Phase boundary motion in an elastic bar of finite length

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 finite elastic bar initially in an equilibrium state that involves two material phases separated by a phase boundary at a given location. Interaction between the moving phase boundary and the elastic waves generated by an impact at the end of the bar and subsequent reflections is studied in detail by using a finite difference scheme. The numerical results show that the phase boundary in a finite bar returns to an equilibrium state after a disturbance of finite duration, whether the two-phase material is trilinear or not.