A major serendipitous contribution to continuum mechanics

Abstract

Giving the continuum notion of stress a quantitative atomistic basis is a long-standing issue. It is argued here that a completely satisfactory solution to this problem came from totally unexpected quarters, being contained (implicitly) in the Parrinello-Rahman method of molecular dynamics. Until now, the latent theoretical potential of this method passed unnoticed by molecular dynamics practitioners—who regarded it as a mere computational device— and even more so among scholars of continuum mechanics. The supreme irony is that Parrinello and Rahman themselves knew very little, if any, of continuum mechanics, and could not care less of it. Their unintentional contribution, expounded and extended in this paper, is a major testimony to the heuristic power of computational science. In their quest for a molecular dynamics method suited for studying solid-state phase transitions they were led, by an intrinsic necessity, to allow the computational cell to change its shape in exactly the same way as an infinitesimally small piece of a deformable medium is assumed to do in standard continuum mechanics.