Localized wrinkling instabilities in radially stretched annular thin films

C. D. Coman, D. M. Haughton

Research output: Contribution to journalArticle

42 Citations (Scopus)

Abstract

We investigate a pre-stressed annular thin film subjected to a uniform displacement field along its inner boundary. This loading scenario leads to a variable stress distribution characterized by an orthoradial component that may change sign along a concentric circle within the annular domain. When the intensity of the applied field is strong enough, elastic buckling occurs circumferentially, leading to a localized wrinkling pattern near the inner edge. Using a linear non-homogeneous pre-bifurcation state, the eigenvalue problem describing this instability is cast as a singularly-perturbed fourth-order linear differential equation with variable coefficients. The dependence of the lowest eigenvalue on various non-dimensional quantities is numerically investigated using the compound matrix method. These results are complemented by a WKB analysis which suggests that the qualitative and quantitative features of the full model can be described by a simplified second-order eigenvalue problem which takes into account the finite stiffness of the system.

Original languageEnglish
Pages (from-to)179-200
Number of pages22
JournalActa Mechanica
Volume185
Issue number3-4
Early online date6 Mar 2006
DOIs
Publication statusPublished - Sep 2006
Externally publishedYes

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