The main objective of this study is to implement extended finite element method (XFEM) to two-dimensional (2D) micropolar structures in order to extract basic fracture parameters required in linear elastic fracture mechanics (LEFM) in a computationally efficient manner, and thus to provide basis to explore the crack propagation phenomenon within this framework. The stress and couple-stress intensity factors (SIF and CSIF) are detected with the aid of interaction integral, I-integral, and compared with the ones in the literature for validation purposes while an engineering problem of practical importance; plate with an oblique edge crack, is investigated to demonstrate the applicability of the developed methodology. The approach presents considerable simplification in modeling process owing to ability of XFEM to treat discontinuities and singularities appeared in the cracked domains, and offers a new, and different perspective to available methods (e.g. phase field method and peridynamics), each with their own advantages and limitations, extended to deal with crack and its growth in micropolar structures.

中文翻译：

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通过 XFEM 模型对微极板进行准脆性静态断裂分析


本研究的主要目标是将扩展有限元方法 （XFEM） 应用于二维 （2D） 微极结构，以便以计算高效的方式提取线性弹性断裂力学 （LEFM） 所需的基本断裂参数，从而为在该框架内探索裂纹扩展现象提供基础。应力和耦合-应力强度因子（SIF 和 CSIF）在交互作用积分、I 积分的帮助下进行检测，并与文献中的那些进行比较以进行验证，同时是一个具有实际意义的工程问题;对具有斜边裂纹的板进行研究，以证明所开发方法的适用性。由于 XFEM 能够处理裂纹域中出现的不连续性和奇异性，该方法大大简化了建模过程，并为可用方法（例如相场法和近场动力学）提供了新的、不同的视角，每种方法都有自己的优点和局限性，扩展到处理裂纹及其在微极结构中的生长。