Electroelastic Boundary-Value Problems

Abstract

In this chapter we apply the theory of nonlinear electroelasticity developed in the previous chapter to several representative boundary-value problems using either the constitutive equation with the electric field as the independent electric variable or the electric displacement. First we consider two homogeneous deformations, namely pure homogeneous strain and simple shear of a slab of material with finite thickness and two parallel plane faces. We then examine three non-homogeneous deformations. For the inflation and extension of a thick-walled circular cylindrical tube subject to an axial or radial electric field, we obtain, in particular, expressions for the inflating pressure and the resultant axial load as functions of the electric field in each case. For the helical shear of a thick-walled circular cylindrical tube, we find conditions on the energy function and electric field for which the deformation is admissible. Finally, we study the problem of the radial inflation of a thick-walled spherical shell under a radial electric field and obtain an expression for the inflating pressure for a general form of energy function, and we show, by taking account of the Maxwell stress, that the electric field counteracts the effect of the pressure.