 | | 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. ĐÀÍ. ̀̉̉): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| I.M. Tsvetkov, "Dynamic Regimes of Biaxial Stretching of a Thin Ideally Rigid-Plastic Rectangular Plate," Mech. Solids. 58 (7), 2656-2665 (2023) |
| Year |
2023 |
Volume |
58 |
Number |
7 |
Pages |
2656-2665 |
| DOI |
10.3103/S0025654423070221 |
| Title |
Dynamic Regimes of Biaxial Stretching of a Thin Ideally Rigid-Plastic Rectangular Plate |
| Author(s) |
I.M. Tsvetkov (Lomonosov Moscow State University, Moscow, Russia, cvetkoviv@yandex.ru) |
| Abstract |
The stress–strain state arising during dynamic tension of a homogeneous rectangular plate
of an incompressible ideally rigid–plastic material, which obeys the Mises–Hencky criterion, is considered. The upper and lower bases are stress-free; longitudinal velocities are set at the ends. The possibility of deformation of the upper and lower sides of the plate is taken into account, which simulates
neck formation and further development of the neck. A small geometric parameter is introduced: the
ratio of the average thickness of the plate to its length along one of the directions. At different time
intervals, the order of smallness of the dimensionless functions characterizing the dynamic stretching
mode may be different with respect to the geometric parameter which determines the stretching mode.
Two such characteristic modes are identified: one is associated with a sufficiently high rate of removal
of the ends of the plate from each other, the second with acceleration. In the second case, an analysis
is carried out using the method of asymptotic integration, which allows us to approximately find the
parameters of the stress–strain state. |
| Keywords |
ideal plasticity, yield stress, plate, tension, neck, quasi-static, dynamics, strain rate, stress, asymptotic expansions |
| Received |
18 January 2023 | Revised |
10 May 2023 | Accepted |
20 June 2023 |
| Link to Fulltext |
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