# An Obstacle Problem for Conical Deformations of Thin Elastic Sheets

An Obstacle Problem for Conical Deformations of Thin Elastic Sheets A developable cone (“d-cone”) is the shape made by an elastic sheet when it is pressed at its center into a hollow cylinder by a distance $${\varepsilon}$$ ε . Starting from a nonlinear model depending on the thickness h > 0 of the sheet, we prove a $${\Gamma}$$ Γ -convergence result as $${h \rightarrow 0}$$ h → 0 to a fourth-order obstacle problem for curves in $${\mathbb{S}^2}$$ S 2 . We then describe the exact shape of minimizers of the limit problem when $${\varepsilon}$$ ε is small. In particular, we rigorously justify previous results in the physics literature. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Archive for Rational Mechanics and Analysis Springer Journals

# An Obstacle Problem for Conical Deformations of Thin Elastic Sheets

, Volume 228 (2) – Nov 11, 2017
29 pages

/lp/springer_journal/an-obstacle-problem-for-conical-deformations-of-thin-elastic-sheets-LIKMgCr1X5
Publisher
Springer Berlin Heidelberg
Subject
Physics; Classical Mechanics; Physics, general; Theoretical, Mathematical and Computational Physics; Complex Systems; Fluid- and Aerodynamics
ISSN
0003-9527
eISSN
1432-0673
D.O.I.
10.1007/s00205-017-1195-z
Publisher site
See Article on Publisher Site

### Abstract

A developable cone (“d-cone”) is the shape made by an elastic sheet when it is pressed at its center into a hollow cylinder by a distance $${\varepsilon}$$ ε . Starting from a nonlinear model depending on the thickness h > 0 of the sheet, we prove a $${\Gamma}$$ Γ -convergence result as $${h \rightarrow 0}$$ h → 0 to a fourth-order obstacle problem for curves in $${\mathbb{S}^2}$$ S 2 . We then describe the exact shape of minimizers of the limit problem when $${\varepsilon}$$ ε is small. In particular, we rigorously justify previous results in the physics literature.

### Journal

Archive for Rational Mechanics and AnalysisSpringer Journals

Published: Nov 11, 2017

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