Directional mechanical response in the bulk of topological metamaterials

TL;DR

This paper demonstrates that topological properties of Maxwell lattices enable directional bulk mechanical responses, allowing stress and strain to be directed selectively within the structure, which can inform design of advanced mechanical metamaterials.

Contribution

It introduces a bulk metric for mechanical polarization based on topological invariants and explores how bond removal affects floppy modes and bulk responses in Maxwell lattices.

Findings

Applying force in the bulk induces directional stress or strain.

Topological invariants predict mechanical polarization.

Bond removal alters floppy modes and bulk response patterns.

Abstract

Mechanical metamaterials are those structures designed to convey force and motion in novel and desirable ways. Recently, Kane and Lubensky showed that lattices at the point of marginal mechanical stability (Maxwell lattices) possess a topological invariant that describes the distribution of floppy, zero-energy edge modes. Here, we show that applying force at a point in the bulk of these lattices generates a directional mechanical response, in which stress or strain is induced only on one side of the force. This provides both a bulk metric for mechanical polarization and a design principle to convey stresses and strains towards or away from parts of the structure. We also characterize the effects of removing bonds on the material's structure and floppy modes, establishing a relationship between edge modes and bulk response.