Plastic Flow in a Thin Layer: the Theory, Formulations of the Boundary- Value Problems and the Applications

Abstract

Two-dimensional, averaged over the thickness of the layer, mathematical theory of the spreading of a plastic layer on the plane has been studied. General and simplified mathematical formulations of boundary value problem were presented. The problem of plastic stretching of a strip by forces applied on its “clamped” ends was investigated. The analysis of various modes of the process was carried out, which are determined by both the total compression force of the ends and the total tensile force. Mathematical analogy between the process of the free spreading of a plastic layer on the plane and the process of heat transfer was studied. For known forms of a domain occupied by a thin plastic layer at the initial time and for a given law of convergence of the plates, the evolution of the boundary of a plastic layer spreading was described. The exact particular solutions of the aforementioned problem was obtained.