Auxetic behavior on demand: a three steps recipe for new designs

Auxetic behavior is a fascinating mechanical property which probably represents the paradigm of mechanical metamaterials. Despite that nowadays it is a widely known phenomenon, a fundamental micro-mechanical understanding which allows the proper control and design of new auxetic material remains mystified. In this letter we show an important step forward setting a unified framework for a large class of auxetic materials composed of 2D rotating rigid units. In addition, a simple pathway for the design of new auxetic material is established based on three simple rules. In particular, we construct for the first time exotic crystals, quasi-crystal and isotropic materials with negative Poisson ratio, which in an ideal design reach the perfect auxetic limit. At the core of this behavior is a low energy mode reminiscent of a non trivial floppy mode that exists in the idealized scenario. A natural connection between 2D rotating rigid auxetic with an antiferromagnetic spin is established which allows to identify general properties of the material. Finally, we show that the auxetic response is robust under small perturbation in the design.