Computational Mechanics

, Volume 52, Issue 6, pp 1381–1393 | Cite as

Local/global non-intrusive crack propagation simulation using a multigrid X-FEM solver

  • Jean-Charles PassieuxEmail author
  • Julien Réthoré
  • Anthony Gravouil
  • Marie-Christine Baietto
Original Paper


A Local/global non-intrusive coupling algorithm is proposed for the analysis of mixed-mode crack propagation. It is based on a three scale multigrid and extended finite element method, that was proposed recently for the direct estimation of stress intensity factors of static cracks. The algorithm couples a linear elastic global model (possibly performed by a industrial software) with an enhanced local model capable of modeling a crack and accurately estimating SIFs (performed by a separate research code). It is said non-intrusive since it does not modify the global mesh, its connectivity and solver. For the global model, the contribution of the local patch consists in additional nodal efforts near the crack, which makes it compatible with most softwares. Further the shape of the domain over which the local model is applied is automatically adapted during propagation.


Nested models Mixed mode Localized multigrid  Williams Stress intensity factors 



The first author would like to acknowledge the financial support of the Agence Nationale de la Recherche under Grant ICARE ANR-12-MONU-0002. The support of the Agence Nationale de la Recherche under grant RUPXCUBE ANR-09-BLAN-0009-01 RUPX CUBE is also gratefully acknowledged by the authors.


