- componentthe component of the displacement vector this kernel is working on: component == 0, ==> X component == 1, ==> Y component == 2, ==> Z
C++ Type:unsigned int
Unit:(no unit assumed)
Controllable:No
Description:the component of the displacement vector this kernel is working on: component == 0, ==> X component == 1, ==> Y component == 2, ==> Z
- displacementsthe string containing displacement variables
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:the string containing displacement variables
- neighbor_varThe variable on the other side of the interface.
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:The variable on the other side of the interface.
- 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
CZMInterfaceKernelTotalLagrangian
Assembles the integrated first Piola-Kirchhoff traction computed by a cohesive zone model
Description
This class assembles the integrated first Piola-Kirchhoff traction computed by a cohesive zone model (CZM) to the system residual vector, which ensures traction equilibrium across an interface. A CZMInterfaceKernelTotalLagrangian acts only on one displacement component and therefore the user must set up a separate instance of this kernel for each dimension of the problem. The CZMInterfaceKernelTotalLagrangian uses the PK1 traction and its derivatives provided by a CZM Compute Global Traction Total Lagrangian to impose the appropriate residual and to provide the appropriate Jacobian. This kernel accounts for both interface area changes and rotations.
Residual
The strong form of the force equilibrium equation in vector form can be written as: where superscripts and identify the primary and secondary surfaces of the cohesive zone, respectively. Furthermore, represents the force, the first Piola-Kirchhoff traction, and the undeformed area. The primary surface is the one where the interface normal is computed.
By utilizing the principle of virtual work and recognizing that forces are work conjugate of displacements, the weak form of the equilibrium equation can be written as where is a vector of test functions. Each of the test function in is associated to a specific displacement component.
In the undeformed configuration, and . Therefore, the equilibrium equation for the displacement component can be rewritten as Therefore the residual for the primary and secondary surfaces, for a specific test function can be rewritten as
These are the residual equations implemented in the CZMInterfaceKernelTotalLagrangian. The traction vector by the CZM Equilibrium Traction Calculator Total Lagrangian
Jacobian
The Jacobian for this model is exact. The Jacobian requires calculating the derivative of the residual with respect to the discrete displacements .
Assuming the traction is only a function of the midplane deformation gradient,, and of the displacement jump in global coordinates, , the partial derivatives of the traction can be rewritten using the chain rule as: Substituting the last two equations in the Jacobian definition one obtains the equation implemented in this kernel.
The CZM Equilibrium Traction Calculator Total Lagrangian provides and . This kernel is responsible for computing and .
Displacement Jump and deformation gradient derivatives
Recalling and that we can write,
Recalling and that we can write
Example Input File Syntax
This object is automatically added from the Cohesive Zone Physics when strain=FINITE.
Input Parameters
- base_nameMaterial property base name
C++ Type:std::string
Unit:(no unit assumed)
Controllable:No
Description:Material property base name
- boundaryThe list of boundaries (ids or names) from the mesh where this object applies
C++ Type:std::vector<BoundaryName>
Unit:(no unit assumed)
Controllable:No
Description:The list of boundaries (ids or names) from the mesh where this object applies
- 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.
- traction_global_namePK1traction
Default:PK1traction
C++ Type:std::string
Unit:(no unit assumed)
Controllable:No
- 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.
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)
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)
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.)
- diag_save_in_var_sideThis parameter must exist if diag_save_in variables are specified and must have the same length as diag_save_in. This vector specifies whether the corresponding aux_var should save-in jacobian contributions from the primary ('p') or secondary side ('s').
C++ Type:MultiMooseEnum
Unit:(no unit assumed)
Controllable:No
Description:This parameter must exist if diag_save_in variables are specified and must have the same length as diag_save_in. This vector specifies whether the corresponding aux_var should save-in jacobian contributions from the primary ('p') or secondary side ('s').
- 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.)
- save_in_var_sideThis parameter must exist if save_in variables are specified and must have the same length as save_in. This vector specifies whether the corresponding aux_var should save-in residual contributions from the primary ('p') or secondary side ('s').
C++ Type:MultiMooseEnum
Unit:(no unit assumed)
Controllable:No
Description:This parameter must exist if save_in variables are specified and must have the same length as save_in. This vector specifies whether the corresponding aux_var should save-in residual contributions from the primary ('p') or secondary side ('s').
- 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