Latitude-and-longitude-inspired three-dimensional auxetic metamaterials

Abstract As we all know, compression in one direction will cause expansion in the orthogonal direction for conventional materials. Similarly, stretching in one direction will give rise to contraction in the vertical direction. It is hence possible to combine these two properties to obtain a novel mechanism to create 3D structures with negative Poisson’s ratio (PR) in some directions and positive PR in other ones (partial auxetics). The latitude-and-longitude-inspired double-elliptic-ring structures (DERs) with tunable Poisson’s ratio and Young’s modulus are designed and studied in this work, which offers an effective way for achieving this mechanism. A 3D structure with negative Poisson’s ratio in three directions is also obtained via arranging the DERs alternately. Meanwhile, theoretical results show that the magnitude of Poisson’s ratio of DERs can reach -18.3. Experimental and simulation consequences indicate that the DERs can effectively reduce stress concentration and fracture possibility due to its smooth geometry. Another advantage of DERs is that it still has negative Poisson’s ratio effect under large levels of compression. This work can provide a useful reference for the design of 3D auxetic metamaterials with excellent properties, which is promising in some structural and functional applications.