Abstract In this paper, a J-integral formula and numerical calculation method are presented, which confirm the path-independence of a J-integral, considering the mixed-mode fracture in a chemo-mechanical coupled medium. The Jk-integral denotes a two-dimensional vector consisting of the components J1 and J2. Using the Equivalent Domain Integral (EDI) method, the chemo-mechanical coupled J2-integral, with an equivalent domain form that includes both a surface integral and a line integral, is deduced using a poroelastical model. Based on a semi-analytical method, an auxiliary -integral is derived to develop a finite element calculation program. By choosing two characteristic lengths, near the crack tip, the mixed-mode fracture parameters, and (T stress) at the crack tip, can be calculated. The mixed-mode fracture problems, which are related to center-cracked and edge-cracked plates, are numerically studied for certain chemo-mechanical coupled boundary conditions. The accuracy of this method is verified with numerical examples, which shows the path-independence of the J-integral for chemo-mechanical coupling. The stress fields of two different cracked hydrogel plates are analyzed with different boundary conditions under the chemo-mechanical coupled mixed-mode fracture. This work provides new insights into the mixed-mode fracture mechanics of a chemo-mechanical coupled medium.

中文翻译：

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化学-机械耦合断裂力学混合模式断裂理论与计算

摘要 本文提出了J-积分公式和数值计算方法，确定了J-积分的路径无关性，考虑了化学-机械耦合介质中的混合模式断裂。Jk 积分表示由分量 J1 和 J2 组成的二维向量。使用等效域积分 (EDI) 方法，使用多孔弹性模型推导出具有等效域形式的化学-机械耦合 J2 积分，其中包括表面积分和线积分。基于半解析方法，推导出辅助积分，开发有限元计算程序。通过选择裂纹尖端附近的两个特征长度，可以计算出裂纹尖端的混合模式断裂参数和（T 应力）。混合模式断裂问题，与中心裂纹和边缘裂纹板有关，对某些化学-机械耦合边界条件进行了数值研究。数值例子验证了该方法的准确性，这表明了化学-机械耦合的 J 积分的路径无关性。在化学-机械耦合混合模式断裂下，分析了不同边界条件下两种不同裂纹水凝胶板的应力场。这项工作为化学-机械耦合介质的混合模式断裂力学提供了新的见解。在化学-机械耦合混合模式断裂下，分析了不同边界条件下两种不同裂纹水凝胶板的应力场。这项工作为化学-机械耦合介质的混合模式断裂力学提供了新的见解。在化学-机械耦合混合模式断裂下，分析了不同边界条件下两种不同裂纹水凝胶板的应力场。这项工作为化学-机械耦合介质的混合模式断裂力学提供了新的见解。