Int J Fract (2008) 149:11–30 DOI 10.1007/s10704-008-9215-5 ORIGINAL PAPER Numerical simulation of crack deflection and penetration at an interface in a bi-material under dynamic loading by time-domain boundary element method Jun Lei · Yue-Sheng Wang · Dietmar Gross Received: 12 September 2007 / Accepted: 5 May 2008 / Published online: 27 June 2008 © Springer Science+Business Media B.V. 2008 Abstract The hybrid time-domain boundary element method (BEM), together with the multi-region technique, is applied to simulate the dynamic process of crack deflection/ penetration at an interface in a bi-material. The whole bi-material is divided into two re- gions along the interface. The traditional displacement boundary integral equations (BIEs) are employed with respect to the exterior boundaries; meanwhile, the non-hypersingular trac- tion BIEs are used with respect to the part of the crack in the matrix. Crack propagation along the interface is numerically modelled by releasing the nodes in the front of the moving crack tip and crack propagation in the matrix is modeled by adding new elements of constant length to the moving crack tip. The dynamic behaviours of the crack deflection/penetration at an interface, propagation in the matrix or along the interface and kinking out off the interface, are controlled by criteria developed from the quasi-static ones. The numerical results of the crack growth trajectory for different inclined interface and bonded strength are computed and compared with the corresponding experimental results. Agreement between numerical and experimental results implies that the present time-domain BEM can provide a simulation for the dynamic propagation and deflection of a crack in a bi-material. Keywords Dynamic fracture · Bi-material · Interface · Crack · Crack deflection and penetration · Fracture criterion · Time-domain boundary element method J. Lei · Y.-S Wang (B ) Institute of Engineering Mechanics, Beijing Jiaotong University, Beijing 100044, People’s Republic of China e-mail: yswang@bjtu.edu.cn J. Lei Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, People’s Republic of China D. Gross Department 13, Mechanics, TU Darmstadt, Hochschulstrasse 1, D-64289 Darmstadt, Germany 123