On the multiscale modeling

Dear all

 I wonder what the status of the multiscale modeling in (computational) solid mechanics is. I read several papers on the coupling of atom and continuum based on some hypotheses such as Cauchy-Born hypothesis, Virial stress theorem etc. My questions are; 1. Are these hypotheses also valid for inhomogeneous/heterogeneous media? 2. All I’ve seen was for elastic media. Are there any references on the atomistic calculation describing plastic deformation of solids? 3. I think that the classical (bulk) Cauchy-Born hypothesis does not validate materials including some pre-existing crack surfaces or developing crack surfaces.Am I right? If then, what alternatives can I think of?

Sincerely,

S. Ha