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.

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.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• 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: 0001-5970
• ISSN (Online): 1619-6937
• Published Online: 06 March 2006