Dynamics of phase transitions and hysteresis in a viscoelastic Ericksen's bar on an elastic foundation

This work is a follow-up on the study [32] of interface dynamics and hyster esis in materials undergoing solid-solid phase transitions. We consider the dynamics of a viscoelastic bar with a nonmonotone stress-strain relation a nd viscous stress linearly proportional to the strain rate. The bar is plac ed on an elastic foundation with stiffness beta mimicking the interaction o f phases in higher dimensions. Time-dependent displacement-controlled loadi ng of the bar results in a tilted and serrated hysteresis loop, in qualitat ive agreement with some experimental observations in shape-memory alloys. T he model exhibits three phase transition processes: phase nucleation, inter face slip and phase annihilation. Between these dynamic processes the syste m gets stuck in local minimizers of the potential energy. As beta increases from zero, a slip-dominated solution behavior transforms to the one where slip and annihilation events are preceded by a step-by-step nucleation proc ess. We show that this transition is caused by an interplay between the sli p-favoring inertia term and the nucleation-favoring elastic foundation term s.