 | | 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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| L. M. Zubov and M. S. Lastenko, "On the instability of equilibrium a cylinder made of a hardening material subjected to tension," Mech. Solids. 39 (3), 109-116 (2004) |
| Year |
2004 |
Volume |
39 |
Number |
3 |
Pages |
109-116 |
| Title |
On the instability of equilibrium a cylinder made of a hardening material subjected to tension |
| Author(s) |
L. M. Zubov (Rostov-on-Don)
M. S. Lastenko (Rostov-on-Don) |
| Abstract |
On the basis of the equations of three-dimensional nonlinear elasticity, the stability of a circular cylinder subjected to uniform axial tension is analyzed. Axisymmetric modes of instability corresponding to neck formation in the extended rod are investigated. An isotropic incompressible material of the rod possesses a power-law hardening and is described by the logarithmic strain tensor. As a result of solving the linearized equations of stability for the cylinder subjected to tension, the spectrum of critical values of the longitudinal strain and fig of buckling are determined. It is established that the bifurcation modes of equilibrium, which are associated with neck formation, appear when the elongation slightly exceeds the value corresponding to the maximum point in the stress-strain diagram of the rod. It is shown that different modes of instability have close eigenvalues, which is a specific feature of the neck-type instability. Qualitatively similar results were obtained previously [1] for the problem of neck formation in a rectangular beam under the conditions of plane strain. |
| References |
| 1. | L. M. Zubov and A. N. Rudev, "On the stability of an extended nonlinearly elastic beam," PMM [Applied Mathematics and Mechanics], Vol. 60, No. 5, pp. 786-798, 1996. |
| 2. | A. I. Lur'e, Nonlinear Theory of Elasticity [in Russian], Nauka,
Moscow, 1980. |
| 3. | V. V. Novozhilov, "On the principles of processing of the results of statical tests for isotropic materials," PMM [Applied Mathematics and Mechanics], Vol. 15, No. 6, pp. 709-722, 1951. |
| 4. | A. Nadai, Plasticity and Fracture of Solids [Russian translation],
Moscow, IL, 1954. |
| 5. | L. M. Kachanov, Fundamentals of the Fracture Mechanics [in Russian],
Nauka, Moscow, 1974. |
| 6. | J. F. Bell, Experimental Fundamentals of the Mechanics of
Solids. Part 1. Finite Strains [Russian translation], Nauka, Moscow, 1984. |
| 7. | V. A. Eremeev and L. M. Zubov, "Some problems of stability of three-dimensional nonlinearly elastic bodies," Izv. Vuzov. Sev.-Kavkaz Region. Estestv. Nauki., No. 1, pp. 42-47, 1999. |
| 8. | V. D. Klyushnikov, Stability of Elastoplastic Systems [in Russian],
Nauka, Moscow, 1980. |
| 9. | L. M. Zubov and S. I. Moiseenko, "Buckling of an elastic cylinder subjected to torsion and compression," Izv. AN. MTT [Mechanics of Solids],
No. 5, pp. 78-84, 1994. |
| 10. | L. V. Nikitin and E. I. Ryzhak, "On the implementation of the state of a material, which corresponds to the descending part of the stress-strain curve," Izv. AN. MTT [Mechanics of Solids], No. 2, pp. 155-161, 1986. |
| 11. | E. I. Ryzhak, "The implementation of uniaxial postcritical deformation in testing on a rigid triaxial machine," Izv. AN. MTT [Mechanics of Solids], No. 1, pp. 111-127, 1991. |
| 12. | E. I. Ryzhak, "On the stable postcritical deformation in a non-rigid triaxial test machine," Doklady AN, Vol. 330, No. 2, pp. 197-199, 1993. |
| 13. | E. I. Ryzhak, "On the stable postcritical deformation of
elastoplastic specimens constrained by a frame of fixed stiffness," Izv. AN. MTT [Mechanics of Solids], No. 3, pp. 117-135, 1995. |
|
| Received |
13 December 2001 |
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