 | | 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 |
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| V. A. Kolesnikov, "Inertial expansion of a cylindrical cavity in an elastic-plastic medium," Mech. Solids. 36 (5), 94-100 (2001) |
| Year |
2001 |
Volume |
36 |
Number |
5 |
Pages |
94-100 |
| Title |
Inertial expansion of a cylindrical cavity in an elastic-plastic medium |
| Author(s) |
V. A. Kolesnikov (Moscow) |
| Abstract |
The problem of expansion of a cylindrical cavity was previously studied
for an ideal medium (the so-called plastic gas) in [1],
for elastic-plastic materials of Saint-Venant-von Mises type in [2, 3],
and in [4], for viscoplastic media.
In this paper, a material with compaction is considered.
Initially, a model of such media in this form was proposed by
A. Yu. Ishlinskii. Its further justification was given in [5].
In the problem considered here, the expansion obeys the general law
r=R(t) and there is no self-similarity.
We are interested in the inertial motion of the cavity and its backward
motion until a complete stop. In the process of solving the problem, we
find the dimensions of the cavity and the duration of its inertial motion.
This problem can be used to model growth of a cavity
due to soil penetration by cylindrical bodies.
When constructing the solution, we take into account the load-relief
from the shear plastic state for the backward motion of
the cavity boundary. The simplicity of the model used here allows
us to construct analytical solutions. |
| References |
| 1. | A. Ya. Sagomonyan, "Penetration of soil by a gas jet,"
Vestnik MGU. Ser. Mat., Mekh. [Bulletin of Moscow State University],
No. 5, pp. 60-64, 1979. |
| 2. | A. G. Bagdoev, Nonstationary Spatial Motions of a Continuum
[in Russian], Izd-vo AN ArmSSR, Erevan, 1961. |
| 3. | V. A. Kolesnikov and L. M. Flitman, "A self-similar problem for a
cylinder expanding and moving along its axis in an elastic-plastic
environment," in Problems of Interaction Dynamics of Solids
[in Russian], pp. 175-176, Izd-vo AN ArmSSR, Erevan, 1984. |
| 4. | V. N. Kukudzhanov,
"Shock waves in a visco-plastic medium with compaction,"
Izv. AN ArmSSR. Ser. Fiz. Mat., Vol. 11, No. 6, pp. 61-72, 1958. |
| 5. | A. Yu. Ishlinskii, N. V. Zvolinskii, and I. Z. Stepanenko,
"On soil dynamics," Doklady AN SSSR, Vol. 95, No. 4, pp. 729-731, 1954. |
| 6. | V. A. Kolesnikov, "Expansion of a cylindrical cavity
in an elastic-plastic medium under dynamic loading,"
Izv. AN. MTT [Mechanics of Solids], No. 5, pp. 65-71, 2000. |
|
| Received |
12 April 2001 |
| << Previous article | Volume 36, Issue 5 / 2001 | Next article >> |
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