Cohesive and non‐cohesive fracture by higher‐order enrichment of XFEM

Abstract

SUMMARYA comprehensive study is performed on the use of higher-order terms of the crack tip asymptotic fields as enriching functions for the eXtended FEM (XFEM) for both cohesive and traction-free cracks. For tractionfree cracks, the Williams asymptotic field is used to obtain highly accurate stress intensity factors (SIFs), directly from the enriched degrees of freedom without any post-processing. The low accuracy of the results of the original research on this subject by Liu et al. [Int. J. Numer. Meth. Engng., 2004; 59:1103-1118 is remedied here by appropriate modifications of the enrichment scheme. The modifications are simple and can be easily included into an XFEM computer code. For cohesive cracks, the relevant asymptotic field is used, and two widely used criteria including the SIFs criterion and the stress criterion are examined for the crack growth simulation. Both linear and nonlinear cohesive laws are used. For the stress criterion, averaging is avoided due to the highly accurate crack tip approximation because of the higherorder enrichment. Then, a modified stress criterion is proposed, which is shown to be applicable to a wider class of problems. Several numerical examples, including straight and curved cracks, stationary and growing cracks, single and multiple cracks, and traction-free and cohesive cracks, are studied to investigate in detail the robustness and efficiency of the proposed enrichment scheme.

Computational Methods for Fracture in Brittle and Quasi-Brittle Solids: State-of-the-Art Review and Future Perspectives

“…Hence, the SIFs can be obtained directly from the numerical analysis without computing the J-integral or interaction integral. However, it was shown by Zamani et al [224,225] that such approaches are less accurate. The extrinsic PU enrichment is comparable to an XFEM enrichment.…”

A High‐order extended finite element method for extraction of mixed‐mode strain energy release rates in arbitrary crack settings based on Irwin's integral

“…Several benchmark examples are studied, and the results show that high accuracy can be achieved with high-order enrichment terms. High-order terms have also been studied by [23][24][25][26][27][28]. In particular, the enrichment of the approximation space by higher-order terms of asymptotic field using h-p clouds were studied by Liszka et al [23] and Duarte et al [24].…”

Probabilistic Model Updating for Sizing of Hole-Edge Crack Using Fiber Bragg Grating Sensors and the High-Order Extended Finite Element Method

“…Since the extracted reflection intensity spectrum relies heavily on the accuracy of the strain field, we propose to use not only the leading, but also the higher-order terms of the Williams asymptotic solution [36] as the enrichment functions. While the idea of incorporating the high-order enrichment was explored in the previous studies [37,38,39] mainly for direct extraction of stress intensity factors, the motivation here is to effectively improve the accuracy of the simulated strain field and, in turn, the reflection intensity spectrum.…”