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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.
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