The shape of low energy configurations of a thin elastic sheet with a single disclination

Abstract

We consider a geometrically fully nonlinear variational model for thin elastic sheets that contain a single disclination. The free elastic energy contains the thickness $h$ as a small parameter. We give an improvement of a recently proved energy scaling law, removing the next-to leading order terms in the lower bound. Then we prove the convergence of (almost-)minimizers of the free elastic energy towards the shape of a radially symmetric cone, up to Euclidean motions, weakly in the spaces $W^{2,2}(B_1\setminus B_{\rho };{\mathbb{R}}^3)$ for every $0<\rho <1$, as the thickness $h$ is sent to 0.

18 pages, 3 figures

References in corpus (3)

• Virus shapes and buckling transitions in spherical shells
• Convex integration for the Monge-Ampère equation in two dimensions
• Energy scaling law for the regular cone

Cited by in corpus (2)

• On a boundary value problem for conically deformed thin elastic sheets
• Wrinkling of an elastic sheet floating on a liquid sphere