Synthetically Non-Hermitian Nonlinear Wave-like Behavior in a Topological Mechanical Metamaterial

TL;DR

This paper explores large deformation nonlinear wave phenomena in a 2D topological Maxwell lattice, revealing new behaviors and mapping them to non-Hermitian wave equations, expanding applications in smart materials and mechanical logic.

Contribution

It introduces a nonlinear, large deformation analysis of topological Maxwell lattices and establishes an equivalence with non-Hermitian wave systems, broadening the understanding of topological metamaterials.

Findings

Observation of harmonic generation and localized domain switching

Identification of amplification-enhanced frequency conversion

Detection of solitary wave phenomena

Abstract

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, non-reciprocal, 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 new 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 exceeding conventional elasticity.