Phase transitions in hierarchical, multi-stable metamaterials

Abstract

In this article, we consider the dynamics of transition waves in phase-transforming metamaterials with hierarchical architecture, i.e., 1D/2D periodic systems comprising a network of intersecting chains of elastically-coupled bi-stable elements. To this end, we develop continuum models of discrete 1D systems that, nevertheless, also elucidate the transition wave dynamics in 2D environments, which have received little attention in the literature. We find the potential driving and the wavelength relative to the hierarchical dimensions to play important roles in determining the wave mobility. The unique construction provokes some interesting results, including the growth of non-circular domains and the stabilization of domains of arbitrarily prescribed morphology; the latter representing an avenue toward reconfigurable performance via domain patterning. Altogether, in a break from the paradigm of homogeneity, the results not only elucidate the influence of hierarchy on the dynamics of phase-transforming metamaterials, but also its potential utility.