Asymptotic phenomena in pressurized thin films

Ciprian D. Coman, Miccal T. Matthews, Andrew P. Bassom

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

An asymptotic study of the wrinkling of a pressurized circular thin film is performed. The corresponding boundary-value problem is described by two nondimensional parameters; a background tension ì 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 ì 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.

LanguageEnglish
Article number20150471
Pages1-19
Number of pages19
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume471
Issue number2182
DOIs
Publication statusPublished - 8 Oct 2015
Externally publishedYes

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Wrinkling
wrinkling
Boundary value problems
Thin Films
Thin films
rims
Direct numerical simulation
thin films
boundary value problems
Bifurcation
Boundary Value Problem
direct numerical simulation
Two Parameters
Numerical Study
derivation
Limiting
Tend
Scenarios
Configuration
Necessary

Cite this

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abstract = "An asymptotic study of the wrinkling of a pressurized circular thin film is performed. The corresponding boundary-value problem is described by two nondimensional parameters; a background tension {\`i} 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 {\`i} 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.",
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Asymptotic phenomena in pressurized thin films. / Coman, Ciprian D.; Matthews, Miccal T.; Bassom, Andrew P.

In: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 471, No. 2182, 20150471, 08.10.2015, p. 1-19.

Research output: Contribution to journalArticle

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