Energy Scaling Laws for Conically Constrained Thin Elastic Sheets |
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Authors: | Jeremy Brandman Robert V Kohn Hoai-Minh Nguyen |
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Institution: | 1. Corporate Strategic Research Laboratory, ExxonMobil Research and Engineering Company, Annandale, NJ, 08801, USA 2. Courant Institute of Mathematical Sciences, New York University, New York, NY, 10012, USA 3. Department of Mathematics, University of Minnesota, Minneapolis, MN, 55455, USA
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Abstract: | We investigate low-energy deformations of a thin elastic sheet subject to a displacement boundary condition consistent with a conical deformation. Under the assumption that the displacement near the sheet’s center is of order h|logh|, where h?1 is the thickness of the sheet, we establish matching upper and lower bounds of order h 2|logh| for the minimum elastic energy per unit thickness, with a prefactor determined by the geometry of the associated conical deformation. These results are established first for a 2D model problem and then extended to 3D elasticity. |
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