Please Help solving VEM with finite strains per Wrigger's paper.

Hello iMechanica,

I have been trying to implement the Virtual Element Method formulation for finite strains described in the paper by Wrigger's et al.  It can be found at the following link:

Link to Wrigger's Paper

https://www.researchgate.net/publication/315974511_Efficient_virtual_el…

I have been partially successful for certain simple problems.  However, for most problems I have been unsuccessful.  Severe problems arise with stability/convergence as I increase the number of virtual elements, and all bending problems fail.  Although I have tried to implement the stabilization described in the paper, clearly stability seems to still be a problem.  I have no doubt there is an error somewhere in my MATLAB computer code, or an error or omission in my understanding of how to implement what is described in the paper.  I have extensively tried to fix the issue, but have run out of ideas to try to find the problem (several weeks and still no luck).

Please, has anyone been successful implementing the formulation in the paper?  Would anyone be willing to discuss with me/ help me figure this out?

thanks for any ideas you may have to offer,

sincerely,

Louie

Below are some examples of my results (a few good, but mostly bad), all using virtual elements:

Axial Extrusion (good behavior, convegence works correctly)

Axial Extrusion (different virtual element discretization, bad behavior, won't converge, stability poor)

Axial Extrusion (with quadrilateral virtual elements, good behavior, convegence works correctly)

Axial Extrusion (a few increments of displacement with quadrilateral virtual elements, bad behavior, won't converge, poor stability, more steps and it crashes badly)

Cantilever with tip load (with virtual elements, clearly unstable, it can't even do a few small incremental steps correctly)

Cantilever with tip load (with quadrilateral virtual elements, clearly unstable, it can't even do a few small incremental steps correctly)