Phase transformations in substrate-free dissipative multistable metamaterials

We show that propagating transitions fronts observed recently in multistable structural networks are analogous to solid-solid phase transformations in crystals and can therefore be described quantitatively as propagating shock fronts. We demonstrate that the well-established sharp-interface theory from shock physics agrees well with the exact and approximate wave solutions obtained from treating the multistable metamaterial as a discrete chain and as a homogenized continuum, respectively. We further discuss the energy transport that governs the underlying dynamic transition phenomenon. Through numerical examples we showcase the diverse nature of the achievable transition effects depending on the interplay between inertia and dissipation in the multistable network, which enables wave tailoring and guidance. We further confirm applicability of the theory by comparison to experimental data. Though focusing on one-dimensional transition front propagation as the most fundamental problem, our results and conclusions admit extension to higher dimensions. (C) 2020 Elsevier Ltd. All rights reserved.