Localized wrinkling instabilities in radially stretched annular thin films

Coman, C.D. and Haughton, D.M. (2006) Localized wrinkling instabilities in radially stretched annular thin films. Acta Mechanica, 185(3-4), pp. 179-200.

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Publisher's URL: http://dx.doi.org/10.1007/s00707-005-0307-2


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.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Coman, Dr Ciprian and Haughton, Dr David
Authors: Coman, C.D., and Haughton, D.M.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Acta Mechanica
Journal Abbr.:Acta Mech
ISSN (Online):1619-6937
Published Online:06 March 2006

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