Non-orientable order and non-Abelian response in frustrated metamaterials

A little frustration to sharpen the metamaterial

“…In their recent preprint, Guo et al [1] design materials in which frustration becomes naturally wedded to global, topological properties. Although locally, it may seem that every element can satisfy its preferred configuration, globally, it is impossible for every element to simultaneously satisfy this configuration.…”

“…The topological feature that Guo et al [1] exploit is orientability. Heuristically, an orientable surface is one that encloses an "inside" volume and separates it from an "outside."…”

“…2) are non-orientable, which translates into surprising mechanics. When Guo et al [1] squeeze a Möbius strip from all sides, they show that a part of the shape remains undeformed because it does not know which way to buckle.…”

“…Although the ideas of topology and non-orientability appear abstract, Guo et al [1] bring them into the material world using state-of-the-art 3D printing of mechanical meta-surfaces and meta-rings. In the ring, Fig.…”

“…Just like for the orientation of a Möbius strip, the sense (a) (b) Introducing a new materials design principle of topological frustration is exciting, because we never know where these discoveries may lead. Guo et al [1] present one possible application: mechanical computers. The defects resulting from frustration can be thought of as bits in a computer, and manipulating several of these bits at once allows for simple arithmetic operations to be performed.…”