IDR/Collaborative Research: Experimental and Computational Foundations for Nonlinear Pattern Formation in the Deposition of Elastic Rods

IDR/合作研究：弹性棒沉积中非线性图案形成的实验和计算基础

• 批准号: 1129917
• 负责人: Eitan Grinspun
• 金额: $ 32.1万
• 依托单位: Columbia University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-09-01 至 2015-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1129917&HistoricalAwards=false
• 关键词: IDR; Collaborative; Research; Experimental; Computational

The goal of this research grant is to elucidate the mechanism and predictively understand the physics of coiling patterns obtained when thin flexible elastic filaments (rods) are deposited onto rigid substrates. The investigation requires the complementary interplay between high-precision model experiments and computational geometric mechanics codes. An important aspect of the project is the porting of techniques from the field of computer graphics as predictive engineering tools. The first stage of research examines the base configuration, in which a rod is injected onto a static or moving conveyor belt, generating a series of coiling patterns. The transitions between coiling phases are mapped and rationalized through mathematical modeling. The second stage of research examines more complicated forms of loading of the thin rod including (a) torsion as a control parameter to precisely generate the coiling patterns, (b) aerodynamic drag of the hanging filament, and (c) adhesion onto the substrate. The third stage studies coiling over non-flat complex topographies, seeking to develop a generalized statistical description of the resulting coiling trajectories. The construction of more predictive models for the motion of flexible filaments will help addressing engineering problems spanning a wide range of physical scales: from micro-fabrication of electronic components using the coiling of nanotubes, serpentine interconnects for stretchable electronics, and 3D-printing technologies, to the laying down of transoceanic cable and pipelines onto the seabed in a more efficient and resilient manner. A mathematical, physical and scalable understanding of the deformation of filaments is also a step towards addressing the fundamental question of how geometry governs the mechanics of thin structures; a topic that is currently receiving interest from both the physics and mechanics communities. The computational codes developed in this project will be broadly disseminated. These, together with the gained fundamental understanding, will serve as new design tools for engineers and physicists who deal with slender filaments in diverse fields including automotive-, aerospace-, biomedical-, civil-, environmental-, geological-, and mechanical-engineering.

这项研究资助的目标是阐明机制并预测性地了解当薄的柔性弹性丝（棒）沉积到刚性基材上时获得的卷绕图案的物理原理。该研究需要高精度模型实验和计算几何力学代码之间的互补相互作用。该项目的一个重要方面是将计算机图形领域的技术移植为预测工程工具。研究的第一阶段检查基本配置，其中将杆注入静态或移动的传送带上，产生一系列卷绕图案。通过数学建模绘制卷绕阶段之间的过渡并使其合理化。研究的第二阶段研究更复杂的细棒加载形式，包括（a）扭转作为控制参数以精确生成卷绕图案，（b）悬挂灯丝的空气动力阻力，以及（c）粘附到基板上。第三阶段研究非平坦复杂地形上的盘绕，寻求对所产生的盘绕轨迹进行广义统计描述。为柔性细丝的运动构建更具预测性的模型将有助于解决跨越广泛物理尺度的工程问题：从使用纳米管卷绕的电子元件的微制造、用于可拉伸电子产品的蛇形互连以及 3D 打印技术，以更高效、更有弹性的方式将跨洋电缆和管道铺设到海底。对细丝变形的数学、物理和可扩展理解也是解决几何学如何控制薄结构力学这一基本问题的一步。这是目前物理学界和力学界都感兴趣的话题。该项目开发的计算代码将被广泛传播。这些知识加上所获得的基本理解，将成为工程师和物理学家在汽车、航空航天、生物医学、土木、环境、地质和机械工程等不同领域处理细长丝的新设计工具。 。