Finite deformations of an electroelastic circular cylindrical tube

Melnikov, A. and Ogden, R. W. (2016) Finite deformations of an electroelastic circular cylindrical tube. Zeitschrift für Angewandte Mathematik und Physik, 67, 140. (doi: 10.1007/s00033-016-0733-0)

Abstract

In this paper the theory of nonlinear electroelasticity is used to examine deformations of a pressurized thick-walled circular cylindrical tube of soft dielectric material with closed ends and compliant electrodes on its curved boundaries. Expressions for the dependence of the pressure and reduced axial load on the deformation and a potential difference between, or uniform surface charge distributions on, the electrodes are obtained in respect of a general isotropic electroelastic energy function. To illustrate the behaviour of the tube, specific forms of energy functions accounting for different mechanical properties coupled with a deformation independent quadratic dependence on the electric field are used for numerical purposes, for a given potential difference and separately for a given charge distribution. Numerical dependences of the non-dimensional pressure and reduced axial load on the deformation are obtained for the considered energy functions. Results are then given for the thin-walled approximation as a limiting case of a thick-walled cylindrical tube without restriction on the energy function. The theory described herein provides a general basis for the detailed analysis of the electroelastic response of tubular dielectric elastomer actuators, which is illustrated for a fixed axial load in the absence of internal pressure and fixed internal pressure in the absence of an applied axial load.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Ogden, Professor Raymond
• Authors: Melnikov, A., and Ogden, R. W.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Zeitschrift für Angewandte Mathematik und Physik
• Publisher: Springer International Publishing
• ISSN: 0044-2275
• ISSN (Online): 1420-9039
• Published Online: 22 October 2016
• Copyright Holders: Copyright © 2016 The Authors
• First Published: First published in Zeitschrift für Angewandte Mathematik und Physik 67:140
• Publisher Policy: Reproduced under a Creative Commons License