In this paper, distributed strain nucleus is presented to compute the modes I/II stress intensity factors (SIFs) and electric displacement intensity factors (EDIFs) for multiple unequal cracks placed between a functionally graded piezoelectric materials (FGPMs) and a piezoelectric half-plane. Employing the Fourier transform, the governing electro-elastic equations are solved in terms of the Burgers vectors , and . These equations converted into a system of singular integral equations with Cauchy type then are solved numerically with the help of collocation methods. Crack problems can be solved by establishing the stress and displacement fields in the crack's absence and distributing strain nuclei along the line of the crack. The distributed strain nucleus is a powerful method to calculate accurate solutions to plane crack problems. In fact, the technique is excellent for solutions of complex crack patterns and it is suitable to analyze multiple cracks. Hence this technique allows considering multiple cracks with arbitrary lengths and positions at the interface. The validation of results has been checked by available analytical, finite element and experimental papers. The primary objective of this paper is to study the interacting effects among multiple unequal interface cracks, the non-homogeneity parameter, geometry and material properties and loading parameters on the field intensity factors. Numerical results show that the normalized modes I/II SIFs and EDIFs decreasing with increasing stiffness and thickness of coating.

中文翻译：

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分布应变核在功能梯度压电层和压电基板之间产生多条不等裂纹


本文提出了分布式应变核来计算功能梯度压电材料 (FGPM) 和压电半平面之间的多个不等裂纹的 I/II 型应力强度因子 (SIF) 和电位移强度因子 (EDIF) 。利用傅里叶变换，控制电弹性方程根据 Burgers 矢量 、 和 来求解。将这些方程转化为柯西型奇异积分方程组，然后借助配置方法进行数值求解。裂纹问题可以通过在没有裂纹的情况下建立应力场和位移场并沿裂纹线分布应变核来解决。分布式应变核是计算平面裂纹问题精确解的有力方法。事实上，该技术非常适合解决复杂的裂纹模式，并且适合分析多个裂纹。因此，该技术允许考虑界面处具有任意长度和位置的多个裂纹。结果的验证已通过可用的分析、有限元和实验论文进行了检查。本文的主要目的是研究多个不等界面裂纹、非均匀参数、几何形状和材料特性以及载荷参数对场强因子的相互作用影响。数值结果表明，归一化模式 I/II SIF 和 EDIF 随着涂层刚度和厚度的增加而减小。