Exact solution of the 3-D-problem of an interface semi-infinite plane crack

Journal of the Mechanics and Physics of Solids

Volumn 47, Issue 5, 1999, Pages 1051-1093

  Antipov, Y A ^a  

^a University of Bath   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

CRACKS; INTEGRAL EQUATIONS; INTERFACES (MATERIALS); MATHEMATICAL TRANSFORMATIONS; PROBLEM SOLVING; STRESS INTENSITY FACTORS;

INTERFACE CRACKS; SEMI-INFINITE PLANE CRACKS;

FRACTURE MECHANICS;

EID: 0032644328     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-5096(98)00096-9     Document Type: Article

References (27)

1. Bueckner, H.F., 1987. Weight functions and fundamental fields for the penny-shaped and the half-plane crack in three-space. Int. J. Solids Structures 23, 57-93.
2. Câmara, G.N., Lebre, A.B., Speck, F.-O., 1993. Generalised factorisation for a class of Jones form matrix functions. Proc. R. Soc. Edinburgh 123A, 401-422.
3. Chebotarev, G.N., 1956. On closed-form solution of a Riemann boundary value problem for n pairs of functions. Uchen. Zap. Kazan. Univ. 116 (4) , 31-58.
4. Duduchava, R., Wendland, W.L., 1995. The Wiener-Hopf method for systems of pseudodifferential equations with an application to crack problems. Integral Equations and Operator Theory 23, 294-335.
5. Duduchava, R., Sändig, A.M., Wendland, W.L., 1996. The Wiener-Hopf method in crack and interface problems. Z. für Angew. Math. und Mech. (ZAMM) 75/2, 113-116.
6. Gakhov, F.D., 1952. A Riemann boundary value problem for a system of n pairs of functions. Russian Mathematical Surveys 7 (4) (50) , 3-54.
7. Gakhov, F.D., 1966. Boundary Value Problems. Pergamon Press, Oxford.
8. Jones, D.S., 1984. Commutative Wiener-Hopf factorization of a matrix. Proc. R. Soc. Lond. A 393, 185-192.
9. Kassir, M.K., Sih, G.C., 1973. Application of Papkovich-Neuber potentials to a crack problem. Int. J. Solids and Structures 9, 643-654.
10. Khrapkov, A.A., 1971. Certain cases of the elastic equilibrium of an infinite wedge with a non-symmetric notch at the vertex, subjected to concentrated forces. J. Appl. Maths Mechs (PMM) 35, 625-637.
11. Lazarus, V., Leblond, J.B., 1998a. Three-dimensional crack-face weight functions for the semi-infinite interface crack - I: Variation of the stress intensity factors due to some small perturbation of the crack front. J. Mech. Phys. Solids 46, 489-511.
12. Lazarus, V., Leblond, J.B., 1998b. Three-dimensional crack-face weight functions for the semi-infinite interface crack - II. Integrodifferential equations on the weight functions and resolution. J. Mech. Phys. Solids 46, 513-536.
13. Meister, E., Speck, F.-O., 1989. The explicit solution of elastodynamical diffraction problems by symbol factorization. Z. Anal. Anw. 8, 307-328.
14. Moiseyev, N.G., Popov, G.Y., 1990. An exact solution of the problem on bend of a semi-infinite plate bonded completely with an elastic half-space. Izv. AN SSSR, Mech. Tverdogo Tela (MTT) 25 (6) , 112-123.
15. Movchan, A.B., Gao, H., Willis, J.R., 1998. On perturbations of plane cracks. Int. J. Solids Structures 35, 3419-3453.
16. Muskhelishvili, N.I., 1953. Singular Integral Equations. Noordhoff, Groningen.
17. Noble, B., 1988. Methods Based on the Wiener-Hopf Technique, 2nd ed. Chelsea, New York.
18. Rapoport, I.M., 1948. On a class of singular integral equations. Dokl. Akad. Nauk SSSR 59 (8) , 1403-1406.
19. Sih, G.C., Rice, J.R., 1964. The bending of plates of dissimilar materials with cracks. J. of Appl. Mech.; Trans. ASME, Series E 86, 477-482.
20. Tichomirov, V.V., 1994. Stressed state of a composite space with a semi-infinite interfacial crack. Izv. RAN, Mech. Tverdogo Tela (MTT) 29 (6) , 51-56.
21. Tichomirov, V.V., 1996. An interfacial crack in a transversely isotropic composite medium. J. Appl. Maths Mechs (PMM) 60, 833-838.
22. Uflyand, Ya.S., 1965. Survey of Articles on the Application of Integral Transforms in the Theory of Elasticity. North Carolina State University.
23. Williams, M.L., 1959. The stresses around a fault or crack in dissimilar media. Bull. of the Seismolog. Soc. of America 49, 199-204.
24. Willis, J.R., 1971a. Fracture mechanics of interfacial cracks. J. Mech. Phys. Solids 19, 353-368.
25. Willis, J.R., 1971b. Interfacial stresses induced by arbitrary loading of dissimilar elastic half-spaces joined over a circular region. J. Inst. Math. Appl. 7, 179-197.
26. Willis, J. R., 1972. The penny-shaped crack on an interface. Quart. J. Mech. Appl. Math. 25, 367-385.
27. Wiener, N., Hopf, E., 1931. Über eine klasse singulärer integralgleichungen. Sitz. Berlin. Akad. Wiss pp. 696-706.