-0.4 -0.2 0 0.2 0.4 -0.4-0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 y x aint sadim=2.8 sadim=2.5 sadim=2.0 sadim=1.5 sadim=1 sadim=0.5 sadim=0.001 (a) Successive positions of the crack 0 0.5 1 1.5 2 2.5 3 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 sig adim aint/b single coalescence (b) Critical loading during propagation Figure 5: β =30, N=160, δamax/l =0.001, a0/b =0.1, remesh each 1000 numerical cycles Acknowledgements [1] A. F. Bower, M. Ortiz, 1990, Solution of three-dimensional crack problems by a finite perturbation method, J. of the Mechanics and Physics of Solids 38(4), 443 480. [2] Y. Chen, K. Y. Lee, 2002, Solution of flat crack problem by using variational principle and differential-integral equation, Int. J. of Solids and Structures 39 (23), 578797. [3] V. Fabrikant, 1987, Close interaction of coplanar circular cracks in an elastic medium, Acta Mechanica 67, 3959. [4] M. Isida, K. Hirota, H. Noguchi, T. Yoshida, 1985, Two parallel elliptical cracks in an infinite solid subjected to tension, Int. J. of Fracture 27, 3148. [5] M. Kachanov, J.-P Laures, 1989, Three-dimensional problems of strongly interacting arbitrarily located pennyshaped cracks, Int. J. of Fracture 41, 289313. [6] V. Lazarus, 2003, Brittle fracture and fatigue propagation paths of 3D plane cracks under uniform remote tensile loading, Int. J. of Fracture 122 (1-2), 2346. [7] J. R. Rice, 1989, Weight function theory for three-dimensional elastic crack analysis, in R. P. Wei and R. P. Gangloff, eds, Fracture Mechanics: Perspectives and Directions (Twentieth Symposium), American Society for Testing and Materials STP 1020, Philadelphia, USA, pp. 2957. [8] S. Zhan, T. Wang, 2006, Interactions of penny-shaped cracks in three-dimensional solids, Acta Mechanica Sinica 22, 341353. 8
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