Structure design of arc-shaped auxetic metamaterials with tunable Poisson’s ratio

Metamaterials with negative Poisson’s ratios, showing unusual properties, are worth studying and tunability for Poisson’s ratio is still a difficult problem. In this study, a 2 D/3D arc-shaped lattice metamaterial with tunable Poisson’s ratio is designed and fabricated by additive manufacturing technology. Experimental and numerical results indicate that structures with distinct geometric features exhibit different auxetic effects, which is attributed to the deformation mode shifting from bending to stretching of the arc-shaped beams. In the bending deformation stage, the designed structure exhibits a constant negative Poisson’s ratio. In the stretching deformation, Poisson’s ratio begins to increase. The calculation formula of Poisson's ratio has been theoretically deduced for auxetic metamaterial and verified by experiments and simulations. The Poisson’s ratio of structure can be designed by adjusting the angle of the arc-shaped ligaments. Three-dimensional (3 D) auxetic structures are designed by the periodic distribution of 2D structures horizontally and vertically, and exhibit auxetic behavior perpendicular to the loading direction. The results of 2D structures also can be applied to 3 D structures. The Poisson's ratio can also be adjusted by changing geometric parameters of 3D structures. These findings can offer new insight for the design and manufacturing of metamaterials with negative Poisson’s ratio.