Abstract By adopting mathematical and physical covers, the Numerical Manifold Method (NMM) simulates cracks with geometrically elaborate patterns in a unified manner. In this contribution, we propose a high-order NMM together with a direct SIF extraction method for crack modeling. In the proposed framework, SIFs are computed in closed-form upon the solution of the NMM discrete system. This novel formulation avoids cumbersome post-processing procedures and results in naturally decomposed SIFs. In order to meet different accuracy needs, we further generalize the original concept of singular physical covers by defining a parametric enrichment zone, for which high-order asymptotic basis functions derived from Williams’ solution are adopted. Several benchmark examples are presented to validate the excellent performance of the proposed framework. The effect of enrichment zone size as well as enrichment function order on the SIF accuracy is systematically investigated. Furthermore, we discuss the appropriate enrichment scheme as crack tips are in close proximity. The capacity of the proposed framework to address branched and coalescent cracks is demonstrated through the last two examples.

中文翻译：

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使用高阶数值流形法直接提取几何精细裂纹的应力强度因子

摘要 数值流形法（NMM）通过采用数学和物理覆盖，以统一的方式模拟具有几何精细图案的裂缝。在这个贡献中，我们提出了一种高阶 NMM 以及一种用于裂纹建模的直接 SIF 提取方法。在所提出的框架中，SIF 是根据 NMM 离散系统的解决方案以封闭形式计算的。这种新颖的配方避免了繁琐的后处理程序，并导致自然分解的 SIF。为了满足不同的精度需求，我们通过定义一个参数富集区，进一步推广了奇异物理覆盖的原始概念，为此采用了由威廉姆斯解导出的高阶渐近基函数。提供了几个基准示例来验证所提出框架的出色性能。系统地研究了富集区大小以及富集函数顺序对 SIF 精度的影响。此外，我们讨论了适当的富集方案，因为裂纹尖端非常接近。所提出的框架解决分支和聚结裂缝的能力通过最后两个例子得到了证明。