Abstract In this study, we examine the fracture analysis of a non-homogeneous half-layer reinforced by a magneto-electro-elastic (MEE) coating with multiple interface and embedded cracks in a non-homogeneous substrate under impact loadings. Material properties of the functionally graded (FG) orthotropic substrate are assumed to vary exponentially in the thickness direction of the half-layer. First, the analytical solution is developed by considering a dynamic mechanical dislocation with time-dependent Burgers vector be situated at the substrate and interface by means of the Fourier and Laplace transform. The solutions are used to derive singular integral equations for the medium containing embedded and interface cracks. Then, the integral equations are solved numerically for the density of dislocations on a crack surface. The dislocation densities are employed to determine the dynamic stress intensity factors (DSIFs). The effects of crack spacing, the length and position of the cracks and FGM exponent as well as crack interaction are studied.

中文翻译：

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与磁电弹性涂层结合的非均匀半层中几个裂纹的瞬态响应

摘要 在这项研究中，我们研究了由磁电弹性 (MEE) 涂层增强的非均匀半层在冲击载荷下的断裂分析，该涂层具有多个界面和嵌入裂纹的非均匀基材。假设功能梯度 (FG) 正交各向异性衬底的材料特性在半层的厚度方向上呈指数变化。首先，通过傅立叶和拉普拉斯变换考虑位于衬底和界面处的动态机械位错与时间相关的 Burgers 向量来开发解析解。这些解用于导出包含嵌入裂纹和界面裂纹的介质的奇异积分方程。然后，对裂纹表面位错密度的积分方程进行数值求解。位错密度用于确定动态应力强度因子 (DSIF)。研究了裂纹间距、裂纹长度和位置、FGM 指数以及裂纹相互作用的影响。