A mixed interface finite element for cohesive zone models

Computer Methods in Applied Mechanics and Engineering

Volumn 198, Issue 2, 2008, Pages 302-317

  Lorentz, E ^a  

^a EDF R AND D   (France)

Author keywords

Augmented Lagrangian; Cohesive zone model; Fracture mechanics; Interface finite element; Mixed finite element

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; FRACTURE MECHANICS; LAGRANGE MULTIPLIERS; LAWS AND LEGISLATION; MECHANICS; NEWTON-RAPHSON METHOD; STRENGTH OF MATERIALS; THEOREM PROVING; THREE DIMENSIONAL; THREE DIMENSIONAL COMPUTER GRAPHICS; UNLOADING;

3D SIMULATIONS; AUGMENTED LAGRANGIAN; CLASSICAL SOLUTIONS; COHESIVE FORCES; COHESIVE LAWS; COHESIVE ZONE MODEL; COHESIVE ZONE MODELS; COMPLEMENTARY; CONSTITUTIVE LAWS; CONTACT CONDITIONS; CONTACT MECHANICS; CRACK LIPS; CRACK PATHS; DEGREES OF FREEDOMS; FINITE ELEMENTS; INTERFACE FINITE ELEMENT; KEY FACTORS; LBB-CONDITION; MIXED FINITE ELEMENT; NEWTON METHODS; NUMERICAL INVESTIGATIONS; PRACTICAL; REGULARISATION; UNIQUE SOLUTIONS; VARIATIONAL FORMULATIONS;

FINITE ELEMENT METHOD;

EID: 54949090719     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2008.08.006     Document Type: Article

References (44)

