A low porosity perforated mechanical metamaterial with negative Poisson’s ratio and band gaps

Auxetic perforated mechanical metamaterials (APMMs) with artificially designed architectures have attracted growing attention in recent years due to the relatively simple fabrication process and their unusual physical properties for broad ranges of potential applications. We present a new topological configuration of APMMs with low porosity that simultaneously exhibits the properties of negative Poisson's ratio and band gaps. The finite element method is employed to investigate the effects of the parameters of void porosity, aspect ratio and chord length on the Poisson's ratio and the range of band gaps. Our results demonstrate that a large range of Poisson's ratio can be achieved with low porosity, and interestingly, the Poisson's ratio and the frequency of lower band gap edge are decreased monotonically as the chord length increases. Furthermore, the comparison of stress–strain behaviors, tensile strength, and acoustic transmission characteristics between the proposed and the classical configurations of low porosity APMMs is given. The results show that the new configuration owns special underlying tensile deformation pattern and long ligament, which effectively alleviates the stress concentration caused by cusp and enhances the tensile strength of the structure. Moreover, compared to previous structural configurations, the proposed configuration shows lower bandwidth and better vibration control property.