Kinetics of Martensitic Phase Transitions: Lattice model

Abstract. We obtain a closing kinetic relation for a mixed type hyperbolic-elliptic p-system originating in the theory of martensitic phase transitions by replacing continuum model with its natural discrete prototype. The procedure can be viewed as either regularization by discretization or as a physically motivated account of underlying discrete (atomic or mesoscopic) microstructure. Our fully inertial lattice model describes an isolated phase boundary and its novelty is in taking into account nonlocality in the form of general harmonic long-range interactions. Although the model is Hamiltonian at the microscale, it generates a nontrivial macroscopic jump relation between the velocity of the discontinuity and the conjugate configurational force. This relation characterizes the rate of (apparent) dissipation, respects entropy inequality but is supplementary to the usual RankineHugoniot jump conditions. The dissipation at the macrolevel is due to the induced radiation of lattice waves carrying energy away from the propagating front. We show that sufficiently strong nonlocality has a significant effect on the kinetic relation in both near-sonic and small-velocity regions.