Abstract In this paper, the mixed mode problem for a magneto-electro-elastic (MEE) material containing multiple cracks under in-plane magneto-electro-mechanical loads is analyzed. First, the solution to an generalized dislocation is obtained in the infinite MEE plane. The Fourier transform is employed to derive closed-form expressions for the stress, electric displacement and magnetic induction components. The solution to the problem is consequently reduced to derive singular integral equations for dislocation density functions on the surfaces of cracks. The equations are then solved numerically to determine field intensity factors for cracks. At the final step, the numerical results of calculated field intensity factors are presented for multiple curved cracks under certain ratios of the applied magnetical and electrical loads to mechanical loads. Also, the field intensity factors are calculated for various crack patterns with different geometries. Moreover, the analysis can be applied for any number of cracks with arbitrary arrangement in the MEE regions under in-plane condition.

中文翻译：

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磁电弹性面多裂纹的混合模式分析

摘要 本文分析了面内磁机电载荷下含多裂纹磁电弹性(MEE)材料的混合模态问题。首先，在无限 MEE 平面中获得广义位错的解。傅里叶变换用于推导出应力、电位移和磁感应分量的闭式表达式。因此，该问题的解被简化为推导出裂纹表面位错密度函数的奇异积分方程。然后对方程进行数值求解以确定裂缝的场强因子。在最后一步，给出了在施加的磁和电负载与机械负载的特定比率下，多个弯曲裂纹的计算场强因子的数值结果。此外，还针对具有不同几何形状的各种裂纹模式计算了场强因子。此外，该分析可以应用于面内条件下 MEE 区域中任意排列的任意数量的裂纹。