期刊
ENGINEERING FRACTURE MECHANICS
卷 199, 期 -, 页码 235-256出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.engfracmech.2018.05.018
关键词
Path-following methods; Cohesive cracks; Extended finite element method; High-order enrichment; Irwin's integral
类别
资金
- Department of Energy through the Early Career Research Program [DE-SC0008196]
- Open Research Fund Program of State Key Laboratory of Water Resources and Hydropower Engineering Science [2016SGK01]
- U.S. Department of Energy (DOE) [DE-SC0008196] Funding Source: U.S. Department of Energy (DOE)
Numerical modeling of cohesive crack growth in quasi-brittle materials is challenging, primarily due to the combination of (i) nonlinearity associated with the fracture process zone (FPZ), (ii) arbitrary directions to which a crack may propagate, and (iii) snap-back or snap-through instabilities encountered in the response of the structure. To address these challenges, we propose a novel arc-length method that can follow the equilibrium path of cohesive crack propagation. The proposed approach is based on the extended finite element method (XFEM) with scalar high-order enrichment functions and Irwin's crack closure integral, which allows for direct control of the applied loads necessary to propagate cohesive cracks. This is achieved by augmenting a constraint equation written in terms of stress intensity factors (SIFs), and expressed explicitly in terms of the enriched degrees of freedom, which is an attractive feature achieved with Irwin's integral, since SIFs can be written in closedform. Note that singular enrichments are active in an unstable crack propagation state and automatically vanish in stable crack configurations. Furthermore, to propagate cracks in arbitrary directions, we employ a maximum circumferential stress criterion implemented by (i) direct usage of the SIFs, and by (ii) a new stress-based nonlocal implementation of this principle. Various benchmark problems including pure mode I and mixed-mode fracture are solved to demonstrate the predictive capability of the present framework for cohesive crack modeling.
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