 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
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| In English (Mech. Solids): | | 3212 |
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| A. A. Kulikov and S. N. Nazarov, "Correspondence principle in plane problems of rectilinear crack growth," Mech. Solids. 39 (1), 56-64 (2004) |
| Year |
2004 |
Volume |
39 |
Number |
1 |
Pages |
56-64 |
| Title |
Correspondence principle in plane problems of rectilinear crack growth |
| Author(s) |
A. A. Kulikov (St. Petersburg)
S. N. Nazarov (St. Petersburg) |
| Abstract |
It is shown that the processes of quasistatic rectilinear crack growth in
plane orthotropic algebraically equivalent materials occur in a similar manner.
A correspondence principle is formulated for media whose elastic and strength
characteristics are related by the same affine transformation. Some relations
are discovered between stress singularity exponents for anisotropic wedges
with clamped or free faces. Some relevant examples are discussed. |
| References |
| 1. | S. G. Lekhnitskii,
Theory of Elasticity of Anisotropic Bodies [in Russian], Nauka, Moscow, 1977. |
| 2. | N. B. Alfutova, A. B. Movchan, and S. A. Nazarov,
"Algebraic equivalence of plane problems for orthotropic and anisotropic media,"
Vestnik LGU, Ser. 1, Vol. 3, No. 15, pp. 64-68, 1991. |
| 3. | A. A. Kulikov, S. A. Nazarov, and M. A. Narbut,
"Affine transformations in the plane problem of anisotropic elasticity,"
Vestnik SPbGU, Ser. 1, Vol. 3, No. 8, pp. 91-95, 2000. |
| 4. | S. A. Nazarov,
"Derivation of a variational inequality for the shape of small increment
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| 5. | S. A. Nazarov, "Interaction of cracks under brittle fracture.
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| 6. | I. I. Argatov and S. A. Nazarov,
"A Comparison of the Griffith and Irwin criteria for a
non-symmetrically growing crack in a plane," Fiz.-Khim. Mekh. Mater.,
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| 7. | V. Z. Parton and E. M. Morozov,
Mechanics of Elastic-Plastic Fracture [in Russian], Nauka, Moscow, 1974. |
| 8. | G. P. Cherepanov, Mechanics of Brittle Fracture [in Russian], Nauka, Moscow, 1974. |
| 9. | S. A. Nazarov, "A crack at the juncture of anisotropic bodies.
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pp. 489-502, 1998. |
| 10. | S. A. Nazarov and O. P. Polyakova,
"Fracture criteria, asymptotic conditions at crack tips and self-adjoint
solutions of the Lamé operator," Trudy Moskov. Matem. Ob-va, Vol. 57,
pp. 16-75, 1996. |
| 11. | S. A. Nazarov, "Weight functions and invariant integrals,"
Vychisl. Mekh. Deform. Tverd. Tela, No. 1, pp. 17-31, 1990. |
| 12. | H. F. Bueckner, "A novel principle for the computation of stress intensity factor,"
ZAMM, Vol. 50, No. 9, pp. 529-546, 1970. |
| 13. | V. G. Maz'ja and B. A. Plamenevskii,
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domains with conical points," Math. Nachr., Bd. 76, S. 29-60, 1977. |
| 14. | E. M. Morozov,
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| 15. | S. Nemat-Nasser, Y. Sumi, and L. M. Keer,
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snap-through and imperfection sensitivity," Int. J. Solids and Struct.,
Vol. 16, No. 11, pp. 1017-1033, 1980. |
| 16. | L. I. Sedov, Continuum Mechanics [in Russian], Nauka,
Moscow, 1976. |
| 17. | Yu. A. Bogan, "Asymptotic behavior of boundary value problems for an
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Mekhaniki i Tekhn. Fiziki, No. 6, pp. 118-122, 1980. |
| 18. | Yu. A. Bogan, "Some variational problems of elasticity with a
small parameter," PMM [Applied Mathematics and Mechanics], Vol. 49, No. 4, pp. 604-607, 1985. |
| 19. | S. G. Lekhnitskii, Anisotropic Plates [in Russian], Gostekhizdat, Moscow, 1957. |
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variable thickness (shallow shell)," Matem. Sbornik, Vol. 191, No. 7,
pp. 129-159, 2000. |
|
| Received |
23 July 2001 |
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