How to resolve the element-size dependence problem of strain-softening materials?

I also came into the same problem. It is almost impossible to get an element-size convegent result for highly deformed materials with strain-softening. I think the main reason is due to the material model we are using is a local plasticity model. You can try some other non-local plasticity models, which take the strain gradient into account.

Hi Zhang,

There are basically two remedies to mesh sensitivity of softening material models. The first one is the so-called crack band theory developed by Bazant where the softening modulus is adjusted according to the element size. With this way, you get mesh independent solution but the result, damage pattern still strongly depends on the mesh structure. I am talking about mesh bias of the solution.

The second one, having more rigourous mathematical foundations, is to introduce a length scale into the constitutive equations. You can find nonlocal integral models or gradient models belonging to this category.

The reason for this mesh dependency is probably the change of the underlying PDE's type.

Hope that is helps.

 Phu

Hope it helps.

 Prediction of ductile fracture in tension by
bifurcation, localization, and imperfection
analyses
International Journal of Plasticity, Available online 19
July 2008
Yaning
Li, Dale G. Karr

http://www.sciencedirect.com/science?_ob=ArticleListURL&_method=list&_Ar...

Yaning

Zehnnan,

To answer your original question, the fundamental issue at hand is that a continuum strain softening model dissipates energy on a per unit volume basis.  As a localization zone shrinks in size with mesh refinement the energy dissipation in the compuation changes.  Thus there is a need to modify a naive strain softening model with a length parameter to make the dissipation energy per unit area (i.e. fracture like).  Better of course is to start with a sound mechanical model with the correct type of dissipation mechanism (traction - separation law) and then do your modeling.

Prof. Dr. Sanjay Govindjee
University of California, Berkeley