Closed-form expressions for the effective properties of piezoelastic composites reinforced with cylindrical fibers by Maxwell scheme

Abstract

In this work, the Maxwell scheme is implemented to characterize the effective properties of piezoelastic fiber composites reinforced by unidirectional cylindrical fibers distributed along the x3-axis. The piezoelastic composites are assumed to have transversely isotropic constituent materials. Analytical expressions for the effective properties (elastic, piezoelectric, and dielectric) are reported. The Mori–Tanaka approach is also developed for piezoelastic composites and it is shown that their analytical results coincide with the Maxwell scheme and the effective field method. Numerical analysis and comparisons with the two-scale asymptotic homogenization method and the semi-analytical finite element method are shown and discussed. As a summary, the novelty value of this work is that the Maxwell and Mori–Tanaka schemes have been extended to heterogeneous piezoelectric structures. Closed formulas are derived for the effective elastic, piezoelectric, and dielectric moduli. A numerical implementation of the effective moduli is carried out and the overall properties are validated with other methods.