Analytically determining the mechanical properties of 2D and 3D auxeti̇c materials

In this study, the mechanical properties of different auxetic materials that are used in literature are analyzed by the finite element method. Also, a novel auxetic material is designed and its mechanical properties compared with the other auxetic materials. The novel auxetic material called as RDN and the materials that are named Re-entrant, Arrowhead, Lozenge Grids, Anti Tetrachiral and Elliptic Holes are modelled in 2D and 3D. Thus, 6 materials in 2D and 10 different materials in 3D are analyzed. The Poisson's ratio and stiffness values of the materials, under the influence of tensile loading in 2D and tensile as well as compression in 3D, are obtained by the linear analysis in ANSYS. Moreover, by considering the stresses as in the materials, weak regions are determined. For in 2D, the highest negative Poisson's ratio and stiffness values are obtained by Re-entrant material. Among 3D materials, the highest negative Poisson's ratio is obtained by Anti Tetrachiral material, and the highest stiffness value is obtained by Re-entrant material with an internal angle of 40o.