The influence of elastic compressibility (Poisson's ratio) on the stress-strain state of a plastic-elastic body in plane-strain problems is investigated. The problem of expansion of a thick-walled tube by internal and external pressures, the problem of expansion in the x and y directions of an infinite medium, when the relation between axial forces takes different values, and the problem of expansion in the x and y directions of an infinite medium with a cylindrical cavity (L.A. Galin's problem) are considered. It is assumed that the material is isotropic hardening with a constant rate of hardening or zero hardening. The von Mises yield criterion is used. For a number of problems analytic solutions are obtained; in most cases, the numerical solution is obtained by the finite element method. It is shown that, contrary to the established opinion, the influence of elastic compressibility may be important, and use of the hypotheses about the size of the axial stress accepted in the literature is not always justified.
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