Mechanical properties of 3D auxetic structure: Emergence of transverse isotropy

Abstract

The 3D auxetic structure (3D-AS) is designed, whose transverse isotropy at small deformations depends strongly on certain geometric parameters. Poisson's ratio and Young's modulus of the 3D-AS in each loading direction are calculated by using the energy method based on the periodic boundary condition at small deformations, and parametric analysis is performed. The effects of θ, t, and b on Poisson's ratio and Young's modulus of the 3D-AS are determined by theoretical analysis, experiments, and numerical simulations. The results show that θ and t are important factors affecting the Poisson's ratio and Young's modulus of 3D-AS, and that b mainly affects Young's modulus. In particular, the transverse isotropy of 3D-AS is analyzed in detail. Through numerical simulations, it is proved that the 3D-AS exhibits transverse isotropic elasticity within a certain parameter range. The 3D-AS exhibits transverse isotropic elasticity in the XY plane when θ ≥ 55°, t ≤ 0.7 mm, or b ≥ 3 mm. The transverse isotropic effective elastic properties can be largely adjusted by modifying the structural geometry. The more desired transverse isotropic elastic properties can be obtained by changing the parameters θ, t, or b of the unit cell. The experimental results agree well with the theoretical analysis and numerical simulations, and prove their accuracy.