Matrix laminate composites: Realizable approximations for the effective moduli of piezoelectric dispersions

This paper is concerned with the effective piezoelectric moduli of a specia l class of dispersions called matrix laminates composites that are known to possess extremal elastic and dielectric moduli. It is assumed that the mat rix material is an isotropic dielectric, and the inclusions and composites are transversely isotropic piezoelectrics that share the same axis of symme try. The exact expressions for the effective coefficients of such structure s are obtained. They can be used to approximate the effective properties of any transversely isotropic dispersion. The advantages of our approximation s are that they are (i) realizable, i.e., correspond to specific microstruc tures; (ii) analytical and easy to compute even in nondegenerate cases; (ii i) valid for the entire range of phase volume fractions; and (iv) character ized by two free parameters that allow one to "tune" the approximation and describe a variety of microstructures. The new approximations are compared with known ones.