Unstable kinetic relations and the dynamics of solid-solid phase transitions

In recent continuum-mechanical models of phase transitions in solids, the kinetic relation for a transition is usually assumed to be such that the driving force acting on a phase boundary is a monotonically increasing function of phase boundary velocity. The present paper explores the implications of relinquishing this assumption in the dynamics of one-dimensional elastic bars undergoing stress-induced transitions. Among other results, it is found that, for a class of non-monotonic kinetic relations, models of the kind discussed here permit stick-slip motions of a phase boundary, as observed in certain experiments.