基于MLS的数值流形法模拟多裂纹扩展

doi:10.13722/j.cnki.jrme.2014.1512

Abstract
Figure/Table
References
Related Citation (15)

Download: PDF (765 KB) HTML (1 KB)
Export: BibTeX | EndNote (RIS)

Abstract The full response of a brittle structure containing multiple cracks under the servo loading condition is of vital importance in the evaluation of properties of the structure. Due to the mathematical covers and physical covers，numerical manifold method is able to simulate the initiation and growth of multiple cracks in a natural way. In order to handle the junction of cracks more straightly，the MLS-based numerical manifold method was used，and the physical patches containing crack tips were enriched to describe the singularity. During the crack growth，crack tips can be located anywhere in the background meshes. Several numerical issues encountered in the simulation were discussed and solved. Besides，a simple algorithm for multiple crack propagation was presented to satisfy the fracture toughness closely. Several numerical examples are illustrated to demonstrate the efficiency and robustness of the proposed method in the simulation of multiple crack propagation.

Key words： numerical analysis moving least square interpolation(MLS) numerical manifold method multiple cracks crack propagation fracture toughness

	Service

	E-mail this article
	Add to my bookshelf
	Add to citation manager
	E-mail Alert
	RSS
	Articles by authors

Cite this article:

URL:

https://rockmech.whrsm.ac.cn/EN/10.13722/j.cnki.jrme.2014.1512 OR https://rockmech.whrsm.ac.cn/EN/Y2016/V35/I1/76

