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

这项研究拨款的目的是阐明机制，并预测性地理解当弹性细丝(棒)沉积在刚性衬底上时所获得的卷曲图案的物理性质。这项研究需要高精度模型试验和计算几何力学程序之间的互补作用。该项目的一个重要方面是将计算机图形学领域的技术作为预测工程工具进行移植。研究的第一阶段考察了底座结构，在底座结构中，将一根杆子注入静止或移动的传送带上，产生一系列卷曲图案。通过数学建模，对卷取阶段之间的过渡进行了映射和合理化。第二阶段的研究考察了细杆的更复杂的载荷形式，包括(A)作为控制参数的扭转以精确地生成卷绕图案，(B)悬挂细丝的气动阻力，以及(C)对衬底的附着。第三阶段研究在非平坦的复杂地形上的盘绕，寻求开发所产生的盘绕轨迹的通用统计描述。建立更具预测性的柔性细丝运动模型将有助于解决跨越各种物理尺度的工程问题：从使用纳米管缠绕的电子部件的微型制造、用于可拉伸电子设备的蛇形互连和3D打印技术，到以更有效和更有弹性的方式将跨洋电缆和管道铺设到海床上。对细丝变形的数学、物理和可扩展的理解也是朝着解决几何如何管理薄结构的力学这一基本问题迈出的一步；这是目前物理学和机械界都感兴趣的话题。在该项目中开发的计算代码将得到广泛传播。这些，再加上所获得的基本认识，将成为工程师和物理学家处理不同领域的细丝的新设计工具，这些领域包括汽车、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.