Finite deformations of an electroelastic circular cylindrical tube

Andrey Melnikov,Ray W Ogden

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.

Highlights

Recent successes in the technological production of new dielectric elastomeric materials has instigated a rapid development of devices which employ the properties of such materials, including, for example, actuators and sensors, as well as noise cancelling and energy conversion devices and prototype artificial muscles
The associated nonlinear electromechanical interaction requires, in general, a rigorous continuum electromechanical theory, the development of which can be traced to the middle of the last century in the seminal work of Toupin [1], who was concerned with the theory governing elastic dielectric materials
As far as the application of the tube geometry to actuator technology is concerned a more realistic setup involves a tube with compliant electrodes coated on its curved boundaries, and this is the arrangement that is considered in the present paper

Summary

Introduction

Recent successes in the technological production of new dielectric elastomeric materials has instigated a rapid development of devices which employ the properties of such materials, including, for example, actuators and sensors, as well as noise cancelling and energy conversion devices and prototype artificial muscles. The approach to the theory in the form described by Dorfmann and Ogden [6], has led to further developments and has proved to be amenable to the solution of boundary-value problems, as exemplified in [7] and the recent monograph by Dorfmann and Ogden [8] and references therein Included in the latter works was the analysis of the deformation of a circular cylindrical tube subject to a radial electric field with the field permeating both the interior and exterior spaces. As far as the application of the tube geometry to actuator technology is concerned a more realistic setup involves a tube with compliant electrodes coated on its curved boundaries, and this is the arrangement that is considered in the present paper This was one of the possible actuator geometries mentioned in [9,10] in which prototype actuators were considered as proof of concept for actuating dielectric elastomers by an electric field. The corresponding problem for a spherical shell subject to internal pressure and compliant electrodes on its inner and outer surfaces was analysed in [11]

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