Nonlinear response of an electroelastic spherical shell

In this paper the theory of nonlinear electroelasticity is used to examine radial deformations of a thick-walled spherical shell of soft dielectric material with compliant electrodes on its inner and outer surfaces combined with an internal pressure. A general expression for the dependence of the pressure on the deformation and a potential difference between the electrodes, or uniform surface charge distributions on the electrodes, is obtained in respect of a general incompressible isotropic electroelastic energy function. To illustrate the behavior of the shell specific forms of energy functions are used for numerical purposes, for either fixed potential difference or fixed charge distribution. Explicit general results are given for the limiting case of a thin-walled (or membrane) shell. Depending on the elastic part of the energy function (as distinct from that part which involves the electric field) different behaviors are obtained, including non-monotonicity of the pressure–radius relationship reminiscent of that known in the purely elastic situation, but moderated by the presence of an electric field.