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Asymptotic phenomena in pressurized thin films

Citation

Coman, CD and Matthews, MT and Bassom, AP, Asymptotic phenomena in pressurized thin films, Proceedings of the Royal Society of London A, 471, (2182) Article 20150471. ISSN 1364-5021 (2015) [Refereed Article]

Copyright Statement

Copyright 2015 The Author(s)

DOI: doi:10.1098/rspa.2015.0471

Abstract

An asymptotic study of the wrinkling of a pressurized circular thin film is performed. The corresponding boundary-value problem is described by two non-dimensional parameters; a background tension μ and the applied loading P. Previous numerical studies of the same configuration have shown that P tends to be large, and this fact is exploited here in the derivation of asymptotic descriptions of the elastic bifurcation phenomena. Two limiting cases are considered; in the first, the background tension is modest, while the second deals with the situation when it is large. In both instances, it is shown how the wrinkling is confined to a relatively narrow zone near the rim of the thin film, but the mechanisms driving the bifurcation are different. In the first scenario, the wrinkles are confined to a region which, though close to the rim, is asymptotically separate from it. By contrast, when μ is larger, the wrinkling is within a zone that is attached to the rim. Predictions are made for the value of the applied loading P necessary to generate wrinkling, as well as details of the corresponding wrinkling pattern, and these asymptotic results are compared to some direct numerical simulations of the original boundary-value problem.

Item Details

Item Type:Refereed Article
Keywords:wrinkling instabilities, thin films, boundary layers, perturbation analysis
Research Division:Mathematical Sciences
Research Group:Applied Mathematics
Research Field:Theoretical and Applied Mechanics
Objective Division:Expanding Knowledge
Objective Group:Expanding Knowledge
Objective Field:Expanding Knowledge in the Mathematical Sciences
Author:Bassom, AP (Professor Andrew Bassom)
ID Code:105658
Year Published:2015
Web of Science® Times Cited:5
Deposited By:Mathematics and Physics
Deposited On:2016-01-12
Last Modified:2016-10-03
Downloads:0

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