Shape and Motion of a Ruck in a Rug

John M Kolinski , Pascale M Aussillous (1) , L M Mahadevan (2, 3, 4, 5)

1 IUSTI - Institut universitaire des systèmes thermiques industriels
2 SEAS - Harvard John A. Paulson School of Engineering and Applied Sciences
3 Wyss Institute for Biologically Inspired Engineering [Harvard University]
4 Harvard University
5 KIBST - Kavli Institute for Bionano Science & Technology [Harvard University]

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.

Domaines: Matière Molle [cond-mat.soft]

John M Kolinski, Pascale M Aussillous, L M Mahadevan. Shape and Motion of a Ruck in a Rug. Physical Review Letters, 2009, 103, ⟨10.1103/PhysRevLett.103.174302⟩. ⟨hal-01431999⟩