Putting a spin on metamaterials: Mechanical incompatibility as magnetic frustration

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 general 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 nontrivial manner and can inspire the design of materials with hitherto unknown complex mechanical response.

Automated summary

Mechanical metamaterials provide a promising platform for seemingly impossible mechanics. By analogizing to ferromagnetic and antiferromagnetic binary spin interactions, identifying and analyzing topological mechanical defects for arbitrary building blocks becomes possible. These topological defects can steer stresses and strains in a controlled and nontrivial manner, inspiring the design of materials with complex mechanical response.