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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 required keywords in the SIF file for this solver are:
Solver 1 Equation = String "StressSolver" Procedure = File "ComputeDevStressNS" "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" ! the name of the stress solution (default is 'stress') !----------------------------------------------------------------------- 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
Download an example using this solver. TODO
When used 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.