Closed-form solutions to the effective properties of fibrous magnetoelectric composites and their applications

Magnetoelectric coupling is of interest for a variety of applications, but is weak in natural materials. Strain-coupled fibrous composites of piezoelectric and piezomagnetic materials are an attractive way of obtaining enhanced effective magnetoelectricity. This paper studies the effective magnetoelectric behaviors of two-phase multiferroic composites with periodic array of inhomogeneities. For a class of microstructures called periodic E-inclusions, we obtain a rigorous closed-form formula of the effective magnetoelectric coupling coefficient in terms of the shape matrix and volume fraction of the periodic E-inclusion. Based on the closed-form formula, we find the optimal volume fractions of the fiber phase for maximum magnetoelectric coupling and correlate the maximum magnetoelectric coupling with the material properties of the constituent phases. Based on these results, useful design principles are proposed for engineering magnetoelectric composites.