title: Wrinkling hierarchy in constrained thin sheets from suspended graphene to curtains.
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.
authors.affiliation: Laboratoire Interfaces et Fluides Complexes, CIRMAP, Université de Mons, Mons, Belgium.
authors.forename: Hugues
authors.initials: H
authors.lastname: Vandeparre
authors.forename: Miguel
authors.initials: M
authors.lastname: Piñeirua
authors.forename: Fabian
authors.initials: F
authors.lastname: Brau
authors.forename: Benoit
authors.initials: B
authors.lastname: Roman
authors.forename: José
authors.initials: J
authors.lastname: Bico
authors.forename: Cyprien
authors.initials: C
authors.lastname: Gay
authors.forename: Wenzhong
authors.initials: W
authors.lastname: Bao
authors.forename: Chun Ning
authors.initials: CN
authors.lastname: Lau
authors.forename: Pedro M
authors.initials: PM
authors.lastname: Reis
authors.forename: Pascal
authors.initials: P
authors.lastname: Damman