Dynamic Axisymmetric Tension of a Thin Round Ideally Rigid-Plastic Layer

We consider the stress-strain state that occurs during dynamic tension of a homogeneous round layer of an incompressible ideally rigid-plastic material that obeys the Mises–Genka criterion. The upper and lower bases are stress-free, and the radial velocity is set on the lateral boundary. The possibility of thickening or thinning of the layer is taken into account, which simulates neck formation and further development of the neck. Two characteristic tension modes are revealed. First one is associated with a rather high rate of removal of the side boundary of the layer from the center, the second one is associated with acceleration. In the second case, we have carried out an analysis using the method of asymptotic integration, which makes it possible to approximately find the parameters of the stress-strain state.