An analysis of piezoelectric composite materials containing ellipsoidal inhomogeneities

Abstract

A set of four tensors corresponding to Eshelby's tensor in elasticity are obtained for an ellipsoidal inclusion embedded in an infinite piezoelectric medium. These tensors, which describe the elastic, piezoelectric, and dielectric constraint of the matrix, are obtained from W. F. Deeg's solution to inclusion and inhomogeneity problems in piezoelectric solids. These tensors are then used as the backbone in the development of a micromechanics theory to predict the effective elastic, dielectric, and piezoelectric moduli of particle and fibre reinforced composite materials. The effects of interaction among inhomogeneities at finite concentrations are approximated through the Mori-Tanaka mean field approach. This approach, although widely utilized in the study of uncoupled elastic and dielectric behaviour, has not before been applied to the study of coupled behaviour. To help ensure confidence in the theory, the analytical predictions are proven to be self-consistent, diagonally symmetric, and to exhibit the correct behaviour in the low and high concentration limits. Finally, numerical results are presented to illustrate the effects of the concentration, shape, and material properties of the reinforcement on the effective properties of piezoelectric composites and analytical predictions are shown to result in good agreement with existing experimental data.