Topological defects steer stresses in two- and three-dimensional combinatorial mechanical metamaterials

Mechanical metamaterials present a promising platform for seemingly impossible mechanics. They often require frustration 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 mechanical defects in two and three dimensions and for arbitrary building blocks. We apply this method to two- and three-dimensional metamaterials, and show how topological defects can be implemented to steer stresses and strains in a controlled and non-trivial manner. This can inspire constructing materials with hitherto unknown complex mechanical response.