We present a new methodology for the systematic reduction of a continuum theory of martensitic transformations to a spin system whose dynamics can be described by an automaton. Our prototypical model reproduces most of the experimental observations in martensites associated with criticality and power law acoustic emission. In particular, it explains in a natural way why cyclic training is necessary to reach scalefree behavior.
Perez-Reche, F. J., Truskinovsky, L., & Zanzotto, G. (2009). Martensitic transformations: from continuum mechanics to spin models and automata. Continuum Mechanics and Thermodynamics, 21(1), 17-26. https://doi.org/10.1007/s00161-009-0096-2