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Idealized 3D Auxetic Mechanical Metamaterial: An Analytical Numerical and Experimental Study

机译：理想化的3D辅助机械超材料：分析数值和实验研究

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摘要

Mechanical metamaterials are man-made rationally-designed structures that present unprecedented mechanical properties not found in nature. One of the most well-known mechanical metamaterials is auxetics, which demonstrates negative Poisson’s ratio (NPR) behavior that is very beneficial in several industrial applications. In this study, a specific type of auxetic metamaterial structure namely idealized 3D re-entrant structure is studied analytically, numerically, and experimentally. The noted structure is constructed of three types of struts—one loaded purely axially and two loaded simultaneously flexurally and axially, which are inclined and are spatially defined by angles θ and φ. Analytical relationships for elastic modulus, yield stress, and Poisson’s ratio of the 3D re-entrant unit cell are derived based on two well-known beam theories namely Euler–Bernoulli and Timoshenko. Moreover, two finite element approaches one based on beam elements and one based on volumetric elements are implemented. Furthermore, several specimens are additively manufactured (3D printed) and tested under compression. The analytical results had good agreement with the experimental results on the one hand and the volumetric finite element model results on the other hand. Moreover, the effect of various geometrical parameters on the mechanical properties of the structure was studied, and the results demonstrated that angle θ (related to tension-dominated struts) has the highest influence on the sign of Poisson’s ratio and its extent, while angle φ (related to compression-dominated struts) has the lowest influence on the Poisson’s ratio. Nevertheless, the compression-dominated struts (defined by angle φ) provide strength and stiffness for the structure. The results also demonstrated that the structure could have zero Poisson’s ratio for a specific range of θ and φ angles. Finally, a lightened 3D re-entrant structure is introduced, and its results are compared to those of the idealized 3D re-entrant structure.
机译：机械超材料是人造理性设计的结构，其在自然界中没有发现前所未有的机械性能。最着名的机械超材料之一是辅助物品，其展示了几个工业应用中非常有益的负泊松比（NPR）行为。在本研究中，在数值上，数值和实验研究了一种特定类型的辅助超材料结构即理想化的3D再参赛体结构。所述结构由三种类型的支柱构成，纯度轴向装载，并且同时弯曲和轴向加载，其倾斜并且通过角度θ和φ在空间限定。基于两个众所周知的光束理论导出了弹性模量，屈服应力和泊松比的分析关系，即Euler-Bernoulli和Timoshenko。此外，两个有限元基于光束元件接近一个，并且基于体积元素的一个。此外，几种样品被橡皮地制造（3D印刷）并在压缩下进行测试。分析结果与一方面的实验结果吻合良好，另一方面，体积有限元模型结果。此外，研究了各种几何参数对结构的机械性能的影响，结果表明角度θ（与张力主导的Struts相关）对泊松比的标志及其程度的影响最高，而角φ （与压缩主导的Struts相关）对泊松比的影响最低。然而，压缩主导的支柱（由角度φ）限定了结构的强度和刚度。结果还证明该结构可以具有零泊松的比率为θ和φ角度。最后，引入了一种照明的3D再参赛体结构，并将其结果与理想化的3D再参赛体结构的结果进行比较。

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