Calculus of Variations and Geometric Measure Theory

A. Figalli - C. Mooney

An obstacle problem for conical deformations of thin elastic sheets

created by figalli on 27 Oct 2017


Accepted Paper

Inserted: 27 oct 2017
Last Updated: 27 oct 2017

Journal: Arch. Ration. Mech. Anal.
Year: 2017


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.