title: Shape and motion of a ruck in a rug.
abstract: The motion of a ruck in a rug is used as an analogy to explain the role of dislocations in crystalline solids. We take literally one side of this analogy 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 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 inclination of the plane reaches a critical angle, at a speed determined by a simple power balance. We find that the angle at which rolling starts is larger than the angle at which the ruck stops; i.e., static rolling friction is larger than dynamic rolling friction. We conclude with a generalization of our results to wrinkles in soft adherent extensible films.
authors.affiliation: School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA.
authors.forename: John M
authors.initials: JM
authors.lastname: Kolinski
authors.forename: Pascale
authors.initials: P
authors.lastname: Aussillous
authors.forename: L
authors.initials: L
authors.lastname: Mahadevan