Elastic-plastic torsion of a two-layer rod

We study the elastic-plastic torsion of a two-layer rod under the action of torque in this article. It is assumed that the rod consists of two layers. Each layer has its own elastic properties, but the plastic properties of both layers are the same. The contact boundary of the layers is located along the oh axis. The lateral boundary of the rod is stress-free, displacements and stresses are continuous at the interface. The components of the stress tensor at a point are calculated using contour integrals derived from conservation laws calculated along the lateral boundary. Next, the second invariant of the stress tensor is compared with the yield strength. At those points where the yield point is reached, the plastic state is realized, in the rest - elastic. This allows you to build a boundary between the plastic and elastic regions. This technique provides a way to calculate elastic-plastic boundaries for the main rolling profiles of rods. This is supposed to be done in subsequent works. We remind you that earlier, with the help of conservation laws, the main 35 boundary value problems for a plastic two-dimensional medium, elastic-plastic torsion of isotropic rods and elastic media for bodies of finite dimensions were solved.