A new way to treat material discontinuities in the numerical manifold method

Computer Methods in Applied Mechanics and Engineering

Volumn 200, Issue 47-48, 2011, Pages 3296-3308

  An, Xinmei ^a   Ma, Guowei ^b   Cai, Yongchang ^c   Zhu, Hehua ^c  

^a NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

^b UNIVERSITY OF WESTERN AUSTRALIA   (Australia)

^c TONGJI UNIVERSITY   (China)

Author keywords

Material interface; Numerical manifold method; Partition of unity; Weak discontinuity

Indexed keywords

FIRST DERIVATIVE; LOCAL APPROXIMATION; MATERIAL DISCONTINUITY; MATERIAL INTERFACES; NUMERICAL MANIFOLD METHOD; PARTITION OF UNITY; WEAK DISCONTINUITY;

INTERFACES (MATERIALS); MATERIALS;

NUMERICAL METHODS;

EID: 80052545409     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2011.08.004     Document Type: Article

References (31)

1. Babuska I., Caloz G., Osborn J.E. Special finite element methods for a class of second order elliptic problems with rough coefficients. SIAM J. Numer. Anal. 1994, 31:945-981.
2. Belytschko T., Black T. Elastic crack growth in finite elements with minimal remeshing. Int. J. Numer. Meth. Engrg. 1999, 45(5):601-620.
3. Moes N., Dolbow J., Belytschko T. A finite element method for crack growth without remeshing. Int. J. Numer. Meth. Engrg. 1999, 46:131-150.
4. Strouboulis T., Babuska I., Copps K. The design and analysis of the generalized finite element method. Comput. Methods Appl. Mech. Engrg. 2000, 181:43-69.
5. Strouboulis T., Copps K., Babuska I. The generalized finite element method: an example of its implementation and illustration of its performance. Int. J. Numer. Meth. Engrg. 2000, 47:1401-1417.
6. Belytschko T., Gracie R., Ventura G. A review of extended/generalized finite element methods for material modeling. Model. Simul. Mater. Sci. Engrg. 2009, 17:1-24.
7. Fries T.P., Belytschko T. The extended/generalized finite element method: an overview of the method and its applications. Int. J. Numer. Meth. Engrg. 2010, 84:253-304.
8. Duarte C.A., Babuska I., Oden J.T. Generalized finite element methods for three-dimensional structural mechanics problems. Comput. Struct. 2000, 77:215-232.
9. G.H. Shi, Manifold method of material analysis, in: Trans. 9th Army Conf. on Applied Mathematics and Computing, Minneapolis, Minnesota, 1991, pp. 57-76.
10. Ma G.W., An X.M., Zhang H.H., Li L.X. Modeling complex crack problems with numerical manifold method. Int. J. Fract. 2009, 156:21-35.
11. Zhang H.H., Li L.X., An X.M., Ma G.W. Numerical analysis of 2-D crack propagation problems using the numerical manifold method. Engrg. Anal. Bound. Elem. 2010, 34:41-50.
12. X.M. An, G.Y. Fu, G.W. Ma, A comparison between the NMM and the XFEM in discontinuity modeling, Int. J. Comput. Methods (in press).
13. Terada K., Asai M., Yamagishi M. Finite cover method for linear and non-linear analyses of heterogeneous solids. Int. J. Numer. Methods Engrg. 2003, 58:1321-1346.
14. Terada K., Ishii T., Kyoya T., Kishino Y. Finite cover method for progressive failure with cohesive zone fracture in heterogeneous solids and structures. Comput. Mech. 2007, 39:191-210.
15. Kurumatani M., Terada K. Finite cover method with multi-cover layers for the analysis of evolving discontinuities in heterogeneous media. Int. J. Numer. Methods Engrg. 2009, 79(1):1-24.
16. Ma G.W., An X.M., He L. The numerical manifold method - a review. Int. J. Comput. Methods 2010, 7:1-32.
17. Li S., Cheng Y., Wu Y.F. Numerical manifold method based on the method of weighted residuals. Comput. Mech. 2005, 35:470-480.
18. Krongauz Y., Belytschko T. EFG approximation with discontinuous derivatives. Int. J. Numer. Meth. Engrg. 1998, 41:1215-1233.
19. Osher S., Fedkiw R.P. Level set methods: an overview and some recent results. J. Comput. Phys. 2001, 169:463-502.
20. Sukumar N., Chopp D.L., Moes N., Belytschko T. Modeling holes and inclusions by level sets in the extended finite-element method. Comput. Methods Appl. Mech. Engrg. 2001, 190:6183-6200.
21. Belytschko T., Black T., Moes N., Sukumar N., Usui S. Structured extended finite element methods of solids defined by implicit surfaces. Int. J. Numer. Meth. Engrg. 2003, 56:609-635.
22. Moes N., Cloirec M., Cartraud P., Remacle J.F. A computational approach to handle complex microstructure geometries. Comput. Methods Appl. Mech. Engrg. 2003, 192:3163-3177.
23. Fries T.P. A corrected XFEM approximation without problems in blending elements. Int. J. Numer. Meth. Engrg. 2008, 75:503-532.
24. An X.M., Li L.X., Ma G.W., Zhang H.H. Prediction of rank deficiency in partition of unity-based methods with plane triangular or quadrilateral meshes. Comput. Methods Appl. Mech. Engrg. 2011, 200:665-674.
25. Tian R., Yagawa G., Terasaka H. Linear dependence problems of partition of unity-based generalized FEMs. Comput. Methods Appl. Mech. Engrg. 2006, 195:4768-4782.
26. Tian R., Yagawa G. Generalized nodes and high-performance elements. Int. J. Numer. Meth. Engrg. 2005, 64:2039-2071.
27. Riker C., Holzer S.M. The mixed-cell-complex partition-of-unity method. Comput. Methods Appl. Mech. Engrg. 2009, 198:1235-1248.
28. Rajendran S., Zhang B.R. A "FE-meshfree" QUAD4 element based on partition of unity. Comput. Methods Appl. Mech. Engrg. 2007, 197:128-147.
29. Ooi E.T., Rajendran S., Yeo J.H., Zhang B.R. A mesh distortion tolerant 8-node solid element based on the partition of unity method with inter-element compatibility and completeness properties. Finite Elem. Anal. Des. 2007, 43:771-787.
30. Lin J.S. A mesh-based partition of unity method for discontinuity modeling. Comput. Meth. Appl. Mech. Engrg. 2003, 192:1515-1532.
31. Shi G.H. Simplex integration for manifold method, FEM, DDA and analytical analysis. Proceedings of the First International Forum on Discontinuous Deformation Analysis (DDA) and Simulations of Discontinuous Media 1996, 205-262. TSI Press, Albuquerque, New Mexico, USA.