A level set based model for damage growth: The thick level set approach

International Journal for Numerical Methods in Engineering

Volumn 86, Issue 3, 2011, Pages 358-380

  Moes N ^a   Stolz, C ^b   Bernard, P E ^a   Chevaugeon, N ^a  

^a UNIVERSITÉ DE NANTES   (France)

^b LABORATOIRE DE MÉCANIQUE DES SOLIDES   (France)

Author keywords

Damage; Fracture; Level set; X FEM

Indexed keywords

FRACTURE;

CONFIGURATIONAL FORCE; CRITICAL LENGTH; DAMAGE; DAMAGE GROWTH; DAMAGE VARIABLES; DAMAGED ZONES; LEVEL SET; THICK LEVEL SETS;

TOPOLOGY;

EID: 79952759911     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.3069     Document Type: Article

References (51)

1. Kachanov L. Time of rupture process under creep conditions. Izvestiia Akademii Nauk SSSR, Otdelenie Tekhmlchesikh Nauk 1958; 8:26-31.
2. Lemaitre J. A Course on Damage Mechanics. Springer: Berlin, 1992.
3. Peerlings R. Gradient damage for quasi-brittle materials. Master Thesis, University of Eindhoven, 1994.
4. Peerlings R, de Borst R, Brekelmans W, De Vree J. Gradient enhanced damage for quasi-brittle materials. International Journal for Numerical Methods in Engineering 1996; 39:3391-3403.
5. Bazant Z, Belytschko T, Chang T. Continuum theory fo strain-softening. Journal of Engineering Mechanics 1984; 110:1666-1692.
6. Pijaudier-Cabot G, Bazant Z. Non-local damage theory. Journal of Engineering Mechanics 1987; 113:1512-1533.
7. Aifantis E. On the structural origin of certain inelastic models. Journal of Engineering Materials and Technology 1984; 106:326-330.
8. Triantafyllidis N, Aifantis E. A gradient approach to localization of deformation: I. Hyperelastic model. Journal of Elasticity 1986; 16:225-237.
9. Schreyer H, Chen Z. One-dimensional softening with localization. Journal of Applied Mechanics 1986; 53:791-979.
10. Mühlhaus H, Vardoulakis I. The thickness of shear bands in granular materials. Géotechnique 1987; 37:271-283.
11. Fremond M, Nedjar B. Damage, gradient of damage and principle of virtual power. International Journal of Solids and Structures 1996; 3(8):1083-1103.
12. Pijaudier-Cabot G, Burlion N. Damage and localisation in elastic materials with voids. Mechanics of Cohesive-frictional Materials 1996; 1:129-144.
13. Nguyen QS, Andrieux S. The non-local generalized standard approach: a consistent gradient theory. Comptes Rendus Académie des Sciences de Paris, Série II 2005; 333:139-145.
14. Peerlings R, Geers M, de Borst R, Brekelmans W. A critical comparison of non-local and gradient-enhanced softening continua. International Journal of Solids and Structures 2001; 38(44-45):7723-7746.
15. Hakim V, Karma A. Laws of crack motion and phase-field models of fracture. Journal of Mechanics and Physics of Solids 2009; 57(2):342-368.
16. Hakim V, Karma A. Crack path prediction in anisotropic brittle materials. Physical Review Letters 2005; 95:235501.
17. Karma A, Kessler D, Levine H. Phase field of mode III dynamic fracture. Physical Review Letters 2001; 8704:045501.
18. Francfort GA, Marigo J-J. Revisiting brittle fracture as an energy minimization problem. Journal of Mechanics and Physics of Solids 1998; 46(8):1319-1342.
19. Bourdin B, Francfort GA, Marigo J-J. Numerical experiments in revisited brittle fracture. Journal of Mechanics and Physics of Solids 2000; 48(4):797-826.
20. Bourdin B, Francfort GA, Marigo J-J. The variational approach to fracture. Journal of Elasticity 2008; 91:5-148.
21. Allaire G, Van Goethem N, Jouve F. A level set method for the numerical simulation of damage evolution, Technical Report, 629, Note École Polytechnique, Centre de Mathématiques Appliquées, 2007.
22. Pradeilles-Duval RM, Stolz C. On the evolution of solids in the presence of irreversible phase transformation. Comptes Rendus Académie des Sciences de Paris, Série II 1991; 313(3):297-302.
23. Pradeilles-Duval RM, Stolz C. Mechanical transformations and discontinuities along a moving surface. Journal of Mechanics and Physics of Solids 1995; 43(1):91-121.
24. Moës N, Chevaugeon N, Dufour F. A Regularized Brittle Damage Model Solved by a Level Set Technique, IUTAM Book Series, Cape Town, South Africa, 2008.
