The interaction of cracks in brittle fracture. Force and energy approaches

Journal of Applied Mathematics and Mechanics

Volumn 64, Issue 3, 2000, Pages 465-475

  Nazarov, S A ^a  

^a NONE   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034347984     PISSN: 00218928     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0021-8928(00)00070-8     Document Type: Article

References (27)

1. Nemat-Nasser, S., Sumi, Y. and Keer, L. M., Unstable growth of tension cracks in brittle solids: Stable and unstable bifurcation, snap-through and imperfection sensitivity. Int. J. Solids and Structures, 1980, 16, 11, 1017-1033.
2. Nazarov, S.A., The derivation of a variational inequality for the shape of a small increment of a tension crack. Izv. Akad. Nauk SSSR. MTT, 1989, 2, 152-160.
3. Nguen Quoc Son, Stabilité et bifurcation en rupture et an plasticité. C. R. Acad. Sci. Paris, Sér. 2. 1981, 292, 11, 817-820.
4. Nazarov, S. A. and Polyakova, O. R. The equivalence of the fracture criteria for a tension crack in an elastic space. Izv. Ross. Akad. Nauk MTT, 1992, 2, 101-113.
5. Nazarov, S. A. and Polyakova, O. R., Fracture criteria, asymptotic conditions at crack tips, and self-adjoint expansions of the Lamé operator. Tr. Mask. Mat. Obsch., 1996, 57, 16-75.
6. Bueckner, H. F., A novel principle for the computation of stress intensity factors. ZAMM, 1970, 50, 9, 529-546.
7. Maz'ya, V. G. and Plamenevskii, B. A., The coefficients in the asymptotic form of the solutions of elliptic boundary-value problems in a region with conical points. Math. Nachr., 1977, 76, 29-60.
8. Nazarov. S. A., Local stability and instability of normal tension cracks. Izv. Akad. Nauk SSSR. MTT, 1988, 3, 124-129.
9. Nazarov, S. A. and Plamenevskii, V. A. Elliptic Problems in Domains with Piecewise Smooth Boundaries. Walter de Gruyter, Berlin, 1994.
10. Van Dyke, M., Perturbation Methods in Fluid Mechanics. Academic Press, New York/London, 1964.
11. Il'in, A. M. Matching of the Symptotic Expansions of the Solutions of Boundary-value Problems. Nauka. Moscow, 1989.
12. Nazarov, S. A., Weighting functions and invariant integrals. Vychisl. Mekhanika Deformiruyemogo Tverdogo Tela, 1990, 1, 17-31.
13. Nazarov, S. A., The interface crack in anisotropic bodies. Stress singularities and invariant integrals. Prikl. Mat. Mekh., 1998, 62, 3, 489-502.
14. Kolton, L. H. and Nazarov, S. A., Quasistatic propagation of a mode-1 crack in an elastic space. C. R. Acad. Sci. Paris. Sér. 2, 1992, 315, 12, 1453-1457.
15. Lions, J.-L., Some Quelgues Méthodes de Résoltuion des Problems and Limites Non Linéaires. Dunod, Paris, 1969.
16. SI. G. and Libowitz. H., Mathematical theory of brittle fracture. In Fracture, Vol. 2 (Edited by Libowitz, H.). Academic Press. New York, 1968.
17. Sedov, L. I., Continum Mechanics. Vol. 2. Nauka, Moscow, 1976.
18. Maz'ya, V. G., Nazarov S. A. and Plamenevskii, B. A., Asymptotishe Theorie Elliptischer Randwertaugaben in Singulär Gestörten Gebieten, Vol. 1. Akademie, Berlin, 1990.
19. Nazarov, S. A. and Specovius-Neugebauer, M. The approximation of unbounded regions by bounded ones. Boundary-value problems for the Lamé operator. Algebra i Analiz, 1996, 8, 5, 229-268.
20. Nazarov. S. A. and Speciovius-Newgebauer, M., The errors due to approximating unbounded elastic bodies by bounded ones. Prikl. Mat. Mekh., 1988, 62, 4, 650-663.
21. Movchan, A. B. and Nazarov, S. A., The occurrence of a Griffith's crack in an inhomogeneous stress field. Fiz.-Khim. Mekhanika Materialov, 1990, 1, 26-31.
22. Savruk, M. P., Stress intensity factors in bodies with cracks. Naukova Dumka, Kiev, 1988. (Fracture Mechanics and Strength of Materials, Vol. 2).
23. Kolton, L. G., Slow growth of a system of cracks. Izv. Akad. Nauk SSSR. MTT, 1989, 5, 95-100.
24. Banichuk, N. V, Determination of shape of a curvilinear crack by the small-parameter method. Izv. Akad. Nauk SSSR. MTT, 1970, 2, 130-137.
25. Gol'dshtein, R. V. and Salganik, R. L., The plane problem of curvilinear cracks in an elastic body. Izv. Akad. Nauk SSSR. MTT, 1970, 3, 69-82.
26. Melin, S., Fracture from a straight crack subjected to mixed mode loading. Int. J. Fracture, 1987, 32, 4, 257-263.
27. Movchan, A. B. Nazarov, S. A. and Polyakova, O. R., The increment of the stress intensity factors during the extension of a curvilinear crack. Izv. Ross. Akad. Nauk, MTT, 1992, 1, 84-93.