ИСТИНА

The exact analytical solution of the problem of finite axial shear of a cylindrical layer fixed on the inner surface is obtained. On the outer surface either axial tangential stress or axial movement is specified. The model of hypoelasticity with objective stress rates of the corotation type is adopted: the Jaumann stress rate and the Green-McInnis-Naghdi stress rate. It is assumed that at any point of the layer only the axial displacement differs from zero, and it depends on the radius. Such a motion is isochoric. All components of the Cauchy stress tensor are found and a numerical-graphical illustration of the obtained solutions is presented. The analytical solution of the problem is compared with the numerical solution obtained in the ANSYS software package for the hypoelastic material model using the Green-McInnis-Naghdi stress rate. Analysis of solutions shows the presence of the Poynting effect for the stress tensor.