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## Solver ComputeStrainRate

**Solver Fortran File:** `ComputeStrainRate.f90`

**Solver Name:** `ComputeStrainRate`

**Required Output Variable(s):** default is `StrainRate`

(else in `StrainRate Variable Name`

)

**Required Input Variable(s):** A `Flow Solution`

(in `Flow Solution Name`

)

**Optional Output Variable(s):** None

**Optional Input Variable(s):** None

### General Description

The aim of this solver is to compute the strain-rate tensor from the flow solution. For a 2D simulation there are 5 DOFs `(E11, E22, E33, E12, Eii)`

and for a 3D simulation, 2 additional (7 DOFs) are being solved for `(E11, E22, E33, E12, E23, E31, Eii)`

. This solver uses a dummy variable and solves 5 (7 in 3D) times a 1 DOF system for each strain-rate components and the trace of the strain-rate tensor `(Eii)`

.

The Strain-rate tensor is computed using:

where is the velocity vector solution of the Stokes problem.

### SIF contents

The required keywords in the SIF file for this solver are:

Solver 1
Equation = "Strain Rate"
Procedure = "ElmerIceSolvers" "ComputeStrainRate"
! this is just a dummy, hence no output is needed
!-----------------------------------------------------------------------
Variable = -nooutput "Eij"
Variable DOFs = 1
Exported Variable 1 = "StrainRate"
Exported Variable 1 DOFs = 5 !in 2D, 7 in 3D
! the name of the variable containing the flow solution (U,V,W,Pressure)
!-----------------------------------------------------------------------
Flow Solver Name = String "Flow Solution"
! the name of the strain-rate solution (default is 'StrainRate')
StrainRate Variable Name = String "StrainRate"
Linear System Solver = Direct
Linear System Direct Method = umfpack
End

### Examples

An example using this solver can be found in `[ELMER_TRUNK]/elmerice/examples/Test_StrainRate`

.