Abstract Critical drawback of poor stiffness in traditional auxetic materials limits them to be applied where negative Poisson’s ratio behavior and excellent load-bearing capacity are simultaneously desired. In this work, a general prescription for designing auxetic lattice structures with high stiffness and controllable isotropic/anisotropic elastic properties is proposed. Based on it, we rationally design a class of novel auxetic lattice structures whose deformation is mainly governed by the stretching mechanisms and conducted an investigation on a tree-like re-entrant structure. A combination of theoretical predictions, numerical simulations and tensile test experiments have been carried out to gain a comprehensive understanding of the structural in-plane elastic mechanical properties along both the principal axes as well as in the off-axis directions. Besides, theoretical model for designing tree-like re-entrant structure with isotropic elastic properties is established and experimentally verified with specimens fabricated with CFRP composite. The results of this research has proven the tree-like re-entrant structure exhibits excellent effective Young’s modulus, shear modulus and obvious negative Poisson’s ratio effect along omni-direction. Investigation on the directional dependence of structural effective elastic properties has further indicated the proposed structure presents a great potential for designing auxetic material with controllable anisotropic elastic properties. In particular, the proposed structure is capable in achieving isotropic design with any negative Poisson’s ratio between −1 and 0. The design philosophy presented in this paper provides a general prescription for solving the challenge of poor stiffness in traditional auxetic materials and paves a new way for isotropic auxetic design.

中文翻译：

---

具有高刚度和可控弹性各向异性的复合树状折返结构

摘要 传统拉胀材料刚度差的严重缺陷限制了它们在同时需要负泊松比行为和优异承载能力的情况下的应用。在这项工作中，提出了设计具有高刚度和可控各向同性/各向异性弹性特性的拉胀晶格结构的通用方法。在此基础上，我们合理设计了一类变形主要受拉伸机制控制的新型拉胀晶格结构，并对树状可重入结构进行了研究。结合理论预测，已经进行了数值模拟和拉伸试验实验，以全面了解沿主轴和离轴方向的结构面内弹性力学性能。此外，建立了设计具有各向同性弹性特性的树状折返结构的理论模型，并用CFRP复合材料制成的试样进行了实验验证。研究结果证明，树状凹入结构在全方向上表现出优异的有效杨氏模量、剪切模量和明显的负泊松比效应。对结构有效弹性特性的方向依赖性的研究进一步表明，所提出的结构在设计具有可控各向异性弹性特性的拉胀材料方面具有巨大的潜力。特别是，所提出的结构能够在-1和0之间的任何负泊松比下实现各向同性设计。 本文提出的设计理念为解决传统拉胀材料刚度差的挑战提供了一般性的解决方案，并开辟了一条新的途径用于各向同性拉胀设计。