 | | 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: | | 13653 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8223
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| In English (Mech. Solids): | | 5430 |
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| S.L. Subbotin, A.A. Alekseev, and V.I. Gultyaev, "Technique of Determining Plasticity Functionals for a Plane Strain Trajectory Based on Experimental Data," Mech. Solids. 60 (8), 6667-6678 (2025) |
| Year |
2025 |
Volume |
60 |
Number |
8 |
Pages |
6667-6678 |
| DOI |
10.1134/S002565442560552X |
| Title |
Technique of Determining Plasticity Functionals for a Plane Strain Trajectory Based on Experimental Data |
| Author(s) |
S.L. Subbotin (Tver State Technical University, Tver, 170026 Russia, sbtn@yandex.ru)
A.A. Alekseev (Tver State Technical University, Tver, 170026 Russia, alexeew@bk.ru)
V.I. Gultyaev (Tver State Technical University, Tver, 170026 Russia, vig0@mail.ru) |
| Abstract |
The article presents calculation formulas and a technique for the practical determination of the functionals of the theory of elastic-plastic processes based on experimental data for plane strain trajectories. To obtain the calculation formulas, a vector representation of stresses and strains is used, and a constitutive relation in the form of A.A. Ilyushin’s coplanarity hypothesis is applied. In the presented method for calculating stress vector components, experimental data are recalculated to equally spaced points along the strain trajectory using linear interpolation. The resulting data are smoothed to reduce random experimental errors using the least-squares method and known formulas. Using the smoothed data and numerical differentiation formulas, the derivatives of the stress vector components along the strain trajectory are found, and from these, the values of the plasticity functionals along the given strain trajectory are determined. The accuracy of the result using the applied methodology is assessed by the proximity of the experimental values of the stress vector components to the coplanarity hypothesis relations calculated by numerical integration. The results of processing an experiment involving complex loading in the deviatoric stress space with axial force and torque (P+M experiment) on a thin-walled tubular specimen made of 45 steel are presented. The results of calculating the plasticity functionals along a plane curved strain trajectory consisting of eight successive semicircles are presented in clear graphical form. The functionals are often complex, which complicates their direct use in mathematical models of plasticity theory. Therefore, approximations of the functionals are often used, allowing them to be replaced with simpler expressions while ensuring sufficient accuracy. The presented method for determining plasticity functionals can be used to process experimental data and construct approximations of the functionals. |
| Keywords |
plasticity, complex loading, coplanarity hypothesis, plasticity functionals, experimental data processing |
| Received |
10 May 2025 | Revised |
11 August 2025 | Accepted |
24 December 2025 |
| Link to Fulltext |
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