The Shape and Motion of a Ruck in a Rug

TL;DR

This paper investigates the shape and motion of a ruck in a rug, using experiments and analysis to understand how it starts rolling on inclined surfaces, with implications for soft interface mechanics.

Contribution

It provides a detailed study of the static and dynamic behavior of a ruck in a thin sheet, including the critical angle for motion and the relation between speed and inclination.

Findings

Ruck shape quantified on horizontal planes.

Critical inclination angle for rolling identified.

Ruck speed proportional to sine of inclination angle.

Abstract

The motion of a ruck in a rug is used as an analogy to explain the role of dislocations in the deformation of crystalline solids. We take the analogy literally and study the shape and motion of a bump, wrinkle or ruck in a thin sheet in partial contact with a rough substrate in a gravitational field. Using a combination of experiments, scaling analysis and numerical solutions of the governing equations, we first quantify the static shape of a ruck on a horizontal plane. When the plane is inclined, the ruck becomes asymmetric and moves by rolling only when the the inclination of the plane reaches a critical angle. We find that the angle at which this first occurs is larger than the angle at which the ruck stops, i.e. static rolling friction is larger than dynamic rolling friction. Once the ruck is in motion, it travels at a constant speed proportional to the sine of the angle of inclination, a result that we rationalize in terms of a simple power balance. We conclude with a simple implication of our study for the onset of rolling motion at soft interfaces.