Documentation + large deformation stress about raccoon

[hugary1995]

It turns out I don't need to change anything to convert the Kirchhoff stress to the Mandel stress -- for isotropic materials, they coincide.

[hugary1995]

Thanks for pointing out the typos, I'll fix them.

Regarding the Kirchhoff stress, this is a very good question. There are some historical reasons for this discrepancy. The relation between the Kirchhoff stress (\tau) and the Mandel stress (M) is given by

\tau = F^e^{-T} M F^e^T

where F^e is the elastic deformation gradient. In most of the existing FEM packages for finite deformation (crystal)plasticity, it is assumed that F^e is close to identity when plasticity occurs, which leads to the approximation \tau ~= M. This assumption is particularly good for many metals. I kept this approximation so that I can benchmark my results with those obtained from other packages.

I'll add the above explanation as comment in the code.

As I'm drafting this answer, I realize that adding an extra operation to convert the Kirchhoff stress to the Mandel stress in computeMandelStressNoDecomposition and computeMandelStressVolDevDecomposition is probably not a bad idea. I'll do some testing and see how much of an additional cost as a result of that. If it is cheap, then why not? :)

[Sina-av]

Thank you so much @hugary1995 for the explanation. It is really helpful.
I also think that adding the extra operation to convert the stress might be a good idea (of course after considering its cost). (Also this conversion might be helpful for cases that one might just use CNH model in an elastic simulation where there is no plasticity at all).
Thanks again.

[Sina-av]

Hi @hugary1995! I was going over this issue again. Looking at your last comment. I was wondering if you have a reference that I can look into regarding "Kirchhoff stress and the Mandel stress -- for isotropic materials, they coincide". I'm still not sure how this can happen (for the most general case).
Thanks a lot!
Edit: I think I found that this is due to commute of the Mandel stress and the right stretch tensor in isotropic elasticity.