Controlling the Deformation of Metamaterials: Corner Modes via Topology

Abstract

Topological metamaterials have invaded the mechanical world, demonstrating acoustic cloaking and waveguiding at finite frequencies and variable, tunable elastic response at zero frequency. Zero frequency topological states have previously relied on the Maxwell condition, namely that the system has equal numbers of degrees of freedom and constraints. Here, we show that otherwise rigid periodic mechanical structures are described by a map with a nontrivial topological degree (a generalization of the winding number introduced by Kane and Lubensky) that creates, directs and protects modes on their boundaries. We introduce a model system consisting of rigid quadrilaterals connected via free hinges at their corners in a checkerboard pattern. This bulk structure generates a topological linear deformation mode exponentially localized in one corner, as investigated numerically and via experimental prototype. Unlike the Maxwell lattices, these structures select a single desired mode, which controls variable stiffness and mechanical amplification that can be incorporated into devices at any scale.

arXiv comment12 pages, 5 figures

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Cited by in corpus (6)

• Band theory and boundary modes of high-dimensional representations of infinite hyperbolic lattices
• Topology in non-linear mechanical systems
• Universal Continuum Theory for Topological Edge Soft Modes
• Soft topological modes protected by symmetry in rigid mechanical metamaterials
• Mirror-symmetry protected higher-order topological zero-frequency boundary and corner modes in Maxwell lattices
• Zero-frequency corner modes in mechanical graphene