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Wrinkling of pre-stressed annular thin films under azimuthal shearing

Citation

Coman, CD and Bassom, AP, Wrinkling of pre-stressed annular thin films under azimuthal shearing, Mathematics and Mechanics of Solids, 13, (6) pp. 513-531. ISSN 1081-2865 (2008) [Refereed Article]

Copyright Statement

Copyright 2008 SAGE Publications

DOI: doi:10.1177/1081286507077107

Abstract

The wrinkling instabilities of a pre-tensioned annular thin film undergoing azimuthal shearing are investigated within the framework of the linearized Donnell—von Kármán bifurcation equation for thin plates. The main objective here is to provide a rational understanding of the role played by the presence of finite bending stiffness and to explain the nature of the localized deformation patterns observed in experiments. In order to achieve this, the eigenvalue problem is formulated as a differential equation with variable coefficients depending on a large parameter. The singular perturbation nature of this equation arises from a combination involving both the pre-stress and the geometrical features of the annular domain. The localization mechanism of the corresponding eigenmodes is then unravelled with the help of a WKB analysis motivated by the qualitative behavior of the neutral stability curves. We show that the asymptotic findings are in very good agreement with the results of direct numerical simulations of the original bifurcation equation.

Item Details

Item Type:Refereed Article
Keywords:thin films, azimuthal shearing, wrinkling, singular perturbations, WKB techniques
Research Division:Mathematical Sciences
Research Group:Applied Mathematics
Research Field:Theoretical and Applied Mechanics
Objective Division:Expanding Knowledge
Objective Group:Expanding Knowledge
Objective Field:Expanding Knowledge in the Mathematical Sciences
Author:Bassom, AP (Professor Andrew Bassom)
ID Code:105657
Year Published:2008
Web of Science® Times Cited:6
Deposited By:Mathematics and Physics
Deposited On:2016-01-12
Last Modified:2016-08-03
Downloads:0

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