Geared topological metamaterials with tunable mechanical stability

Abstract

The classification of materials into insulators and conductors has been shaken up by the discovery of topological insulators that conduct robustly at the edge but not in the bulk. In mechanics, designating a material as insulating or conducting amounts to asking if it is rigid or floppy. Although mechanical structures that display topological floppy modes have been proposed, they are all vulnerable to global collapse. Here, we design and build mechanical metamaterials that are stable and yet capable of harboring protected edge and bulk modes, analogous to those in electronic topological insulators and Weyl semimetals. To do so, we exploit gear assemblies that, unlike point masses connected by springs, incorporate both translational and rotational degrees of freedom. Global structural stability is achieved by eliminating geometrical frustration of collective gear rotations extending through the assembly. The topological robustness of the mechanical modes makes them appealing across scales from engineered macrostructures to networks of toothed microrotors of potential use in micro-machines.

15 pages, 8 figures; new title, added discussion and appendices; see http://wwwhome.lorentz.leidenuniv.nl/~paulose/topological-gears/ for accompanying videos. To appear in PRX

References in corpus (14)

• Topological Photonics
• Observation of phononic helical edge states in a mechanical 'topological insulator'
• Topological Phononic Crystals with One-Way Elastic Edge Waves
• Topological mechanics of gyroscopic metamaterials
• Topologically protected elastic waves in phononic metamaterials
• Topological modes bound to dislocations in mechanical metamaterials
• Nonlinear conduction via solitons in a topological mechanical insulator
• Selective buckling via states of self-stress in topological metamaterials
• Topological mechanics of origami and kirigami
• Mechanical Weyl Modes in Topological Maxwell Lattices
• Force Mobilization and Generalized Isostaticity in Jammed Packings of Frictional Grains
• Rigid cluster decomposition reveals criticality in frictional jamming
• Transmission of torque at the nanoscale
• Topological boundary modes in jammed matter

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• Topological nodal states in circuit lattice
• Many-Body Topological and Skin States without Open Boundaries
• Non-Hermitian Topological Metamaterials with Odd Elasticity
• Switchable phonon diodes using nonlinear topological Maxwell lattices
• Nonlinearity-induced transition in nonlinear Su-Schrieffer-Heeger model and nonlinear higher-order topological system
• Extreme Spatial Dispersion in Nonlocally-Resonant Elastic Metamaterials
• Directional mechanical response in the bulk of topological metamaterials
• Localizing softness and stress along loops in three-dimensional topological metamaterials
• Kink-antikink asymmetry and impurity interactions in topological mechanical chains
• Nonlinear Topological Mechanics in Elliptically Geared Isostatic Metamaterials
• Signatures of Topological Phonons in Superisostatic Lattices
• Origin and localization of topological band gaps in gyroscopic metamaterials
• Topological Toda lattice and nonlinear bulk-edge correspondence
• Self-Assembly of Isostatic Self-Dual Colloidal Crystals
• Quench dynamics and bulk-edge correspondence in nonlinear mechanical systems
• Controlling the Deformation of Metamaterials: Corner Modes via Topology
• Electric Circuit Realizations of Fracton Physics
• Supersymmetry on the lattice: Geometry, Topology, and Flat Bands
• Nonlinear topological phase diagram in dimerized sine-Gordon model
• Topological Micro-Electro-Mechanical Systems
• Classifying topological floppy modes in the continuum
• Nonlinear dynamical topological phases in Cooper-pair box array