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Asymptotic phenomena in pressurized thin films

journal contribution
posted on 2023-05-18, 15:42 authored by Coman, CD, Matthews, MT, Andrew BassomAndrew Bassom
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.

History

Publication title

Proceedings of the Royal Society of London A

Volume

471

Issue

2182

Article number

20150471

Number

20150471

Pagination

1-19

ISSN

1364-5021

Department/School

School of Natural Sciences

Publisher

Royal Soc London

Place of publication

6 Carlton House Terrace, London, England, Sw1Y 5Ag

Rights statement

Copyright 2015 The Author(s)

Repository Status

  • Restricted

Socio-economic Objectives

Expanding knowledge in the mathematical sciences

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