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arXiv · 1707.02940

An obstacle problem for conical deformations of thin elastic sheets

Alessio Figalli·Connor Mooney
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Abstract

A developable cone ("d-cone") is the shape made by an elastic sheet when it is pressed at its center into a hollow cylinder by a distance $ε$. Starting from a nonlinear model depending on the thickness $h > 0$ of the sheet, we prove a $Γ$-convergence result as $h \rightarrow 0$ to a fourth-order obstacle problem for curves in $\mathbb{S}^2$. We then describe the exact shape of minimizers of the limit problem when $ε$ is small. In particular, we rigorously justify previous results in the physics literature.

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Alessio Figalli, Connor Mooney. 2017-07-10. An obstacle problem for conical deformations of thin elastic sheets. https://doi.org/10.1007/s00205-017-1195-z

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