Tunable Topological Wave Control in a Three-Dimensional Metastable Elastic Metamaterial

Abstract The concepts of topological insulators in condensed matter physics have been harnessed in elastic metamaterials to obtain quasi-lossless and omnidirectional guiding of elastic waves. Initial studies concerning topological wave propagation in elastic metamaterials focused on localizing waves in 1D or 2D mechanical structures. More recent investigations involving topological metamaterials have uncovered methodologies to achieve unprecedented control of elastic waves in 3D structures. However, a 3D topological metamaterial that can be tuned online to expand functionalities and respond to external conditions has yet to be developed. To advance the state of the art, this research proposes a tunable 3D elastic metamaterial that enables the reconfiguration of a topological waveguide through the switching of metastable states. Through careful design of internal bistable elements in the metastable unit cell, a switching methodology is developed to obtain topologically distinct lattices and a full topological bandgap. Analysis of the dispersion relation for a supercell reveals the presence of a topological surface state at the interface of topologically distinct lattices. Full-scale finite element simulations illustrate topological wave propagation in a 3D structure with a path that can be tailored on-demand. The research outcomes presented in this paper could be beneficial to potential applications requiring programmable and robust energy transport in 3D mechanical structures and serve as an inspiration for further work in adaptive 3D topological metamaterials.