Geometry, topology and mechanics of twisted elastic fibers

Abstract

Elastic rods and fibers are ubiquitous in physical and biological systems across a range of length scales, from microtubules to construction beams. In this thesis, we explore the impact of twist on the failure and stability of elastic rods by studying fragmentation and knot dynamics. We begin with a famous phenomenon in elastic rod fragmentation observed by Feynman, who discovered that dry spaghetti typically breaks into three or more pieces when exposed to large bending stresses. Combining theory, experiments and analytic scaling arguments, we demonstrate that twist may be used to achieve binary fracture of brittle elastic rods. Additionally, we show that quenching allows for robust control of the fragmentation cascade. In the second half of this thesis, we use twist to investigate the stability of softer fibers in knotted configurations. We identify twist-based topological counting rules that explain the relative stability of bend knots, which are used to tie two ropes together. These counting rules reveal an underlying stability phase diagram which agrees with numerical simulations and experimental testing of several climbing and sailing knots. Combining the notions of structural and topological stability, we then investigate the energy discharge dynamics of a knotted elastic fiber after it is broken. We show that this class of topological batteries contains special topologically resonant states for which energy release is superslow. Finally, we apply our topological model to surgical knots. Through numerical simulation, we show that topology can be used to identify mechanically stable and balanced suture knots.