High-order extended finite element method for cracked domains

International Journal for Numerical Methods in Engineering

Volumn 64, Issue 3, 2005, Pages 354-381

  Laborde, Patrick ^a   Pommier, Julien ^a   Renard, Yves ^a   Salaün, Michel ^b  

^a CNRS   (France)

^b UNIVERSITÉ DE TOULOUSE   (France)

Author keywords

Extended finite element method; Finite elements; Fracture; Rate of convergence

Indexed keywords

APPROXIMATION THEORY; BOUNDARY CONDITIONS; COMPUTER SIMULATION; CONVERGENCE OF NUMERICAL METHODS; CRACKS; DEGREES OF FREEDOM (MECHANICS); FRACTURE; INTEGRATION; MATHEMATICAL MODELS; STRESS INTENSITY FACTORS;

EXTENDED FINITE ELEMENT METHOD; OPTIMAL CONVERGENCE;

FINITE ELEMENT METHOD;

FINITE ELEMENT METHOD; FRACTURE MECHANICS;

EID: 24944495351     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/nme.1370     Document Type: Article

References (29)

1. Anderson TL. Fracture Mechanics: Fundamentals and Applications (2nd edn). CRC Press: Boca Raton, FL, 1994.
2. Shah SP. Fracture Mechanics of Concrete: Applications of Fracture Mechanics to Concrete, Rock and Other Quasi-Brittle Materials. Wiley: New York, 1995.
3. Sun TC. Mechanics of Aircraft Structures. Wiley: New York, 1998.
4. Strang G, Fix GJ. An Analysis of the Finite Element Method. Prentice-Hall: Englewood Cliffs, NJ, 1973.
5. Babuška I, Caloz G, Osborn J. Special finite element methods for a class of second order elliptic problems with rough coefficients. SIAM Journal on Numerical Analysis 1994; 31:945-981.
6. Melenk JM, Babuška I. The partition of unity finite element method: basic theory and applications. Computer Methods in Applied Mechanics and Engineering 1996; 139:289-314.
7. Babuška I, Melenk JM. The partition of unity method. International Journal for Numerical Methods in Engineering 1997; 40:27-758.
8. Duarte CAM, Babuška I, Oden JT. Generalized finite element method for three-dimensional structural mechanics problems. Computers and Structures 2000; 77:219-232.
9. Strouboulis T, Babuška I, Copps T. The design and analysis of the generalized finite element method. Computer Methods in Applied Mechanics and Engineering 2000; 181:43-69.
10. Strouboulis T, Copps K, Babuška I. The generalized finite element method. Computer Methods in Applied Mechanics and Engineering 2001; 190:4081-4193.
11. Babuška I, Banerjee U, Osborn JE. Survey of meshless and generalized finite element methods: a unified approach. Acta Numerica 2003; 1-125.
12. Moës N, Dolbow J, Belytschko T. A finite element method for crack growth without remeshing. International Journal for Numerical Methods in Engineering 1999; 46:131-150.
13. 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.
14. Dolbow J, Moës N, Belytschko T. An extended finite element method for modeling crack growth with frictional contact. Computer Methods in Applied Mechanics and Engineering 2001; 190:6825-6846.
15. Sukumar N, Moës N, Moran B, Belytschko T. Extended finite element method for three dimensional crack modelling. International Journal for Numerical Methods in Engineering 2000; 48:1549-1570.
16. Belytschko T, Moës N, Usui S, Parimi C. Arbitrary discontinuities in finite elements. International Journal for Numerical Methods in Engineering 2000; 50(4):993-1013.
17. 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(11): 2569-2586.
18. Sukumar N, Chopp DL, Moës N, Belytschko T. Modeling holes and inclusions by level sets in the extended finite element method. Computer Methods in Applied Mechanics and Engineering 2001; 90 (46,47):6183-6200.
19. Moës N, Belytschko T. Extended finite element method for cohesive crack growth. Engineering Fracture Mechanics 2002; 69 (7):813-833.
20. 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(11):2549-2568.
21. Stazi FL, Budyn E, Chessa J, Belytschko T. An extended finite element method with higher-order elements for curved cracks. Computational Mechanics 2003; 31:38-48.
22. Chessa J, Wang HW, Belytschko T. On construction of blending elements for locally partition of unity enriched finite element methods. International Journal for Numerical Methods in Engineering 2003; 57(7): 1015-1038.
23. Grisvard P. Singularities in Boundary Value Problems. Masson: Paris, 1992.
24. Lemaitre J, Chaboche J-L. Mechanics of Solid Materials. Cambridge University Press: Cambridge, 1994.
25. Sukumar N, Préévost J-H. Modeling quasi-static crack growth with the extended finite element method, part I: computer implementation. International Journal of Solids and Structures 2003; 40:7513-7537.
26. Béchet E, Minnebo H, Moës N, Burgardt B. Improved implementation and robustness study of the X-FEM method for stress analysis around cracks. International Journal for Numerical Methods in Engineering, 2005, in press.
27. Yau J, Wang S, Corten H. A mixed-mode crack analysis of isotropic solids using conservation laws of elasticity. Journal of Applied Mechanics 1980; 47:335-341.
28. Destuynder Ph, Djaoua M. Mathematical Methods in the Applied Sciences 1981; 3:70-87.
29. Pommier J, Renard Y. Getfem ++. An open source generic C++ it library for finite element methods, http://www-gmm.insa-toulouse.fr/getfem.