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)PRLTAO0031-900710.1103/PhysRevLett.106.074301]. 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.
- Publication:
-
Physical Review Letters
- Pub Date:
- June 2011
- DOI:
- 10.1103/PhysRevLett.106.224301
- arXiv:
- arXiv:1012.4325
- Bibcode:
- 2011PhRvL.106v4301V
- Keywords:
-
- 46.32.+x;
- Static buckling and instability;
- Condensed Matter - Materials Science;
- Condensed Matter - Soft Condensed Matter;
- Nonlinear Sciences - Adaptation and Self-Organizing Systems
- E-Print:
- 7 pages, 4 figures, added references, submitted for publication