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

Abstract

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