Electrostriction and modelling of finitely deformable dielectrics

The paper investigates models of electrostriction by following a new approach though within the basic laws of continuum mechanics. Three general requirements are considered. Firstly, in a three-dimensional setting the balance of angular momentum implies a symmetry condition for the Cauchy stress tensor, the electric field and the electric polarization. By checking the thermodynamic consistency it is observed that constitutive equations with a separate dependence on the deformation gradient and the electric field does not satisfy the symmetry condition. Instead the symmetry is shown to hold for variables involving jointly the deformation gradient and the electric field or the polarization. This scheme in turn is found to satisfy both the thermodynamic consistency and the objectivity principle. Next electrostriction is examined by determining the deformation of an isotropic elastic solid induced by an electric field. Furthermore, it is shown that a proper dependence on the polarization or on the electric field results in elongations or contractions just as it is observed in real materials.