A novel auxetic unit cell for 3D metamaterials of designated negative Poisson's ratio

Metamaterials have promising applications in many fields such as those in medical, electronic and civil engineering. However, the existing unit cell designs for metamaterials are with limited range of achievable properties, and establishing an auxetic unit cell for general three-dimensional (3D) metamaterial structures is so far a challenge. This work proposes a novel unit cell design for metamaterials of designated 3D negative Poisson's ratios (NPR). Theoretical formulas accommodating complex mechanics quantities that govern the substructural deformation in metamaterials were first established to predict the NPR. Based on this, some 3D metamaterials were fabricated with the aid of an additive manufacturing technique. The properties of the metamaterials were examined both experimentally and numerically against the theoretical predictions. It was found that the new auxetic unit cell and the theoretical formulas can effectively realize the design of metamaterials with predic table 3D-NPR metamaterials for practical applications.