CZM InterfaceKernel !syntax description /InterfaceKernels/CZMInterfaceKernel

Description

This class assembles the integrated traction computed by a cohesive zone model (CZM) to the system residual vector, which ensures traction equilibrium across an interface. A CZMInterfaceKernel acts only on one displacement component and therefore the user must set up a separate instance of this kernel for for each dimension of the problem. The CZMInterfaceKernel uses the traction and its derivatives provided by a CZMMaterial to compute the appropriate residual and Jacobian.

Residual

The strong form of the force equilibrium equation in vector form can be written as: $var element = document.getElementById("moose-equation-ec295e4d-b4c8-4010-a27c-646def982fd7");katex.render(" F^- -F^+ = \\int_{A^-}{T^- dA^-} - \\int_{A^+}{T^+ dA^+} = 0", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ where superscripts $var element = document.getElementById("moose-equation-f33fea25-4ba5-4eb1-aab5-2af36f62040a");katex.render("+", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ and $var element = document.getElementById("moose-equation-774f271b-d926-4013-b2cb-0647f19d0dfd");katex.render("-", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ identify the master and slave surfaces of the cohesive zone, respectively. Furthermore, $var element = document.getElementById("moose-equation-b3e0db2f-6826-489a-8bbd-2c2ec9b1ea7e");katex.render("F", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ represents the force, $var element = document.getElementById("moose-equation-9139fde2-7dea-42df-b5f9-7c2781a63680");katex.render("T", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ the traction, and $var element = document.getElementById("moose-equation-ecaefa0c-0ae2-4b0b-88fe-8a8c99111272");katex.render("A", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ the area. The master 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 $var element = document.getElementById("moose-equation-7281351c-b5b8-46e5-aa35-66ec8c85ae35");katex.render(" \\int_{A^-}{T^- \\psi^- dA^-} - \\int_{A^+}{T^+ \\psi^+ dA^+} = 0", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ where $var element = document.getElementById("moose-equation-fcdf53f2-7581-4d29-928d-d1ed072f9830");katex.render("\\psi", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is a vector of test functions. Each of the test function in $var element = document.getElementById("moose-equation-8f6766e2-40f4-4d1e-b053-9e43b8323a63");katex.render("\\psi", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is associated to a specific displacement component.

Because of the small deformation assumption $var element = document.getElementById("moose-equation-681c3c46-913a-4085-8c11-5d1942391071");katex.render("A^-=A^+=A", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ and $var element = document.getElementById("moose-equation-787bdc78-15ef-493b-945e-a67e4939824e");katex.render("T^+=T^-=T", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ . Therefore, the equilibrium equation for the displacement component $var element = document.getElementById("moose-equation-9bb47383-1cea-4112-8e2c-e46aca3c59d1");katex.render("i", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ can be rewritten as $var element = document.getElementById("moose-equation-20cc966f-2e62-4929-ac48-975c6ab63c26");katex.render(" T_i (\\psi^- - \\psi^+) = 0", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ Therefore the residual for the master and slave surfaces can be rewritten as $var element = document.getElementById("moose-equation-3d1efb20-b6fe-47a5-85f1-1bad57fb1fa0");katex.render("\\begin{aligned} R_i^+ & = & - T_i \\psi^+ \\\\ R_i^- & = & T_i \\psi^- \\end{aligned}", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$

These are the residual equations implemented in the CZMInterfaceKernel. The traction vector $var element = document.getElementById("moose-equation-f14b11f8-25e7-45aa-ad52-01ee4fb5a3b2");katex.render("T", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ is provided to the CZMInterfaceKernel by the CZMMaterial.

