Impact induced propagation of phase transformation in a shape memory alloy rod

In this work we study the propagation of a phase-transformation front induced by an impact loading. Our main goals in this paper are to demonstrate the wave structure of the solution to the impact loading and to estimate the velocity of phase front propagation using a thermodynamically based constitutive model for SMAs with internal variables. First, we study the impact problem in an isothermal setting; this study provides an important insight into the wave structure of the solution. The non-uniqueness issue inherent to such problems due to nonconvex SMA constitutive models is thoroughly discussed. Then we develop the solution for an adiabatic approximation for a simplified SMA model. Several numerical examples based on a first order Lax-Friedrichs finite difference scheme are presented.