Hysteresis in multi-stable lattices with non-local interactions

We study a model for martensitic phase transitions represented by a lattice of mass points connected by bi-stable nearest neighbor (NN) springs and harmonic next to nearest neighbor (NNN) springs. Our main assumption of weak NNN interactions allows us to obtain a fully analytical representation of the quasistatic evolution of the overdamped system, including both the ‘non-local’ interaction with the external load and the presence of imperfections. This simple model reproduces the experimental observation of different evolution strategies, with internal or boundary nucleation and with the possibility of one or more coherently propagating phase fronts. The model describes also the observation of a Peierls stress higher or lower than the nucleation stress. We show that all these properties are also preserved in the ‘continuum’ limit.