The objective of this work is to study the effect of strain gradient, electric field gradient, and magnetic field gradient on the potential and field distributions of multiferroic fibrous composites subjected to generalized anti-plane shear deformation. A detailed energy variational formulation with strain, strain gradient, electric field, electric field gradient, magnetic field, and magnetic field gradient as independent variables is provided, and the equilibrium equations with the complete boundary conditions are simultaneously determined. Three internal characteristic lengths of the underlying microstructure are introduced in the constitutive equations. The general solutions in cylindrical polar coordinates consisting of the modified Bessel functions of first and second kind are derived. One inclusion problem’s solution is also obtained. The derived solutions are applied to a \(\hbox {CoFe}_{2}\hbox {O}_{4}\)-PZT-4 composite to demonstrate the effect of strain gradient, electric field gradient, and magnetic field gradient. Numerical results provide insights into the role of characteristic lengths on the potential and field distributions of a multiferroic fibrous composite.

这项工作的目的是研究应变梯度，电场梯度和磁场梯度对承受广义反平面剪切变形的多铁纤维复合材料的电势和场分布的影响。提供了以应变，应变梯度，电场，电场梯度，磁场和磁场梯度为自变量的详细能量变化公式，并同时确定了具有完整边界条件的平衡方程。本构方程中介绍了底层微观结构的三个内部特征长度。推导了由第一和第二种修正贝塞尔函数组成的圆柱极坐标系的一般解。还获得了一个包含问题的解决方案。\（\ hbox {CoFe} _ {2} \ hbox {O} _ {4} \）- PZT-4复合材料，以演示应变梯度，电场梯度和磁场梯度的影响。数值结果提供了洞察特征长度在多铁纤维复合材料的电势和场分布中的作用。