Stress-induced phase transitions in elastic solids

This paper describes a continuum model, developed recently by R. Abeyaratne and the author, for the response of elastic solids capable of undergoing stress-induced phase transitions. Models of the kind sketched here and their generalizations are intended to apply to both quasi-static and dynamic experiments for shape memory alloys and to impact-induced phase changes in ceramics. The present discussion is confined to a purely mechanical theory, omitting thermal effects, so that the natural setting is the nonlinear theory of elasticity. The presentation below is limited to one space dimension.