Ghavidelnia Naeim, Bodaghi Mahdi, Hedayati Reza
Department of Mechanical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Hafez Ave, Tehran 1591634311, Iran.
Department of Engineering, School of Science and Technology, Nottingham Trent University, Nottingham NG11 8NS, UK.
Materials (Basel). 2021 Feb 20;14(4):993. doi: 10.3390/ma14040993.
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.
机械超材料是人工设计的结构，具有自然界中未曾发现的前所未有的机械性能。最著名的机械超材料之一是负泊松比材料，它表现出负泊松比（NPR）行为，这在多个工业应用中非常有益。在本研究中，对一种特定类型的负泊松比超材料结构，即理想化的三维凹角结构进行了分析、数值和实验研究。该结构由三种类型的支柱组成——一种仅承受轴向载荷，另外两种同时承受弯曲和轴向载荷，它们相互倾斜，并由角度θ和φ在空间上定义。基于两个著名的梁理论，即欧拉 - 伯努利梁理论和铁木辛柯梁理论，推导了三维凹角单元胞的弹性模量、屈服应力和泊松比的解析关系。此外，实施了两种有限元方法，一种基于梁单元，另一种基于体积单元。此外，通过增材制造（3D打印）制作了多个试样，并在压缩状态下进行测试。一方面，解析结果与实验结果吻合良好，另一方面，与体积有限元模型结果也吻合良好。此外，研究了各种几何参数对结构力学性能的影响，结果表明，角度θ（与受拉主导的支柱相关）对泊松比的符号及其大小影响最大，而角度φ（与受压主导的支柱相关）对泊松比的影响最小。然而，受压主导的支柱（由角度φ定义）为结构提供强度和刚度。结果还表明，对于特定范围的θ和φ角度，该结构的泊松比可以为零。最后，引入了一种轻量化的三维凹角结构，并将其结果与理想化的三维凹角结构的结果进行比较。
