Vol. 11, No. 5, 2018

Download this article
Download this article For screen
For printing
Recent Issues

Volume 12
Issue 4, 867–1148
Issue 3, 605–866
Issue 2, 259–604
Issue 1, 1–258

Volume 11, 8 issues

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editors’ Interests
Scientific Advantages
Submission Guidelines
Submission Form
Editorial Login
Ethics Statement
Contacts
Author Index
To Appear
 
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
The shape of low energy configurations of a thin elastic sheet with a single disclination

Heiner Olbermann

Vol. 11 (2018), No. 5, 1285–1302
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 W2,2(B1 Bρ; 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