Collaborative Research: Dynamics of Snapping of Tethers

这笔拨款将资助研究，使用于降落伞、系泊绳、牵引电缆、安全带和能量收集装置的柔性绳索的性能、可靠性和安全性的精确设计成为可能，从而促进科学进步，促进国家繁荣。无论是自由末端还是系在有效载荷上，在工程应用中，只有考虑到松弛物体突然被拉紧的潜在损伤诱发的断裂动力学，才能正确理解柔性绳索的行为。由于动能集中在电缆另一端附近的一个小区域，即使是在电缆一端轻微的拉扯也很容易将加速度和张力放大几个数量级。断裂过程的时间短暂性和相应的强空间能量局部化可能导致结构失效，但也可能是操纵有效载荷的一种方法。为了使研究人员和工程师能够量化、解释和预测一系列应用中的捕捉现象，该项目将建立理论和计算模型，这些模型将通过实验观察得到信息，并通过物理测试进行验证。为了鼓励参与STEM，将为内华达大学和德克萨斯大学奥斯汀分校的高中生开发一个关于蹦极动力学的教育模块。本研究旨在为柔性物体在有效不可扩展惯性运动到拉伸和弹性波产生之间的快速、非线性、松弛-紧绷转换建模方法奠定基础，并将该方法转化为有效的仿真技术。它将通过推导新的边界层渐近性和尺度分析来实现这些结果，这些分析可以捕捉突然出现的大空间张力梯度，以及动能与弹性势能之间的快速交换。然后，它建立在这样的技术在开发的降阶模型和异步时间积分器，克服了独特的数值挑战与几乎奇异的捕捉动力学。最后，将进行重力驱动的断裂实验，以探索不同的行为机制，并获得与理论和模拟比较的数据。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This grant will fund research that enables accurate design for performance, reliability, and safety of flexible ropes used in parachutes, mooring lines, towing cables, safety harnesses, and energy harvesting devices, thereby promoting the progress of science, and advancing the national prosperity. Whether free-ended or tethered to payloads, the behavior of flexible ropes in engineering applications can be properly understood only by accounting for potentially damage-inducing snapping-like dynamics whereby a slack object is suddenly pulled taut. Even mild yanking at one end of a cable can easily amplify accelerations and tensions by several orders of magnitude, as kinetic energy is focused on a small region near the cable’s other end. The temporal brevity of the snapping process and the corresponding strong spatial localization of energy may lead to structural failures but can also be a way to manipulate a payload. To allow researchers and engineers to quantify, explain, and predict snapping phenomena across a range of applications, this project will build theoretical and computational models that are informed by experimental observations and validated against physical tests. To encourage participation in STEM, an educational module on bungee jump dynamics will be developed for summer camp programs for high school students at the University of Nevada and the University of Texas at Austin.This research aims to develop the foundations of a modeling method for rapid, nonlinear, slack-taut transitions between effectively inextensible inertial motion to stretching and elastic wave generation of flexible objects, and to translate this method into efficient simulation techniques. It will accomplish these outcomes by deriving new boundary-layer asymptotics and scaling analyses that capture a sudden onset of large spatial gradients in tension and rapid exchange of kinetic energy to elastic potential energy and back again. It then builds on such techniques in the development of reduced order models and asynchronous time integrators that overcome unique numerical challenges associated with the nearly singular snapping dynamics. Finally, experiments on gravity-driven snapping will be performed to explore different regimes of behavior and to obtain data for comparison with theory and simulation.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.