Statics and inertial dynamics of a ruck in a rug

TL;DR

This paper investigates the formation, stability, and motion of a ruck in a rug, revealing critical compression thresholds and inertial traveling solutions, with experimental validation and implications for contact slip dynamics.

Contribution

It introduces a detailed analysis of the critical conditions for ruck formation and inertial traveling solutions, combining theoretical modeling with experimental confirmation.

Findings

A critical initial compression threshold for ruck flattening.

Existence of a traveling ruck solution with specific energy-tension relations.

Experimental validation of theoretical predictions.

Abstract

We consider the familiar problem of a bump, or ruck, in a rug. Under lateral compression, a rug bends out of the plane forming a ruck -- a localized region in which it is no longer in contact with the floor. We show that when the external force that created the ruck is removed, the ruck flattens out unless the initial compression is greater than a critical value, which we determine. We also study the inertial motion of a ruck that is generated when one end of the rug is moved rapidly. We show that the equations of motion admit a travelling ruck solution for which a linear combination of the tension and kinetic energy is determined by the ruck size. We confirm these findings experimentally. We end by discussing the potential implications of our work for the analogous propagation of localized slip pulses in the sliding of two bodies in contact.