title: Wrinkles and folds in a fluid-supported sheet of finite size.
abstract: A laterally confined thin elastic sheet lying on a liquid substrate displays regular undulations, called wrinkles, characterized by a spatially extended energy distribution and a well-defined wavelength λ. As the confinement increases, the deformation energy is progressively localized into a single narrow fold. An exact solution for the deformation of an infinite sheet was previously found, indicating that wrinkles in an infinite sheet are unstable against localization for arbitrarily small confinement. We present an extension of the theory to sheets of finite length L, accounting for the experimentally observed wrinkle-to-fold transition. We derive an exact solution for the periodic deformation in the wrinkled state, and an approximate solution for the localized, folded state. We find that a second-order transition between these two states occurs at a critical confinement Δ(F)=λ(2)/L.
authors.affiliation: Raymond & Beverly Sackler School of Physics & Astronomy, Tel Aviv University, Tel Aviv 6997801, Israel.
authors.forename: Oz
authors.initials: O
authors.lastname: Oshri
authors.affiliation: Nonlinear Physical Chemistry Unit, Université libre de Bruxelles (ULB), CP231, B-1050 Brussels, Belgium.
authors.forename: Fabian
authors.initials: F
authors.lastname: Brau
authors.affiliation: Raymond & Beverly Sackler School of Chemistry, Tel Aviv University, Tel Aviv 6997801, Israel.
authors.forename: Haim
authors.initials: H
authors.lastname: Diamant