A one-dimensional variational formulation for quasibrittle fracture

Journal of Mechanics of Materials and Structures

Volumn 1, Issue 8, 2006, Pages 1323-1343

  Comi, Claudia ^a   Mariani, Stefano ^a   Negri, Matteo ^b   Perego, Umberto ^a  

^a POLITECNICO DI MILANO   (Italy)

^b UNIVERSITY OF PAVIA   (Italy)

Author keywords

Cohesive crack; Finite step problem; Variational formulation

Indexed keywords

FRACTURE;

CRACK INITIATION AND PROPAGATION; CRACK SURFACE ENERGY; DISCONTINUOUS SOLUTIONS; DISPLACEMENT DISCONTINUITY; INITIATION AND PROPAGATION; QUASI-BRITTLE FRACTURE; QUASIBRITTLE MATERIAL; VARIATIONAL FORMULATION;

CRACKS;

EID: 68149097899     PISSN: 15593959     EISSN: None     Source Type: Journal    
DOI: 10.2140/jomms.2006.1.1323     Document Type: Article

References (22)

1. L. Ambrosio, N. Fusco, and D. Pallara, Functions of bounded variation and free discontinuity problems, Oxford University Press, Oxford, 2000.
2. M. Angelillo, E. Babilio, and A. Fortunata, "A computational approach to fracture of brittle solids based on energy minimization", Preprint, Università di Salerno, 2003.
3. H. Askes and L. J. Sluys, "Remeshing strategies for adaptive ALE analysis of strain localisation", Eur. J. Mech. A:Solids 19:3 (2000), 447-467.
4. B. Bourdin, G. Francfort, and J. J. Marigo, "Numerical experiments in revisited brittle fracture", J. Mech. Phys. Solids 48:4 (2000), 797-826.
5. A. Braides, G. Dal Maso, and A. Garroni, "Variational formulation of softening phenomena in fracture mechanics: the one-dimensional case", Arch. Ration. Mech. An. 146:1 (1999), 23-58.
6. A. Chambolle, "A density result in two-dimensional linearized elasticity and applications", Arch. Ration. Mech. An. 167:3 (2003), 211-233.
7. G. Dal Maso and R. Toader, "A model for the quasi-static growth of brittle fractures: existence and approximation results", Arch. Ration. Mech. An. 162:2 (2002), 101-135.
8. G. Dal Maso and C. Zanini, "Quasistatic crack growth for a cohesive zone model with prescribed crack path", Proc. R. Soc. Edin. A Math. 137 (2007), 1-27.
9. G. Del Piero and L. Truskinovsky, "Macro-and micro-cracking in one-dimensional elasticity", Int. J. Solids Struct. 38:6-7 (2001), 1135-1148.
10. P. Dumstorff and G. Meschke, "Modelling of cohesive and non-cohesive cracks via X-FEM based on global energy criteria", pp. 565-568 in COMPLAS VIII, VIII International Conference on Computational Plasticity, edited by E. Onate and D. R. J. Owen, CIMNE, Barcelona (Spain), 2005.
11. G. A. Francfort and C. J. Larsen, "Existence and convergence for a quasi-static evolution in brittle fracture", Commun. Pur. Appl. Math. 56:10 (2003), 1465-1500.
12. G. Francfort and J. J. Marigo, "Revisiting brittle fracture as an energy minimization problem", J. Mech. Phys. Solids 46:8 (1998), 1319-1342.
13. S. Mariani and U. Perego, "Extended finite element method for quasi-brittle fracture", Int. J. Numer. Methods Eng. 58:1 (2003), 103-126.
14. N. Moës and T. Belytschko, "Extended finite element method for cohesive crack growth", Eng. Fract. Mech 69:7 (2002), 813-833.
15. N. Moës, J. Dolbow, and T. Belytschko, "A finite element method for crack growth without remeshing", Int. J. Numer. Methods Eng. 46:1 (1999), 131-150.
16. M. Negri, "A finite element approximation of the Griffith's model in fracture mechanics", Numer. Math. 95:4 (2003), 653-687.
17. J. Oliver, A. E. Huespe, M. D. G. Pulido, and E. Chaves, "From continuum mechanics to fracture mechanics: the strong discontinuity approach", Eng. Fract. Mech. 69:2 (2002), 113-136.
18. J. Oliver, A. E. Huespe, and E. Samaniego, "A study on finite elements for capturing strong discontinuities", Int. J. Numer. Methods Eng. 56:14 (2003), 2135-2161.
19. A. Pandolfi and M. Ortiz, "An efficient adaptive procedure for three-dimensional fragmentation simulations", Eng. Comput. 18:2 (2002), 148-159.
20. A. Rodríguez-Ferran and A. Huerta, "Error estimation and adaptivity for nonlocal damage models", Int. J. Solids Struct. 37:48-50 (2000), 7501-7528.
21. J. C. Simo, J. Oliver, and F. Armero, "An analysis of strong discontinuities induced by strain softening in rate-independent inelastic solids", Comput. Mech. 12:5 (1993), 277-296.
22. G. N. Wells and L. J. Sluys, "A new method for modelling cohesive cracks using finite elements", Int. J. Numer. Methods Eng. 50:12 (2001), 2667-2682.