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.

设计了 3D 拉胀结构 (3D-AS)，其在小变形时的横向各向同性在很大程度上取决于某些几何参数。利用基于小变形周期性边界条件的能量法计算了3D-AS在每个加载方向上的泊松比和杨氏模量，并进行了参数分析。θ、t和b对 3D-AS 的泊松比和杨氏模量的影响通过理论分析、实验和数值模拟确定。结果表明，θ和t是影响3D-AS泊松比和杨氏模量的重要因素，b主要影响杨氏模量。特别是详细分析了 3D-AS 的横向各向同性。通过数值模拟，证明3D-AS在一定参数范围内表现出横向各向同性弹性。当θ ≥ 55°、t  ≤ 0.7 mm 或b  ≥ 3 mm时，3D-AS 在XY平面中表现出横向各向同性弹性。横向各向同性有效弹性特性可以通过修改结构几何形状进行大幅度调整。通过改变参数θ、t或b可以获得更理想的横向各向同性弹性特性的单元格。实验结果与理论分析和数值模拟吻合良好，证明了其准确性。