25. Nguyen QS, Pradeilles RM, Stolz C. Sur une loi régularisante en rupture et endommagement fragile. Comptes Rendus Académie des Sciences de Paris, Série II 1989; 309:1515-1520.
26. Stolz C. Bifurcation of equilibrium solutions and defects nucleation. International Journal of Fracture 2007; 147:103-107.
27. Salac D, Lu W. A level set approach to model directed nanocrack patterns. Computer Material Sciences 2007; 39(4):849-856.
28. Simone A, Wells GN, Sluys LJ. From continuous to discontinuous failure in a gradient-enhanced continuum damage model. Computer Methods in Applied Mechanics and Engineering 2003; 192(41-42):4581-4607.
29. Simone A, Sluys LJ. The use of displacement discontinuities in a rate-dependent medium. Computer Methods in Applied Mechanics and Engineering 2004; 193(27-29):3015-3033.
30. Comi C, Mariani S, Perego U. An extended FE strategy for transition from continuum damage to mode I cohesive crack propagation. International Journal for Numerical Analysis and Methods in Geomechanics 2007; 31(2):213-238.
31. Saanouni K, Belamri N, Autesserre P. Finite element simulation of 3D sheet metal guillotining using advanced fully coupled elastoplastic-damage constitutive equations. Finite Elements in Analysis and Design 2010; 46(7):535-550.
32. Mazars J, Pijaudier-Cabot G. From damage to fracture and conversely: a combined approach. International Journal of Solids and Structures 1996; 33(20-22):3327-3342.
33. Stolz C. On the propagation of discontinuity and shock generating function in anelastic solids mechanics. Comptes Rendus Académie des Sciences de Paris, Série II 1989; 308:1-3.
34. Stolz C. Thermodynamical description of running discontinuities. In Continuum Thermodynamics, Maugin GA et al. (eds). Kluwer Academic Publishers: Dordrecht, 2000; 401-412.
35. Dequiedt JL, Stolz C. Propagation of shock discontinuity in an elasto-plastic materials: constituitve relations. Archives of Mechanics 2004; 56:5.
36. Lorentz E, Andrieux S. Analysis of non-local models through energetic formulations. International Journal of Solids and Structures 2003; 40(12):2905-2936.
37. Simone A, Askes H, Sluys LJ. Incorrect initiation and propagation of failure in non-local and gradient-enhanced media. International Journal of Solids and Structures 2004; 41:351-363.
38. 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.
39. Belytschko T, Moës N, Usui S, Parimi C. Arbitrary discontinuities in finite elements. International Journal for Numerical Methods in Engineering 2001; 50(4):993-1013.
40. 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; 48:1741-1760.
41. Sethian JA. Level Set Methods and Fast Marching Method: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science. Cambridge University Press: Cambridge, 1999.
42. Osher S, Fedkiw R. Level Set Methods and Dynamic Implicit Surfaces. Springer: Berlin, 2002.
43. Ben Dhia H, Vautier I, Zarroug M. Problèmes de contact frottant en grandes transformations: du continu au discret. Revue Européenne des Éléments Finis 2000; 9:243-261.
44. Zarroug M. Eléments Mixtes de Contact Frottant en Grandes Transformation et Applications. Ecole Centrale de Paris, 2002.
45. Verhoosel CV, Remmers JJC, Gutiérrez MA. A dissipation-based arc-length method for robust simulation of brittle and ductile failure. International Journal for Numerical Methods in Engineering 2009; 77:9.
46. Lemaitre J, Desmorat R. Engineering Damage Mechanics: Ductile, Creep, Fatigue and Brittle Failures. Springer: Berlin, 2005.
47. Bazant ZP, Gettu R. Rate effects and load relaxation in static fracture of concrete. ACI Materials Journal 1992; 89(5):456-468.
48. Carpinteri A, Colombo G. Numerical analysis of catastrophic softening behavior (snap-back instability). Computers and Structures 1989; 31:607-636.
49. Melin S. Why do cracks avoid each other. International Journal of Fracture 1983; 23(1):37-45.
50. Sumi Y, Wang ZN. A finite-element simulation method for a system of growing cracks in a heterogeneous materials. Mechanics of Materials 1998; 28:197-206.
51. Budyn E, Zi G, Moës N, Belytschko T. A model for multiple crack growth in brittle materials without remeshing. International Journal for Numerical Methods in Engineering 2004; 61:10.