# Rank Two Aux

Access a component of a RankTwoTensor

## Description

The AuxKernel RankTwoAux is used to save single components of Rank-2 tensors into an AuxVariable for visualization and/or post-processing purposes. An antisymmetric Rank-2 tensor would require nine separate RankTwoAux AuxKernel-AuxVariable pairs to store all of the components of the antisymmetric Rank-2 tensor; six separate AuxKernel-AuxVariable pairs are required to print out all the unique components of a symmetric Rank-2 tensor. Quantities commonly examined with RankTwoAux are stress () and strain ().

The RankTwoAux takes as arguments the values of the index_i and the index_j for the single tensor component to save into an AuxVariable. Eq. (1) shows the index values for each Rank-2 tensor component. (1)

If desired, RankTwoAux can be restricted to save data from a Rank-2 tensor at a single specified quadrature point per element. This option is generally used for debugging purposes.

## AuxVariable Order

note:Elemental vs Nodal Visualization of Quadrature Field Values

Results will have different quality based on the AuxVariable:

• Elemental Constant Monomial Using an AuxVariable with family = MONOMIAL and order = CONSTANT will give a constant value of the AuxVariable for the entire element, which is computed by taking a volume-weighted average of the integration point quantities. This is the default option using TensorMechanics Action and requires the least computational cost.

• Elemental Higher-order Monomial Using an AuxVariable with family = MONOMIAL and order = FIRST or higher will result in fields that vary linearly (or with higher order) within each element. Because the Exodus mesh format does not support higher-order elemental variables, these AuxVariables are output by libMesh as nodal variables for visualization purposes. Using higher order monomial variables in this way can produce smoother visualizations of results for a properly converged simulation.

• Nodal Lagrange Using an AuxVariable with family = LAGRANGE will result in a smooth nodal field of the material property, constructed using nodal patch recovery. patch_polynomial_order is set to equal the order of the AuxVariable by default. Use this option for the best (smoothest, most accurate) results, but there is some additional computational cost. Furthermore, this method is suitable only for serial simulations at present.

## Example Input File Syntax

[./stress_xy]
type = RankTwoAux
rank_two_tensor = stress
variable = stress_xy
index_i = 0
index_j = 1
[../]

(modules/tensor_mechanics/test/tests/elastic_patch/elastic_patch.i)

An AuxVariable is required to store the RankTwoAux AuxKernel information. Note that the name of the AuxVariable is used as the argument for the variable input parameter in the RankTwoAux block.

[./stress_xy]
order = CONSTANT
family = MONOMIAL
[../]

(modules/tensor_mechanics/test/tests/elastic_patch/elastic_patch.i)

## Input Parameters

• rank_two_tensorThe rank two material tensor name

C++ Type:MaterialPropertyName

Options:

Description:The rank two material tensor name

• variableThe name of the variable that this object applies to

C++ Type:AuxVariableName

Options:

Description:The name of the variable that this object applies to

• index_jThe index j of ij for the tensor to output (0, 1, 2)

C++ Type:unsigned int

Options:

Description:The index j of ij for the tensor to output (0, 1, 2)

• index_iThe index i of ij for the tensor to output (0, 1, 2)

C++ Type:unsigned int

Options:

Description:The index i of ij for the tensor to output (0, 1, 2)

### Required Parameters

• execute_onLINEAR TIMESTEP_ENDThe list of flag(s) indicating when this object should be executed, the available options include NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, FINAL, CUSTOM, PRE_DISPLACE.

Default:LINEAR TIMESTEP_END

C++ Type:ExecFlagEnum

Options:NONE INITIAL LINEAR NONLINEAR TIMESTEP_END TIMESTEP_BEGIN FINAL CUSTOM PRE_DISPLACE

Description:The list of flag(s) indicating when this object should be executed, the available options include NONE, INITIAL, LINEAR, NONLINEAR, TIMESTEP_END, TIMESTEP_BEGIN, FINAL, CUSTOM, PRE_DISPLACE.

• 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

• 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

### Optional Parameters

• selected_qpEvaluate the tensor at this specific quadpoint

C++ Type:unsigned int

Options:

Description:Evaluate the tensor at this specific quadpoint

• enableTrueSet the enabled status of the MooseObject.

Default:True

C++ Type:bool

Options:

Description:Set the enabled status of the MooseObject.

• 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.

• patch_polynomial_orderPolynomial order used in least squares fitting of material property over the local patch of elements connected to a given node

C++ Type:MooseEnum

Options:CONSTANT FIRST SECOND THIRD FOURTH

Description:Polynomial order used in least squares fitting of material property over the local patch of elements connected to a given node

• 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