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1. Introduction
Magnetoelectric (ME) composite materials, composed of magnetostrictive and ferroelectric materials, are effective in converting magnetic field into electric signal. In particular, the magnetic field deforms the magnetostrictive material due to magnetostriction effect, which then stresses the ferroelectric material through interfacial mechanical coupling, and finally the ferroelectric material generates electric field due to its piezoelectric property. ME composite is able to generate a magnetoelectric coefficient of several V/cm-Oe, much higher than single-phase material, which makes it a good candidate for potential applications in sensors, transformers, energy harvesters, and so on [1].
The studies on ME composites can be dated back to 1972 when van Suchtelen proposed the idea of ME conversion through mechanical coupling between two-phase materials [4]. Since then, several researchers fabricated such composite and the obtained ME coefficient has been increasing [5–12]. At the same time, much attention is also focused on the theoretical and numerical investigations. Harshe et al. developed a theoretical model dealing with the linear behavior of ME composites [13]. Nan et al. predicted a giant magnetoelectric effect of Terfenol-D and P (VDF-TrFE) composites using Green’s function technique [14, 15]. The shear-lag and demagnetization effects in laminated ME composites were considered by Chang and Carman [16]. Nan et al. discussed the influence of interfacial bonding on the magnetoelectric coefficient [17]. The resonance behavior of ME composite was investigated in [18–20]. Numerically, Liu et al. [21] and Zhou et al. [22] calculated the magnetoelectric effect using finite element method (FEM). In their models, the nonlinear behavior of magnetostrictive material is considered. Linnemann et al. [23] proposed a constitutive model for magnetostrictive and piezoelectric materials and gave FEM examples. Nguyen et al. [24] modeled the nonlinear behavior of magnetic sensor using FEM. In recent years, there...