Jacobian

Assuming the traction to be only a function of the displacement jump vector $var element = document.getElementById("moose-equation-7dd89de0-7234-4b89-86ba-d55fc8bb95ba");katex.render("\\Delta U", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ : $var element = document.getElementById("moose-equation-680aa517-f4b8-40a2-849a-e1de718811e0");katex.render(" \\Delta U = u^- - u^+", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ the component $var element = document.getElementById("moose-equation-14584225-4221-46a1-9eff-9e10e891110d");katex.render("i,j", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ of of the residual's Jacobian for the master surface can be written as $var element = document.getElementById("moose-equation-548d64ab-ff00-4a99-99bb-ccc093a9fd8e");katex.render("\\begin{aligned} \\frac{\\partial R_i^+}{\\partial u_j^+} & = & -\\frac{\\partial T_i(\\Delta U)}{\\partial \\Delta U_j} \\frac{\\partial \\Delta U}{\\partial u_j^+} \\psi^+ \\\\ \\frac{\\partial R_i^+}{\\partial u_j^-} & = & -\\frac{\\partial T_i(\\Delta U)}{\\partial \\Delta U_j} \\frac{\\partial \\Delta U}{\\partial u_j^-} \\psi^+ \\end{aligned}", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$

By noticing that $var element = document.getElementById("moose-equation-f4ee22ea-9b60-46fe-a15b-05b4e8fe20a8");katex.render("\\begin{aligned} \\frac{\\partial \\Delta U}{\\partial u_j^+} & = & -\\phi^+ \\\\ \\frac{\\partial \\Delta U}{\\partial u_j^-} & = & \\phi^- \\end{aligned}", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ the Jacobian of the master surface can be rewritten as $var element = document.getElementById("moose-equation-a61318d5-ad68-406f-89b5-8cf3164408f4");katex.render("\\begin{aligned} \\frac{\\partial R_i^+}{\\partial u_j^+} & = & \\frac{\\partial T_i(\\Delta U)}{\\partial \\Delta U_j} \\phi^+ \\psi^+ \\\\ \\frac{\\partial R_i^+}{\\partial u_j^-} & = & -\\frac{\\partial T_i(\\Delta U)}{\\partial \\Delta U_j} \\phi^- \\psi^+ \\end{aligned}", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ Similarly, the Jacobian of the slave surface can be written as $var element = document.getElementById("moose-equation-ab4742ee-8e75-4e2b-b9aa-8ff327a15314");katex.render("\\begin{aligned} \\frac{\\partial R_i^-}{\\partial u_j^+} & = & -\\frac{\\partial T_i(\\Delta U)}{\\partial \\Delta U_j} \\phi^+ \\psi^- \\\\ \\frac{\\partial R_i^-}{\\partial u_j^-} & = & \\frac{\\partial T_i(\\Delta U)}{\\partial \\Delta U_j} \\phi^- \\psi^- \\end{aligned}", element, {displayMode:true,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$

The last two sets of equations are implemented as Jacobian terms in the CZMInterfaceKernel. The derivatives of the traction with respect to the displacement jump, e.g. $var element = document.getElementById("moose-equation-67916d08-0bc6-4933-8f79-74dd17cb2661");katex.render("\\frac{dT_i(\\Delta U)}{\\Delta U_j)}", element, {displayMode:false,throwOnError:false,macros:{"\\pf":"\\frac{\\partial #1}{\\partial #2}"}});$ are provided by the CZMMaterial.

Input Parameters

componentthe component of the displacement vector this kernel is working on: component == 0, ==> X component == 1, ==> Y component == 2, ==> Z
C++ Type:unsigned int
Options:
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
Options:
Description:the string containing displacement variables
neighbor_varThe variable on the other side of the interface.
C++ Type:std::vector
Options:
Description:The variable on the other side of the interface.
variableThe name of the variable that this boundary condition applies to
C++ Type:NonlinearVariableName
Options:
Description:The name of the variable that this boundary condition applies to

Required Parameters

boundaryThe list of boundary IDs from the mesh where this boundary condition applies
C++ Type:std::vector
Options:
Description:The list of boundary IDs from the mesh where this boundary condition applies
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
Options:
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 master ('m') or slave side ('s').
C++ Type:MultiMooseEnum
Options:m s
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 master ('m') or slave side ('s').
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
Options:
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 master ('m') or slave side ('s').
C++ Type:MultiMooseEnum
Options:m s
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 master ('m') or slave side ('s').

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector
Options:
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Options:
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
Options:
Description:Determines whether this object is calculated using an implicit or explicit form
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
Options:
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

extra_matrix_tagsThe extra tags for the matrices this Kernel should fill
C++ Type:std::vector
Options:
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
Options:
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
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
Description:The tag for the vectors this Kernel should fill

Tagging Parameters

Description
Input Parameters

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