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

Olbermann, Heiner

doi:10.2140/apde.2018.11.1285

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

Heiner Olbermann

Vol. 11 (2018), No. 5, 1285–1302

DOI: 10.2140/apde.2018.11.1285

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 $W^{2, 2} (B_{1} ∖ B_{ρ}; ℝ^{3})$ for every $0 < ρ < 1$ , as the thickness $h$ is sent to 0.

Keywords

nonlinear elasticity, thin elastic sheets, d-cones, Hessian determinant

Mathematical Subject Classification 2010

Primary: 49Q10, 74K20

Milestones

Received: 20 July 2017

Revised: 9 October 2017

Accepted: 22 November 2017

Published: 11 April 2018

Authors

Heiner Olbermann
Universität Leipzig Leipzig Germany

Vol. 11, No. 5, 2018