Compression induced folding of a sheet: an integrable system
arXiv:1107.5505 · doi:10.1103/PhysRevLett.107.164302
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 wavevector 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 wavevector whose magnitude remains invariant with compression.
4 pages
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