Stability of crack fronts under Griffith criterion: A computational approach using integral equations and domain derivatives of potential energy

Computer Methods in Applied Mechanics and Engineering

Volumn 173, Issue 3-4, 1999, Pages 337-364

  Bonnet, Marc ^a  

^a ECOLE POLYTECHNIQUE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY ELEMENT METHOD; FRACTURE MECHANICS; GALERKIN METHODS; INTEGRAL EQUATIONS; POTENTIAL ENERGY;

GRIFFITH CRITERION;

CRACK PROPAGATION;

EID: 0032688894     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(98)00290-4     Document Type: Article

References (27)

1. [1] P. Berest, Q.S. Nguyen and R.M. Pradeilles-Duval, Stability and bifurcation of plane cracks of arbitrary shape, in: Computational Modelling of Free and Moving Boundary Problem (Comput. Mech. Publ., Southampton, 1993) 409-418.
2. [2] M. Bonnet, Méthode des équations intégrales régularisées en élastodynamique tridimensionnelle, Ph.D. Thesis, Ecole Nationale des Ponts et Chaussées, Paris (Nov. 1986), publiée dans le Bulletin EDF/DER série C, 1/2, 1987.
3. [3] M. Bonnet, Equations intégrales et éléments de frontière, CNRS Editions/Eyrolles, Paris, France, 1995.
4. [4] M. Bonnet, Regularized BIE formulations for first-and second-order shape sensitivity of elastic fields, Comput. Struct. 56 (1995) 799-811. (Invited paper, special issue, S. Saigal, guest editor).
5. [5] M. Bonnet, Regularized direct and indirect symmetric variational BIE formulations for three-dimensional elasticity, Engrg. Anal. Bound. Elem. 15 (1995) 93-102.
6. [6] M. Bonnet, G. Maier and C. Polizzotto, On symmetric Galerkin boundary element method, Appl. Mech. Rev. 51 (1998) 669-704.
7. [7] T.A. Cruse, Boundary Element Analysis in Computational Fracture Mechanics (Kluwer Academic Publishers, 1988).
8. [8] T.A. Cruse and P.M. Besuner, Residual life prediction for surface cracks in complex structural details, J. Aircraft 12 (1975) 369-375.
9. [9] H.G. Delorenzi, On the energy release rate and the J-integral for 3-D crack configurations, Int. J. Fract. 19 (1982) 183-194.
10. [10] Ph. Destuynder, M. Djaoua and S. Lescure, Quelques remarques sur la mécanique de la rupture élastique, J. Mécan. Théor. Appl. 2 (1983) 113-135.
11. [11] B. Doubrovine, S. Novikov and A. Fomenko, Géométrie contemporaine, méthodes et applications (première partie: géométrie des surfaces, des groupes de transformations et des champs) (Editions de Moscou, 1979).
12. [12] T.K. Hellen, On the method of virtual crack extension, Int. J. Numer. Methods Engrg. 9 (1975) 187-207.
13. [13] S. Li, M.E. Mear and L. Xiao, Symmetric weak-form integral equation method for three-dimensional fracture analysis, Comput. Methods Appl. Mech. Engrg. 151 (1998) 435-459.
14. [14] P. Mialon, Calcul de la dérivée d'une grandeur par rapport à un fond de fissure par la méthode θ, Bulletin EDF/DER série c vol. 3, Electricité de France, 1987.
15. [15] J.C. Nedelec, Integral equations with non integrable kernels, Integral Equations and Operator Theory 5 (1982) 562-572.
16. [16] Q.S. Nguyen, Bifurcation and stablity of time-independent dissipative systems. Advanced course on bifurcation and stability of dissipative systems, CISM Lectures, Udine, Italy, 1991.
17. [17] Q.S. Nguyen, Bifurcation and stability in dissipative media (plasticity, friction, fracture), Appl. Mech. Rev. 47 (1994) 1-31.
18. [18] Q.S. Nguyen, C. Stolz and G. Debruyne, Energy methods in fracture mechanics: stability, bifurcation and second variations, Engrg. Struct. 9 (1990) 157-173.
19. [19] N. Nishimura and S. Kobayashi, A boundary integral equation method for an inverse problem related to crack detection, Int. J. Numer. Methods Engrg. 32 (1991) 1371-1387.
20. [20] K. Ohtsuka, Generalized J-integral and three-dimensional fracture mechanics, Hiroshima Math. J. 11 (1981) 21-52.
21. [21] D.M. Parks, A stiffness derivative finite element technique for determination of crack tip stress intensity factors, Int. J. Fract. 10 (1974) 487-501.
22. [22] H. Petryk and Z. Mroz, Time derivatives of integrals and functionals defined on varying volume and surface domains. Arch. Mech. 38 (1986) 694-724.
23. [23] S. Sirtori, G. Maier, G. Novati and S. Miccoli, A Galerkin symmetric boundary element method in elasticity: formulation and implementation, Int. J. Numer. Methods Engrg. 35 (1992) 255-282.
24. [24] J. Sokolowski and J.P. Zolesio, Introduction to shape optimization. Shape sensitivity analysis, Vol. 16 of Springer Series in Computational Mathematics (Springer-Verlag, 1992).
25. [25] X.Z. Suo and A. Combescure, Sur une formulation mathématique de la dérivée de l'énergie potentielle en théorie de la rupture fragile, C.R. Acad. Sci. Paris, série II 308 (1122-1989) 1119.
26. [26] H. Tada, P. Paris and G. Irwin, The stress analysis of cracks handbook, Tech. Rep., Del. Research Corporation, Hellertown, Pennsylvania, USA, 1973.
27. [27] Y. Wadier and O. Malak, The theta method applied to the analysis of 3D-elastic-plastic cracked bodies, in SMIRT Proceedings, 1989.