The Life and Times of a Ruck in a Rug

We study the familiar problem of a ruck in a rug. Under lateral compression, a rug bends out of the plane forming a ruck - a localised region in which it is no longer in contact with the floor. We consider the equilibrium of such a ruck. Once the external force that caused the compression is removed, experience tells us that the ruck may either remain or flatten out under its own weight. We quantify the conditions under which each of these two scenarios occurs. We also consider how the propagation of a ruck along the carpet facilitates large-scale sliding.