title: Compression induced folding of a sheet: an integrable system.
abstract: The apparently intractable shape of a fold in a compressed elastic film lying on a fluid substrate is found to have an exact solution. Such systems buckle at a nonzero wave vector set by the bending stiffness of the film and the weight of the substrate fluid. Our solution describes the entire progression from a weakly displaced sinusoidal buckling to a single large fold that contacts itself. The pressure decrease is exactly quadratic in the lateral displacement. We identify a complex wave vector whose magnitude remains invariant with compression.
authors: Raymond & Beverly Sackler School of Chemistry, Tel Aviv University, Tel Aviv 69978, Israel. hdiamant@tau.ac.il
authors: Haim
authors: H
authors: Diamant
authors: Thomas A
authors: TA
authors: Witten
mesh_terms: D004548:Elasticity; D055595:Mechanical Phenomena; D017711:Nonlinear Dynamics