*Accepted Paper*

**Inserted:** 27 oct 2017

**Last Updated:** 27 oct 2017

**Journal:** Arch. Ration. Mech. Anal.

**Year:** 2017

**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 $\epsilon$. Starting from a nonlinear model depending on the thickness $h > 0$ of the sheet, we prove a $\Gamma$-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 $\epsilon$ is small. In particular, we rigorously justify previous results in the physics literature.

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