Ordinary State-based Peridynamic Mechanics Kernel

Description

The MechanicsOSPD Kernel calculates the residual and jacobian of the force density integral for 2D, and 3D ordinary state-based peridynamic models under infinitesimal strain assumptions.

Force state

The force state for each Edge2 element, i.e., bond, is

where is the unit vector in deformed configuration.

where is the bond stretch, is the dilatation at a material point, parameters , and are model parameters which can be expressed in terms of the material constants.

More details on the residual and Jacobian formulation can be found in Ref. (Hu et al., 2018).

Input Parameters

  • componentAn integer corresponding to the variable this kernel acts on (0 for x, 1 for y, 2 for z)

    C++ Type:unsigned int

    Controllable:No

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

  • 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

  • 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

  • displacementsThe displacements

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

    Controllable:No

    Description:The displacements

  • full_jacobianFalseWhether to include coupling terms with nodes connected to neighbors in the Jacobian matrix for state based formulations

    Default:False

    C++ Type:bool

    Controllable:No

    Description:Whether to include coupling terms with nodes connected to neighbors in the Jacobian matrix for state based formulations

  • out_of_plane_strainNonlinear variable name for the out_of_plane strain for plane stress analysis using NOSPD formulation

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

    Controllable:No

    Description:Nonlinear variable name for the out_of_plane strain for plane stress analysis using NOSPD formulation

  • 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.

  • temperatureNonlinear variable name for the temperature

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

    Controllable:No

    Description:Nonlinear variable name for the temperature

  • 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.

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_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

References

  1. Yile Hu, Hailong Chen, Benjamin W. Spencer, and Erdogan Madenci. Thermomechanical peridynamic analysis with irregular non-uniform domain discretization. Engineering Fracture Mechanics, 2018. URL: https://doi.org/10.1016/j.engfracmech.2018.02.006, doi:10.1016/j.engfracmech.2018.02.006.[BibTeX]