Non-symmetric localized fold of a floating sheet

An elastic sheet lying on the surface of a liquid, if axially compressed, shows a transition from a smooth sinusoidal pattern to a well-localized fold. This wrinkle-to-fold transition is a manifestation of a localized buckling. The symmetric and antisymmetric shapes of the fold have recently been described by Diamant and Witten (2011), who found two exact solutions of the nonlinear equilibrium equations. In this Note, we show that these solutions can be generalized to a continuous family of solutions, which yields non-symmetric shapes of the fold. We prove that non-symmetric solutions also describe the shape of a soft strip withdrawn from a liquid bath, a physical problem that allows us to easily observe portions of non-symmetric profiles. (C) 2013 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.