On the Dynamic Tension of a Thin Round Perfectly Rigid-Plastic Layer Made of Transversely Isotropic Material

We study a system of equations modeling the dynamic tension of a homogeneous roundlayer of incompressible perfectly rigid-plastic transversely isotropic material obeying theMises–Hencky criterion. The upper and lower bases are stress-free, the radial velocity is set on thelateral boundary, and the possibility of thickening or thinning of the layer, simulating formationand further development of a neck, is taken into account. Using the method of asymptoticintegration, two characteristic tension modes are identified, that is, relations of dimensionlessparameters are determined that necessitate taking into account inertial terms. An approximatesolution of the problem is constructed when considering the mode associated with the accelerationon the lateral face reaching its critical values.