Unlike regular elastic materials, when auxetic materials are compressed, they become thinner in the direction perpendicular to the applied force. Despite their outstanding mechanical properties, a systematic design of new and controlled auxetics remains underdeveloped. Here we establish a unified framework to describe bidimensional perfect auxetics with potential use in the design of new materials. Inspired by a natural connection between rotating rigid units and antiferromagnetic spin systems, we unveil the conditions for the emergence of a non-trivial floppy mode responsible for the auxetic behaviour. This model establishes three simple steps to design new auxetics. In particular, we constructed an exotic crystal, a Penrose quasi-crystal and the long-desired isotropic auxetic. The auxeticity of these designs is robust under small structural disturbances, as seen from experiments and numerical simulations. We expect that this work will allow the implementation of auxetic behaviour into advanced materials to enhance their functionalities, with a promising extension into 3D auxetics.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.