Packing of elastic rings with friction

TL;DR

This study investigates how elastic rings deform within shrinking circular boundaries considering friction, revealing complex behaviors like sliding, bifurcations, and scaling laws influenced by friction levels.

Contribution

It introduces a spring-lattice computational model to analyze frictional effects on elastic ring deformations under confinement, highlighting new scaling laws and deformation sequences.

Findings

Deformation sequences involve spiraling and bifurcations depending on friction.

Elastic energy scales with wall radius, affected by friction coefficient.

High friction leads to buckling near the boundary.

Abstract

We study the deformations of elastic filaments confined within slowly-shrinking circular boundaries, under contact forces with friction. We perform computations with a spring-lattice model that deforms like a thin inextensible filament of uniform bending stiffness. Early in the deformation, two lobes of the filament make contact. If the friction coefficient is small enough, one lobe slides inside the other; otherwise, the lobes move together or one lobe bifurcates the other. There follows a sequence of deformations that is a mixture of spiraling and bifurcations, primarily the former with small friction and the latter with large friction. With zero friction, a simple model predicts that the maximum curvature and the total elastic energy scale as the wall radius to the -3/2 and -2 powers respectively. With nonzero friction, the elastic energy follows a similar scaling but with a prefactor up to 8 times larger, due to delayering and bending with a range of small curvatures. For friction coefficients as large as 1, the deformations are qualitatively similar with and without friction at the outer wall. Above 1, the wall friction case becomes dominated by buckling near the wall.