Wrinkling Hierarchy in Constrained Thin Sheets from Suspended Graphene to Curtains

• Main Authors: Vandeparre, Hugues (Author), Pineirua, Miguel (Author), Brau, Fabian (Author), Roman, Benoit (Author), Bico, Jose (Contributor), Gay, C. (Author), Bao, Wenzhong (Author), Lau, Chun Ning (Author), Reis, Pedro Miguel (Contributor), Damman, Pascal (Author)
• Other Authors: Massachusetts Institute of Technology. Department of Civil and Environmental Engineering (Contributor), Massachusetts Institute of Technology. Department of Mechanical Engineering (Contributor)
• Format: Article
• Language: English
• Published: American Physical Society, 2011-10-12T15:06:20Z.
• Subjects: Article
• Online Access: Get fulltext

 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.