Abstract
A system of equations modeling the dynamic stretching of a homogeneous circular layer of incompressible ideally rigid-plastic transversely isotropic material obeying the Mises–Hencky criterion is studied. The upper and lower bases are stress-free, the radial velocity is set at the lateral boundary, and the possibility of thickening or thinning of the layer is taken into account, which simulates neck formation and further development of the neck. Using the method of asymptotic integration, two characteristic stretching modes are identified, that is, the relations of dimensionless parameters are determined, in which consideration of inertial terms is necessary. When considering the regime associated with the achievement of acceleration on the side face of its critical values, an approximate solution of the problem was constructed.