Abstract

Auxetics are an unusual family of materials that, for instance, when stretched in a particular direction will exhibit an expansion of the dimensions that are perpendicular to the applied stress; however, despite many known examples of auxectics there is no universal description of the material properties. Here, the authors report a model based on antiferromagnetic spins and demonstrate how this can be used to design a auxetic material with a Poisson ratio of -1 over a range of finite strain. 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.