1. Leguillon D. Strength or toughness ? A criterion for crack onset at a notch. Eur. J. Mech. A/Solids 21 (2002) 61-72
2. Marigo J.-J., and Truskinovsky L. Initiation and propagation of fracture in the models of Griffith and Barenblatt. Continuum. Mech. Thermodyn. 16 (2004) 391-409
3. Wadier Y., and Lorentz E. Mécanique de la rupture fragile en présence de plasticité: modélisation de la fissure par une entaille. C.R. Mécanique 332 (2004) 979-986
4. Dugdale D.S. Yielding of steel sheets containing slits. J. Mech. Phys. Solids 8 (1960) 100-104
5. Barenblatt G.I. The mathematical theory of equilibrium cracks in brittle fracture. Adv. Appl. Mech. 7 (1962) 55-129
6. Francfort G., and Marigo J.-J. Revisiting brittle fracture as an energy minimization problem. J. Mech. Phys. Solids 46 8 (1998) 1319-1342
7. Charlotte M., Laverne J., and Marigo J.-J. Initiation of cracks with cohesive force models: a variational approach. Eur. J. Mech. A/Solids 25 (2006) 649-669
8. Bourdin B., Francfort G.A., and Marigo J.-J. Numerical experiments in revisitted brittle fracture. J. Mech. Phys. Solids 48 4 (2000) 797-826
9. Fraternali F. Free discontinuity finite element models in two-dimensions for in-plane crack problems. Theoret. Appl. Fract. Mech. 47 (2007) 274-282
10. Alfaiate J., Wells G.N., and Sluys L.J. On the use of embedded discontinuity element with crack path continuity for mode I and mixed-mode fracture. Engrg. Fract. Mech. 69 (2002) 661-686
11. De Borst R. Numerical aspects of cohesive-zone models. Engrg. Fract. Mech. 70 (2003) 1743-1757
12. Jirasek M., and Zimmermann T. Embedded crack model: Part II: Combination with smeared cracks. Int. J. Numer. Methods Engrg. 50 (2001) 1291-1305
13. Gasser T., and Holzapfel G. 3D crack propagation in unreinforced concrete. A two-step algorithm for tracking 3D crack paths. Comput. Methods Appl. Mech. Engrg. 195 (2006) 5198-5219
14. Sam C.-H., Papoulia K.D., and Vavasis S.A. Obtaining initially rigid cohesive finite element models that are temporally convergent. Engrg. Fract. Mech. 72 (2005) 2247-2267
15. Réthoré J., Gravouil A., and Combescure A. An energy-conserving scheme for dynamic crack growth using the extended finite element method. Int. J. Numer. Methods Engrg. 63 5 (2005) 631-659
16. Oliver J., and Huespe A.E. Theoretical and computational issues in modelling material failure in strong discontinuity scenarios. Comput. Methods Appl. Mech. Engrg. 193 (2004) 2987-3014
17. Schellekens J.C.J., and de Borst R. On the Numerical Integration of Interface Elements 36 (1993) 43-66
18. M. Fortin, Error estimates and contact problems. Courtesy of Pr. Fortin, GIREF internal report, université Laval, Québec.
19. Fortin M., and Glowinski R. Augmented lagrangian methods: application to the numerical solution of boundary-value problems. Studies in Mathematics and its Applications vol. 15 (1983), North-Holland
20. Ben Belgacem F. The mortar finite element method with Lagrange multipliers. Numer. Math. 84 (1999) 173-197
21. Puso M.A., and Laursen T.A. A mortar segment-to-segment frictional contact method for large deformations. Comput. Methods Appl. Mech. Engrg. 193 (2004) 4891-4913
22. Moes N., Dolbow J., and Belytschko T. A finite element method for crack growth without remeshing. Int. J. Numer. Methods Engrg. 46 (1999) 131-150
23. 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
24. Geniaut S., Massin P., and Moes N. A stable 3D contact formulation for cracks using X-FEM. Eur. J. Comp. Mech. 16 1 (2007)
25. Jirasek M. Comparative study on finite elements with embedded discontinuities. Comput. Methods Appl. Mech. Engrg. 188 (2000) 307-330
26. Oliver J., Huespe A.E., and Sanchez P.J. A comparative study on finite elements for capturing strong discontinuities: E-FEM vs. X-FEM. Comput. Methods Appl. Mech. Engrg. 195 (2006) 4732-4752
27. Jirasek M., and Zimmermann T. Embedded crack model: I. Basic formulation. Int. J. Numer. Methods Engrg. 50 (2001) 1269-1290
28. Manzoli O.L., and Shing P.B. A general technique to embed non-uniform discontinuities into standard solid finite elements. Comput. Struct. 84 (2006) 742-757
29. 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
30. M. Fortin, N. Tardieu, E. Chamberland, Un algorithme de sous-gradient pour le traitement du contact frottant, in: Proceedings " 7è colloque national en calcul des structures", Giens, France, 2005.
31. Alart P., and Curnier A. A mixed formulation for frictional contact problems prone to Newton like solution methods. Comput. Methods Appl. Mech. Engrg. 92 (1991) 353-375
32. Ladeveze P. Mécanique Non linéaire des Structures (1996), Hermes
33. D. Doyen, Modélisation et simulation de la propagation quasi-statique des fissures - livrable 1. EDF R& D Internal Report, SINETICS/2008, cow. Duwig V., Ern A., Piperno S., 2008.
34. Lorentz E., and Benallal A. Gradient constitutive relations: numerical aspects and application to gradient damage. Comput. Methods Appl. Mech. Engrg. 194 (2005) 5191-5220
35. Bathe K.J., and Brezzi F. Stability of finite element mixed interpolation for contact problems. Rend. Mat. Acc. Lincei 12 9 (2001) 167-183
36. Stadler G. Path-following and augmented Lagrangian method for contact problems in linear elasticity. J. Comput. Appl. Math. 203 (2007) 533-547
37. Bathe K.J. The inf-sup condition and its evaluation for mixed finite element methods. Comput. Struct. 79 (2001) 243-252
38. Talon C., and Curnier A. A model of adhesion coupled to contact and friction. Eur. J. Mech. A/Solids 22 4 (2003) 545-565
39. Del Piero G., and Truskinovsky L. Macro- and micro- cracking in one dimensional elasticity. Int. J. Solids Struct. 38 (2001) 1135-1148
40. Clarke F.H. Optimization and non smooth analysis. Classics in Applied Mathematics vol. 5 (1990), SIAM
41. J. Laverne, Formulation énergétique de la rupture par des modèles de forces cohésives: considérations théoriques et implantations numériques, Thèse de doctorat de l'université Paris XIII, 2004.
42. Code_Aster. Open Source Finite Element Software. , courtesy of EDF.
43. Lorentz E., and Badel P. A new path-following constraint for strain-softening finite elements simulations. Int. J. Numer. Methods Engrg. 60 (2004) 499-526
44. Alfano G., and Crisfield M.A. Finite element interface models for the delamination analysis of laminated composites: mechanical and computational issues. Int. J. Numer. Methods Engrg. 50 7 (2001) 1701-1736