Elastic deformations and instabilities in thin fibers and films

Abstract

Systems across nearly all length scales can experience elastic deformations. The details of how a system deforms is generally determined by i) the way stresses and loads are applied, ii) size, shape, geometry, and physical constraints, and iii) the material properties of the system. Although the physical forces causing deformations are often simple in origin, the interplay between these forces and the physical constraints of these systems can produce instabilities – situations where small changes in loading can cause large and sometimes surprising mechanical effects. From an application-based perspective, These effects can lead to interesting and useful techniques as well as sometimes beautiful patterns and features reminiscent of complex, natural systems. This thesis centres on three research manuscripts, each concerning different elastic instabilities observed in slender elastic fibers. In the first paper (Chapter 3, published in the European Physical Journal E) we explore the effect of tension, compression, and torsion on slender fibers, and explain the looping and twisting behaviour observed with a simple linear elasticity model. The second paper (Chapter 4, published in Physical Review Letters), presents a novel interaction between slender elastic fibers and liquid-air bubbles on the surface of a liquid bath. We fi nd that for certain combinations of fiber and bubble (depending on size, thickness, material, etc), a fiber may partially penetrate and spontaneously wrap around the bubble at its liquid-air interface. In the third paper (Chapter 5, to be submitted), considers the elastic response of coupled elastic systems with incompatible strains. In this case a thin film is pre-strained before a slender fiber is affixed to its surface, acting like a strut or support. Then, biaxial tension and/or compression is applied to the film, causing the fiber to buckle and rotate in and out of the plane of the film in, ultimately, predictable and controllable ways. Lastly, an appendix is included, featuring several examples of the science writing I have done for less technical audiences, broadly related to the themes presented in this thesis.