A topological derivative is defined, which is caused by kinking of a crack, thus, representing the topological change. Using variational methods, the anti-plane model of a solid subject to a non-penetration condition imposed at the kinked crack is considered. The objective function of the potential energy is expanded with respect to the diminishing branch of the incipient crack. The respective sensitivity analysis is provided by a Saint-Venant principle and a local decomposition of the solution of the variational problem in the Fourier series.

中文翻译：

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关于非穿透裂纹扭结的拓扑导数。反平面模型。

定义了一个拓扑导数，它是由裂缝的扭结引起的，因此，代表了拓扑变化。使用变分方法，考虑在扭结裂纹处施加非渗透条件的固体的反平面模型。势能的目标函数相对于初始裂纹的递减分支展开。各自的敏感性分析由圣维南原理和傅立叶级数中变分问题的解的局部分解提供。