Piezoelectric composites with periodic multi-coated inhomogeneities

A new, robust homogenization scheme for determination of the effective properties of a periodic piezoelectric composite with general multi-coated inhomogeneities is developed. In this scheme the coating does not have to be thin, the shape and orientation of the inclusion and coatings do not have to be identical, their centers do not have to coincide, their properties do not have to remain uniform, and the microstructure can be with the 2D elliptic or the 3D ellipsoidal inclusions. The development starts from the local electromechanical equivalent inclusion principle through the introduction of the position-dependent equivalent eigenstrain and electric field. Then with a Fourier series expansion and a superposition procedure, the volume-averaged equivalent eigenstrain and electric field for each phase are obtained. The results in turn are used in an energy equivalent criterion to determine the effective properties of the composite. In this model the interphase interactions in each multi-coated particle and the long-range interactions between the periodically distributed particles are fully accounted for. To demonstrate its wide range of applicability, we applied it to examine the properties of several periodic composites: (i) piezoelectric PZT spherical particles in a polymer matrix, (ii) continuous glassy fibers with thin PZT coating in an epoxy matrix, (iii) spherical PZT particles coated by thick or functionally graded piezoelectric layer, (iv) spheroidal voids coated with a thick non-piezoelectric layer in a PZT matrix, and (v) spherical piezoelectric inhomogeneities with eccentric, non-uniform thickness coating. The calculated results reflect the complex nature of interplay between the properties of core, matrix, and coating, as well as whether the coating is uniform, functionally graded, or eccentric. The accuracy of this new scheme is checked against the double-inclusion and other micromechanics models, and good agreement is observed.