A continuous/discontinuous deformation analysis (CDDA) method based on deformable blocks for fracture modeling

Yongchang CAI, Hehua ZHU, Xiaoying ZHUANG

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PDF(638 KB)
Front. Struct. Civ. Eng. ›› 2013, Vol. 7 ›› Issue (4) : 369-378. DOI: 10.1007/s11709-013-0222-x
RESEARCH ARTICLE

A continuous/discontinuous deformation analysis (CDDA) method based on deformable blocks for fracture modeling

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Abstract

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.

Keywords

fracture / crack / propagation / deformable block / continuous/discontinuous deformation analysis (CDDA)

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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 https://doi.org/10.1007/s11709-013-0222-x

References

[1]
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
CrossRef Google scholar
[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
CrossRef Google scholar
[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
CrossRef Google scholar
[5]
Belytschko T, Fleming M. Smoothing, enrichment and contact in the element-free Galerkin method. Computers & Structures, 1999, 71(2): 173-195
CrossRef Google scholar
[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
CrossRef Google scholar
[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
CrossRef Google scholar
[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
CrossRef Google scholar
[10]
Moes N, Dolbow J, Belytschko T. A finite element method for crack growth without remeshing. International Journal for Numerical Methods in Engineering, 1999, 46(1): 131-150
CrossRef Google scholar
[11]
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
CrossRef Google scholar
[12]
Sukumar N, Chopp D L, Béchet E, Moës 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
CrossRef Google scholar
[13]
Fleming M, Chu Y A, Moran B, Belytschko T. Enriched element-free Galerkin methods for crack tip fields. International Journal for Numerical Methods in Engineering, 1997, 40(8): 1483-1504
CrossRef Google scholar
[14]
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
CrossRef Google scholar
[15]
Hellen T K. On the method of virtual crack extensions. International Journal for Numerical Methods in Engineering, 1975, 9(1): 187-207
CrossRef Google scholar
[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
CrossRef Google scholar
[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
CrossRef Google scholar
[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
CrossRef Google scholar
[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
CrossRef Google scholar
[27]
Ingraffea A R, Grigoriu M. Probabilistic fracture mechanics: A validation of predictive capability, Report 90-8. Department of Structural Engineering, Cornell University, 1990.

Acknowledgements

The authors gratefully acknowledge the support of Nature Science Foundation of China (NSFC 41130751), National Basic Research Program of China (Grant No.: 2011CB013800), and New Century Excellent Talents Project in China (NCET-12-0415).

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2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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