Turn of an elastic-plastic rod under pressure that varies linearly along the forming

The article continues a series of articles devoted to the use of the method of conservation laws of differential equations for solving problems in the mechanics of deformable solids. Elastoplastic problems in the mechanics of a deformable solid take into account the nonlinear relationship between stresses and deformations under the influence of various loads. Such problems arise in structures where materials are characterized by different physical properties; taking into account elastic-plastic deformations is important for predicting the operation of structures, as well as for ensuring their durability. Currently, solutions to elastoplastic problems continue to be the focus of researchers' attention. New analytical approaches to solving these problems are emerging, and numerical methods are being improved. The authors contribute to solving the problems of mechanics of deformable solids using conservation laws. The use of conservation laws makes it possible to reduce the finding of the stress tensor components at each point to a contour integral along the boundary of the region under consideration, which makes it possible to construct a previously unknown elastoplastic boundary. The article considers an elastoplastic rod of constant cross-section, which is under the influence of linear hydrostatic pressure and a pair of forces that twist it around a central axis coinciding with the oz axis. The lateral surface of the rod is stress-free and in a plastic state. The constructed conservation laws allow us to find the components of the stress tensor. The components of the stress tensor make it possible to determine the elastoplastic boundary in the rod under consideration.