Snap Buckling in Overhand Knots
Snap Buckling in Overhand Knots
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反手结中的卡扣屈曲
DOI：
10.1115/1.4056478
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发表时间：
2023
期刊：
影响因子：
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通讯作者：
Khalid Jawed, Mohammad
中科院分区：
文献类型：
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作者：
Tong, Dezhong;Choi, Andrew;Joo, Jungseock;Borum, Andy;Khalid Jawed, Mohammad
当弹性杆上的上手结被拉紧时，它可能会通过卡扣发生形状的突然变化。在这篇文章中，我们使用的离散微分几何（DDG）为基础的模拟和桌面实验相结合，探讨作为结拓扑结构，杆的几何形状和摩擦的函数屈曲的发病。在我们的设置中，两个开放的两端一个上手结慢慢拉开，这将导致在结环扣。我们称这种现象为“反转”，因为环似乎从结的一边到另一边移动得很厉害。由于编织物（结的自接触部分）和环（结的两端连接到编织物的部分）之间的弹性能量耦合，发生这种反转。实现了一个数值框架，结合离散的弹性杆与基于约束的摩擦接触的方法，探索反演在上手结。数值模拟鲁棒捕获反转的结，并发现是在良好的协议与实验结果。为了获得对反演过程的物理洞察，我们还开发了一个简化的结模型，该模型不需要模拟自接触，这使我们能够可视化导致卡扣屈曲的分叉。
When an overhand knot tied in an elastic rod is tightened, it can undergo a sudden change in shape through snap buckling. In this article, we use a combination of discrete differential geometry (DDG)-based simulations and tabletop experiments to explore the onset of buckling as a function of knot topology, rod geometry, and friction. In our setup, two open ends of an overhand knot are slowly pulled apart, which leads to snap buckling in the knot loop. We call this phenomenon “inversion” since the loop appears to move dramatically from one side of the knot to the other. This inversion occurs due to the coupling of elastic energy between the braid (the portion of the knot in self-contact) and the loop (the portion of the knot with two ends connected to the braid). A numerical framework is implemented that combines discrete elastic rods with a constraint-based method for frictional contact to explore inversion in overhand knots. The numerical simulation robustly captures inversion in the knot and is found to be in good agreement with experimental results. In order to gain physical insight into the inversion process, we also develop a simplified model of the knot that does not require simulation of self-contact, which allows us to visualize the bifurcation that results in snap buckling.