A geometrically nonlinear FE approach for the simulation of strong and weak discontinuities

Computer Methods in Applied Mechanics and Engineering

Volumn 195, Issue 37-40, 2006, Pages 5037-5052

  Mergheim, Julia ^a   Steinmann, Paul ^a  

^a University of Koblenz Landau   (Germany)

Author keywords

Crack propagation; Discontinuous finite elements; Geometrically nonlinear; Material interfaces; Nitsche's method

Indexed keywords

COMPUTATIONAL GEOMETRY; COMPUTER SIMULATION; CRACK PROPAGATION; CRACKS; DEFORMATION; ELASTICITY; INTERFACES (MATERIALS); MATHEMATICAL MODELS;

DISCONTINUOUS FINITE ELEMENTS; GEOMETRICALLY NONLINEAR; NITSCHE'S METHOD;

FINITE ELEMENT METHOD;

COMPUTATIONAL GEOMETRY; COMPUTER SIMULATION; CRACK PROPAGATION; CRACKS; DEFORMATION; ELASTICITY; FINITE ELEMENT METHOD; INTERFACES (MATERIALS); MATHEMATICAL MODELS;

EID: 33744937342     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2005.05.057     Document Type: Article

References (36)

1. Hansbo A., and Hansbo P. An unfitted finite element method, based on Nitsche's method for elliptic interface problems. Comput. Methods Appl. Mech. Engrg. 191 (2002) 5537-5552
2. Hansbo A., and Hansbo P. A finite element method for the simulation of strong and weak discontinuities in solid mechanics. Comput. Methods Appl. Mech. Engrg. 193 (2004) 3523-3540
3. Nitsche J. Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, Die keinen Randbedingungen unterworfen sind. Abh. Math. Univ. Hamburg 36 (1970) 9-15
4. Ortiz M., Leroy Y., and Needleman A. A finite element method for localized failure analysis. Comput. Methods Appl. Mech. Engrg. 61 (1987) 189-214
5. Belytschko T., Fish J., and Engelmann B.E. A finite element with embedded localization zones. Comput. Methods Appl. Mech. Engrg. 70 (1988) 59-89
6. Klisinski M., Runesson K., and Sture S. Finite element with inner softening band. J. Engrg. Mech., ASCE 117 (1991) 575-587
7. Jirásek M. Comparative study on finite elements with embedded cracks. Comput. Methods Appl. Mech. Engrg. 188 (2000) 307-330
8. Armero F., and Garikipati K. An analysis of strong discontinuities in multiplicative finite strain plasticity and their relation with the numerical simulation of strain localization in solids. Int. J. Solids Struct. 33 (1996) 2863-2885
9. Oliver J., Huespe A.E., Pulido M.D.G., and Samaniego E. On the strong discontinuity approach in finite deformation setting. Int. J. Numer. Methods Engrg. 56 (2003) 1051-1082
10. Gasser T.C., and Holzapfel G.A. Geometrically nonlinear and consistently linearized embedded strong discontinuity models for 3d problems with an application to the dissection analysis of soft biological tissues. Comput. Methods Appl. Mech. Engrg. 192 (2003) 5059-5098
11. Babuška I., and Melenk J.M. The partition of unity method. Int. J. Numer. Methods Engrg. 40 (1997) 727-758
12. Belytschko T., and Black T. Elastic crack growth in finite elements with minimal remeshing. Int. J. Numer. Methods Engrg. 45 (1999) 601-620
13. Moës N., Dolbow J., and Belytschko T. A finite element method for crack growth without remeshing. Int. J. Numer. Methods Engrg. 46 (1999) 131-150
14. Dolbow J., Möes N., and Belytschko T. An extended finite element method for modeling crack growth with friction contact. Comput. Methods Appl. Mech. Engrg. 190 (2001) 6825-6846
