Equivalent mechanical properties of auxetic lattices from discrete homogenization

Auxetic materials having a network like structure are analyzed in terms of their deformation mechanisms and equivalent homogenized mechanical properties thanks to the discrete asymptotic homogenization method. This systematic and predictive methodology is exemplified for five different 2D periodical lattices: the re-entrant hexagonal, hexachiral, cross chiral, rafters and the re-entrant square. The equivalent moduli and Poisson’s ratio are expressed in closed form versus the microbeam geometrical parameters and rigidities. As a novel result, the predicted homogenized properties depend on the slenderness of the beam, hence providing more accurate results in comparison to the literature. The studied lattices allow to explore the two main mechanisms responsible for negative Poisson’s ratio, the re-entrant and the rolling-up mechanism. Non-standard overall behaviors, such as traction-shear coupling occurring for the cross chiral lattice, are evidenced. Negative values of the Poisson’s ratio are obtained in a certain range of the configuration parameter of each lattice. Comparisons of the obtained homogenized moduli with finite element simulations show a very good accuracy of the predicted effective mechanical behavior.