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An explicit representation of cracks in the variational phase field method for brittle fractures
Computer Methods in Applied Mechanics and Engineering ( IF 7.2 ) Pub Date : 2021-09-22 , DOI: 10.1016/j.cma.2021.114127
Liang Yang 1, 2 , Yongtao Yang 1 , Hong Zheng 3 , Zhijun Wu 4
Affiliation  

The phase field method (PFM) by means of regularization fractures has become a promising and popular method for complex crack propagation, especially in geotechnical applications. Attractive as it is, a challenge exists for the PFM to obtain explicit representation of cracks and jump displacement field across cracks that are essential and crucial for some applications, e.g., hydraulic fracturing, leakage problems, and contact problems. In the present paper, an algorithm in which the values of phase field are regarded as the indicator to identify crack paths is proposed. Then physical patches are cut by the reconstructed crack paths to obtain explicit cracks and jump displacement field in the context of the numerical manifold method (NMM). The numerical examples investigate that various explicit cracks, including a straight crack, a curve crack, the branching cracks, and the merging cracks, predicted by the proposed method are in good agreement with the literature. Besides, the Sneddon’s example verifies that the discontinuous displacement field across explicit cracks is in line with the closed form solution. The proposed numerical model deserves a further investigation.



中文翻译:

脆性断裂变相场法中裂纹的显式表示

借助正则化裂缝的相场法(PFM)已成为复杂裂纹扩展的一种有前途和流行的方法,特别是在岩土工程应用中。. 尽管很有吸引力,但 PFM 存在一个挑战,即获得裂缝的明确表示和跨裂缝的跳跃位移场,这对于某些应用至关重要,例如水力压裂、泄漏问题和接触问题。本文提出了一种以相场值为指标的裂纹路径识别算法。然后通过重建的裂纹路径切割物理补丁,以在数值流形方法 (NMM) 的背景下获得显式裂纹和跳跃位移场。数值算例研究了各种显性裂纹,包括直线裂纹、曲线裂纹、分支裂缝和合并裂缝,所提出的方法预测与文献吻合良好。此外,Sneddon 的例子验证了跨越显式裂缝的不连续位移场与封闭形式解是一致的。所提出的数值模型值得进一步研究。

更新日期:2021-09-23
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