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

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.

12 pages, 7 figures

References in corpus (9)

• Topological Acoustics
• Topological modes bound to dislocations in mechanical metamaterials
• Nonlinear conduction via solitons in a topological mechanical insulator
• Nonlinear control of PT-symmetry and non-Hermitian topological states
• Topological solitons as addressable phase bits in a driven laser
• A road to reality with topological superconductors
• Intrinsically polar elastic metamaterials
• Modelling planar kirigami metamaterials as generalized elastic continua
• Nonlinear Topological Edge States: from Dynamic Delocalization to Thermalization

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• Nonlinear Topological Mechanics in Elliptically Geared Isostatic Metamaterials
• Percolation-induced PT symmetry breaking
• Strongly Nonlinear Topological Phases of Cascaded Topoelectrical Circuits
• Fully-Polarized Topological Isostatic Metamaterials in Three Dimensions
• Opening and closing a bandgap via alternating softening and hardening nonlinearities