Mechanics of Dynamic Discontinuities

随着柔性物体的移动，它们的形状经常会出现不连续性。感兴趣的不连续性是诸如尖锐褶皱、与障碍物和引导物的接触或撕裂的特征。这项工作旨在了解这些不连续性的力学和动力学，并研究它们如何移动，以及它们如何影响整个柔性物体的运动。基础工程科学成果最终可能应用于许多不同的技术领域。弦、电缆、薄板和平板等薄而柔性的结构是许多工程系统的重要组成部分，包括能量收集技术、传感器、海洋和航空航天结构等。制造技术，如转移印刷和纺织加工也涉及薄，柔性结构及其接触不连续性的动态行为。机械超材料和变形装置依赖于通过铰链或其他尖锐特征连接的薄板或条带的操纵和响应。该项目还将通过向公众展示令人兴奋的现象，提供关于力学主题的宣传和教育机会。不连续面的动力学行为是分析力学中的一个基本课题。这项工作将适用于一个新的统一变分框架的非材料和结构的不连续性，包括扭结和折叠，移动接触和影响，剥离和撕裂的前线。该方法是新的，因为它把所有这些对象作为时间依赖的边界。这项工作是围绕三个项目组织的，每个项目代表不同类别的不连续性：1）电缆和胶带的拾取，冲击和剥离，2）膜，板和壳中的折叠，以及3）片材的破裂，撕裂和切割。这项工作将产生新的理论结果的动量和能量平衡，在这些系统中，和不连续运动的解析解。带链条的桌面实验将提供不连续动态接触的实验数据。

As flexible objects move, they often develop discontinuities in their shapes. Discontinuities of interest are features such as sharp folds, contacts with obstacles and guides, or tears. This work seeks to understand the mechanics and dynamics of these discontinuities and investigates how they move, and how they affect the motion of the flexible object as a whole. Fundamental engineering science outcomes may eventually be applied to many different technology domains. Thin, flexible structures like strings, cables, sheets, and plates are important components of many engineered systems, including, among other things, energy harvesting technologies, sensors, marine and aerospace structures. Manufacturing technologies such as transfer printing and textile processing also involve the dynamical behavior of thin, flexible structures and their contact discontinuities. Mechanical metamaterials and morphing devices rely on the manipulation and response of thin plates or strips linked by hinges or other sharp features. The project will also provide opportunities for outreach and education on topics in mechanics, through demonstration of exciting phenomena insightful to the general public. The dynamical behavior of discontinuities is a fundamental topic in analytical mechanics. The work will apply a new unifying variational framework for non-material discontinuities in materials and structures, including kinks and folds, moving contacts and impacts, and peeling and tearing fronts. The approach is new in that it treats all of these objects as time-dependent boundaries. The work is organized around three projects, each representing a different class of discontinuity: 1) Pickup, impact, and peeling of cables and tapes, 2) Propagating folds in membranes, plates, and shells, and 3) Cracking, tearing, and cutting of sheets. The work will generate novel theoretical results on momentum and energy balances in these systems, and analytical solutions for motions of discontinuities. Tabletop experiments with chains will provide experimental data on discontinuous dynamic contacts.