Re-entrant auxetic lattices with enhanced stiffness: A numerical study

Traditional auxetic lattices are featured with negative Poisson's ratio but weak stiffness. In this work, a set of auxetic lattices with enhanced stiffness are proposed by adding a strengthening rib into conventional auxetic unit cells in a direction perpendicular to the re-entrant direction. The effective mechanical properties of these variants are calculated using the fast Fourier transform-based homogenization method, which show that their Young's modulus in 2D can be improved by approximately 200% along the strengthening direction without significant sacrifice of auxetic property. However, such an enhancement is weakened in 3D as the variant of a tetrahedral cell has an approximate 100% improvement of Young's modulus only at low relative density. Though the stiffness of a variant hexahedral cell can be doubled in 3D at a wide range of relative density, its Poisson's ratio remains negative only in a narrow range of relative density. The findings in this work will offer new opportunities for the applications of auxetic materials which not only need negative Poisson's ratio but also high stiffness.