Modeling of the out-of-plane mechanical response of a laminated cellular structure showing negative Poisson’s ratio under uniaxial tensile deformation

Abstract

In this study, we analyze the mechanical responses of the two types of laminated cellular structures using finite element models based on a homogenization method. In the numerical simulations, we obtain the homogenized elastic modulus tensors for the two structural units and show that the cellular structure, which is bridged by additional beams, exhibits strong auxeticity with high negative values of Poisson's ratio in the lamination direction, while retaining the in-plane negative Poisson's ratios. We then assess the sensitivity of the linear and nonlinear out-of-plane response to changes in the component geometry. According to the analytical results, we propose a simple periodic framework consisting polyhedron blocks and spherical joints, which can represent the similar auxetic behavior the cellular structure exhibits in the in-plane and out-of-plane directions.