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~~NOTOC~~
===== Solver ComputeDevStress =====

==== General Informations ====
  * **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


==== General Description ====
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:\\

<m>sigma_{ij}  = 2 {eta}  {epsilon}_{ij} - p delta_{ij} </m> \\

where <m>epsilon</m> is directly evaluated from the velocity field and <m>p</m> 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 ([[solvers:aiflow|AIFlow Solver]]) and the snow/firn ([[solvers:porous|Porous Solver]]) rheologies. Nevertheless, these two solvers have intrinsic functions which allow to compute the stress directly. 


==== SIF contents ====
The required keywords in the SIF file for this solver are:
<code>
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
</code>

==== Examples ====
A 2D example can be found in ''[ELMER_TRUNK]/elmerice/Tests/ComputeDevStress''.
==== Reference ====
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.