The role of extensibility in the birth of a ruck in a rug

TL;DR

This paper investigates how finite extensibility of a rug allows for the formation of a ruck when its ends are brought together, resolving a paradox in classical inextensible models through theory and experiments.

Contribution

It introduces a model accounting for finite extensibility to explain ruck formation, supported by experimental validation.

Findings

Finite extensibility enables ruck formation with finite end-shortening.

Classical inextensible models predict infinite force for ruck creation.

Experimental results confirm the theoretical predictions.

Abstract

Everyday experience suggests that a `ruck' forms when the two ends of a heavy carpet or rug are brought closer together. Classical analysis, however, shows that the horizontal compressive force needed to create such a ruck should be infinite. We show that this apparent paradox is due to the assumption of inextensibility of the rug. By accounting for a finite extensibility, we show that rucks appear with a finite, non-zero end-shortening and confirm our theoretical results with simple experiments. Finally, we note that the appropriate measure of extensibility, the stretchability, is in this case not determined purely by geometry, but incorporates the mechanics of the sheet.