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Mathematical Problems in Engineering
Volume 2013, Article ID 157130, 13 pages
Research Article

The Numerical Simulation of the Crack Elastoplastic Extension Based on the Extended Finite Element Method

1State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing 210098, China
2Department of Engineering Mechanics, Hohai University, Nanjing 210098, China
3School of Civil and Transportation Engineering, Guangdong University of Technology, Guangzhou 510006, China
4Communication and Electron College, Jiangxi Science & Technology Normal University, Nanchang 330013, China

Received 19 July 2013; Revised 22 September 2013; Accepted 22 September 2013

Academic Editor: Zhiqiang Hu

Copyright © 2013 Xia Xiaozhou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In the frame of the extended finite element method, the exponent disconnected function is introduced to reflect the discontinuous characteristic of crack and the crack tip enrichment function which is made of triangular basis function, and the linear polar radius function is adopted to describe the displacement field distribution of elastoplastic crack tip. Where, the linear polar radius function form is chosen to decrease the singularity characteristic induced by the plastic yield zone of crack tip, and the triangle basis function form is adopted to describe the displacement distribution character with the polar angle of crack tip. Based on the displacement model containing the above enrichment displacement function, the increment iterative form of elastoplastic extended finite element method is deduced by virtual work principle. For nonuniform hardening material such as concrete, in order to avoid the nonsymmetry characteristic of stiffness matrix induced by the non-associate flowing of plastic strain, the plastic flowing rule containing cross item based on the least energy dissipation principle is adopted. Finally, some numerical examples show that the elastoplastic X-FEM constructed in this paper is of validity.