A novel contour integral approach termed Medg is introduced for computation of the surface energy required for the formation of multiple edge cracks. The method is developed by reinterpretation of the conventional M-integral with deliberate delimitation of integration contour and selection of coordinate origin. Due to path independence, this method is efficient, easy to implement by using finite elements, and does not require a complicated mesh around the crack tips for good accuracy. Attention is also addressed to discussion of the size effects on proper interpretation of its physical meaning. The adequacy of the numerical results computed for the finite size corrections has been validated by using some of the available empirical formulations. It is observed that the size effect can be neglected when the crack size remains under one-tenth of the structure size. The results of a specific multi-cracked geotechnical structure suggest that, the damage state such as degradation of the structural stiffness due to the presence of edge cracks can be properly inspected by using Medg.

中文翻译：

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使用 Medg-integral 评估形成多边缘裂纹的表面能

引入了一种称为 Medg 的新型轮廓积分方法来计算形成多边缘裂纹所需的表面能。该方法是通过重新解释传统的 M 积分而开发的，故意划定积分轮廓并选择坐标原点。由于路径独立性，该方法效率高，易于使用有限元实现，并且不需要在裂纹尖端周围进行复杂的网格划分以获得良好的精度。还注意讨论尺寸对正确解释其物理意义的影响。已通过使用一些可用的经验公式验证了为有限尺寸校正计算的数值结果的充分性。据观察，当裂纹尺寸保持在结构尺寸的十分之一以下时，尺寸效应可以忽略不计。一个特定的多裂缝岩土结构的结果表明，由于边缘裂缝的存在，结构刚度下降等破坏状态可以通过使用 Medg 来正确检查。