An analytical model for nonlinear magnetoelectric effect in laminated composites


Magnetoelectric (ME) composites have found numerous applications owing to their unique ferroic properties. These composites can achieve ME effects via mechanical coupling between two constituent phases. Among the available ME composites, laminated composites have recently attracted research attention as potential candidates for numerous applications since they exhibit strong-mediated ME coupling at room temperature. Over the years, the theories proposed for studying the ME effects of laminated composites have mainly focused on understanding the effects of materials’ linear characteristics with little contribution to nonlinear characteristics observed in these materials. This can be attributed to the nonlinearity in the ME coupling of the laminated composites due to the materials’ strong nonlinear behaviors at a high bias magnetic field.

The study of nonlinear ME interactions is of great interest because accurate prediction of nonlinear ME effects is critical for designing high-performing devices. Typically, the nonlinear ME interaction in laminated composites occurs in two ways, namely, due to signal dependencies on the external stimuli and the signal distortions due to high order harmonics. Currently, most existing nonlinear ME models do not entirely give a clear revelation about the origin and control mechanism of high order ME signals that are critical in eliminating signal distortions. From the point view of applications, these models adopted complex expressions with an implicit form of the inverse function in magnetization equation and a piecewise function to describe the pre-stress. This seriously restrict applications in practical engineering, especially in nonlinear devices.

Recently, the development of an explicit nonlinear magneto-thermo-mechanical model for describing tensile and compressive stresses opened a way for enhanced nonlinear ME effects analysis via analytical and explicit solutions. Motivated by these results, Xidian University researchers: Dr.Yang Shi, Ms. Ni Li, Professor Yongkun Wang, and Professor Junjie Ye proposed an analytical and explicit theoretical model for studying nonlinear ME effects in laminated composites taking into account the multi-field coupled properties of magnetostrictive materials. The authors hoped to tune the frequency-multiplying behavior of the laminated composites using the bias magnetic field and to understand all nonlinear ME behaviors. Their research work is currently published in the journal, Composite Structures.

In their approach, the authors expanded the magnetostriction as a Taylor series in the applied bias magnetic field to obtain the explicit nonlinear constitutive equation. Additionally, the field-dependent material’s parameters were derived as functions of bias field and stress, while the analytical solutions of the nonlinear ME voltages were simultaneously obtained using boundary conditions and mechanical differential and electric equations. Also, the origin of the dual-peak phenomena as well as the occurrence of harmonics in the presence and absence of the bias field, were investigated.

The authors achieved a high-performance ME device with low input frequency attributed to mechanical resonance of the ME composite by high-order harmonics. Even harmonics were observed in the presence of bias field, while odd harmonics in the absence of the bias field. As such, a high-performance ME sensor with improved linearity, high piezomagnetic effects, and strong ME coupling could be achieved by increasing the bias field to the optimal value. Furthermore, the dual peaks in the voltages were induced by the combined effects of the pre-stress and resonance response under a fixed bias field. Due to this phenomenon, the available ME coupling could effectively achieve a wider bias field range.

The study reported the development of a more concise analytical and theoretical model for studying nonlinear ME effects. By considering the multi-field coupled properties of the magnetostrictive materials, and adopting the explicit form of the magnetization equation and the field-related equivalent material parameter, the proposed model addressed the drawbacks of the previously used models. Moreover, the obtained numerical results agreed well with the experimental data, indicating the feasibility of using the model in various practical applications. The research work, therefore, provides a basic guide for understanding the emerging nonlinear ME technology and can potentially be applied to investigate nearly all nonlinear ME behaviors besides designing high-performance ME-based devices.


Shi, Y., Li, N., Wang, Y., & Ye, J. (2021). An analytical model for nonlinear magnetoelectric effect in laminated compositesComposite Structures, 263, 113652.

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