Synthetically non-Hermitian nonlinear wave-like behavior in a topological mechanical metamaterial

Topological mechanical metamaterials have enabled new ways to control stress and deformation propagation. Exemplified by Maxwell lattices, they have been studied extensively using a linearized formalism. Herein, we study a two-dimensional topological Maxwell lattice by exploring its large deformation quasi-static response using geometric numerical simulations and experiments. We observe spatial nonlinear wave-like phenomena such as harmonic generation, localized domain switching, amplification-enhanced frequency conversion, and solitary waves. We further map our linearized, homogenized system to a non-Hermitian, nonreciprocal, one-dimensional wave equation, revealing an equivalence between the deformation fields of two-dimensional topological Maxwell lattices and nonlinear dynamical phenomena in one-dimensional active systems. Our study opens a regime for topological mechanical metamaterials and expands their application potential in areas including adaptive and smart materials and mechanical logic, wherein concepts from nonlinear dynamics may be used to create intricate, tailored spatial deformation and stress fields greatly transcending conventional elasticity.

Automated summary

In this study, a two-dimensional topological Maxwell lattice is investigated through geometric numerical simulations and experiments, revealing spatial nonlinear wave-like phenomena and an equivalence between the deformation fields of two-dimensional topological Maxwell lattices and nonlinear dynamical phenomena in one-dimensional active systems. This research opens up new possibilities for topological mechanical metamaterials and expands their application potential in areas such as adaptive and smart materials and mechanical logic, enabling the creation of intricate, tailored spatial deformation and stress fields using concepts from nonlinear dynamics.