An analytical model for nonlinear magnetoelectric effect in laminated composites

Abstract This paper presents an analytical and explicit theoretical model for the nonlinear magnetoelectric (ME) effect in laminated composites, in which the multi-field coupled properties of magnetostrictive materials are taken into account. The adopted explicit nonlinear constitutive equation is equivalent to the one in series form through expanding the magnetostriction as a Taylor series in the vicinity of the applied bias field. Then the field-dependent materials’ parameters are derived as functions of bias field and stress. Analytical solutions of nonlinear ME voltages in various modes are obtained simultaneously using mechanical differential equations, boundary conditions, and electric equations. It is predicted that the frequency-multiplying behavior observed in the composites can be tuned by bias magnetic field. Only even harmonics occur in the absence of bias field, while odd harmonics appear once a bias field is applied. An optimal bias field corresponding to the maximum linear voltage and zero nonlinear voltage is obtained, where the highest piezomagetic effect generates. It is proved that the ME distortions under a fixed ac field is actually caused by the competition results between the linear piezomagnetic effect and high-order magnetostrictive effect. Moreover, pre-stress may enhance ME voltages and reduce the optimal field due to the multi-field coupled character, and control the resonance frequency via ΔE effect. Eventually, the origin of the observed dual-peak phenomenon around resonance frequencies is revealed and explained theoretically, indicating that strong ME effect may be achieved in a wider bias field range. The analytical solutions from this study can be applied to design tunable ME sensors, energy harvesters, and some other nonlinear devices via manipulating the external bias field and pre-stress.