compressible elastic-plastic medium, generalized Tresca’s yield criterion, plane strain, plasticity theory.

A comparative analysis of the theories of Saint-Venant, Levy and Mises has been presented. Comparison of condition of proportionality of stress deviator and plastic strain deviator has been given taking into account coaxiality of these two tensors. For plane strain case, the problem of obtaining of medium principle stress is discussed within different plastic flow theories. It is pointed out that the value of medium principle stress is undetermined in case of the Tresca plastic law. The consequences of associated flow rule for regular isotropic and normally isotropic medium have been discussed in case of smooth and piecwise smooth flow functions. The particularities of the alternative forms of statement of the Tresca yiled criterion are considered and respective modifications are discussed. For ideal rigid-plastic and compressible elasto-plastic medium, the plane strain axisymmetric problem is considered. Stress range variations at the boundaries, within which the only one plastic regime takes place for the Tresca yield criterion, have been obtained. Particular cases are considered when the problem is statically determined. It is shown that for some stress values at the solution region boundaries the completely plastic regime takes place. Generalized forms of statements for the Tresca, Shmidt-Ishlinskii and Mises yield criterions proposed by A. V. Hershey, W. F. Hosford, F. Barlat, A. P. Karafillis, M. C. Boyce, F. Bron, J. Besson as functions of principle values of stress deviator have been presented via quadratic and cubic stress tensor invariants. 

1. Artemov Mikhail Anatolievich Dr. Sci. Phys. & Math., Professor, Head of the Chair, Voronezh State University, Voronezh

2. Baranovskii Evgenii Sergeevich PhD, Assoc. Professor, Voronezh State University, Voronezh