Tunable Topologically Protected Waveguiding in Auxetic Nonlinear Metamaterials

In this paper, we discuss the possibility of achieving tunable topologically protected edge modes through the application of uniaxial prestrain in an auxetic metamaterial. The proposed structure consists of a thin slab with oriented cuts in a hexagonal lattice, where topologically protected band gaps are opened by introducing a controlled variation in selected cut lengths. Numerical simulations demonstrate the existence of topologically protected and scatter-free wave propagation in the structure at the interface between two subdomains with modified cells, in distinct frequency ranges. For the metamaterial considered in this study, this happens only in the presence of auxeticity. In addition, exploiting geometrical nonlinearity, the application of a uniaxial prestrain can be used to close the band gaps or to modify their frequency range, i.e., to weaken the localization effects or to shift the frequency at which they occur. The spatial and temporal variation of the applied strain field can thus be used for the dynamic tuning of metamaterial topological waveguiding properties, with applications in mechanical devices for logic operations and computation.