Dynamic behavior of the interface between two solid phases in an elastic bar

Using the continuum mechanical model of solid-solid phase transitions of Abeyaratne and Knowles, this paper examines the large time dynamical behavior of a phase boundary. The problem studied concerns a semi-infinite elastic bar initially in an equilibrium state that involves two material phases separated by a phase boundary at a given location. Interaction between the phase boundary and the elastic waves generated by an impact at the end of the bar and subsequent reflections is studied in detail, and an exact solution of the dynamical problem, which is governed by a nonlinear resursive formula, is obtained. It is shown that the phase boundary reaches a new equilibrium state for large time. Numerical calculations based on the recursive formula are carried out to illustrate analytical results.Address after August 15, 1995: Department of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, Blacksburg, VA24061, USA.