## Information and Tools

Stress divergence kernel with automatic differentiation for the Cartesian coordinate system

## Description

The ADStressDivergenceTensors kernel calculates the residual of the stress divergence for 1D, 2D, and 3D problems in the Cartesian coordinate system. Forward mode automatic differentiation is used to compute an exact Jacobian.

Either 1, 2, or 3 displacement variables can be used in the stress divergence calculator for the Cartesian system.

## Residual Calculation

The stress divergence kernel handles the calculation of the residual, , from the governing equation and the calculation of the Jacobian using forward mode automatic differentiation. From the strong form of the governing equation for mechanics, neglecting body forces,

(1)

the weak form, using Galerkin's method and the Gauss divergence theorem, becomes

(2)

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 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.

note:Automatic Differentiation Materials

The computation of a correct Jacobian contribution requires the use of compatible automatic differentiation materials ([ADMaterials]).

## Input Parameters

• variableThe name of the variable that this Kernel operates on

C++ Type:NonlinearVariableName

Options:

Description:The name of the variable that this Kernel operates on

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

C++ Type:unsigned int

Options:

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

Options:

Description:The string of displacements suitable for the problem statement

### Required Parameters

• volumetric_locking_correctionFalseSet to false to turn off volumetric locking correction

Default:False

C++ Type:bool

Options:

Description:Set to false to turn off volumetric locking correction

• blockThe list of block ids (SubdomainID) that this object will be applied

C++ Type:std::vector

Options:

Description:The list of block ids (SubdomainID) that this object will be applied

• base_nameMaterial property base name

C++ Type:std::string

Options:

Description:Material property base name

### Optional Parameters

• enableTrueSet the enabled status of the MooseObject.

Default:True

C++ Type:bool

Options:

Description:Set the enabled status of the MooseObject.

• 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.)

• 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.

• 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.

• seed0The seed for the master random number generator

Default:0

C++ Type:unsigned int

Options:

Description:The seed for the master random number generator

• 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.)

• 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

• 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

• 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

• 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