  [left]
    type = DirichletBC
    preset = false
    variable = disp_r
    boundary = left
    value = 0.0
  []
  [right]
    type = FunctionDirichletBC
    preset = false
    variable = disp_r
    boundary = right
    function = 't'
  []
[]

[Materials]
  [elastic_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 1000.0
    poissons_ratio = 0.25
  []
  [compute_stress]
    type = ComputeLagrangianLinearElasticStress
  []
  [compute_strain]
    type = ComputeLagrangianStrainCentrosymmetricSpherical
  []
[]

[Executioner]
  type = Transient

  solve_type = NEWTON

  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  automatic_scaling = true

  nl_abs_tol = 1e-10
  nl_rel_tol = 1e-10

  dt = 0.1
  num_steps = 5
[]

(modules/solid_mechanics/test/tests/lagrangian/centrosymmetric_spherical/total/thermal_expansion/jactest.i)

[GlobalParams]
  displacements = 'disp_r'
  large_kinematics = true
  stabilize_strain = true
[]

[Mesh]
  type = GeneratedMesh
  dim = 1
  nx = 2
  coord_type = RSPHERICAL
[]

[Variables]
  [disp_r]
    [InitialCondition]
      type = RandomIC
      min = 0
      max = 0.02
    []
  []
  [temperature]
  []
[]

[Kernels]
  [sdr]
    type = TotalLagrangianStressDivergenceCentrosymmetricSpherical
    variable = disp_r
    component = 0
    temperature = temperature
    eigenstrain_names = "thermal_contribution"
  []
  [temperature]
    type = Diffusion
    variable = temperature
  []
[]

[BCs]
  [T_left]
    type = DirichletBC
    variable = temperature
    boundary = left
    value = 0
    preset = false
  []
  [T_right]
    type = DirichletBC
    variable = temperature
    boundary = right
    value = 1
    preset = false
  []
[]

[Materials]
  [elastic_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 100000.0
    poissons_ratio = 0.3
  []
  [compute_stress]
    type = ComputeLagrangianLinearElasticStress
  []
  [compute_strain]
    type = ComputeLagrangianStrainCentrosymmetricSpherical
    eigenstrain_names = 'thermal_contribution'
  []
  [thermal_expansion]
    type = ComputeThermalExpansionEigenstrain
    temperature = temperature
    thermal_expansion_coeff = 1.0e-3
    eigenstrain_name = thermal_contribution
    stress_free_temperature = 0.0
  []
[]

[Executioner]
  type = Transient
  solve_type = NEWTON
  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  automatic_scaling = true
  end_time = 1
  dt = 1
[]

(modules/solid_mechanics/test/tests/lagrangian/centrosymmetric_spherical/total/jacobian/neumann.i)

[GlobalParams]
  displacements = 'disp_r'
  large_kinematics = true
  stabilize_strain = true
[]

[Mesh]
  [gmg]
    type = GeneratedMeshGenerator
    dim = 1
    nx = 5
  []
  coord_type = RSPHERICAL
[]

[Variables]
  [disp_r]
  []
[]

[Kernels]
  [sdr]
    type = TotalLagrangianStressDivergenceCentrosymmetricSpherical
    variable = disp_r
    component = 0
  []
[]

[BCs]
  [top]
    type = FunctionDirichletBC
    preset = false
    variable = disp_r
    boundary = right
    function = 't'
  []
[]

[Materials]
  [elastic_tensor]
    type = ComputeIsotropicElasticityTensor
    youngs_modulus = 1000.0
    poissons_ratio = 0.25
  []
  [compute_stress]
    type = ComputeLagrangianLinearElasticStress
  []
  [compute_strain]
    type = ComputeLagrangianStrainCentrosymmetricSpherical
  []
[]

[Executioner]
  type = Transient

  solve_type = NEWTON

  petsc_options_iname = '-pc_type'
  petsc_options_value = 'lu'
  automatic_scaling = true

  nl_abs_tol = 1e-10
  nl_rel_tol = 1e-10

  dt = 0.1
  num_steps = 5
[]

Overview
Input Parameters
Input Files