Amit Acharya's blog

The main idea is the following: a most natural mathematical setup for considering the motion of the void-solid interface of an expanding void is that of the traveling wave. Thus, a theory for macroscopic damage evolution may be suspected as being a homogenized version of basic theory that has such wave phenomena as an essential ingredient. This paper is a first step in probing such questions. 

I came across some content I used to have on my webpage a long time ago.

http://www.ce.cmu.edu/~amita/webpage_misc.html

A technique for setting up generalized continuum theories based on a balance law and nonlocal thermodynamics is suggested. The methodology does not require the introduction of gradients of the internal variable in the free energy. Elements of a generalized damage model with porosity as the internal variable are developed as an example.

A field theory of dislocation mechanics and plasticity is illustrated through new results at the nano, meso, and macro scales. Specifically, dislocation nucleation, the occurrence of wave-type response in quasi-static plasticity, and a jump condition at material interfaces and its implications for analysis of deformation localization are discussed.

 The Koiter-Sanders-Budiansky bending strain measure and a nonlinear generalization

 We know from strength of materials that non-uniform stretching of fibers along the cross section of a beam produces bending moments. But does this situation necessarily correspond to a 'bending' deformation? For that matter, what do we exactly mean kinematically when we talk about a bending deformation?

Attached is a paper outlining ideas for averaging autonomous dynamics, based on a dynamical systems point of view.

People interested in computational multiscale modeling, especially of the sequential kind, as well as nonequilibrium statistical mechanics may find these ideas useful.