Effect of geometry on homogenised properties of selected auxetic metamaterials

Abstract

Our study investigates the influence of geometrical parameters of two types of auxetic metamaterials on their effective properties. In particular, we focus on three-dimensional lattice structures, which we represent with discrete beam models of their respective Periodic Unit Cells (PUCs). Limiting the scope of the study to linear elasticity, we compute the effective response of PUCs by plugging the kinematic ansatz of the first-order numerical homogenisation into the strain energy expression arising from the Direct Stiffness Method and minimising the energy with respect to the periodic fluctuation field. The obtained effective stiffness matrices are post-processed to arrive at elastic parameters as Poisson’s ratios coefficients, that are reported in different directions with respect to the key geometrical parameters.