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

这项研究的目的是阐明机制，并预测性地理解当薄的柔性弹性细丝（棒）沉积在刚性基板上时获得的卷曲模式的物理。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学领域的技术移植为预测工程工具。研究的第一阶段检查基础配置，其中一根杆注入到静态或移动的传送带上，产生一系列的盘绕模式。通过数学建模，映射和合理化了线圈之间的过渡阶段。第二阶段的研究考察了更复杂的细杆加载形式，包括(a)以扭转为控制参数以精确生成盘绕模式，(b)悬挂灯丝的气动阻力，以及(c)附着在基板上。第三阶段研究非平坦复杂地形上的卷绕，寻求对卷绕轨迹的广义统计描述。为柔性细丝的运动建立更多的预测模型将有助于解决跨越各种物理尺度的工程问题：从使用纳米管卷曲的电子元件的微制造，可拉伸电子设备的蛇形互连和3d打印技术，到以更高效和更有弹性的方式在海底铺设跨洋电缆和管道。对细丝变形的数学、物理和可扩展的理解也是解决几何如何支配薄结构力学的基本问题的一步；这是目前物理界和力学界都很感兴趣的一个话题。本项目编制的计算代码将广泛传播。这些，连同获得的基本理解，将成为工程师和物理学家在不同领域处理细长细丝的新设计工具，包括汽车、航空航天、生物医学、土木、环境、地质和机械工程。

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.