Harmonic enrichment functions: A unified treatment of multiple, intersecting and branched cracks in the extended finite element method

International Journal for Numerical Methods in Engineering

Volumn 85, Issue 10, 2011, Pages 1306-1322

  Mousavi, S E ^a   Grinspun, E ^b   Sukumar, N ^a  

^a Davis   (United States)

^b Fu Foundation School of Engineering and Applied Science   (United States)

Author keywords

Branched crack; Curved crack; Extended finite element method (X FEM); Harmonic enrichment; Intersecting crack; Partition of unity method (PUM); Stress intensity factors

Indexed keywords

BRANCHED CRACKS; CURVED CRACK; EXTENDED FINITE ELEMENT METHOD; HARMONIC ENRICHMENT; INTERSECTING CRACK; PARTITION-OF-UNITY METHOD (PUM);

BOUNDARY CONDITIONS; FINITE ELEMENT METHOD; HARMONIC ANALYSIS; HARMONIC FUNCTIONS; INTEGRATION; LAPLACE EQUATION; STRESS INTENSITY FACTORS;

CRACKS;

EID: 79851504685     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.3020     Document Type: Article

References (44)

1. 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.
2. 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.
3. 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.
4. Babuška I, Melenk JM. The partition of unity method. International Journal for Numerical Methods in Engineering 1997; 40:727-758.
5. Shi G-H. Manifold method of material analysis. Transactions of the Ninth Army Conference on Applied Mathematics and Computing, Minneapolis, MN, 1991; 57-76.
6. Ma GW, An XM, Zhang HH, Li LX. Modeling complex crack problems using the numerical manifold method. International Journal of Fracture 2009; 156:21-35.
7. Ma GW, An XM, He L. The numerical manifold method: a review. International Journal of Computational Methods 2010; 7(1):1-32.
8. Terada K, Asai M, Yamagishi M. Finite cover method for linear and non-linear analyses of heterogeneous solids. International Journal for Numerical Methods in Engineering 2003; 58:1321-1346.
9. Hansbo A, Hansbo P. A finite element method for the simulation of strong and weak discontinuities in solid mechanics. Computer Methods in Applied Mechanics and Engineering 2004; 193(33-35):3523-3540.
10. Kaufmann P, Martin S, Botsch M, Grinspun E, Gross M. Enrichment textures for detailed cutting of shells. ACM Transactions on Graphics 2009; 28(3):50:1-50:10.
11. Daux C, Moës N, Dolbow J, Sukumar N, Belytschko T. Arbitrary branched and intersecting cracks with the extended finite element method. International Journal for Numerical Methods in Engineering 2000; 48(12):1741-1760.
12. Belytschko T, Moës N, Usui S, Parimi C. Arbitrary discontinuities in finite elements. International Journal for Numerical Methods in Engineering 2001; 50:993-1013.
13. Simone A, Duarte CA, Van der Giessen E. A generalized finite element method for polycrystals with discontinuous grain boundaries. International Journal for Numerical Methods in Engineering 2006; 67:1122-1145.
14. Duarte CA, Reno LG, Simone A. A high-order generalized FEM for through-the-thickness branched cracks. International Journal for Numerical Methods in Engineering 2007; 72:325-351.
15. Dolbow J, Moës N, Belytschko T. Discontinuous enrichment in finite elements with a partition of unity method. Finite Elements in Analysis and Design 2000; 36:235-260.
16. Dolbow J, Moës N, Belytschko T. Modeling fracture in Mindlin-Reissner plates with the extended finite element method. International Journal of Solids and Structures 2000; 37:7161-7183.
17. Sukumar N, Huang ZY, Prévost J-H, Suo Z. Partition of unity enrichment for bimaterial interface cracks. International Journal for Numerical Methods in Engineering 2004; 59(8):1075-1102.
18. Asadpoure A, Mohammadi S. Developing new enrichment functions for crack simulation in orthotropic media by the extended finite element method. International Journal for Numerical Methods in Engineering 2007; 69:2150-2172.
19. Béchet E, Scherzer M, Kuna M. Application of the X-FEM to the fracture of piezoelectric materials. International Journal for Numerical Methods in Engineering 2009; 77:1535-1565.
