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 the elastic energy with the sheet thickness \(h\). Following recent work of Brandman et al. (2012) 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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