International Journal of Fracture

, Volume 156, Issue 1, pp 21–35 | Cite as

Modeling complex crack problems using the numerical manifold method

  • G. W. Ma
  • X. M. An
  • H. H. Zhang
  • L. X. Li
Original Paper


In the numerical manifold method, there are two kinds of covers, namely mathematical cover and physical cover. Mathematical covers are independent of the physical domain of the problem, over which weight functions are defined. Physical covers are the intersection of the mathematical covers and the physical domain, over which cover functions with unknowns to be determined are defined. With these two kinds of covers, the method is quite suitable for modeling discontinuous problems. In this paper, complex crack problems such as multiple branched and intersecting cracks are studied to exhibit the advantageous features of the numerical manifold method. Complex displacement discontinuities across crack surfaces are modeled by different cover functions in a natural and straightforward manner. For the crack tip singularity, the asymptotic near tip field is incorporated to the cover function of the singular physical cover. By virtue of the domain form of the interaction integral, the mixed mode stress intensity factors are evaluated for three typical examples. The excellent results show that the numerical manifold method is prominent in modeling the complex crack problems.


Numerical manifold method Mathematical cover Physical cover Weight function Cover function Complex crack problems 


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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • G. W. Ma
    • 1
  • X. M. An
    • 1
  • H. H. Zhang
    • 1
    • 2
  • L. X. Li
    • 1
    • 2
  1. 1.School of Civil and Environmental EngineeringNanyang Technological UniversitySingaporeSingapore
  2. 2.MOE Key Laboratory for Strength and VibrationXi’an Jiaotong UniversityXi’anPeople’s Republic of China

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