Asymptotic phenomena in pressurized thin films

C.D. Coman, Miccal Matthews, Andrew Bassom

    Research output: Contribution to journalArticle

    8 Citations (Scopus)

    Abstract

    © 2015 The Author(s) Published by the Royal Society. All rights reserved. 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.
    Original languageEnglish
    Pages (from-to)1-19
    JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
    Volume471
    Issue number2182
    DOIs
    Publication statusPublished - 2015

    Fingerprint

    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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    title = "Asymptotic phenomena in pressurized thin films",
    abstract = "{\circledC} 2015 The Author(s) Published by the Royal Society. All rights reserved. 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.",
    author = "C.D. Coman and Miccal Matthews and Andrew Bassom",
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    language = "English",
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    pages = "1--19",
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    Asymptotic phenomena in pressurized thin films. / Coman, C.D.; Matthews, Miccal; Bassom, Andrew.

    In: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 471, No. 2182, 2015, p. 1-19.

    Research output: Contribution to journalArticle

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    AU - Matthews, Miccal

    AU - Bassom, Andrew

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    N2 - © 2015 The Author(s) Published by the Royal Society. All rights reserved. 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.

    AB - © 2015 The Author(s) Published by the Royal Society. All rights reserved. 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.

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