Hierarchical design of auxetic metamaterial with peanut-shaped perforations for extreme deformation: Self-similar or not?

Hierarchical designs have exhibited great potential in reducing structural weight and improving mechanical properties. However, the hierarchical design of perforated auxetic metamaterials with curved holes is rarely investigated and the choice of self-similar hierarchical design or not still confuses us. In this study, two types of hierarchical designs with self-similar and non-self-similar features for the auxetic metamaterial with peanut-shaped perforations are realized and compared. First, the printed hierarchical auxetic metamaterials via additive manufacturing technology are tested by quasi-static tension to explore their mechanical performance in different directions. Correspondingly, the computational homogenization model is established to characterize their full elastic properties and its effectiveness is verified by the experimental results. Subsequently, the deformation mechanisms of the proposed hierarchical metamaterials are numerically analyzed to address the superiority of self-similar design over the non-self-similar design. Finally, the influences of microstructural parameters and hierarchy order on the effective elastic constants of the proposed hierarchical metamaterial are considered and the optimal topology with extreme auxetic behavior is recommended. The results indicate that the proposed self-similar hierarchical design exhibits significant anisotropic feature, which can serve the multidirectional mechanical requirements, and the remarkable enhancement in auxeticity can be attributed to the synergistic deformation of tetrachiral sub-elements. Besides, the increase of hierarchy order does not continuously enhance the auxetic behavior of hierarchical metamaterial, although it can effectively change the porosity of structure. Through such investigations, a meaningful guidance of property map is provided for the hierarchical design of auxetic metamaterial perforated by curved cuts.