Non-symmetric localized fold of a floating sheet

Marco Rivetti

doi:10.1016/j.crme.2013.01.005

Non-symmetric localized fold of a floating sheet

Marco Rivetti ^1,²

¹ Université Pierre-et-Marie-Curie, UMR 7190, Institut Jean-Le-Rond-dʼAlembert, 4, place Jussieu, 75252 Paris cedex 05, France
² CNRS, UMR 7190, Institut Jean-Le-Rond-dʼAlembert, 4, place Jussieu, 75252 Paris cedex 05, France

Comptes Rendus. Mécanique, Volume 341 (2013) no. 3, pp. 333-338.

Abstract
Résumé

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 We prove that non-symmetric solutions also describe the shape of a soft strip withdrawn from a liquid bath, a physical problem that allows us to easily observe portions of non-symmetric profiles.

Le flambage dʼune poutre posée à la surface dʼun liquide présente un phénomène de localisation, qui consiste en une transition dʼun état de déformations distribuées et sinusoïdales vers un état avec un pli localisé. Les formes symétriques et antisymétriques du pli ont été récemment décrites par Diamant et Witten (2011), qui ont trouvé une solution exacte des équations non linéaires dʼéquilibre. Dans cette Note, on généralise ces solutions et on montre quʼil existe une famille continue de solutions dʼéquilibre qui donnent des formes de pli généralement non symétriques. On montre que les solutions non symétriques décrivent aussi la forme dʼune lamelle élastique retirée dʼun bain liquide. Cette dernière expérience permet dʼobserver facilement des portions de solutions non symétriques.

Received: 2012-10-09
Accepted: 2013-01-28
Published online: 2013-02-11

DOI: 10.1016/j.crme.2013.01.005

Keywords: Localized buckling, Wrinkle-to-fold transition, Integrable systems
Mots-clés : Flambage localisé, Transition rides-pli, Systèmes intégrables

Author's affiliations:

Marco Rivetti ^{1, 2}

¹ Université Pierre-et-Marie-Curie, UMR 7190, Institut Jean-Le-Rond-dʼAlembert, 4, place Jussieu, 75252 Paris cedex 05, France
² CNRS, UMR 7190, Institut Jean-Le-Rond-dʼAlembert, 4, place Jussieu, 75252 Paris cedex 05, France

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     author = {Marco Rivetti},
     title = {Non-symmetric localized fold of a floating sheet},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {333--338},
     publisher = {Elsevier},
     volume = {341},
     number = {3},
     year = {2013},
     doi = {10.1016/j.crme.2013.01.005},
     language = {en},
}

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Marco Rivetti. Non-symmetric localized fold of a floating sheet. Comptes Rendus. Mécanique, Volume 341 (2013) no. 3, pp. 333-338. doi : 10.1016/j.crme.2013.01.005. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2013.01.005/

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