A local multigrid X-FEM strategy for 3-D crack propagation

International Journal for Numerical Methods in Engineering

Volumn 77, Issue 4, 2009, Pages 581-600

  Rannou, J ^a   Gravouil, Anthony ^a   Baietto Dubourg M C ^a  

^a UNIVERSITÉ DE LYON   (France)

Author keywords

3 D crack growth; Fatigue; Level sets; Multigrid; X FEM

Indexed keywords

CRACK PROPAGATION; CRACKING (CHEMICAL); FINITE ELEMENT METHOD; LEVEL MEASUREMENT; STRENGTH OF MATERIALS;

3-D CRACK GROWTH; FATIGUE; LEVEL SETS; MULTIGRID; X-FEM;

CRACKS;

EID: 60949097838     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.2427     Document Type: Article

References (31)

1. Moës 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.
2. Belytschko T, Black T. Elastic crack growth in finite elements with minimal remeshing. International Journal for Numerical Methods in Engineering 1999; 45(5):601-620.
3. Gravouil A, Moës N, Belytschko T. Non-planar 3D crack growth by the extended finite element and level sets - part II: level set update. International Journal for Numerical Methods in Engineering 2002; 53:2569-2586.
4. Sethian JA. Level Set Methods and Fast Marching Methods. Cambridge University Press: Cambridge, 1999.
5. Duflot M. A study of the representation of cracks with level sets. International Journal for Numerical Methods in Engineering 2006; 70(11):1261-1302.
6. Pommier S, Risbet M. Time-derivative equations for fatigue crack growth in metals. International Journal of Fracture 2005; 131(1):79-106.
7. Ribeaucourt R, Baïetto-Dubourg MC, Gravouil A. A new fatigue frictional contact crack propagation model with the coupled X-FEM/LATIN method. Computer Methods in Applied Mechanics and Engineering 2007; 196(33-34):3230-3247.
8. Elguedj T, Gravouil A, Combescure A. A mixed augmented Lagrangian-extended finite element method for modelling elastic-plastic fatigue crack growth with unilateral contact. International Journal for Numerical Methods in Engineering 2007; 71(13):1569-1597.
9. Elkhodja N, Ben Dhia H, Roux FX. Modélisation de structures multi-défauts dans le cadre arlequin et approches par sous-domaines. Actes du huitième colloque national en calcul des structures, Giens, France, vol. 1, 2007; 467-472.
10. Guidault PA, Allix O, Champaney L, Navarro JP. A multiscale computational strategy for crack propagation with local enrichment. USNCCM 8 - 8th US National Congress on Computational Mechanics, Austin, U.S.A., 2005.
11. Bellec J, Dolbow JE. A note on enrichment functions for modelling crack nucleation. Communications in Numerical Methods in Engineering 2003; 19(12):921-932.
12. Melenk JM, Babuska I. The partition of unity finite element method: basic theory and applications. Computer Methods in Applied Mechanics and Engineering 1996; 139(1):289-314.
13. Qian D, Wagner GJ, Liu WK. A multiscale projection method for the analysis of carbon nanotubes. Computer Methods in Applied Mechanics and Engineering 2004; 19(17):1603-1632.
14. Fish J, Yuan Z. Multiscale enrichment based on partition of unity. International Journal for Numerical Methods in Engineering 2005; 62:1341-1359.
15. Brandt A. Multigrid Techniques: 1984 Guide. The Weizmann Institute of Science: Rehovot, Israel, 1984.
16. Lubrecht AA, Venner CH. Multilevel Methods in Lubrication. Elsevier: Amsterdam, 2000.
17. Parsons ID, Hall JF. The multigrid method in solid mechanics: part I - algorithm description and behaviour. International Journal for Numerical Methods in Engineering 1990; 29:719-737.
18. Parsons ID, Hall JF. The multigrid method in solid mechanics. II: practical applications. International Journal for Numerical Methods in Engineering 1990; 29(4):739-753.
19. Rannou J, Gravouil A, Combescure A. A multi-grid extended finite element method for elastic crack growth simulation. European Journal of Computational Mechanics 2007; 16:161-182.
20. Brandt A. Multi-level adaptive solutions to boundary-value problems. Mathematics of Computation 1977; 31(138):333-390.
21. Gravouil A, Combescure A. Multi-time-step explicit-implicit method for non-linear structural dynamics. International Journal for Numerical Methods in Engineering 2001; 50:199-225.
22. Dureisseix D, Bavestrello H. Information transfer between incompatible finite element meshes: application to coupled thermo-viscoelasticity. Computer Methods in Applied Mechanics and Engineering 2006; 195(44-47):6523-6541.
23. Béchet E, Minnebo H, Moës N, Burgardt B. Improved implementation and robustness study of the X-FEM for stress analysis around cracks. International Journal for Numerical Methods in Engineering 2005; 64(8): 1033-1056.
24. Laborde P, Pommier J, Renard Y, Salaün M. High order extended finite element method for cracked domains. International Journal for Numerical Methods in Engineering 2005; 64:354-381.
25. Bui HD, Germain P. Mécanique de la rupture fragile. Masson: Paris, 1978.
26. Prabel B, Combescure A, Gravouil A, Marie S. Level set X-FEM non-matching meshes: application to dynamic crack propagation in elastic-plastic media. International Journal for Numerical Methods in Engineering 2006; 69:1553-1569.
27. 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.
28. Ferrie E, Buffiere JY, Ludwig W, Gravouil A, Edwards L. Fatigue crack propagation: in situ visualization using X-ray microtomography and 3D simulation using the extended finite element method. Acta Materialia 2006; 54(4):1111-1122.
29. Moës N, Gravouil A, Belytschko T. Non-planar 3D crack growth by the extended finite element and level sets - part I: mechanical model. International Journal for Numerical Methods in Engineering 2002; 53:2549-2568.
30. Newman JC, Raju IS, Langley Research Center. Stress-intensity Factor Equations for Cracks in Three-dimensional Finite Bodies Subjected to Tension and Bending Loads. National Aeronautics and Space Administration, Langley Research Center. For sale by the National Technical Information Service, 1984.
31. Cavin P, Gravouil A, Lubrecht AA, Combescure A. Efficient FEM calculation with predefined precision through automatic grid refinement. Finite Elements in Analysis and Design 2005; 41(11-12):1043-1055.