On the Cauchy—Born Rule

Abstract

To relate continuum theories of elastic phenomena to typical atomic or molecular theories, one needs some way of correlating changes in positions of the entities in the latter with descriptions of deformation used in the former. For crystals, the most commonly used bridge used for this is the Cauchy—Born rule. In recent years, there has been a flurry of activity aimed at better understanding it and in trying to generalize it. I will describe and comment on important ideas that have been generated, point out some successes and failures of the rule and indicate kinds of applications that have motivated such work.