A numerical method for fracture of rods

Lecture Notes in Applied and Computational Mechanics

Volumn 23, Issue , 2005, Pages 277-292

  Angelillo, Maurizio ^a   Babilio, Enrico ^a   Fortunato, Antonio ^a  

^a UNIVERSITY OF SALERNO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

FRACTURE; ITERATIVE METHODS; ONE DIMENSIONAL; POTENTIAL ENERGY;

DISPLACEMENT FIELD; ENERGY DENSITY; ENERGY MINIMIZATION; FRACTURE PROBLEMS; INTERFACE ENERGY; NONCONVEX FUNCTIONAL; ONE-DIMENSIONAL BODY; TOTAL POTENTIAL ENERGY;

NUMERICAL METHODS;

EID: 84866549230     PISSN: 16137736     EISSN: None     Source Type: Book Series    
DOI: 10.1007/3-540-32399-6_14     Document Type: Article

References (18)

1. Ambrosio, L. (1989) Compactness theorem for a special class of functions of bounded variation. Boll. Un. Mat. Ital.3-B, 857-881.
2. Ambrosio, L. (1989) Variational problems in SBV and image segmentation. Acta Appl. Math. 17, 1-40.
3. Ambrosio, L. (1990) Existence theory for a new class of variational problems. Arch. Rat. Mech. Anal. 111, 291-322.
4. Ambrosio, L. (1995) A new proof of the SBV compactness theorem. Calc. Var. 3, 127-137.
5. Ambrosio, L., Braides, A. (1997) Energies in SBV and variational models in fracture mechanics. Homogenization and Applications to Material Sciences (D. Cioranescu, A. Damlamian, P. Donato eds.), GAKUTO, Gakkōtosho, Tokio, Japan, 1-22.
6. Ambrosio, L., Fusco, N., Pallara, D. (2000) Functions of bounded variation and free discontinuity problems. Clarendon Press, Oxford.
7. Bourdin, B. (2000) Francfort, G. A., Marigo, J. J., Numerical experiments in revisited brittle fracture. J. Mech. Phys. Solids, 48 (4), 797-826.
8. Braides, A. (1998) Approximation of Free-Discontinuity Problems. Lecture Notes in Mathematics, Vol. 1694, Springer, Berlin.
9. Brakke, K. A. (1999) Surface Evolver Manual. Mathematics Department, Susquehanna University, Selinsgrove. Available at http://www.susqu.edu/facstaff/b/brakke/evolver.
10. Dal Maso, G., Toader, R. (2002) A model for the quasi-static growth of brittle fractures: existence and approximation results. Arch. Rational Mech. Anal. 162, 101-135.
11. Dal Maso, G., Toader, R. (2002) A model for the quasi-static growth of brittle fractures based on local minimization. Math. Models Methods Appl. Sci., 12 (12), 1773-1799.
12. De Giorgi, E., Ambrosio, L. (1988) Un nuovo tipo di funzionale del calcolo delle variazioni. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. s. 8 82, 199-210.
13. Del Piero, G. (2000) On the role of interface energies in the description of material behaviour. Lecture notes, Graduate School of Structural Engineering, Dip. Ing. Civ., Università di Salerno.
14. Del Piero, G., Truskinovsky, L. (1998) A one-dimensional model for localized and distributed fracture. J. de Physique IV 8, 95-102.
15. Del Piero, G., Truskinovsky, L. (2001) Macro- and micro-cracking in one- dimensional elasticity. Int. J. Solids and Structures, 38, 1135-1148.
16. Francfort, G. A., Marigo, J. J. (1998) Revisiting brittle fracture as an energy minimization problem. J. Mech. Phys. Solids, 46(8), 1319-1342.
17. Negri, M. (2003) A finite element approximation of the Griffith's model in fracture mechanics. Numerische Mathematik, 95, 653-687.
18. Negri, M. (2001) Numerical methods for free-discontinuity problems based on approximations by Γ-convergence. PhD Theses.