Abstract In this paper, dual boundary element method (DBEM) is combined with interaction integral (I-integral) to evaluate stress intensity factors (SIFs) and T-stress simultaneously for mixed-mode crack analyzing. DBEM is proved to be one of the most efficient boundary element methods (BEM) for solving crack problems with boundary-only discretization, however its current implementation is in lack of efficient methods to evaluate fracture parameters. The available geometrical extrapolation method and J-integral technique for calculating fracture parameters in combination with DBEM are imprecise and difficult to be implemented in mix-mode crack analysis. The presented combined DBEM and I-integral approach can be easily used to extract SIFs and T-stress for mixed-mode cracks, which does not need the decomposition of elastic field into symmetric and antisymmetric components. The fundamental basis lies in the introduction of auxiliary fields for some proper defined single mode crack, then fracture parameters are calculated by evaluating the formulated I-integral in terms of DBEM solution and auxiliary elastic fields. In this paper, the basis of DBEM is illustrated at first, then the explicit expressions for auxiliary fields of displacement gradients are derived, then an automatic scheme for generating the path of I-integral is presented. Several numerical examples are given to validate correctness of the presented method.

中文翻译：

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使用相互作用积分技术的 T 应力和混合模式 SIF 的 DBEM 计算

摘要 本文将双边界元法(DBEM)与相互作用积分(I-integral)相结合，同时评估应力强度因子(SIFs)和T-应力，进行混合模式裂纹分析。DBEM 被证明是解决仅边界离散化裂纹问题的最有效的边界元方法 (BEM) 之一，但其目前的实现缺乏评估断裂参数的有效方法。现有的几何外推法和 J 积分技术结合 DBEM 计算断裂参数不精确，难以在混合模式裂纹分析中实施。提出的组合 DBEM 和 I 积分方法可以很容易地用于提取混合模式裂纹的 SIF 和 T 应力，不需要将弹性场分解为对称分量和反对称分量。其基本基础在于为一些适当定义的单模裂纹引入辅助场，然后通过根据DBEM解和辅助弹性场评估公式化的I-积分来计算断裂参数。本文首先说明了DBEM的基础，然后推导了位移梯度辅助场的显式表达式，然后提出了一种自动生成I-积分路径的方案。给出了几个数值例子来验证所提出方法的正确性。然后通过根据 DBEM 解和辅助弹性场评估公式化的 I 积分来计算断裂参数。本文首先说明了DBEM的基础，然后推导了位移梯度辅助场的显式表达式，然后提出了一种自动生成I-积分路径的方案。给出了几个数值例子来验证所提出方法的正确性。然后通过根据 DBEM 解和辅助弹性场评估公式化的 I 积分来计算断裂参数。本文首先说明了DBEM的基础，然后推导了位移梯度辅助场的显式表达式，然后提出了一种自动生成I-积分路径的方案。给出了几个数值例子来验证所提出方法的正确性。