  1. 1.
    Moës N, Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. Int J Numer Methods Eng 46(1):131–150CrossRefzbMATHGoogle Scholar
  2. 2.
    Chiaruttini V, Feyel F, Chaboche JL (2010) A robust meshing algorithm for complex 3D crack growth simulations. In: European congress on computational mechanics, Venice, ItalyGoogle Scholar
  3. 3.
    Barsoum R (1974) Application of quadratic isoparametric elements in linear fracture mechanics. Int J Fract 10:603–605CrossRefGoogle Scholar
  4. 4.
    Passieux JC, Gravouil A, Réthoré J, Baietto MC (2011) Direct estimation of generalized stress intensity factors using a three-scale concurrent multigrid X-FEM. Int J Numer Meth Eng 85(13):1648–1666CrossRefzbMATHGoogle Scholar
  5. 5.
    Réthoré J, Roux S, Hild F (2010) Hybrid analytical and extended finite element method (HAX-FEM): a new enrichment procedure for cracked solids. Int J Numer Methods Eng 81(3):269–285CrossRefzbMATHGoogle Scholar
  6. 6.
    Williams M (1957) On the stress distribution at the base of a stationary crack. ASME J Appl Mech 24:109–114zbMATHGoogle Scholar
  7. 7.
    Pereira J, Duarte C (2005) Extraction of stress intensity factors from generalized finite element solutions. Eng Anal Boundary Elem 29:397–413CrossRefzbMATHGoogle Scholar
  8. 8.
    Rannou J, Gravouil A, Baietto-Dubourg MC (2008) A local multigrid X-FEM strategy for 3-D crack propagation. Int J Numer Methods Eng 77:581–600MathSciNetCrossRefGoogle Scholar
  9. 9.
    Berger-Vergiat L, Waisman H, Hiriyur B, Tuminaro R, Keyes D (2012) Inexact Schwarz-algebraic multigrid preconditioners for crack problems modeled by extended finite element methods. Int J Numer Methods Eng 90(3):311–328MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Guidault PA, Allix O, Champaney L, Cornuault C (2008) A multiscale extended finite element method for crack propagation. Comput Methods Appl Mech Eng 197(5):381–399CrossRefzbMATHGoogle Scholar
  11. 11.
    Lozinski A, Pironneau O (2011) Numerical zoom for localized multiscales. Numer Methods Partial Differential Equ 27:197–207MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Gerstenberger A, Tuminaro R (2012) An algebraic multigrid approach to solve XFEM based fracture problems. Int J Numer Methods Eng 94(3):248–272Google Scholar
  13. 13.
    Kim DJ, Pereira J, Duarte C (2010) Analysis of three-dimentional fracture mechanics problems: a two-scale approach using coarse-generalized fem meshes. Int J Numer Methods Eng 81:335–365zbMATHGoogle Scholar
  14. 14.
    Pereira J, Kim D, Duarte C (2012) A two-scale approach for the analysis of propagating three-dimensional fractures. Comput Mech 49(1):99–121MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Holl M, Loehnert S, Wriggers P (2013) An adaptive multiscale method for crack propagation and crack coalescence. Int J Numer Methods Eng 93(1):23–51MathSciNetCrossRefGoogle Scholar
  16. 16.
    Ben Dhia H, Jamond O (2010) On the use of XFEM within the arlequin framework for the simulation of crack propagation. Comput Methods Appl Mech Eng 199(21–22):1403–1414MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Chahine E, Laborde P, Renard Y (2011) A non-conformal extended finite element approach: integral matching XFEM. Appl Numer Math 61(3):322–343MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Gendre L, Allix O, Gosselet P (2009) Non-intrusive and exact global/local techniques for structural problems with local plasticity. Comput Mech 44:233–245MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Glowinski R, He J, Lozinski A, Rappaz J, Wagner J (2005) Finite element approximation of multi-scale elliptic problems using patches of elements. Numer Math 101(4):663–687MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Lozinski A (2010) Méthodes numériques et modélisation pour certains problèmes multi-échelles. Habilitation à diriger des recherches. Université Paul Sabatier, Toulouse, FranceGoogle Scholar
  21. 21.
    Allix O, Gendre L, Gosselet P, Guguin G (2011) Non-intrusive coupling: An attempt to merge industrial and research software capabilities. In: Mueller-Hoeppe D, Loehnert S, Reese S (eds) Recent developments and innovative application in computational mechanics, chap. 15, pp. 125–133. Springer, BerlinGoogle Scholar
  22. 22.
    Gendre L, Gosselet Allix OP (2011) A two-scale approximation of the schur complement and its use for non-intrusive coupling. Int J Numer Methods Eng 87:889–905CrossRefzbMATHGoogle Scholar
  23. 23.
    Brandt A (1984) Multigrid techniques: 1984 guide with applications to fluid dynamics. The Weizmann Institute of Science, RehovotzbMATHGoogle Scholar
  24. 24.
    Parsons I, Hall J (1990) The multigrid method in solid mechanics: part I-algorithm description and behaviour. Int J Numer Methods Eng 29:719–737CrossRefzbMATHGoogle Scholar
  25. 25.
    Rannou J, Gravouil A, Combescure A (2007) A multi-grid extended finite element method for elastic crack growth simulation. Eur J Comput Mech 16:161–182zbMATHGoogle Scholar
  26. 26.
    Pierrès E, Baietto MC, Gravouil A (2010) A two-scale extended finite element method for modelling 3D crack growth with interfacial contact. Comput Methods Appl Mech Eng 199(17–20):1165–1177CrossRefzbMATHGoogle Scholar
  27. 27.
    Passieux JC, Ladevèze P, Néron D (2010) A scalable time-space multiscale domain decomposition method: adaptive time scale separation. Comput Mech 46(4):621–633MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Gravouil A, Moës N, Belytschko T (2001) Non-planar crack growth by the extended finite element and level sets. Part II: Level-set Update. Int J Numer Methods Eng 53(11):2569–2586CrossRefGoogle Scholar
  29. 29.
    Prabel B, Combescure A, Gravouil A, Marie S (2006) Level set X-FEM non-matching meshes: application to dynamic crack propagation in elastic-plastic media. Int J Numer Methods Eng 69:1553–1569 Google Scholar
  30. 30.
    Geniaut S, Galenne E (2012) A simple method for crack growth in mixed mode with X-FEM. Int J Solids Struct 49(15–16):2094–2106Google Scholar
  31. 31.
    Bui H (1978) Mécanique de la Rupture Fragile. Masson, ParisGoogle Scholar
  32. 32.
    Cormier N, Smallwood B, Sinclair G, Meda G (1999) Aggressive submodelling of stress concentrations. Int J Numer Methods Eng 46(6):889–909CrossRefzbMATHGoogle Scholar
  33. 33.
    Ingraffea A, Grigoriu M (1990) Probabilistic fracture mechanics: a validation of predictive capability. Technical Report 90–98, Department of Structural Engineering, Cornell UniversityGoogle Scholar
  34. 34.
    Häusler SM, Lindhorst K, Horst P (2011) Combination of the material force concept and the extended finite element method for mixed mode crack growth simulations. Int J Numer Methods Eng 85(12):1522–1542CrossRefzbMATHGoogle Scholar
  35. 35.
    Bittencourt TN, Wawrzynek PA, Ingraffea AR, Sousa JL (1996) Quasi-automatic simulation of crack propagation for 2D lefm problems. Eng Fracture Mech 55(2):321–334CrossRefGoogle Scholar
  36. 36.
    Réthoré J, Roux S, Hild F (2010) Mixed-mode crack propagation using a hybrid analytical and extended finite element method. Comptes Rendus de Mécanique 338:121–126CrossRefzbMATHGoogle Scholar
  37. 37.
    Grégoire D, Maigre H, Réthoré J, Combescure A (2007) Dynamic crack propagation under mixed-mode loading - comparison between experiments and x-fem simulations. Int J Solids Struct 44 (20):6517–6534Google Scholar
  38. 38.
    Besnard G, Hild F, Roux S (2006) Finite-element displacement fields analysis from digital images: application to portevinle chtelier bands. Exp Mech 46(6):789–803CrossRefGoogle Scholar
  39. 39.
    Biotteau E, Gravouil A, Lubrecht A, Combescure A (2012) Three dimensional automatic refinement method for transient small strain elastoplastic finite element computations. Comput Mech 49(1):123–136MathSciNetCrossRefzbMATHGoogle Scholar
  40. 40.
    Kerfriden P, Passieux J, Bordas S (2012) Local/global model order reduction strategy for the simulation of quasi-brittle fracture. Int J Numer Methods Eng 89(2):154–179MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Jean-Charles Passieux
    • 1
    Email author
  • Julien Réthoré
    • 2
  • Anthony Gravouil
    • 2
  • Marie-Christine Baietto
    • 2
  1. 1.Université de Toulouse, Institut Clément Ader (ICA), INSA de Toulouse, UPS, Mines Albi, ISAEToulouse CedexFrance
  2. 2.Laboratoire de Mécanique de Contacts et des Structures (LaMCoS)INSA de Lyon/CNRS UMR5259/Université de LyonVilleurbanne CedexFrance

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