15. Sukumar N., Möes N., Moran B., and Belytschko T. Extended finite element method for three-dimensional crack modeling. Int. J. Numer. Methods Engrg. 48 11 (2000) 1549-1570
16. Daux C., Moës N., Dolbow J., Sukumar N., and Belytschko T. Arbitrary branched and intersecting cracks with the extended finite element method. Int. J. Numer. Methods Engrg. 48 (2000) 1741-1760
17. Mergheim J., Kuhl E., and Steinmann P. A finite element method for the computational modelling of cohesive cracks. Int. J. Numer. Methods Engrg. 63 2 (2005) 276-289
18. Dugdale D.S. Yielding of steel sheets containing slits. J. Mech. Solids 8 (1960) 100-108
19. Barenblatt G.I. The mathematical theory of equilibrium of cracks in brittle fracture. Adv. Appl. Mech. 7 (1962) 55-129
20. Hillerborg A., Petersson P.E., and Modéer M. Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cement Concr. Res. 6 (1976) 773-782
21. Ortiz M., and Pandolfi A. Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis. Int. J. Numer. Methods Engrg. 44 (1999) 1267-1282
22. de Borst R., Gutiérrez M.A., Wells G.N., Remmers J.J.C., and Askes H. Cohesive-zone models, higher-order continuum theories and reliability methods for computational failure analysis. Int. J. Numer. Methods Engrg. 60 (2004) 289-315
23. Wells G.N., and Sluys L.J. A new method for modelling cohesive cracks using finite elements. Int. J. Numer. Methods Engrg. 50 (2001) 2667-2682
24. Moës N., and Belytschko T. Extended finite element method for cohesive crack growth. Engrg. Fracture Mech. 69 7 (2002) 813-833
25. Zi G., and Belytschko T. New crack-tip elements for XFEM and applications to cohesive cracks. Int. J. Numer. Methods Engrg. 57 (2003) 2221-2240
26. Wells G.N., Sluys L.J., and de Borst R. A consistent geometrically nonlinear approach for delamination. Int. J. Numer. Methods Engrg. 54 (2002) 1333-1355
27. Gasser T.C., and Holzapfel G.A. Modeling of 3d crack propagation in unreinforced concrete using PUFEM. Comput. Methods Appl. Mech. Engrg. 194 25-26 (2005) 2859-2896
28. Sukumar N., Chopp D.L., Möes N., and Belytschko T. Modelling holes and inclusions by level sets in the extended finite-element method. Comput. Methods Appl. Mech. Engrg. 190 (2001) 6183-6200
29. Ji H., Chopp D., and Dolbow J.E. A hybrid extended finite element/level set method for modeling phase transformations. Int. J. Numer. Methods Engrg. 54 (2002) 1209-1233
30. Chessa J., Smolinski P., and Belytschko T. The extended finite element method (XFEM) for solidification problems. Int. J. Numer. Methods Engrg. 53 8 (2002) 1959-1977
31. Chessa J., and Belytschko T. An extended finite element method for two-phase fluids. J. Appl. Mech. 70 1 (2003) 10-17
32. Hansbo P., and Larson M.G. Discontinuous Galerkin and the Crouzeix-Raviart element: application to elasticity. Math. Modell. Numer. Anal. 37 (2003) 63-72
33. Mergheim J., Kuhl E., and Steinmann P. A hybrid discontinuous Galerkin/interface method for the computational modelling of failure. Commun. Numer. Methods Engrg. 20 (2004) 511-519
34. A. Fritz, S. Hüber, B.I. Wohlmuth, A comparison of mortar and Nitsche techniques for linear elasticity. Preprint, Universität Stuttgart, 008, 2003.
35. Papoulia K.D., Sam C.-H., and Vavasis S.A. Time continuity in cohesive finite element modeling. Int. J. Numer. Methods Engrg. 58 (2003) 679-701
36. Osher S., and Sethian J.A. Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations. J. Comput. Phys. 79 1 (1988) 12-49