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arXiv · 1107.5505

Compression induced folding of a sheet: an integrable system

Haim Diamant·Thomas A. Witten
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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.

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Haim Diamant, Thomas A. Witten. 2011-07-27. Compression induced folding of a sheet: an integrable system. https://doi.org/10.1103/physrevlett.107.164302

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