Plewa Julian, Płońska Małgorzata, Junak Grzegorz
Faculty of Science and Technology, Institute of Materials Engineering, University of Silesia in Katowice, 75 Pułku Piechoty Str. 1a, 41-500 Chorzów, Poland.
Faculty of Materials Engineering, Silesian University of Technology, 44-100 Gliwice, Poland.
Materials (Basel). 2024 Feb 3;17(3):731. doi: 10.3390/ma17030731.
The subject of the work is analysis, which presents a renowned auxetic structure based on so-called rotating polygons, which has been subject to modification. This modification entails introducing pivot points on unit cell surfaces near rectangle corners. This innovative system reveals previously unexplored correlations between Poisson's ratio, the ratio of rectangle side lengths, pivot point placement, and structural opening. Formulas have been derived using geometric relationships to compute the structure's linear dimensions and Poisson's ratio. The obtained findings suggest that Poisson's ratio is intricately tied to the structure's opening degree, varying as the structure undergoes stretching. Notably, there are critical parameter limits beyond which Poisson's ratio turns positive, leading to the loss of auxetic properties. For elongated rectangles, extremely high negative Poisson's ratio values are obtained, but only for small opening angles, while with further stretching, the structure loses its auxetic properties. This observed trend is consistent across a broad category of structures comprised of rotating rectangles.
这项工作的主题是分析，它展示了一种基于所谓旋转多边形的著名负泊松比结构，该结构已经过修改。这种修改需要在矩形角附近的晶胞表面引入枢轴点。这个创新系统揭示了泊松比、矩形边长比、枢轴点位置和结构开口之间以前未被探索的相关性。利用几何关系推导出了计算结构线性尺寸和泊松比的公式。所得结果表明，泊松比与结构的开口程度密切相关，随着结构的拉伸而变化。值得注意的是，存在临界参数极限，超过该极限泊松比变为正值，导致负泊松比特性丧失。对于细长矩形，可获得极高的负泊松比值，但仅在小开口角度时，而随着进一步拉伸，结构会失去其负泊松比特性。在由旋转矩形组成的广泛结构类别中，观察到的这一趋势是一致的。
