• 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.