This paper investigates the Mode-I crack problem that a three-dimensional infinite space of transversely isotropic multi-ferroic composite medium is weakened by multiple coplanar penny-shaped cracks under uniform mechanical, electric and magnetic loadings. These cracks are arbitrarily distributed in an isotropic plane of the material. Four kinds of idealized electro-magnetic crack boundary conditions, which assume a crack to be electrically permeable (or impermeable) and magnetically permeable (or impermeable), are adopted, and all the possible combinations of these electro-magnetic crack boundary conditions are considered. An approximate three-dimensional solution of the field variables and expressions of some important fracture mechanics quantities are proposed, by virtue of Kachanov’s method and the generalized potential theory method. Numerical examples for some particular configurations of cracks are presented. Based on a two-crack system, the validity of the present solution is checked by comparing the results with their counterparts from a finite element simulation. Interaction of cracks is investigated as well, by taking the crack size and distance between two cracks as factors. From the phenomena shown in the numerical examples, a reduced solution and an empirical method for evaluating generalized stress intensity factors are proposed.

本文研究了模式I裂纹问题，即在均匀的机械，电磁和电磁载荷作用下，多个各向同性的便士形裂纹削弱了横向各向同性的多铁性复合介质的三维无限空间。这些裂纹在材料的各向同性平面中任意分布。采用四种理想化的电磁裂纹边界条件，假定裂纹是电可渗透的（或不可渗透的）和磁可渗透的（或不可渗透的），并考虑了这些电磁裂纹边界条件的所有可能组合。利用Kachanov法和广义势理论，提出了场变量的近似三维解和一些重要的断裂力学量的表达式。给出了一些特定的裂纹构型的数值示例。基于双裂纹系统，通过将结果与有限元模拟中的结果进行比较，检查了本解决方案的有效性。还以裂纹的大小和两个裂纹之间的距离为因素，研究了裂纹的相互作用。根据数值示例中显示的现象，提出了一种简化的解决方案和一种评估广义应力强度因子的经验方法。以裂缝的大小和两个裂缝之间的距离为因素。根据数值示例中显示的现象，提出了一种简化的解决方案和一种评估广义应力强度因子的经验方法。以裂缝的大小和两个裂缝之间的距离为因素。根据数值示例中显示的现象，提出了一种简化的解决方案和一种评估广义应力强度因子的经验方法。