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MP: Theoretische und Mathematische Grundlagen der Physik

MP 2: Hauptvorträge II

MP 2.1: Hauptvortrag

Dienstag, 8. März 2005, 16:30–17:25, TU MA043

Isometric embeddings and scaling laws in compressed elastic sheets — •Sergio Conti — Fachbereich Mathematik, Universitaet Duisburg-Essen, Lotharstr. 65, 47057 Duisburg

Crumpling a sheet of paper leads to the formation of complex folding patterns over several length scales. This can be understood on the basis of the interplay of a nonconvex elastic energy, which penalizes local stretching, and a small singular perturbation, which penalizes high curvature. We obtain, using a combination of explicit constructions and general results from differential geometry, an upper bound for the energy of a compressed thin sheet which scales as the thickness to the 5/3. Focussing on a simplified geometry we then prove optimality of this energy scaling.