The Griffith formula and the Rice-Cherepanov integral for crack problems with unilateral conditions in nonsmooth domains

European Journal of Applied Mathematics

Volumn 10, Issue 4, 1999, Pages 379-394

  Khludnev, A M ^a   Sokolowski, J ^b,c  

^a LAVRENTYEV INSTITUTE OF HYDRODYNAMICS   (Russian Federation)

^b UNIVERSITÉ HENRI POINCARÉ NANCY 1   (France)

^c SYSTEMS RESEARCH INSTITUTE   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033434545     PISSN: 09567925     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0956792599003885     Document Type: Article

References (23)

1. DESTUYNDER, P. & JAOUA, M. (1981) Sur une interprétation mathématique de l'intégrale de Rice en théorie de la rupture fragile. Math. Meth. in the Appl. Sci. 3, 70-87.
2. CHEREPANOV, G. P. (1979) Mechanics of Brittle Fracture. McGraw-Hill.
3. BUI, H. D. & EHRLACHER, A. (1997) Developments of fracture mechanics in France in the last decades. In: H. P. Rossmanith (ed.), Fracture Research in Retrospect. A. A. Balkema, Rotterdam, pp. 369-387.
4. SOKOLOWSKI, J. & ZOLÉSIO, J. P. (1992) Introduction to Shape Optimization. Shape Sensitivity Analysis. Springer-Verlag.
5. PARTON, V. Z. & MOROZOV, E. M. (1985) Mechanics of Elastoplastic Fracture. Moscow, Nauka (in Russian).
6. MAZJA, V. G. & NAZAROV, S. A. (1987) Asymptotics of energy integrals for small perturbation of a boundary near corner and conical points. Proc. Moscow Math. Society, Moscow State University, pp. 79-129 (in Russian).
7. GRISVARD, P. (1992) Singularities in Boundary Value Problems. Masson, Springer-Verlag.
8. OHTSUKA, K. (1994) Mathematical aspects of fracture mechanics. Lecture Notes in Numer. Appl. Anal., 13, 39-59.
9. BLAT, J. & MOREL, J. M. (1988) Elliptic problems in image segmentation and their relation to fracture theory. In : P. Benilan, M. Chipot, L. C. Evans and M. Pierre (eds.), Recent Advances in Nonlinear Elliptic and Parabolic Problems: Proc. International Conference. Longman.
10. KHLUDNEV, A. M. (1996) Contact problem for a plate having a crack of minimal opening. Control and Cybernetics, 25 605-620.
11. KHLUDNEV, A. M. (1995) The contact problem for a shallow shell with a crack. J. Appl. Math. Mech. 59, 299-306.
12. KHLUDNEV, A. M. (1996) On equilibrium problem for a plate having a crack under the creep condition. Control & Cybernetics, 25, 1015-1029.
13. KONDRATIEV, V. A., KOPAČHEK, J. & OLEINIK, O. A. (1982) On behaviour of solutions to the second order equations and elasticity equations in a neighbourhood of boundary points. Proc. Petrovsky's Seminar. Moscow, Moscow University Publishers, 8, pp. 135-152 (in Russian).
14. NAZAROV, S. A. & POLYAKOVA, O. P. (1996) Fracture criterions, asymptotic conditions at the crack tips, and selfadjoint extensions of the Lame operator. Proc. Moscow Math. Society, Moscow State University, 57, pp. 16-75 (in Russian).
15. NAZAROV, S. A. & POLYAKOVA, O. P. (1995) Weighted functions and invariant integrals of higher orders. Izviestia Ross. Acad. Nauk, Mekh. tverdogo tela, 1, 104-119 (in Russian).
16. KHLUDNEV, A. M. & SOKOLOWSKI, J. (1997) Modelling and Control in Solid Mechanics. Birkhauser.
17. GRISVARD, P. (1985) Elliptic Problems in Nonsmooth Domains. Pitman.
18. DAUGE, M. (1988) Elliptic Boundary Value Problems on Corner Domains: Lecture Notes in Mathematics 1341. Springer-Verlag.
19. NAZAROV, S. A. & PLAMENEVSKII, B. A. (1991) Elliptic Problems in Domains with Piecewise Smooth Boundaries. Moscow, Nauka (in Russian).
20. BANICHUK, N. V. (1970) The small parameter method of finding a curvilinear crack shape. Izviestia Acad. Nauk USSR, Mekh. tverdogo tela, N.2, 130-137 (in Russian).
21. YAKUNINA, G. V. (1981) Smoothness of solutions of variational inequalities. Partial Diff. Equat., Spectral theory, Leningrad State University, 8, 213-220 (in Russian).
22. KINDERLEHRER, D. & STAMPACCHIA, G. (1980) An Introduction to Variational Inequalities and their Applications.
23. LANDKOF, N. S. (1972) Foundations of Modern Potential Theory. Springer-Verlag.