Periodic tetrahedral auxetic metamaterial

Abstract

In this work, we introduce a novel three-dimensional auxetic mechanical metamaterial consisting of rotating tetrahedra connected by ideal hinges at their vertices, arranged to form a periodic framework structure. Through analytical and kinematic approaches, we evaluated the deformation behavior of the proposed idealized model, revealing Poisson’s ratios ranging between −0.36 and −2.72 and a transverse isotropic response as a result of its geometry. A specimen of the proposed metamaterial concept is designed by introducing deformable ribs between the solid units, and fabricated via additive manufacturing in polymeric material. Auxetic behavior of the prototype was assessed through a compression test and accurately predicted by a full-scale Finite Element model. We envisage that this new metamaterial design can have a significant impact on a wide range of engineering applications, particularly as bone substitute biomaterial.