Valley-protected topological interface state of the elastic wave: From discrete model to multistable mechanical metamaterials

Topological metamaterials provide a new strategy to guide wave energy and exhibit unprecedented robustness. In this study, a novel design strategy is proposed to realize programmable topological metamaterials with local resonant eigenstates. Firstly, in the discrete spring-mass model, two resonant masses and two base masses are introduced into the hexagonal lattice, and a local resonant eigenstate-induced Dirac cone can be formed at the high symmetry point of the Brillouin zone. By introducing the spring stiffness difference, a topological bandgap is opened near the Dirac degeneracy frequency. Thereafter, the nontrivial nature of the bandgap is verified by the theoretical evaluation of the Berry curvature and Chern number. Secondly, the symmetry-breaking configuration is extended to a continuum plate-resonator model. The numerical results demonstrate that the interface state wave propagates along the interface path at a frequency located at the edge-bulk band. Finally, by using the asymmetric effective stiffness of the bistable structure between tension and compression, a programmable topological interface path is realized. The proposed reconfigurable design based on asymmetry significantly expands the design space of metamaterials.