A material multipole theory of elastic dielectric composites

Abstract

This article is concerned with the study of the overall mechanical and electrical properties of elastic dielectric composites by using the concept of material multipoles. In particular, by developing a statistical continuum material multipole theory, the effects of the microstructure of the inhomogeneities on the overall properties of the composites can be derived. In this theory, inhomogeneities are modelled as point material-induced multipoles. The macroscopic fields obtained from the ensemble average of the microscopic fields in the composite with statistically-distributed inhomogeneities in a uniform matrix are described by statistical continuum material multipoles in the matrix. This theory, in comparison with classical effective medium theory, has the possibility of attacking rather complicated problems such as, for instance, electromagnetoelaslic composites. It is shown that the statistical anisotropy and shape effects of microscopic ellipsoidal particles and their orientations on the overall effective properties of dielectric composites may be obtained in an explicit form. Also, the macroscopic constitutive relations of elastic dielectric composites and their macroscopic material parameters accounting for electroelastic interaction may be derived with the use of this statistical continuum multipole theory.