### 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.

Language | English |
---|---|

Article number | 20150471 |

Pages | 1-19 |

Number of pages | 19 |

Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |

Volume | 471 |

Issue number | 2182 |

DOIs | |

Publication status | Published - 8 Oct 2015 |

Externally published | Yes |

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*Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences*,

*471*(2182), 1-19. [20150471]. https://doi.org/10.1098/rspa.2015.0471

}

*Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences*, vol. 471, no. 2182, 20150471, pp. 1-19. https://doi.org/10.1098/rspa.2015.0471

**Asymptotic phenomena in pressurized thin films.** / Coman, Ciprian D.; Matthews, Miccal T.; Bassom, Andrew P.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Asymptotic phenomena in pressurized thin films

AU - Coman, Ciprian D.

AU - Matthews, Miccal T.

AU - Bassom, Andrew P.

PY - 2015/10/8

Y1 - 2015/10/8

N2 - 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 - 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.

KW - Boundary layers

KW - Perturbation analysis

KW - Thin films

KW - Wrinkling instabilities

UR - http://www.scopus.com/inward/record.url?scp=84946025288&partnerID=8YFLogxK

U2 - 10.1098/rspa.2015.0471

DO - 10.1098/rspa.2015.0471

M3 - Article

VL - 471

SP - 1

EP - 19

JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

T2 - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

SN - 0080-4630

IS - 2182

M1 - 20150471

ER -