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

Olbermann, Heiner
(2018) Analysis & PDE — Vol. 11, n° 5, p. 1285-1302 (2018)

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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;ℝ3) for every 0<ρ<1, as the thickness h is sent to 0.
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  • Universität Leipzig

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Olbermann, H. (2018). The shape of low energy configurations of a thin elastic sheet with a single disclination. Analysis & PDE, 11(5), 1285-1302. https://hdl.handle.net/2078.5/125386 (Original work published 2018)