Nonlinear Electroelastic Deformations

Electro-sensitive (ES) elastomers form a class of smart materials whose mechanical properties can be changed rapidly by the appli-cation of an electric field. These materials have attracted consider-able interest recently because of their potential for providing rela-tively cheap and light replacements for mechanical devices, such as actuators, and also for the development of artificial muscles. In this paper we are concerned with a theoretical framework for the analysis of boundary-value problems that underpin the applications of the as-sociated electromechanical interactions. We confine attention to the static situation and first summarize the governing equations for a solid material capable of large electroelastic deformations. The general con-stitutive laws for the Cauchy stress tensor and the electric field vectors for an isotropic electroelastic material are developed in a compact form following recent work by the authors. The equations are then applied, in the case of an incompressible material, to the solution of a number of representative boundary-value problems. Specifically, we consider the influence of a radial electric field on the azimuthal shear response of a thick-walled circular cylindrical tube, the extension and inflation characteristics of the same tube under either a radial or an axial elec-tric field (or both fields combined), and the effect of a radial field on the deformation of an internally pressurized spherical shell