Numerical study on bending response of auxetic 2D-lattice plates

Abstract

In this study, the bending response of 2D-lattice plates having auxetic unit cells is determined by using the homogenization method based on equivalent strain energy. The auxetic unit cells in this study are different topologies of re-entrant hexagonal unit cells. In the homogenization method, the effective out-of-plane elastic properties of an auxetic 2D-lattice plate are obtained from the strain energy values of its unit cell under different curvature modes, determined by the finite element method. In the analysis, the auxetic unit cells are considered as frames whose struts are modeled as Euler beams. The effective elastic properties, i.e., the effective bending moduli, Poisson’s ratios, and shear modulus, are described as the bending response of a 2D-lattice plate subjected to out-of-plane bending. In the validation, the effective elastic properties of some auxetic 2D-lattice plates obtained from their unit cells by the homogenization method are numerically compared with those obtained from direct structural analysis of the plates. Besides, the obtained results show how the bending response of the auxetic 2D-lattice plates can be adjusted by varying their unit-cell geometries, especially the internal cell angle.