Cross-property connections for fiber reinforced piezoelectric materials with anisotropic constituents

The paper addresses the problem of the connection between effective elastic stiffnesses, piezoelectric coefficients and dielectric permeabilities of a fiber reinforced piezoelectric composite with both phases (the matrix and the fibers) being transversely-isotropic. These connections allow one to predict the entire set of macroscopic elastic stiffnesses through one or two measurements of dielectric permeability. The solutions for square and hexagonal arrays of fibers and for randomly located parallel fibers are constructed and compared. The analytical results show very good agreement with available experimental data. As a side result, it is shown that the mutual positions of inhomogeneities produce only a minor effect and that applicability of the non-interaction approximation is much wider than expected.