 | | 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
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| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4810 |
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| Yu. N. Radaev, "To the theory of 3D equations of mathematical plasticity," Mech. Solids. 38 (5), 85-99 (2003) |
| Year |
2003 |
Volume |
38 |
Number |
5 |
Pages |
85-99 |
| Title |
To the theory of 3D equations of mathematical plasticity |
| Author(s) |
Yu. N. Radaev (Samara) |
| Abstract |
We consider 3D equations of mathematical plasticity with Tresca's plasticity condition and the flow law associated with this condition for stress states that correspond to an edge of the yield surface. It is shown that the fields of eigenvectors of the stress tensor that correspond to the greatest or least principal stress are necessarily fiber fields. We introduce curvilinear coordinates such that the equilibrium relations transformed to the new variables are reduced to three integrable equations. Invariants that preserve their values along lines of principal stresses are found. Classes of 3D plasticity problems are singled out for which the stress fields correspond to an edge of Tresca's prism and are fiber fields. It is proved that the integration of the equations of plasticity in these problems can be reduced to the search for canonical transformations of spatial regions. The canonical coordinates are introduced for the spatial, plane, and axially symmetric problems. Equations for generating functions of the desired canonical transformations are investigated for plane and axially symmetric problems of plasticity. |
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|
| Received |
02 August 2001 |
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