Directional instability-driven strain-dependent 3D auxetic metamaterials

Auxetic metamaterials have received increasing interest due to their distinct mechanical properties. However, most developed auxetic metamaterials feature a uniform auxeticity in the elastic deformation stage, which limits their functional applications. Here, based on double-elliptic-ring (DER) partial auxetic structures, an enhanced-double-elliptic-ring (EDER) structure with strain-dependent auxeticity is introduced. The proposed EDERs consist of DERs and an enhanced structure (ES). Under compression, the ES will exhibit directional instability owing to the shrinking of DERs, and these directional instabilities will enhance the auxetic behaviors of EDERs. Analytical and simulation models are carried out to explore the equivalent Young's modulus and Poisson's ratio of EDERs and are validated via experiments. The results show that the strain value in the shrinking direction is different in different regions due to the directional instability of the ES which occurs layer by layer. By varying the geometric parameters of the ES of the EDERs, its deformation can be programmed and EDERs display varying localized deformation mechanisms.