An analogy between rectilinear flow of plastic solids and Saint-Venant torsion

Abstract

This paper presents a new analogy between steady rectilinear flow of plastic materials and Saint-Venant torsion of elastic bars. Material behaviour is modelled as rigid/linear-hardening in conjunction with the von Mises flow rule. Focusing attention on steady flow through pipes with simply connected cross sections and perfectly rough walls, we arrive at a Dirichlet-type problem. The mathematical formulation of this problem is analogous to that of Saint-Venant torsion of elastic bars. This analogy provides a number of exact solutions for steady rectilinear flow of plastic materials, through pipes with various cross sections. A few simple examples are discussed with emphasis on the growth of plastic boundary layers induced by wall friction. The influence of stress singularities near corners, at the boundary, is also investigated.