Calculus of Variations and Geometric Measure Theory
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S. Müller - H. Olbermann

Conical singularities in thin elastic sheets

created by olbermann on 23 Jul 2019

[BibTeX]

preprint

Inserted: 23 jul 2019

Year: 2012

ArXiv: 1208.4298 PDF

Abstract:

When one slightly pushes a thin elastic sheet at its center into a hollow cylinder, the sheet forms (to a high degree of approximation) a developable cone, or "d-cone" for short. Here we investigate one particular aspect of d-cones, namely the scaling of elastic energy with the sheet thickness. Following recent work of Brandman, Kohn and Nguyen we study the Dirichlet problem of finding the configuration of minimal elastic energy when the boundary values are given by an exact d-cone. We improve their result for the energy scaling. In particular, we show that the deviation from the logarithmic energy scaling is bounded by a constant times the double logarithm of the thickness.

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