A metamaterial design method applied to topologically protected mechanical metamaterials

Abstract

Mass-spring models provide a straightforward way to describe complex dynamic behavior of mechanical systems, such as topologically protected and backscattering-free surface phonons. Such discrete models also provide a means to translate these properties, based on the unique class of electronic materials of topological insulators, to the mechanical domain. This talk will discuss a systematic design process to take such a mass-spring model and implement its functionality directly into a metamaterial. The design method uses combinatorial searches plus gradient-based optimizations to determine the configuration of the metamaterial’s building blocks that replicates the behavior of the target mass-spring model. A key aspect of the design method is the use of “perturbative metamaterials”—i.e., metamaterials with weakly interacting unit cells. The weak coupling enables the design space to be divided into smaller sub-spaces that can be independently tuned, which results in an exponential speed-up of the design process. It also allows us to isolate the interactions between vibrational modes of its unit cells within the frequency range of interest, simplifying the inverse problem. The design method is illustrated through the example of engineering a 2D mechanical metamaterial that supports topologically protected and defect-immune edge modes, directly from the mass-spring model of a topological insulator.