Numerical investigation of the mechanical properties of 2D and 3D auxetic structures

Auxetic materials and structures have a negative Poisson's ratio and it is this unique property that differentiates them from traditional materials. In recent years, three-dimensional (3D) auxetic structures have attracted considerable interest with the emergence of advanced manufacturing technologies. Many studies have been carried out to determine the mechanical properties of the existing 3D structures or improve and develop new ones, and extensive research is ongoing. This paper presents a comparative numerical study of two-dimensional (2D) and 3D geometries of four different auxetic structures, namely: elliptic holes, lozenge grids, re-entrant and arrowhead. Among these structures, elliptic holes and lozenge grids are designed and studied in 3D for the first time in this study. The structures are analysed under axial tension and the Poisson's ratio, Young's modulus and stiffness values are obtained from linear finite element model analysis. In addition, the unit cells of the 3D structures are examined. The findings showed that the elliptical holes structure exhibits a higher negative Poisson's ratio than other auxetics and the 3D re-entrant and 2D arrowhead structures outperform the other auxetics with respect to the Young's modulus and stiffness values.