Journal of Shanghai Jiao Tong University ›› 2021, Vol. 55 ›› Issue (6): 689-697.doi: 10.16183/j.cnki.jsjtu.2020.021

Special Issue: 《上海交通大学学报》2021年“土木建筑工程”专题 《上海交通大学学报》2021年12期专题汇总专辑

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Numerical Calculation Method for Crack Dynamic Propagation Based on Newmark Implicit Time Integration Scheme

GUO Deping1,2, LI Zheng3(), PENG Senlin4, ZENG Zhikai3, WU Daifeng3   

  1. 1. Xuzhen Railway Co., Ltd., Zhaotong 657900, Yunnan, China
    2. School of Civil Engineering, Wuhan University, Wuhan 430072, China
    3. Chongqing City Construction Investment (Group) Co., Ltd., Chongqing 400023, China
    4. Department of Civil Engineering, Chongqing University, Chongqing 400045, China
  • Received:2020-01-14 Online:2021-06-28 Published:2021-06-30
  • Contact: LI Zheng


Extended finite element method (XFEM) is based on the idea of unit decomposition. The jump function that can reflect the discontinuity of the crack surface and the progressive displacement field function of the crack tip is added to the conventional finite element displacement mode, which avoids the inconvenience of remeshing the crack tip and the heavy calculation. Then the conventional finite element method calculates the fracture problem, and the crack propagation is independent of the mesh. When the standard finite element deals with time integration, the degree of freedom of the overall stiffness matrix will continue to increase in the process of crack propagation, which makes iterative calculation impossible. This paper proposes a novel Newmark implicit time integration scheme based on the XFEM to simulate dynamic crack growth. This method enriches all the nodes with the Heaviside function and the asymptotic displacement field function at the crack tip, that is, each node has 12 degrees of freedom, so that the overall stiffness matrix is consistent without making iterative calculation impossible. At the same time, a sparse matrix technology is proposed to solve the problems of large memory and long calculation time occupied by the matrix.

Key words: extended finite element method (XFEM), dynamic cracks, Newmark implicit time integration scheme, sparse matrix technique

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