 | | 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: | | 12788 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8028
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| In English (Mech. Solids): | | 4760 |
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| E.A. Lyamina, "A General Axisymmetric Elastic-Plastic Solution for an Arbitrary Isotropic Yield Criterion under Plane Stress," Mech. Solids. 59 (1), 541-554 (2024) |
| Year |
2024 |
Volume |
59 |
Number |
1 |
Pages |
541-554 |
| DOI |
10.1134/S0025654424603100 |
| Title |
A General Axisymmetric Elastic-Plastic Solution for an Arbitrary Isotropic Yield Criterion under Plane Stress |
| Author(s) |
E.A. Lyamina (Ishlinsky Institute for Problems in Mechanics RAS, Moscow, 119526 Russia, lyamina@inbox.ru) |
| Abstract |
Plane stress solutions in plasticity have qualitative features not inherent to other deformation modes. Examples are a particular condition of the non-existence of solutions and the necessity to verify that the conditions under which the assumption of plane stress is acceptable are satisfied. Therefore, analytical and semi-analytical solutions are advantageous over numerical solutions, even though the former require simplified constitutive equations. A typical approach for deriving analytical and semi-analytical solutions to axisymmetric problems is to assume Tresca’s yield criterion or another yield criterion represented by linear equations in terms of the principal stresses. Such yield criteria are piecewise linear, and the solution to a boundary value problem usually involves several plastic regimes, making it cumbersome. Moreover, using piecewise linear yield criteria may significantly affect predicted strain distributions compared to smooth yield criteria, which are more accurate for most metals. The present paper provides a general axisymmetric elastic perfectly plastic solution for an arbitrary isotropic yield criterion under plane stress conditions. The flow theory of plasticity based on the associated plastic flow rule is used. Obtaining quantitative results requires evaluating ordinary integrals by a numerical method. The solution is especially simple if one of the boundary conditions requires that the stress components are constant on a surface surrounded by a plastic region. A numerical example of using the solution is presented. |
| Keywords |
plane stress, axial symmetry, arbitrary yield criterion, analytical solution, flow theory of plasticity |
| Received |
13 March 2024 | Revised |
27 March 2024 | Accepted |
29 March 2024 |
| Link to Fulltext |
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