simpleshear

Concise 2D visco-elasto-plastic Stokes solver

Visco-elasto-plastic rheology for 2D Stokes solvers and continuum mechanics.

👉 Simple shear: The current codes rely on a centres implementation of the VEP rheology (staggered grid). Pure shear configuration results are accurate but simple shear experiments fail to localise compared to vertices only or vertices and centres formulations.

Content

• The fix
• Julia Codes

The fix

Doing the interpolation of the shear stress after the plastic correction:

Txyv[2:end-1,2:end-1].=av(Txy); Txyv[1,:].=Txyv[2,:]; Txyv[end,:].=Txyv[end-1,:]; Txyv[:,1].=Txyv[:,2]; Txyv[:,end].=Txyv[:,end-1]

instead of the visco-elasto-plastic viscosity:

η_vepv[2:end-1,2:end-1].=av(η_vep); η_vepv[1,:].=η_vepv[2,:]; η_vepv[end,:].=η_vepv[end-1,:]; η_vepv[:,1].=η_vepv[:,2]; η_vepv[:,end].=η_vepv[:,end-1]
Txyv   .= 2.0.*η_vepv.*Exyv1

solves the issue.

Julia codes

The Julia codes implementing 2D Stokes equations and visco-elasto-plastic shear rheology in simple shear experiments:

• Stokes2D_vep_reg_simpleshear_c.jl resolve regularised brittle failure of a bloc containing a visco-elastic inclusion in centres only formulation;

• Stokes2D_vep_reg_simpleshear_v.jl resolve regularised brittle failure of a bloc containing a visco-elastic inclusion in vertices only formulation;

• Stokes2D_vep_reg_simpleshear_vc.jl resolve regularised brittle failure of a bloc containing a visco-elastic inclusion in vertices and centres formulation.

• Stokes2D_vep_reg_simpleshear_ctau.jl resolve regularised brittle failure of a bloc containing a visco-elastic inclusion in centres formulation with extrapolation of the corrected shear stress instead of the corrected effective visco-elasto-plastic viscosity.