基于磁致伸缩相与压电相的本构方程,应用弹性力学的方法,建立了功能梯度铁电铁磁复合材料弯曲模态下的磁电耦合静态力学模型。假设铁电和铁磁材料的物理参数均为沿厚度方向的线性或指数函数,分析计算了由PZT作为铁电材料和CoFe2O4作为铁磁材料的双层复合材料的磁电效应。结果表明,在弯曲模态下,磁电电压系数出现两个峰值。负梯度的铁电（或铁磁）材料提高磁电效应,正梯度的铁电（或铁磁）材料降低磁电效应。同号梯度的铁电铁磁材料对磁电效应的影响更大。
Based on the magnetostrictive phase and piezoelectric phase constitutive equations,and the method of elasticity,a static mechanical model is formulated.Assuming all physical parameters of ferroelectric and ferromagnetic material are linear or exponential function along the thickness direction,the magnetoelectric effects of a functionally graded bilayer ferroelectric ferromagnetic composite of PZT as a ferroelectric material and CoFe2O4 as a ferromagnetic material are calculated for bending deformations.Results show that the magnetoelectric voltage coefficient can reach two peaks.When the gradient factor of material parameters of ferroelectric(or ferromagnetic) materials is negative,the magnetoelectric effect is enhanced;the magnetoelectric effect is reduced when the gradient factor is positive;the ferroelectric and ferromagnetic materials are simultaneously graded which results in the greatest magnetoelectric effect.
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