Pipe Flow of Plastic Materials

Abstract

Plastic materials behave as both solids and fluids. When forced to move in a pipe, they flow as a solid plug with a slipping boundary. Depending on the cross-sectional shape of the pipe, the slipping boundary may not coincide with the inner boundary of the pipe. When such is the situation, there exist dead regions in the flow. This is undesirable when the material is time degradable as those encountered in the food processing and chemical industry. Two formulations of nonlinear programming problems governing the pipe flow are presented. They correspond, respectively, to the lower bound and upper bound theorems of plasticity. An efficient method is developed for the nonlinear programming problem formulated from the upper bound theorem. Application of the method to two examples are demonstrated.