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Conical singularities in thin elastic sheets

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Olbermann, Heiner [Universität Hamburg] Müller, Stefan [Universität Bonn]

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.

Document type Article de périodique (Journal article) – Article de recherche
Access type Accès libre
Publication date 2014
Language Anglais
Journal information "Calculus of Variations and Partial Differential Equations" - Vol. 49, no.3, p. 1177-1186 (2014)
Peer reviewed yes
Publisher Springer (Heidelberg)
issn 0944-2669
e-issn 1432-0835
Publication status Publié
Affiliation Universität Hamburg
Links
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Bibliographic reference Olbermann, Heiner ; Müller, Stefan ; et. al. Conical singularities in thin elastic sheets. In: Calculus of Variations and Partial Differential Equations, Vol. 49, no.3, p. 1177-1186 (2014)
Permanent URL http://hdl.handle.net/2078/203007