Bifurcation of finitely deformed thick-walled electroelastic cylindrical tubes subject to a radial electric field

Melnikov, A. and Ogden, R. W. (2018) Bifurcation of finitely deformed thick-walled electroelastic cylindrical tubes subject to a radial electric field. Zeitschrift für Angewandte Mathematik und Physik, 69, 60. (doi: 10.1007/s00033-018-0954-5)

Abstract

This paper is concerned with the bifurcation analysis of a pressurized electroelastic circular cylindrical tube with closed ends and compliant electrodes on its curved boundaries. The theory of small incremental electroelastic deformations superimposed on a finitely deformed electroelastic tube is used to determine those underlying configurations for which the superimposed deformations do not maintain the perfect cylindrical shape of the tube. First, prismatic bifurcations are examined and solutions are obtained which show that for a neo-Hookean electroelastic material prismatic modes of bifurcation become possible under inflation. This result contrasts with that for the purely elastic case for which prismatic bifurcation modes were found only for an externally pressurized tube. Second, axisymmetric bifurcations are analyzed, and results for both neo-Hookean and Mooney–Rivlin electroelastic energy functions are obtained. The solutions show that in the presence of a moderate electric field the electroelastic tube becomes more susceptible to bifurcation, i.e., for fixed values of the axial stretch axisymmetric bifurcations become possible at lower values of the circumferential stretches than in the corresponding problems in the absence of an electric field. As the magnitude of the electric field increases, however, the possibility of bifurcation under internal pressure becomes restricted to a limited range of values of the axial stretch and is phased out completely for sufficiently large electric fields. Then, axisymmetric bifurcation is only possible under external pressure.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Melnikov, Mr Andrey and Ogden, Professor Raymond
• Authors: Melnikov, A., and Ogden, R. W.
• College/School: College of Science and Engineering > School of Mathematics and Statistics; College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Zeitschrift für Angewandte Mathematik und Physik
• Publisher: Springer
• ISSN: 0044-2275
• ISSN (Online): 1420-9039
• Published Online: 04 May 2018
• Copyright Holders: Copyright © 2018 The Authors
• First Published: First published in Zeitschrift für Angewandte Mathematik und Physik 69:60
• Publisher Policy: Reproduced under a Creative Commons License