Directions dependence of the elastic properties of a 3D augmented re-entrant cellular structure

In this paper, a 3D augmented re-entrant cellular structure (ARCS) is proposed and its Poisson's ratios and elastic properties can be modulated in a wide range. Based on the classical beam theory, the elastic properties on the principle directions are obtained as functions of the structural parameters and then are verified by finite element method (FEM) simulations. Compared with the classical 3D re-entrant cellular structure (RCS), the Young's moduli of the new 3D structure on the principal directions show a significant increase, and the Poisson's ratio can be tunable with the control of the internal parameters of cellular structure. In addition, the elastic properties on off-axis directions are obtained by analytical solutions, which show that the Young's moduli on the off-axis directions are much lower than the principle ones. In addition, the shear moduli also show strong dependence on the loading directions. Moreover, by stretching in the principal directions, the ARCS expands in all vertical directions when the moduli ratio is below 0.5. However, stretching in the off-axis directions, the Poisson's ratios are no longer negative in its vertical directions. The results suggest a possible approach to design new auxetic materials with tunable Poisson's ratios for engineering applications.