The evaluation of the stress intensity factors (SIFs), T-stress, and higher-order coefficients in the crack tip asymptotic field in the extended finite element method (XFEM) is investigated based on the over-deterministic displacement field fitting method. Numerical examples of central cracked and edge cracked plate under uniaxial tension exhibit the accuracy of the evaluated coefficients. A convergence study is conducted to explore the influence of fitting parameters: the number of nodes used for fitting, the number of terms in the asymptotic field series used for fitting, and the distance from selected nodes to the crack tip. It indicates that the distance of selected nodes affects the accuracy of coefficients above 3rd order. Besides, the study of enrichment function and strategy demonstrates that adopting higher-order enrichment terms or more enriched layers of elements can improve the accuracy of coefficient evaluation. Particularly, the higher-order coefficients can be evaluated without the enrichment terms of the corresponding order. The analyses verify that the crack tip asymptotic field coefficients can be accurately evaluated in XFEM using this over-deterministic displacement field fitting method with the appropriate setting of enrichment and fitting parameters.

基于超确定性位移场拟合方法，研究了扩展有限元方法（XFEM）中裂纹尖端渐近场中应力强度因子（SIF），T应力和高阶系数的评估。中心裂纹和边缘裂纹板在单轴拉力作用下的数值算例表明了所评估系数的准确性。进行了收敛研究以探讨拟合参数的影响：用于拟合的节点数，用于拟合的渐近场序列中的项数以及从选定节点到裂纹尖端的距离。这表明所选节点的距离会影响三阶以上系数的准确性。除了，富集功能和策略的研究表明，采用高阶富集项或元素的更富集层可以提高系数评估的准确性。特别地，可以在没有相应阶数的富集项的情况下评估高阶系数。分析证明，使用这种超确定性位移场拟合方法，并通过适当设置富集和拟合参数，可以在XFEM中准确评估裂纹尖端的渐近场系数。