 | | 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
|
| In English (Mech. Solids): | | 3212 |
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| I. A. Miklashevich and A. V. Chigirev, "Stability of a crack trajectory in heterogeneous media," Mech. Solids. 37 (4), 93-97 (2002) |
| Year |
2002 |
Volume |
37 |
Number |
4 |
Pages |
93-97 |
| Title |
Stability of a crack trajectory in heterogeneous media |
| Author(s) |
I. A. Miklashevich (Minsk)
A. V. Chigirev (Minsk) |
| Abstract |
We study the stability of a solution of a nonlinear second-order
differential equation describing the trajectory of crack propagation
in heterogeneous media. It is shown that the types of critical points
arising in the system depend on the inhomogeneity of the medium
both in the longitudinal and the orthogonal directions to
the crack trajectory. Initiation of stochastic regimes of crack propagation is investigated.
Conditions ensuring the initiation of deterministic chaos in the behavior of
a crack trajectory
are established. |
| References |
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| 2. | G. P. Cherepanov, A. S. Balankin, and V. S. Ivanova,
"Fractal fracture mechanics- a review," Engng. Fract. Mech.,
Vol. 51, No. 6, pp. 997-1033, 1995. |
| 3. | I. M. Sokolova,
"Dimensions and other critical geometrical characteristics in the theory of
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| 4. | A. S. Balankin,
"Fractal mechanics of deformable media and the topology of
fracture of solids," Doklady AN, Vol. 322, No. 5, pp. 869-874, 1992. |
| 5. | I. A. Miklashevich and A. V. Chigarev,
"Stochastization of crack growth direction in heterogeneous media,"
in 8th Intern. Conf. on Fracture. Ukraine 93. Part 1, p. 227, Kiev, 1993. |
| 6. | I. A. Miklashevich, L. N. Bialiatskaja, and A. V. Chigarev,
"Nonlinear effects at the crack propagation," in
Proc of the 9th Ann. Seminar NPCS'2000, Nonlinear Phenomena in Complex
Systems: Fractals, Chaos, Phase Transitions, Self-Organization,
pp. 206-214, Minsk, 2000. |
| 7. | V. Z. Parton and E. M. Morozov, Mechanics of Elastoplastic Fracture
[in Russian], Nauka, Moscow, 1985. |
| 8. | M. V. Baninchuk,
"On a variational principle in the theory of cracks,"
Izv. AN. MTT [Mechanics of Solids], No. 4, pp. 197-199, 1969. |
| 9. | K. L. Molski, "Problemy modelowania rozwoju pęknięć międzyfazowych," Zeszyty Naukowe
Politechniki Bialostockiej. Nauki Technicznie. Mechanika, Z. 22, No. 134,
pp. 143-159, 2000. |
| 10. | A. V. Chigarev and I. A. Miklashevich,
"Calculation of crack trajectories in composite media in the linear
approximation," Doklady Belarus AN, Vol. 39, No. 2, pp. 114-116, 1995. |
| 11. | I. A. Miklashevich,
"Crack trajectories in heterogeneous media under plane loading,"
Mekh. Komposit. Mat. i Konstr., Vol. 6, No. 3, pp. 408-418, 2000. |
| 12. | F. Verhulst, Nonlinear Differential Equations and
Dynamical Systems, Springer-Verlag, Berlin, 1990. |
| 13. | A. V. Chigarev and Yu. V. Chigarev,
"On possible stochastic instability of rays in heterogeneous media,"
Akust. Zh., Vol. 24, No. 5, pp. 765-771, 1978. |
| 14. | G. M. Zaslavskii and R. Z. Sagdeev,
Introduction to Nonlinear Physics [in Russian], Nauka, Moscow, 1988. |
| 15. | G. P. Cherepanov, Mechanics of Brittle Fracture [in Russian],
Nauka, Moscow, 1974. |
|
| Received |
25 May 2001 |
| << Previous article | Volume 37, Issue 4 / 2002 | Next article >> |
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