On the wrinkling of a pre-stressed annular thin film in tension

Ciprian D. Coman, Andrew P. Bassom

Research output: Contribution to journalArticle

45 Citations (Scopus)

Abstract

Asymptotic properties of the neutral stability curves for a linear boundary eigenvalue problem which models the wrinkling instability of an annular thin film in tension are considered. The film is subjected to imposed radial displacement fields on its inner and outer boundaries and, when these loads are sufficiently large, the film is susceptible to wrinkling. The critical values at which this onset occurs are dictated by the solution of a fourth-order ordinary differential eigensystem whose eigenvalue λ is a function of μ (≫ 1), a quantity inversely proportional to the non-dimensional bending stiffness of the film, and n, the number of half-waves of the wrinkling pattern that sets in around the annular domain. Previously, Coman and Haughton [2006. Localised wrinkling instabilities in radially stretched annular thin films. Acta Mech. 185, 179-200] employed the compound matrix method together with a WKB technique to characterise the form of λ (μ, n) which essentially is related to a turning point in a reduced eigenproblem. The asymptotic analysis conducted therein pertained to the case when this turning point was not too close to the inner edge of the annulus. However, in the thin film limit μ → ∞, the wrinkling load and the preferred instability mode are given by a modified eigenvalue problem that involves a turning point asymptotically close to the inner rim. Here WKB and boundary-layer asymptotic methods are used to examine these issues and comparisons with direct numerical simulations made.

Original languageEnglish
Pages (from-to)1601-1617
Number of pages17
JournalJournal of the Mechanics and Physics of Solids
Volume55
Issue number8
Early online date14 Feb 2007
DOIs
Publication statusPublished - Aug 2007
Externally publishedYes

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wrinkling
Thin films
thin films
eigenvalues
Asymptotic analysis
Direct numerical simulation
asymptotic properties
asymptotic methods
annuli
Boundary layers
rims
direct numerical simulation
matrix methods
Stiffness
boundary layers
stiffness
curves

Cite this

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abstract = "Asymptotic properties of the neutral stability curves for a linear boundary eigenvalue problem which models the wrinkling instability of an annular thin film in tension are considered. The film is subjected to imposed radial displacement fields on its inner and outer boundaries and, when these loads are sufficiently large, the film is susceptible to wrinkling. The critical values at which this onset occurs are dictated by the solution of a fourth-order ordinary differential eigensystem whose eigenvalue λ is a function of μ (≫ 1), a quantity inversely proportional to the non-dimensional bending stiffness of the film, and n, the number of half-waves of the wrinkling pattern that sets in around the annular domain. Previously, Coman and Haughton [2006. Localised wrinkling instabilities in radially stretched annular thin films. Acta Mech. 185, 179-200] employed the compound matrix method together with a WKB technique to characterise the form of λ (μ, n) which essentially is related to a turning point in a reduced eigenproblem. The asymptotic analysis conducted therein pertained to the case when this turning point was not too close to the inner edge of the annulus. However, in the thin film limit μ → ∞, the wrinkling load and the preferred instability mode are given by a modified eigenvalue problem that involves a turning point asymptotically close to the inner rim. Here WKB and boundary-layer asymptotic methods are used to examine these issues and comparisons with direct numerical simulations made.",
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On the wrinkling of a pre-stressed annular thin film in tension. / Coman, Ciprian D.; Bassom, Andrew P.

In: Journal of the Mechanics and Physics of Solids, Vol. 55, No. 8, 08.2007, p. 1601-1617.

Research output: Contribution to journalArticle

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AU - Bassom, Andrew P.

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AB - Asymptotic properties of the neutral stability curves for a linear boundary eigenvalue problem which models the wrinkling instability of an annular thin film in tension are considered. The film is subjected to imposed radial displacement fields on its inner and outer boundaries and, when these loads are sufficiently large, the film is susceptible to wrinkling. The critical values at which this onset occurs are dictated by the solution of a fourth-order ordinary differential eigensystem whose eigenvalue λ is a function of μ (≫ 1), a quantity inversely proportional to the non-dimensional bending stiffness of the film, and n, the number of half-waves of the wrinkling pattern that sets in around the annular domain. Previously, Coman and Haughton [2006. Localised wrinkling instabilities in radially stretched annular thin films. Acta Mech. 185, 179-200] employed the compound matrix method together with a WKB technique to characterise the form of λ (μ, n) which essentially is related to a turning point in a reduced eigenproblem. The asymptotic analysis conducted therein pertained to the case when this turning point was not too close to the inner edge of the annulus. However, in the thin film limit μ → ∞, the wrinkling load and the preferred instability mode are given by a modified eigenvalue problem that involves a turning point asymptotically close to the inner rim. Here WKB and boundary-layer asymptotic methods are used to examine these issues and comparisons with direct numerical simulations made.

KW - Asymptotics

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