In this paper, we develop new asymptotic path-independent integrals for the evaluation of the crack tip parameters in a 2D neo-Hookean material. The new integrals are of both J -integral and interaction energy integral type and rely on the separation of the asymptotic boundary value problem into independent problems for each of the deformed coordinates. Both the plane stress and plane strain cases are considered. The integrals developed are used to compute the amplitude parameters of the asymptotic crack tip fields, which allows for direct extraction of these parameters from numerical results. A long strip with an edge crack under mixed loading modes is considered for both homogeneous and biomaterial cases. It is found that the asymptotic J -integrals produce good results for the first-order parameters while the interactions integrals produce good results for both the first and second-order parameters.

中文翻译：

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用于评估新胡克材料中裂纹尖端参数的渐近路径无关积分

在本文中，我们开发了新的渐近路径无关积分，用于评估 2D 新胡克材料中的裂纹尖端参数。新积分是 J 积分和相互作用能积分类型，依赖于将渐近边值问题分离为每个变形坐标的独立问题。考虑了平面应力和平面应变情况。开发的积分用于计算渐近裂纹尖端场的振幅参数，这允许从数值结果中直接提取这些参数。对于均质和生物材料情况，考虑在混合加载模式下具有边缘裂纹的长条。