Nucleation and phase propagation in a multistable lattice with weak non local interactions

We study the overdamped gradient flowdynamics of a chain of massless points connected by bistable nearest-neighbor (NN) interactions and harmonic next-nearest-neighbor (NNN) interactions under quasistatic loads of assigned displacements. The model reproduces experimental observations on the phase transition of shape-memory wires with the possibility of different microstructure evolution strategies: internal or boundary nucleations and one or two coherently propagating phase fronts. The presence or absence of a stress peak is also obtained by considering nonlocal interaction effects with the loading device. Similar results are also obtained under the hypothesis of global energy minimization. The system also retains the described properties in the continuum limit. Some rate effects are numerically analyzed.