Polarization in dielectrics modeled as micromorphic continua

Abstract

On the basis of an extension of the micromorphic continuum theory accounting for electromagneto-elastic coupling in a consistent way, we develop a continuum formulation of polarization in dielectrics. The introduction of dielectric multipoles by means of the microdisplacement and the exploitation of their linearized evolution equations allows to achieve a representation of the polarization in terms of macroscopic and microscopic strain measures and in particular of the microrotation tensor. The microdeformation is then expressed by means of the macroscopic strain and the dependence of polarization from the gradients of the mechanical displacement is explicitly written, up to the third order in multipoles. Piezoelectric and flexoelectric tensors are thus obtained, and it is shown that they uniquely depend on electric quadrupoles and octupoles. We also discuss the reduction in the present model to micropolar continua, giving a representation of the flexoelectric tensor for isotropic micropolar dielectrics.