Voids

Arash_Yavari — Tue, 12 Aug 2008 16:12:10 -0400

Dear Rezwan:

Thank you for your interest.

Of course you can think of "damage" or any measure that describes "damage" as a microstructure field. However, the question should be how useful the formulation is. My motivation in this paper was to see why there are so many different possibilities for "balance laws" and if there is any way to understand this starting from first principles. In many works balance laws are simply postulated and it's not clear if what one sees is the personal choice of the author(s) or there is more into the given formulation.

For damage you may look at the following paper:

Fu, M.F., Saczuk, J., Stumpf, H. 1998 'On fiber bundle approach to damage analysis' Int J Engng Science 36, 1741-1762.

The presentation is geometric but somewhere in the middle they assume Euclidean ambient spaces. Again, the question you should always ask yourself is whether you can gain anything using geometry. For your damage evolution problem, you should first see why the formulation based on Euclidean ambient spaces is not satisfactory (is this really the case?) and then try to formulate the theory geometrically. I had a look at the paper you sent me (don't want to mention the author) but didn't see anything but some "nice" interpretations of what is already known.

I hope this helps.

Regards,

Arash

RE: Balance Laws in Continua with Microstructure

Rezwanur Rahman — Sun, 10 Aug 2008 15:23:22 -0400

Hi Dr. Arash

This paper is very interesting indeed. This paper can be helpful regarding considering the issue of damages/voids/defects in the continuum (with respect to the microstructure field). I would like to mention that the Article 5.1 named: A Geometric Theory of Elastic Solids with Distributed Voids is expressive about cosidering damages/voids. According to our previous discussion, this material void velocity can be considered as "Local Martingale". And some random nucleation of new void(s) can cause this velocity to be a stochastic process containing sudden jumps. Besides that we can deal with a density function of void velocity instead of a single void. Please let me know about your opinion regarding this.

Thanks

Rezwan

iMechanica - Couple Stress - Comments

Voids

RE: Balance Laws in Continua with Microstructure