# deriveShearRate Subroutine

## public recursive subroutine deriveShearRate(fun, varSys, elempos, time, tree, nElems, nDofs, res)

Calculate the shear rate

The Shear Rate is defined as where $D_{II}$ is the second invariant of the strain rate tensor and defined as where $S_{\alpha\beta}$ is the strain rate tensor.

### Arguments

TypeIntentOptionalAttributesName
class(tem_varSys_op_type), intent(in) :: fun

Description of the method to obtain the variables, here some preset values might be stored, like the space time function to use or the required variables.

type(tem_varSys_type), intent(in) :: varSys

The variable system to obtain the variable from.

integer, intent(in) :: elempos(:)

Position of the TreeID of the element to get the variable for in the global treeID list.

type(tem_time_type), intent(in) :: time

Point in time at which to evaluate the variable.

type(treelmesh_type), intent(in) :: tree

global treelm mesh info

integer, intent(in) :: nElems

Number of values to obtain for this variable (vectorized access).

integer, intent(in) :: nDofs

Number of degrees of freedom within an element.

real(kind=rk), intent(out) :: res(:)

Resulting values for the requested variable.

Linearized array dimension: (n requested entries) x (nComponents of this variable) x (nDegrees of freedom) Access: (iElem-1)fun%nComponentsnDofs + (iDof-1)*fun%nComponents + iComp

## Variables

TypeVisibilityAttributesNameInitial
integer, private :: posStrain
integer, private :: iElem
real(kind=rk), private :: strain(6*nElems)