Abstract In this work, an extended finite element method with partial Heaviside function enrichment (XFEM-P) in the crack tip element is proposed for fracture analysis for the first time. In this method, the crack tip element is divided into cracked and uncracked domains naturally by the crack geometry. In the cracked domain, Heaviside function enrichment is employed to simulate the crack discontinuity across the crack surface. In the uncracked domain, the displacement from standard finite element method is employed. Ramp function is used to ensure the displacement continuity in the method. Through this way, the crack tip can be arbitrarily located inside the crack tip element, which is a great advantage over traditional counterpart, i.e., XFEM with only Heaviside function enrichment (XFEM-H). Thus the mesh work for the XFEM-P is much easier than that of the XFEM-H, resulting in great conveniences for crack propagation. The new method is applied to several examples. From the computed results, it is observed that the XFEM-P offers more accurate results than the XFEM-H in terms of strain energy and SIFs. The XFEM-P performs better than XFEM-H in numerical properties such as convergence rate and condition number.

中文翻译：

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具有部分 Heaviside 函数富集的 XFEM 用于断裂分析

摘要 在这项工作中，首次提出了裂纹尖端单元部分Heaviside函数富集（XFEM-P）的扩展有限元方法用于断裂分析。在这种方法中，裂纹尖端单元被裂纹几何自然分为裂纹域和未裂纹域。在裂纹域中，采用 Heaviside 函数富集来模拟裂纹表面的裂纹不连续性。在未开裂域中，采用标准有限元法的位移。斜坡函数用于保证方法中位移的连续性。通过这种方式，裂纹尖端可以任意位于裂纹尖端单元内部，这比传统的对应物，即仅具有Heaviside函数富集的XFEM（XFEM-H）有很大的优势。因此，XFEM-P 的网格工作比 XFEM-H 的网格工作容易得多，为裂纹扩展带来了极大的便利。新方法应用于几个例子。从计算结果可以看出，XFEM-P 在应变能和 SIF 方面提供比 XFEM-H 更准确的结果。XFEM-P 在收敛速度和条件数等数值属性方面的性能优于 XFEM-H。