A mechanism of transformational plasticity

In order to understand the phenomenon of reversible plasticity exhibited by shape memoryalloys and other smart materials, we study an elementary prototypical model. Building on anoriginal idea of M¨uller and Villaggio [17], we consider an inhomogeneous ensemble of bi-stableelements connected in series and loaded in a soft device. To interpret the fine structure of thehysteresis loops observed experimentally, we assume that the dynamics is maximally dissipativeand investigate different evolutionary strategies for a “driven” system with external forcechanging quasi-statically. Our main result is that the inhomogeneity of the elastic propertiesleads to a distinctive hardening with serrations of a Portevin-Le Chatelier type and producesa realistic memory structure characterized by the “congruency” and “return point memory”properties