Dynamics of martensitic phase boundaries : discreteness , dissipation and inertia

We study a fully inertial model of a martensitic phase transition in a one-dimensional crystal lattice with long-range interactions. The model allows one to represent a broad range of dynamic regimes, from underdamped to overdamped. We systematically compare the discrete model with its various continuum counterparts including elastic, viscoelastic and viscosity-capillarity models. Each of these models generates a particular kinetic relation which links the driving force with the phase boundary velocity. We find that the viscoelastic model provides an upper bound for the critical driving force predicted by the discrete model, while the viscosity-capillarity model delivers a lower bound. We show that at near-sonic velocities, where inertia dominates dispersion, both discrete and continuum models behave qualitatively similarly. At small velocities, and in particular near the depinning threshold, the discreteness prevails and predictions of the continuum models cannot be trusted.