Electric Displacement Gradients in the Elastic Dielectric

Abstract

A variational principle is used to derive a nonlinear theory of the static elastic and dielectric response of an insulator whose energy density is a function of the deformation gradients, the electric displacement components, and the electric displacement gradients. The linearized or small field version of this theory differs from Mindlin's theory of the elastic dielectric with polarization gradient arguments in the energy density. From an application of the linear theory to the determination of the response of a particular system with non-piezoelectric cubic material symmetry, it is concluded that to satisfy all the boundary conditions there can be no explicit displacement gradient dependence in the small field energy density representation. An analogous result holds for Mindlin's theory.We also examine three microscopic model calculations, by Ginzburg, Mindlin, and Askar et al., and we conclude that in each case the effect obtained can be attributed equally well to the presence of arguments other than the polarization gradient. Ginzburg's model is shown to have an energy density with arguments which are the polarization components and the gradients of polarization gradients.