This paper aims at a fundamental perspective of multiple cracks’ interaction on the fracture behavior of magnetoelastic materials. A theoretical study is performed on a soft ferromagnetic solid weakened by an array of periodic cracks under an in-plane magnetic loading. By using the conformal mapping technique and the analytic function boundary value theory, a rigorous analytical solution of the magnetic and stress fields is obtained, and the closed-form expressions for the field intensity factors are presented. Numerical examples of magnetically impermeable and permeable cracks are studied to reveal the relationship of the mode-I stress intensity factor with the period ratio of the cracks, the surrounding medium, and the applied magnetic loading. The analytical solution in this study can serve as a theoretical benchmark for the fracture problem of a magnetoelastic solid containing multiple defects.

中文翻译：

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均匀磁场下软铁磁材料中周期性间隔的共线裂纹

本文旨在从多裂纹相互作用对磁致弹性材料断裂行为的基本观点出发。对在面内磁载荷下被一系列周期性裂纹削弱的软铁磁固体进行了理论研究。利用共形映射技术和解析函数边值理论，得到了磁场和应力场的严格解析解，并给出了场强因子的闭式表达式。研究了不透磁裂缝和透磁裂缝的数值例子，以揭示 I 型应力强度因子与裂缝周期比、周围介质和施加的磁载荷之间的关系。