[1] BOUCHARD P，BAY F，CHASTEL Y，et al. Crack propagation modelling using an advanced remeshing technique[J]. Computer methods in applied mechanics and engineering，2000，189(3)：723–742. [2] BOUCHARD P，BAY F，CHASTEL Y. Numerical modelling of crack propagation：automatic remeshing and comparison of different criteria[J]. Computer Methods in Applied Mechanics and Engineering，2003，192(35/36)：3 887–3 908. [3] MOES 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. [4] BELYTSCHKO T，BLACK T. Elastic crack growth in finite elements with minimal remeshing[J]. International journal for numerical methods in engineering，1999，45(5)：601–620. [5] FLEMING M，CHU Y，MORAN B，et al. Enriched element-free Galerkin methods for crack tip fields[J]. International Journal for Numerical Methods in Engineering，1997，40(8)：1 483–1 504. [6] VENTURA G，XU J，BELYTSCHKO T. A vector level set method and new discontinuity approximations for crack growth by EFG[J]. International Journal for Numerical Methods in Engineering，2002，54(6)：923–944. [7] 蔡永昌，朱合华. 裂纹扩展过程模拟的无网格MSLS方法[J]. 工程力学，2010(7)：21–26. [8] BELYTSCHKO T，LU Y Y，GU L. Element‐free Galerkin methods[J]. International Journal for Numerical Methods in Engineering，1994，37(2)：229–256. [9] SHI G. Manifold method of material analysis. DTIC Document，1992. [10] 王水林，葛修润. 流形元方法在模拟裂纹扩展中的应用[J]. 岩石力学与工程学报，1997，16(5)：405–410. [11] ZHANG G，ZHAO Y，PENG X. Simulation of toppling failure of rock slope by numerical manifold method[J]. International Journal of Computational Methods，2010，7(01)：167–189. [12] ZHENG H，XU D. New strategies for some issues of numerical manifold method in simulation of crack propagation[J]. International Journal for Numerical Methods in Engineering，2014，97(13)：986– 1 010. [13] AZADI H，KHOEI A. Numerical simulation of multiple crack growth in brittle materials with adaptive remeshing[J]. International Journal for Numerical Methods in Engineering，2011，85(8)：1 017–1 048. [14] SUKUMAR N，BELYTSCHKO T. Arbitrary branched and intersecting cracks with the extended finite element method[J]. Int. J. Numer. Meth. Engng，2000，48：1 741–1 760. [15] BUDYN E，ZI G，MO S N，et al. A method for multiple crack growth in brittle materials without remeshing[J]. International Journal for Numerical Methods in Engineering，2004，61(10)：1 741–1 770. [16] 石路杨，余天堂. 多裂纹扩展的扩展有限元法分析[J]. 岩土力学，2014，35(1)：263–272. [17] MURAVIN B，TURKEL E. Multiple crack weight for solution of multiple interacting cracks by meshless numerical methods[J]. International Journal for Numerical Methods in Engineering，2006，67(8)：1 146–1 159. [18] RABCZUK T，BORDAS S，ZI G. A three-dimensional meshfree method for continuous multiple-crack initiation，propagation and junction in statics and dynamics[J]. Computational Mechanics，2007，40(3)：473–495. [19] BARBIERI E，PETRINIC N，MEO M，et al. A new weight-function enrichment in meshless methods for multiple cracks in linear elasticity[J]. International Journal for Numerical Methods in Engineering，2012，90(2)：177–195. [20] SHI J，MA W，LI N. Extended meshless method based on partition of unity for solving multiple crack problems[J]. Meccanica，2013，48(9)：2 263–2 270. [21] TSAY R，CHIOU Y，CHUANG W. Crack growth prediction by manifold method[J]. Journal of engineering mechanics，1999，125(8)：884–890. [22] 张国新，王光纶，裴觉民. 基于流形方法的结构体破坏分析[J]. 岩石力学与工程学报，2001，20(3)：281–287. [23] 张国新，金峰，王光纶. 用基于流形元的子域奇异边界元法模拟重力坝的地震破坏[J]. 工程力学，2001，18(4)：18–27. [24] ZHANG G，SUGIURA Y，HASEGAWA H. Crack propagation by manifold and boundary element method. Proc. Third Int. Conf. Analysis of Discontinuous Deformation(ICADD-3)：1999：273–282. [25] CHIOU Y J，LEE Y M，TSAY R J. Mixed mode fracture propagation by manifold method[J]. International Journal of Fracture，2002，114(4)：327–347. [26] 黄涛，陈鹏万，张国新，等. 岩石双孔爆破过程的流形元法模拟[J]. 爆炸与冲击，2006，26(5)：434–440. [27] 黄涛，陈鹏万，张国新，等. 岩石Hopkinson层裂的流形元法模拟[J]. 高压物理学报，2007，20(4)：353–358. [28] 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. [29] ZHANG H，LI L，AN X，et al. Numerical analysis of 2-D crack propagation problems using the numerical manifold method[J]. Engineering analysis with boundary elements，2010，34(1)：41–50. [30] WU Z，WONG L N Y. Frictional crack initiation and propagation analysis using the numerical manifold method[J]. Computers and Geotechnics，2012，39：38–53. [31] WU Z，WONG L N Y. Modeling cracking behavior of rock mass containing inclusions using the enriched numerical manifold method[J]. Engineering Geology，2013，162：1–13. [32] 徐栋栋，郑宏. 数值流形法在处理强奇异性问题时的网格无关性[J]. 岩土力学，2014，35(8)：2 385–2 394. [33] 徐栋栋，郑宏，夏开文，等. 高阶扩展数值流形法在裂纹扩展中的应用[J]. 岩石力学与工程学报，2014，33(7)：1 375–1 387. [34] 李树忱，程玉民. 基于单位分解法的无网格数值流形方法[J]. 力学学报，2004，36(4)：496–500. [35] 栾茂田，杨新辉，田荣，等. 有限覆盖无单元法在多裂纹岩体断裂特性数值分析中的应用[J]. 岩石力学与工程学报，2005，24(24)：4 403–4 408. [36] 樊成，栾茂田. 有限覆盖Kriging插值无网格法在裂纹扩展中的应用[J]. 岩石力学与工程学报，2008，27(4)：743–748. [37] 刘丰，李春光，郑宏，等. 对有限覆盖无网格法中悬挂节点的研究[J]. 工程力学，2014：(IN PRESS). [38] 刘丰，郑宏，李春光. 基于NMM的EFG方法及其裂纹扩展模拟[J]. 力学学报，2014，46(4)：582–590. [39] ZHENG H，LIU F，LI C. The MLS-based numerical manifold method with applications to crack analysis[J]. International Journal of Fracture，2014，190(1/2)：147–166. [40] LIU G. Meshfree methods：moving beyond the finite element method[M]. Florida：CRC，2009. [41] BAZANT Z，TABBARA M. Bifurcation and stability of structures with interacting propagating cracks[J]. International journal of fracture，1992，53(3)：273–289.