Exact size-dependent connections between effective moduli of fibrous piezoelectric nanocomposites with interface effects

We consider the macroscopic behavior of two-phase fibrous piezoelectric composites. The fibers are of circular cross-section with the same radius. Along the interfaces between the fibers and the matrix we consider the effects of surface stress and surface electric displacement. The constituents are transversely isotropic and exhibit pyroelectricity. We find that the overall thermoelectroelastic moduli of these solids must comply with two sets of exact connections. The first set, similar to Hill's universal connections, provides five constraints between the six axisymmetric overall electroelastic moduli. The second set relates the effective coefficients of thermal stress and pyroelectric coefficients to the effective electroelastic moduli, in analogy with Levin's formula. In contrast to their conventional counterparts, i.e., without surface effects, the presence of surface effects makes both sets of connections dependent on the absolute size of the nanoinclusions.