Examples of auxetic structures with phase transition

Auxetic structures are a distinct type of mechanical metamaterials that contract or expand laterally under compressive or tensile loads in the axial direction. Structures based on rotating polygons are a notable example of metamaterials with these properties. While structures built of rotating squares exhibit a Poisson’s ratio of minus one (–1), in structures of rotating rectangles, this ratio takes on larger negative and positive values. This indicates that a phase transition occurs, which has been confirmed theoretically as well as with physical models. Modified structures of rotating rectangles have been investigated in terms of the magnitude of elongation under tension and the value of Poisson’s ratio, and the necessary conditions for the emergence of mechanical phase transition have been determined. In particular, elongated rectangular unit cells, as well as higher values of the geometric parameter x, yield a range of elongation magnitudes at which Poisson’s ratio changes its sign. The tested structures were assembled from rectangular metal unit cells, which were connected by pivots at overlapping corners. This proven solution guarantees the possibility of cyclically stretching and compressing the structure and determining the critical point of elongation at which the Poisson’s ratio relationship loses continuity and reaches extreme negative and positive values. In addition, metamaterials that are assembled with such a method, whether in 2D or 3D, can be made to any size, allowing them to be designed and reconfigured to tailor them to their desired applications.