20. Moës N, Belytschko T. Extended finite element method for cohesive crack growth. Engineering Fracture Mechanics 2002; 69:813-833.
21. Cox JV. An extended finite element method with analytical enrichment for cohesive crack modeling. International Journal for Numerical Methods in Engineering 2008; 78:48-83.
22. Elguedj T, Gravouil A, Combescure A. Appropriate extended functions for X-FEM simulation of plastic fracture mechanics. Computer Methods in Applied Mechanics and Engineering 2006; 195:501-515.
23. Strouboulis T, Zhang L, Babuška I. Generalized finite element method using mesh-based handbooks: application to problems in domains with many voids. Computer Methods in Applied Mechanics and Engineering 2003; 192:3109-3161.
24. Strouboulis T, Zhang L, Babuška I. p-version of the generalized FEM using mesh-based handbooks with applications to multiscale problems. International Journal for Numerical Methods in Engineering 2004; 60:1639-1672.
25. Duarte CA, Kim D-J. Analysis and applications of a generalized finite element method with global-local enrichment functions. Computer Methods in Applied Mechanics and Engineering 2008; 197:487-504.
26. Ventura G. On the elimination of quadrature subcells for discontinuous functions in the extended finite-element method. International Journal for Numerical Methods in Engineering 2006; 66:761-795.
27. Holdych DJ, Noble DR, Secor RB. Quadrature rules for triangular and tetrahedral elements with generalized functions. International Journal for Numerical Methods in Engineering 2008; 73:1310-1327.
28. Mousavi SE, Xiao H, Sukumar N. Generalized Gaussian quadrature rules on arbitrary polygons. International Journal for Numerical Methods in Engineering 2010; 82:99-113.
29. Mousavi SE, Sukumar N. Generalized Gaussian quadrature rules for discontinuities and crack singularities in the extended finite element method. Computer Methods in Applied Mechanics and Engineering 2010; DOI: 10.1016/j.cma.2010.06.031.
30. Strouboulis T, Babuška I, Copps K. The design and analysis of the generalized finite element method. Computer Methods in Applied Mechanics and Engineering 2000; 181(1-3):43-69.
31. 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.
32. 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.
33. Mousavi SE, Sukumar N. Generalized Duffy transformation for integrating vertex singularities. Computational Mechanics 2010; 45(2-3):127-140.
34. Fries TP, Belytschko T. The extended/generalized finite element method: an overview of the method and its applications. International Journal for Numerical Methods in Engineering 2010; DOI: 10.1002/nme.2914.
35. Sukumar N, Prévost 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(26):7513-7537.
36. Ewalds H, Wanhill R. Fracture Mechanics. Edward Arnold: New York, 1989.
37. Sukumar N, Srolovitz DJ. Finite element-based model for crack propagation in polycrystalline materials. Computational and Applied Mathematics 2004; 23:363-380.
38. Sutradhar A, Paulino GH, Gray LJ. Symmetric Galerkin Boundary Element Method. Springer: Berlin, Heidelberg, 2008.
39. Aliabadi MH, Hall WS. Analytical removal of singularities and one-dimensional integration of three-dimensional boundary element method kernels. Engineering Analysis with Boundary Elements 1987; 4:21-24.
40. Cheung YK, Woo CW, Wang YH. A general method for multiple crack problems in a finite plate. Computational Mechanics 1992; 10:335-343.
41. Chen YZ, Hasebe N. New integration scheme for the branch crack problem. Engineering Fracture Mechanics 1995; 52(5):791-801.
42. Sih GC, Paris PC, Erdogan F. Crack-tip stress intensity factors for plane extension and plane bending problems. Journal of Applied Mechanics 1962; 29:306-312.
43. Huang R, Sukumar N, Prévost J-H. Modeling quasi-static crack growth with the extended finite element method. Part II: numerical applications. International Journal of Solids and Structures 2003; 40:7539-7552.
44. Stazi FL, Budyn E, Chessa J, Belytschko T. An extended finite element method with higher-order elements for curved cracks. Computational Mechanics 2003; 31(1-2):38-48.