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.

从航运到航行再到手术，每天都会使用数千种不同类型的结，每种结都需要特定的力来拉紧，该力通常取决于结的材料特性、摩擦力和拓扑结构。也具有承载能力；超过这个水平的力会导致结解开，并且过度的力可能会导致结的材料断裂，并且有些结在没有任何外力的情况下很容易松散。 ，结可以储存能量这一概念被称为拓扑电池，它对 DNA 中的纳米级结和结构工程中的宏观结都有影响。这项工作将支持研究结的基础科学。与此同时，它将制定实验技术来系统地研究这种力学，并通过开发本科生和研究生课程的教学工具（视频、笔记和演示）来补充该研究。公开发布。该项目的研究目标是量化弹性杆上结的机械响应，该项目将采用（1）受计算机图形学启发的快速数值模拟，（2）具有可定制摩擦力的创新材料，以及（3）自主机器人实验。即使是最基本的结（反手结），打结所需的力也取决于 (1) 弹性、(2) 摩擦力和 (3) 之间复杂的相互作用。拓扑。上手结可能会经历超过临界拉力的突然屈曲不稳定性，这种不稳定性表明了结的机械行为的丰富性。将研究常见的结，例如反手结和鞋带结，利用模拟工具的计算速度和机器人实验的自主性，将量化几种类型结的机械响应，以建立其力学库。用于合理化结的机械响应作为拓扑、材料和摩擦参数的函数的变化，与元素周期表类似，将制定基于力学的结分类方案，其中对结进行分组。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力优点和更广泛的影响审查标准进行评估，被认为值得支持。

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