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 ε . Starting from a nonlinear model depending on the thickness h > 0 of the sheet, we prove a Γ -convergence result as h → 0 to a fourth-order obstacle problem...

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Bibliographic Details
Published in:Archive for rational mechanics and analysis 2018-05, Vol.228 (2), p.401-429
Main Authors: Figalli, Alessio, Mooney, Connor
Format: Article
Language:English
Subjects:
Classical Mechanics
Complex Systems
Fluid- and Aerodynamics
Mathematical and Computational Physics
Physics
Physics and Astronomy
Theoretical
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Summary: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 ε . Starting from a nonlinear model depending on the thickness h > 0 of the sheet, we prove a Γ -convergence result as h → 0 to a fourth-order obstacle problem for curves in S 2 . We then describe the exact shape of minimizers of the limit problem when ε is small. In particular, we rigorously justify previous results in the physics literature.
ISSN:0003-9527
1432-0673
DOI:10.1007/s00205-017-1195-z