Size effects on magnetoelectric response of multiferroic composite with inhomogeneities

This paper investigates the influence of size effects on the magnetoelectric performance of multiferroic composite with inhomogeneities. Based on a simple model of gradient elasticity for multiferroic materials, the governing equations and boundary conditions are obtained from an energy variational principle. The general formulation is applied to consider an anti-plane problem of multiferroic composites with inhomogeneities. This problem is solved analytically and the effective magnetoelectric coefficient is obtained. The influence of the internal length (grain size or particle size) on the effective magnetoelectric coefficients of piezoelectric/piezomagnetic nanoscale fibrous composite is numerically evaluated and analyzed. The results suggest that with the increase of the internal length of piezoelectric matrix (PZT and BaTiO₃), the magnetoelectric coefficient increases, but the rate of increase is ratcheting downwards. If the internal length of piezoelectric matrix remains unchanged, the magnetoelectric coefficient will decrease with the increase of internal length scale of piezomagnetic nonfiber (CoFe₂O₃). In a composite consisiting of a piezomagnetic matrix (CoFe₂O₃) reinforced with piezoelectric nanofibers (BaTiO₃), an increase of the internal length in the piezomagnetic matrix, results to a decrease of the magnetoelectric coefficient, with the rate of decrease diminishing.