 | | 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: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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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
of a tensile crack," Izv. AN SSSR. MTT [Mechanics of Solids], No. 2,
pp. 152-160, 1989. |
| 5. | S. A. Nazarov, "Interaction of cracks under brittle fracture.
Load and Energy Approaches," PMM [Applied Mathematics and Mechanics], Vol. 64, No. 3, pp. 484-496, 2000. |
| 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.,
Vol. 36, No. 4, pp. 77-82, 2000. |
| 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.
Stress singularities and invariant integrals," PMM [Applied Mathematics and Mechanics], Vol. 62, No. 3,
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,
"On coefficients in asymptotic formulas for solutions of elliptic boundary value problems in
domains with conical points," Math. Nachr., Bd. 76, S. 29-60, 1977. |
| 14. | E. M. Morozov,
"A variational principle in fracture mechanics," Doklady AN SSSR,
Vol. 184, No. 6, pp. 1308-1311, 1969. |
| 15. | S. Nemat-Nasser, Y. Sumi, and L. M. Keer,
"Unstable growth of tension cracks in brittle solids: Stable and unstable bifurcations,
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
elastic ring reinforced by fibers of very high rigidity," Zh. Prikl.
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. |
| 20. | S. A. Ambartsumian, Theory of Anisotropic Plates. Strength, Stability, and
Vibrations [in Russian], Nauka, Moscow, 1987. |
| 21. | B. A. Shoikhet, "On asymptotically precise equations of thin plates of
complex structure," PMM [Applied Mathematics and Mechanics], Vol. 37, No. 5, pp. 914-924, 1973. |
| 22. | S. A. Nazarov, "Asymptotic analysis of an arbitrary anisotropic plate of
variable thickness (shallow shell)," Matem. Sbornik, Vol. 191, No. 7,
pp. 129-159, 2000. |
|
| Received |
23 July 2001 |
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