A Reciprocity Relation Couples Newtonian and Eshelbian Mechanics

Abstract

By considering a stressed elastic body subjected sequentially to a material displacement of a defect and the application of a physical force, the authors have succeeded in arriving at a novel type of coupling of Newtonian and Eshelbian mechanics by means of a reciprocity theorem analogous to that of Maxwell. This reciprocity relation is more involved than those in strictly physical or strictly material space. An order of magnitude analysis was required to obtain consistent relations. Several illustrative examples are worked out, and suggestions for some experiments, which in their evaluations would make use of the new expressions, are offered.