In the framework of finite element meshes, a novel continuous/discontinuous deformation analysis (CDDA) method is proposed in this paper for modeling of crack problems. In the present CDDA, simple polynomial interpolations are defined at the deformable block elements, and a link element is employed to connect the adjacent block elements. The CDDA is particularly suitable for modeling the fracture propagation because the switch from continuous deformation analysis to discontinuous deformation analysis is natural and convenient without additional procedures. The SIFs (stress intensity factors) for various types of cracks, such as kinked cracks or curved cracks, can be easily computed in the CDDA by using the virtual crack extension technique (VCET). Both the formulation and implementation of the VCET in CDDA are simple and straightforward. Numerical examples indicate that the present CDDA can obtain high accuracy in SIF results with simple polynomial interpolations and insensitive to mesh sizes, and can automatically simulate the crack propagation without degrading accuracy.
Corresponding Author(s):
CAI Yongchang,Email:yc_cai@163.net
引用本文:
. A continuous/discontinuous deformation analysis (CDDA) method based on deformable blocks for fracture modeling[J]. Frontiers of Structural and Civil Engineering, 2013, 7(4): 369-378.
Yongchang CAI, Hehua ZHU, Xiaoying ZHUANG. A continuous/discontinuous deformation analysis (CDDA) method based on deformable blocks for fracture modeling. Front Struc Civil Eng, 2013, 7(4): 369-378.
Atluri S N. Methods of Computer Modeling in Engineering and the Sciences. Tech Science Press, 2005
2
Tong P, Pian T H H, Lasry S J. A hybrid-element approach to crack problems in plane elasticity. International Journal for Numerical Methods in Engineering , 1973, 7(3): 297-308 doi: 10.1002/nme.1620070307
3
Atluri S N, Kobayashi A S, Nakagaki M. An assumed displacement hybrid finite element model for linear fracture mechanics. International Journal of Fracture , 1975, 11(2): 257-271 doi: 10.1007/BF00038893
4
Xu Y, Saigal S. An element free Galerkin formulation for stable crack growth in an elastic solid. Computer Methods in Applied Mechanics and Engineering , 1998, 154(3-4): 331-343 doi: 10.1016/S0045-7825(97)00133-3
5
Belytschko T, Fleming M. Smoothing, enrichment and contact in the element-free Galerkin method. Computers & Structures , 1999, 71(2): 173-195 doi: 10.1016/S0045-7949(98)00205-3
6
Ching H K, Batra R C. Determination of crack tip fields in linear elastostatics by the Meshless Local Petrov-Galerkin (MLPG) method. Computer Modeling in Engineering & Sciences , 2001, 2(2): 273-290
7
Gu Y T, Wang W, Zhang L C, Feng X Q. An enriched radial point interpolation method (e-RPIM) for analysis of crack tip fields. Engineering Fracture Mechanics , 2011, 78(1): 175-190 doi: 10.1016/j.engfracmech.2010.10.014
8
Ma G W, An X M, Zhang H H, Li L X. Modeling complex crack problems using the numerical manifold method. International Journal of Fracture , 2009, 156(1): 21-35 doi: 10.1007/s10704-009-9342-7
9
Wu Z J, Wong L N Y. Frictional crack initiation and propagation analysis using the numerical manifold method. Computers and Geotechnics , 2012, 39: 38-53 doi: 10.1016/j.compgeo.2011.08.011
Sukumar N, Chopp D L, Moes N, Belytschko T. Modeling holes and inclusions by level sets in the extended finite-element method. Computer Methods in Applied Mechanics and Engineering , 2001, 190(46-47): 6183-6200 doi: 10.1016/S0045-7825(01)00215-8
12
Sukumar N, Chopp D L, Béchet E, Mo?s N. Three-dimensional non-planar crack growth by a coupled extended finite element and fast marching method. International Journal for Numerical Methods in Engineering , 2008, 76(5): 727-748 doi: 10.1002/nme.2344
Gosz M, Dolbow J, Moran B. Domain integral formulation for stress intensity factor computation along curved three-dimensional interface cracks. International Journal of Solids and Structures , 1998, 35(15): 1763-1783 doi: 10.1016/S0020-7683(97)00132-7
15
Hellen T K. On the method of virtual crack extensions. International Journal for Numerical Methods in Engineering , 1975, 9(1): 187-207 doi: 10.1002/nme.1620090114
16
Rybicki E F, Kanninen M F. A finite element calculation of stress intensity factors by a modified crack closure integral. Engineering Fracture Mechanics , 1977, 9(4): 931-938 doi: 10.1016/0013-7944(77)90013-3
17
Raju I S. Calculation of strain-energy release rates with high-order and singular finite-elements. Engineering Fracture Mechanics , 1987, 28(3): 251-274 doi: 10.1016/0013-7944(87)90220-7
18
Xie D, Waas A M, Shahwan K W, Schroeder J A, Boeman R G. Computation of Energy Release Rates for Kinking Cracks based on Virtual Crack Closure Technique. CMES: Computer Modeling in Engineering & Sciences , 2004, 6(6): 515-524
19
Zhu B F. The Finite Element Method Theory and Application. Beijing: China Water Conservancy and Hydropower Press, 1998
20
Irwin G R. One set of fast crack propagation in high strength steel and aluminum alloys. Sagamore Resrach Conference Proceedings , 1956, 2: 289-305
21
Anderson T L. Fracture Mechanics: Foundamentals and Application. 2nd ed. Boca Raton: CRC , 1995
22
John E S. Wide range stress intensity factor expressions for ASTM E399 standard fracture toughness specimens. International Journal of Fracture , 1976, 12: 475-476
23
Gdoutos E. Fracture Mechanics. Boston: Kluver Academics Publisher , 1979
24
Budyn E R L. Mutiple Crack Growth by the Extended Finite Element Method. Northwestern University , 2004
25
Chen Y, Hasebe N. New integration scheme for the branch crack problem. Engineering Fracture Mechanics , 1995, 52(5): 791-801 doi: 10.1016/0013-7944(95)00052-W
26
Bittencourt T N, Wawrzynek P A, Ingraffea A R, Sousa J L. Quasiautomatic simulation of crack propagation for 2d lefm problems. Engineering Fracture Mechanics , 1996, 55(2): 321-334 doi: 10.1016/0013-7944(95)00247-2
27
Ingraffea A R, Grigoriu M. Probabilistic fracture mechanics: A validation of predictive capability, Report 90-8. Department of Structural Engineering, Cornell University , 1990.
