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

Hi, Phu, thanks for your help!

Zhennan Zhang — Tue, 23 Sep 2008 17:41:41 -0400

Zhennan Zhang

Hi,Prof. Govindjee, Thanks a lot for your valuable suggestion

Zhennan Zhang — Tue, 23 Sep 2008 17:40:29 -0400

Zhennan Zhang

References

Julian Hallai — Tue, 23 Sep 2008 12:50:30 -0400

Hi Phu,

Woud you recommend some references on these two approaches?

Thanks

Julian

Strain Softening and Energy Release

Sanjay Govindjee — Tue, 23 Sep 2008 04:29:34 -0400

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

A recent paper addressed mesh-size problem

Yaning Li — Sun, 21 Sep 2008 21:35:29 -0400

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

Hi Zhang, There are

vinh phu nguyen — Sat, 20 Sep 2008 08:55:27 -0400

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

I also had the same problem

Yuanli Bai — Sat, 20 Sep 2008 00:41:52 -0400

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.

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

Zhennan Zhang — Thu, 18 Sep 2008 11:25:40 -0400

In the finite element simulaiton of material failure, the simulaiton results are critically dependent on the element size if the mateiral is described by a softening constitutive relationship. How to resolve this problem? What is the underlying principle of this phenomenon? Thanks!