In this paper, the problem of two equal collinear semi‐permeable cracks is analytically studied for two‐dimensional arbitrarily polarized magneto‐electro‐elastic materials. The electric and magnetic poling directions make arbitrary angles with the crack line. Stroh's formalism and complex variable methodology are utilized to reduce the problem into non‐homogeneous Riemann–Hilbert problem. This numerical problem is then comprehended with the Riemann–Hilbert way to obtain the stress, electric displacement, and magnetic induction components at any point in the domain. The explicit expressions for the crack opening displacement, crack opening potential drop, crack opening induction drop, and the intensity factors are derived. A numerical contextual analysis is displayed for the $BaTi{O}_3-CoF{e}_2{O}_4$ composite. The numerical examination demonstrates that the change in electric/magnetic poling directions influences the different crack parameters.

中文翻译：

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电磁场和磁极化对磁电弹性材料中两个相等的共线半渗透性裂纹的影响

本文分析了二维任意极化的磁电弹性材料的两个相等的共线半渗透裂纹问题。电磁极化方向与裂纹线成任意角度。利用Stroh的形式主义和复杂变量方法将问题简化为非齐次的Riemann-Hilbert问题。然后用黎曼-希尔伯特方法理解该数值问题，以获取域中任意点的应力，电位移和磁感应分量。推导了开裂位移，开裂电位降，开裂感应降和强度因子的显式表达式。将显示以下内容的数字上下文分析：$乙\mathrm{一种}Ť\mathrm{一世}{Ø}_3-CØF{Ë}_2{Ø}_4$综合。数值研究表明，电磁极化方向的变化会影响不同的裂纹参数。