Application of the perturbation method for the determination of stress-strain state of a thick-style two-layer anisotropic shaft of non-circular cross section with elastoplastic torsion

The present work is devoted to the problem of elastoplastic torsion of the two-layer slightly anisotropic non-circular cross section shaft. The cross section is a doubly connected region. The shaft is oriented in a cylindrical coordinate system so that the $Z$ axis is directed along the axis of the shaft. The influence of mass forces is not taken into account. Let the rod twist about the $Z$ axis by equal and opposite pairs of forces. Suppose that the lateral surface of the rod is free of loads. The value of the moment is such that for some parts of the cross section the material passes into a plastic state and plastic zones are formed. The propagation of plastic flow comes from the outer contour inside the section. Suppose that the value of the torque is such that the plastic region entirely covers the outer contour of the cross section, and there is an elastoplastic boundary that is located between the inner contour and the interface of the layers. It is considered as an anisotropic material that in particular cases is in the kinematic properties of the anisotropy and anisotropy according to Hill. Each of the layers has its own anisotropy parameters. With using perturbation method, stress-strain state and elastoplastic boundary at first approximate is defined.