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 $W^{2,2}\left(B_1\setminus B_{\rho };{ℝ}^3\right)$ for every $0<\rho <1$, as the thickness $h$ is sent to 0.