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Putting a spin on metamaterials: Mechanical incompatibility as magnetic frustration

Ben Pisanty, Erdal C. Oguz, Cristiano Nisoli, Yair Shokef

SciPost Phys. 10, 136 (2021) · published 8 June 2021


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.

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