Bifurcation of finitely deformed thick-walled electroelastic spherical shells subject to a radial electric field

Melnikov, A., Dorfmann, L. and Ogden, R. W. (2020) Bifurcation of finitely deformed thick-walled electroelastic spherical shells subject to a radial electric field. International Journal of Non-Linear Mechanics, 121, 103429. (doi: 10.1016/j.ijnonlinmec.2020.103429)

Abstract

This paper is concerned with the bifurcation analysis of a pressurized electroelastic spherical shell with compliant electrodes on its inner and outer boundaries. The theory of small incremental electroelastic deformations superimposed on a radially finitely deformed electroelastic thick-walled spherical shell is used to determine those underlying configurations for which the superimposed deformations do not maintain the perfect spherical shape of the shell. Specifically, axisymmetric bifurcations are analyzed, and results are obtained for three different electroelastic energy functions, namely electroelastic counterparts of the neo-Hookean, Gent and Ogden elastic energy functions. For the neo-Hookean energy function it was reported previously that for the purely mechanical case axisymmetric bifurcations are possible under external pressure only, no bifurcation solutions being possible for internally pressurized spherical shells. In the case of an electroelastic neo-Hookean model bifurcation under internal pressure becomes possible when the potential difference between the electrodes exceeds a certain value, which depends on the ratio of inner to outer undeformed radii. Results obtained for the three classes of model are significantly different and are illustrated for a range of fixed values of the potential difference. Although of less practical significance, results are also shown for fixed charges, and these are both different between the models and different from the case of fixed potential difference.

• Item Type: Articles
• Additional Information: The work of Andrey Melnikov was funded by a University of Glasgow studentship in the period 2012–2016.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Melnikov, Mr Andrey and Ogden, Professor Raymond
• Authors: Melnikov, A., Dorfmann, L., and Ogden, R. W.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: International Journal of Non-Linear Mechanics
• Publisher: Elsevier
• ISSN: 0020-7462
• ISSN (Online): 1878-5638
• Published Online: 24 January 2020
• Copyright Holders: Copyright © 2020 Elsevier Ltd.
• First Published: First published in International Journal of Non-Linear Mechanics 121: 103429
• Publisher Policy: Reproduced in accordance with the publisher copyright policy