Paper by Ellad Tadmor & Nikhil Admal---Atomistic Definition of Stress
For both mechanicians and physicists, linking continuum concepts to the underlying microscopic characteristics of materials has remained a major preoccupation. Certainly, with the recent advent of the so-called "multiscale" modeling approaches, this topic has been brought to a sharp focus. Cauchy stress is one such continuum concept that has courted a fair amount of controversy.
I personally became interested in this topic a few years ago when I initiated research on a quantum definition of stress. This became troublesome quite quickly as I found that (let alone quantum perspective) I was bewildered and confused by even the literature on classical definition of atomistic stress. Papers by Professor Ian Murdoch went a long way in contributing to my understanding of this subject.
Last week, I had the pleasure of reading a pre-print by Ellad Tadmor and his graduate student (Nikhil Admal). This paper (honestly more of a treatise given its scope and length!) provides one of the clearest and most comprehensive yet exposition on this topic---at least for me. Apart from a fresh approach to the derivations, the paper clarifies several mis-notions and establishes connections between the various definitions of atomistic stress that abound in the literature.
The readers can make up their own mind. The pre-print is attached below (with permission from the authors). It will appear in a special issue of Journal of Elasticity honoring Professor Walter Noll. Incidentally, it is worth mentioning that a translation is now available of Professor Noll's relatively lesser known paper on atomistic stress----see also a discussion by Richard LeHoucq . Noll's original paper appeared in 1955 and was in German. Ellad, Ian (Murdoch) and I, all use the results derived by Professor Noll in some form or the other.