Collaborative Research: Mechanics of Knots and Tangles of Elastic Rods

合作研究：弹性杆结和缠结的力学

• 批准号: 2101745
• 负责人: Bashir Khoda
• 金额: $ 14.19万
• 依托单位: University of Maine
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2021
• 资助国家: 美国
• 起止时间: 2021-10-01 至 2024-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2101745&HistoricalAwards=false
• 关键词: Collaborative; Research; Mechanics; Knots; Tangles

In settings from shipping to sailing to surgery, thousands of different types of knots are used every day, each requiring a specific amount of force to tighten. This force depends on the material properties, friction, and the topology of the knot. A knot typically also has a load-bearing capacity; force beyond this level causes the knot to be undone, and excessive force may result in material failure in the knot. Moreover, some knots hold tight without any external force while others easily get untangled. In other words, the knots can store energy in the material. This concept is called a topological battery with implications in nanometer-sized knots in DNA to macroscopic knots in structural engineering. This award supports research to understand the fundamental science of knots. The work will develop modeling and computational methods for the analysis of the mechanics of knots and tangles. In parallel, it will formulate experimental techniques to systematically study this mechanics. The research will be complemented by developing teaching tools (videos, notes, and demonstrations) for undergraduate and graduate courses. The computational software will also be made publicly available. The research objective of this project is to quantify the mechanical response of knots tied in elastic rods. The project will employ (1) fast numerical simulations inspired by computer graphics, (2) innovative materials with customizable friction, and (3) autonomous robotic experiments to untangle the mechanics of knots. Even in the case of the most basic type of knots (overhand knots), the force required to tie the knot depends on an intricate interplay of (1) elasticity, (2) friction, and (3) topology. Interestingly, the overhand knot may undergo a snap-through buckling instability beyond a critical amount of pull. Such instability in a basic knot points to the richness of the mechanical behavior of knots. After developing simulation and experimental tools, the mechanical response and instabilities of a few common knots, e.g. overhand and shoelace knots, will be investigated. Exploiting the computational speed of the simulation tool and autonomy of robotic experiments, the mechanical response of several types of knots will be quantified to build a library of their mechanics. This data will be used to rationalize the variation of a knot’s mechanical response as a function of the topological, material, and frictional parameters. Similar to the periodic table of elements, a mechanics-based classification scheme of knots will be formulated, where the knots will be grouped into various classes, such as, friction-dominated knots, bending-dominated knots, and others.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.

在从运输到航行到手术的设置中，每天都使用数千种不同类型的结，每种结都需要特定的力来拧紧。这种力取决于结的材料特性，摩擦和结的拓扑。结通常还具有承重能力。超出此级别的力会导致结式，过量的力可能导致结的材料故障。此外，有些结不带任何外力，而另一些结则很容易被弄脏。换句话说，结可以将能量存储在材料中。这个概念称为拓扑电池，在DNA中的纳米尺寸结中对结构工程中的宏观结进行了影响。该奖项支持研究以了解结的基本科学。这项工作将开发建模和计算方法，以分析结和缠结的力学。同时，它将制定实验技术，以系统地研究该力学。这项研究将通过为本科和研究生课程开发教学工具（视频，笔记和演示）来完成。计算软件也将公开可用。该项目的研究目的是量化弹性杆中并列的结的机械响应。该项目将采用（1）受计算机图形，（2）具有可自定义摩擦的创新材料启发的快速数值模拟，以及（3）自动机器人实验，以解开结的机械。即使是最基本的结（副结），打结所需的力也取决于（1）弹性，（2）摩擦和（3）拓扑的复杂相互作用。有趣的是，过度结可能会在关键的拉力中发生弯曲的屈曲不稳定。基本结中的这种不稳定性指出了结的机械行为。在开发了模拟和实验工具之后，一些常见结的机械响应和不稳定性，例如将调查过手声和鞋带结。利用模拟工具的计算速度和机器人实验的自主权，将量化几种类型的结的机械响应以构建其机械库。该数据将用于合理化结的机械响应的变化，这是拓扑，材料和滤波器参数的函数。 Similar to the periodic table of elements, a mechanics-based classification scheme of knots will be formulated, where the knots will be grouped into various classes, such as, friction-dominated knots, bending-dominated knots, and others.This award reflects NSF's statutory mission and has been deemed honestly of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

项目成果

Effect of Withdrawal Velocity on Particle Entrainment From Density Mismatched Mixture

退出速度对密度不匹配混合物中颗粒夹带的影响

• DOI: 10.1115/msec2022-85745
• 发表时间: 2022
• 期刊: Proceedings of the ASME 2022 17th International Manufacturing Science and Engineering Conference
• 作者: Shovon, S. M.;Khalil, Ibrahim;Alam, Adeeb;Khoda, Bashir
• 通讯作者: Khoda, Bashir

Size-Based Filtration of Poly-Disperse Micro-Particle by Dipping

基于尺寸的多分散微粒浸渍过滤

• DOI: 10.1115/msec2022-85680
• 发表时间: 2022
• 期刊: Proceedings of the ASME 2022 17th International Manufacturing Science and Engineering Conference
• 作者: Khalil, Md Ibrahim;Khoda, Bashir
• 通讯作者: Khoda, Bashir

Effect of molecular weight on polymer solution facilitated transfer of non-Brownian particles

• DOI: 10.1016/j.porgcoat.2022.107394
• 发表时间: 2023-03
• 期刊: Progress in Organic Coatings
• 影响因子: 6.6
• 作者: Bashir Khoda;W. Gramlich;S. Shovon;I. Khalil