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

这项研究资助的目标是阐明机制，并预测性地理解当薄的柔性弹性细丝（杆）沉积在刚性基底上时获得的卷曲图案的物理学。研究需要高精度模型试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移植计算机图形学领域的技术作为预测工程工具。研究的第一阶段检查了基本配置，其中将杆注入到静态或移动的传送带上，产生一系列盘绕模式。通过数学建模映射并合理化卷绕阶段之间的过渡。研究的第二阶段检查细杆的更复杂的加载形式，包括（a）作为控制参数的扭转以精确地产生卷绕图案，（B）悬挂细丝的空气动力学阻力，以及（c）粘附到基底上。第三阶段研究在非平坦复杂地形上的盘绕，寻求对所得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：从使用纳米管盘绕的电子元件的微制造，用于可拉伸电子产品的蛇形互连和3D打印技术，到以更有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学如何支配薄结构力学这一基本问题的一步;这一主题目前受到物理学和力学界的关注。该项目中开发的计算机代码将广泛传播。这些，以及所获得的基本理解，将作为新的设计工具，为工程师和物理学家谁处理细长细丝在不同领域，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.