A programmable auxetic metamaterial with tunable crystal symmetry

Artificially-structured materials with negative Poisson's ratio, also known as auxetics, have been the focus of numerous studies over the past few decades. In this paper, using a group-theory-based symmetry reduction approach, and based on a structure composed of rotating rigid triangles, we propose a new approach to designing auxetic metamaterials. These metamaterials can be fabricated by using a variety of active or smart structural members that undergo different deformations when subjected to external stimulations, e.g. by using temperature-sensitive members in a temperature-changing environment. Then, by applying controlled stimuli to the initial structure, we obtain desired symmetry-reduced structural configurations which facilitate the programmability of Poisson's ratio. In particular, to demonstrate this programmable metamaterial design approach, starting with an auxetic metamaterial with an initial C3v symmetry, we apply an external stimulus to reduce the symmetry of the initial structural configuration. The deformed configurations, which belong to the symmetry groups C3, CS, and C1, enable us to program the Poisson's ratio of the metamaterial. We derive theoretical expressions for the Poisson's ratio associated with different symmetries, which are subsequently verified by numerical studies and proof-of-concept Kirigami models. We anticipate that this approach to designing programmable structures will open up new avenues of research in metamaterial design.