Flows of Thin Perfectly Rigid-Plastic Bodies: Dynamic Modes and Necking

The presented review consists of two parts. The first one is devoted to research generalizing the classical Prandtl problem in the case of taking into account the inertia of the convergence of rigid plates and dynamic effects occurring in a thin perfect rigid plastic layer. The second part examines the work related to the formation and development of the neck in plastic materials under quasi-static and dynamic loading. In particular, attention is paid to thin solids with a perturbed boundary shape, which have technological significance. The presence of a small geometric parameter allows the use of asymptotic methods.