Finite deformations of a bilayer dielectric nonlinear elastic anisotropic tube under an electric field

Abstract

In this paper the problem of finite deformations of a dielectric tube under the action of an electric field is considered. The tube consists of two layers, each spirally reinforced with fibres. The angles of the fibres in each layer are different. On the inner and outer surfaces of the tube and between the layers are flexible electrodes. The electric field is induced by applying voltage to the first or second layer, i. e. either to the electrodes on the inner side surface and between the layers, or to the electrodes between the layers and on the outer side surface. A simple model of an electroactive anisotropic incompressible material is considered in the analysis. The potential energy function is represented by the sum of the energy of the isotropic matrix in Gent form, the simplest electrical component and the energy of the reinforced fibres. Using a semi-inverse method, the static problem of the three-dimensional body is reduced to integral equations with respect to the tube deformation parameters: the radius of the outer layer, the multiplicity of longitudinal elongation and the twist angle. The influence of layer thickness on tube deformation under quasi-static increase of voltage is investigated. The purpose of this work is to determine the thickness of the layers at which the application of voltage to the different layers will cause the tube to twist in different directions.