Saint-Venant flow in a thin layer under plastic compression

Abstract

The flow of perfectly rigid-plastic material in a thin layer subjected to a load was considered in numerous studies, including the classical ones [1–12]. In the case of rigid plates coinciding with the layer face surfaces and approaching each other in a prescribed way, we deal with the Prandtl problem, which was considered in [1], or with its numerous generalizations (e.g., see [13, 14]). Traditionally, the process of obtaining the Prandtl solution is based on the hypothesis that the tangential stress is linear in thickness and hence the tangential stress attains its maximum absolute value on the surfaces of the rough plates.