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

**Solver Name:**`ComputeDevStress`

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

(else in`Stress Variable Name`

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

(in`Flow Solution Name`

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

The aim of this solver is to compute deviatoric or Cauchy stress from flow solution. For a 2D simulation there are 4 DOFs `(S11, S22, S33, S12)`

, for a 3D simulation, 2 additional are being solved for `(S11, S22, S33, S12, S23, S31)`

. This solver uses a dummy variable and solves 4 (6 in 3D) times a 1 DOF system for each stress components.

The Cauchy stress is computed using:

where is directly evaluated from the velocity field and is the isotropic pressure.The convention is that a positive stress corresponds to a tensile stress (opposite to the isotropic pressure convention).

This solver doesn't work for the GOLF anisotropic (AIFlow Solver) and the snow/firn (Porous Solver) rheologies. Nevertheless, these two solvers have intrinsic functions which allow to compute the stress directly.

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

Solver 1 Equation = String "StressSolver" Procedure = File "ElmerIceSolvers" "ComputeDevStress" ! this is just a dummy, hence no output is needed !----------------------------------------------------------------------- Variable = -nooutput "Sij" Variable DOFs = 1 ! the name of the variable containing the flow solution (U,V,W,Pressure) !----------------------------------------------------------------------- Flow Solver Name = String "Flow Solution" ! no default value anymore for "Stress Variable Name" Stress Variable Name = String 'Sigma' !----------------------------------------------------------------------- Exported Variable 1 = "Sigma" ! [Sxx, Syy, Szz, Sxy] in 2D ! [Sxx, Syy, Szz, Sxy, Syz, Szx] in 3D Exported Variable 1 DOFs = 6 ! 4 in 2D, 6 in 3D Linear System Solver = "Iterative" Linear System Iterative Method = "BiCGStab" Linear System Max Iterations = 300 Linear System Convergence Tolerance = 1.0E-09 Linear System Abort Not Converged = True Linear System Preconditioning = "ILU0" Linear System Residual Output = 1 End Material 1 ... ! we want to have the Cauchy stress !---------------------------------- Cauchy = Logical True End

A 2D example can be found in `[ELMER_TRUNK]/elmerice/Tests/ComputeDevStress`

.

This solver can be cited using the following references:

Gagliardini O., D. Cohen, P. Råback and T. Zwinger, 2007. Finite-Element Modeling of Subglacial Cavities and Related Friction Law. J. of Geophys. Res., Earth Surface, 112, F02027.