Wawrzynek P A, Ingraffea A R. An interactive approach to local remeshing around a propagating crack [J]. Finite Elements in Analysis and Design, 1989, 5(1): 87―96.
Luo Shaoming, Cai Yongchang, Zhang Xiangwei. Study on the numerical nanifold nethod remeshing technique and its application in metal forming processes [J]. Journal of Chongqing University (Natural Science Edition), 2001, 24(4): 34―37, 41. (in Chinese)
[4]
Rashid M M. The arbitrary local mesh replacement method: An alternative to remeshing for crack propagation analysis [J]. Computer Methods in Applied Mechanics and Engineering, 1998, 154(1/2): 133―150.
[5]
R#x000e9;thor#x000e9; J, Gravouil A, Combescure A. A stable numerical scheme for the finite element simulation of dynamic crack propagation with remeshing [J]. Computer Methods in Applied Mechanics and Engineering, 2004, 193(42/43/44): 4493―4510.
Jin Feng, Fang Xiujun. The extended finite element method and its relations with other numerical methods [J]. Engineering Mechanics, 2008, 25(Suppl 1): 1―17. (in Chinese)
[8]
Fries T P, Belytschko T. The extended/generalized finite element method: An overview of the method and its applications [J]. International Journal for Numerical Methods in Engineering, 2010, 84(3): 253―304.
[9]
Ma G W, An X M, He L. The numerical manifold method: A review [J]. International Journal of Computational Methods, 2010, 7(1): 1―32.
Su Haidong. Study on numerical manifold method with fixed meshes [J]. Chinese Journal of Theoretical and Applied Mechanics, 2011, 43(1): 169―178. (in Chinese)
Li Luxian, Liu Shujing, Zhang Huihua, et al. Researching progress of generalized finite element method [J]. Chinese Journal of Applied Mechanics, 2009, 26(1): 96―108. (in Chinese)
[14]
Stolarska M, Chopp D L, Mo#x000eb;s N, et al. Modelling crack growth by level sets in the extended finite element method [J]. International Journal for Numerical Methods in Engineering, 2001, 51(8): 943―960.
[15]
Mo#x000eb;s N, Dolbow J, Belytschko T. A finite element method for crack growth without remeshing [J]. International Journal for Numerical Methods in Engineering, 1999, 46(1): 131―150.
[16]
Cheng K W, Fries T P. Higher-order XFEM for curved strong and weak discontinuities [J]. International Journal for Numerical Methods in Engineering, 2010, 82(5): 564―590.
[17]
Fries T P, Belytschko T. The intrinsic XFEM: A method for arbitrary discontinuities without additional unknowns [J]. International Journal for Numerical Methods in Engineering, 2006, 68(13): 1358―1385.
Fang Xiujun, Jin Feng, Kou Lihang, et al. A new method for constructing the approximations of zigzag-crack-tip elements [J]. Chinese Journal of Computational Mechanics, 2010, 27(1): 95―101. (in Chinese)
[20]
Xiao Q Z, Karihaloo B L. Improving the accuracy of XFEM crack tip fields using higher order quadrature and statically admissible stress recovery [J]. International Journal for Numerical Methods in Engineering, 2006, 66(9): 1378―1410.
[21]
Nakasumi S, Suzuki K, Ohtsubo H. Crack growth analysis using mesh superposition technique and X-FEM [J]. International Journal for Numerical Methods in Engineering, 2008, 75(3): 291―304.
[22]
Karihaloo B L, Xiao Q Z. Modelling of stationary and growing cracks in FE framework without remeshing: A state-of-the-art review [J]. Computers and Structures, 2003, 81(3): 119―129.
Wang Shuilin, Ge Xiurun. Application of manifold method in simulating crack propagation [J]. Chinese Journal of Rock Mechanics and Engineering, 1997, 16(5): 405―410. (in Chinese)
[25]
An X M, Ma G W, Cai Y C, et al. Arbitrary discontinuities in the numerical manifold method [J]. International Journal of Computational Methods, 2011, 8(2): 315―347.
[26]
Ning Y J, Yang J, An X M, et al. Modelling rock fracturing and blast-induced rock mass failure via advanced discretisation within the discontinuous deformation analysis framework [J]. Computers and Geotechnics, 2011, 38(1): 40―49.
[27]
Ma G W, An X M, Zhang H H, et al. Modeling complex crack problems using the numerical manifold method [J]. International Journal of Fracture, 2009, 156(1): 21―35.
Su Haidong, Cui Jianhua, Xie Xiaoling. Initial stress equation for high-order numerical manifold method [J]. Chinese Journal of Computational Mechanics, 2010, 27(2): 270―274. (in Chinese)
Cai Yongchang, Zhu Hehua, Xia Caichu. Automatically forming of cover system in numerical manifold method [J]. Journal of Tongji University, 2004, 32(5): 585―590. (in Chinese)
Li Shuchen, Li Shucai, Zhang Jingwei, Wang Zhaoqing. Numerical manifold method from mathematical theory and its application [J]. Engineering Mechanics, 2007, 24(6): 36―42. (in Chinese)
Guo Chaoxu, Zheng Hong. Study on linear dependence problem in high-order numerical manifold method [J]. Engineering Mechanics, 2012, 29(12): 228―232. (in Chinese)
L#x000fc; Senpeng, Chen Weizhong, Jia Shanpo, et al. Experiential study on brittle rock failure [J]. Chinese Journal of Rock Mechanics and Engineering, 2009, 28(Suppl 1): 2772―2777. (in Chinese)
[40]
Brace W F, Bombolakis E G. A note on brittle crack growth in compression [J]. Journal of Geophysical Research, 1963, 68(12): 3709―3713.
[41]
Horii H, Nemat-Nasser S. Compression-induced microcrack growth in brittle solids: Axial splitting and shear failure [J]. Journal of Geophysical Research, 1985, 90(B4): 3105―3125.
Song Na, Zhou Chuwei. Accuracy study of crack tip field in extended finite element method [J]. Chinese Journal of Computational Mechanics, 2009, 26(4): 544―547. (in Chinese)
