This paper studies the effective moduli of multiferroic fibrous composites with strain gradient and electromagnetic field gradient effects subjected to generalized anti-plane shear deformation. Using the energy variational formulation and the generalized self-consistent method, we can determine the effective moduli of the heterogeneous material. The derived solutions are then applied to a BaTiO₃–CoFe₂O₄ composite to demonstrate the effect of strain gradient, electric field gradient, and magnetic field gradient. Numerical results show that  the gradient effects have significant influence on the effective moduli of the multiferroic composite. We show that the magnetoelectric voltage coefficient, the figure of merit of the multiferroic material, can be enhanced many-fold than that of the classical solution. In addition, most of the effective moduli increase as the radius of the fiber decreases (or equivalently the characteristic length increases).

本文研究了具有广泛的反平面剪切变形的应变梯度和电磁场梯度效应的多铁纤维复合材料的有效模量。使用能量变分公式和广义自洽方法，我们可以确定异质材料的有效模量。然后将衍生的溶液应用于BaTiO ₃ -CoFe ₂ O ₄复合材料，以证明应变梯度，电场梯度和磁场梯度的影响。数值结果表明 梯度效应对多铁复合材料的有效模量有重要影响。我们表明，磁电电压系数，即多铁材料的品质因数，可以比传统解决方案提高很多倍。另外，大多数有效模量随光纤半径的减小而增大（或等效地，特征长度增大）。