A unified design method for 2D auxetic metamaterials based on a minimal auxetic structure

Auxetic metamaterials are architected structures that possess a unique property known as a negative Poisson's ratio. This remarkable characteristic enables them to expand or contract in a direction perpendicular to stretch or compression. Due to their exceptional attributes such as energy absorption and fracture resistance, these auxetic metamaterials hold great promise for various applications across multiple domains. However, the widespread development of these materials has been hindered by the absence of an efficient design method. Addressing this limitation, our work introduces a minimal 2D auxetic structure and a corresponding design approach that comprises two geometric transformations. This design method not only allows for the replication of existing auxetic structures but also facilitates the creation of novel structures. Additionally, it enables the classification of these structures into six distinct categories. To enhance the understanding and standardization of these structures, we propose a naming protocol and define their associated unit cell. Furthermore, we explore the possibilities of tessellations within this framework. Finally, we examine the auxetic structures from the perspective of surface strain, which is closely linked to the Poisson's ratio, the Bulk modulus and compressibility.