Abstract—A moving mesh finite element method is studied for the numerical solution of a phase-field model for brittle fracture and hydraulic fracture. In the phase-field modeling, a continuous phase field variable is introduced to describe the unbroken or broken status of the material, which can model fractures without explicitly tracking discontinuous displacement fields. It has the advantages of being able to handle complex cracks, crack propagation, and creation of new cracks more easily. It is noted that the parameter , which describes the width of smeared cracks, should be chosen small for the model to be sufficiently accurate. On the other hand, the mesh size ( ) should be chosen small typically satisfying or at least . This deems it necessary to use mesh adaptation for an efficient numerical simulation. Moreover, cracks propagate under continuous load, which means the mesh must adapt to the evolving cracks dynamically. In this talk we will employ the moving mesh partial differential equation approach for dynamic mesh adaption. Numerical examples will be presented to show that the moving mesh finite element method is able to adaptively capture the crack propagation and handle multiple crack systems.
Index Terms—Brittle fracture, hydraulic fracture, phase-field model, moving mesh, mesh adaptation.
Fei Zhang and Shicheng Zhang are with College of Petroleum Engineering, China University of Petroleum – Beijing, 18 Fuxue Road, Changping, Beijing 102249, China (email: fzhang_cup@outlook.com, zhangsc@cup.edu.cn).
Weizhang Huang is with Department of Mathematics, the University of Kansas, Lawrence, Kansas 66049, U.S.A. (whuang@ku.edu). Xianping Li is with Department of Mathematics and Statistics, University of Missouri – Kansas City, 5120 Rockhill Road, Kansas City, Missouri 64110, U.S.A. (lixianp@umkc.edu).
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Cite: Fei Zhang, Weizhang Huang, Xianping Li and Shicheng Zhang, "A Study on Moving Mesh Finite Element Solution of Phase-Field Models for Hydraulic Fracturing," International Journal of Chemical Engineering and Applications vol. 9, no. 2, pp. 51-57, 2018.
