Putting a spin on metamaterials: Mechanical incompatibility as magnetic frustration

TL;DR

This paper introduces a universal framework for understanding topological defects in mechanical metamaterials, revealing how incompatibility influences their mechanical behavior and enabling the design of materials with novel responses.

Contribution

It presents an analogy to magnetic spin interactions to analyze topological defects in mechanical metamaterials, advancing understanding of their role and potential for innovative material design.

Findings

Topological defects can steer stresses and strains in complex ways.

Differences between 2D and 3D metamaterials are highlighted.

The approach enables designing materials with unprecedented mechanical responses.

Abstract

Mechanical metamaterials present a promising platform for seemingly impossible mechanics. They often require incompatibility of their elementary building blocks, yet a comprehensive understanding of its role remains elusive. Relying on an analogy to ferromagnetic and antiferromagnetic binary spin interactions, we present a universal approach to identify and analyze topological mechanical defects for arbitrary building blocks. We underline differences between two- and three-dimensional metamaterials, and show how topological defects can steer stresses and strains in a controlled and non-trivial manner and can inspire the design of materials with hitherto unknown complex mechanical response.