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Wrinkling Hierarchy in Constrained Thin Sheets from Suspended Graphene to Curtains

Hugues Vandeparre, Miguel Piñeirua, Fabian Brau, Benoit Roman, José Bico, Cyprien Gay, Wenzhong Bao, Chun Ning Lau, Pedro M. Reis, and Pascal Damman
Phys. Rev. Lett. 106, 224301 – Published 2 June 2011
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Abstract

We show that thin sheets under boundary confinement spontaneously generate a universal self-similar hierarchy of wrinkles. From simple geometry arguments and energy scalings, we develop a formalism based on wrinklons, the localized transition zone in the merging of two wrinkles, as building blocks of the global pattern. Contrary to the case of crumpled paper where elastic energy is focused, this transition is described as smooth in agreement with a recent numerical work [R. D. Schroll, E. Katifori, and B. Davidovitch, Phys. Rev. Lett. 106, 074301 (2011)]. This formalism is validated from hundreds of nanometers for graphene sheets to meters for ordinary curtains, which shows the universality of our description. We finally describe the effect of an external tension to the distribution of the wrinkles.

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  • Received 23 February 2011

DOI:https://doi.org/10.1103/PhysRevLett.106.224301

© 2011 American Physical Society

Synopsis

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A hierarchy of wrinkles

Published 2 June 2011

Thin sheets of length scales ranging from graphene to paper are shown to exhibit a universal behavior of self-similar wrinkling patterns.

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Authors & Affiliations

Hugues Vandeparre1, Miguel Piñeirua2, Fabian Brau1, Benoit Roman2, José Bico2, Cyprien Gay3, Wenzhong Bao4, Chun Ning Lau4, Pedro M. Reis5, and Pascal Damman1,*

  • 1Laboratoire Interfaces et Fluides Complexes, CIRMAP, Université de Mons, 20 Place du Parc, B-7000 Mons, Belgium
  • 2PMMH, CNRS UMR 7636, ESPCI, Paris-Tech, Univ. Paris 6 and Paris 7, 10 Rue Vauquelin, 75231 Paris Cedex 05, France
  • 3Matière et Systèmes Complexes, Université Paris Diderot—Paris 7, CNRS, UMR 7057, Bâtiment Condorcet, F-75205 Paris cedex 13, France
  • 4Department of Physics and Astronomy, University of California, Riverside, California 92521, USA
  • 5Departments of Mechanical Engineering and Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

  • *pascal.damman@umons.ac.be

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Issue

Vol. 106, Iss. 22 — 3 June 2011

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