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.