An Effective Characteristic Method for Plastic Plane Stress Problems

Abstract

Based on the maximum stress deviator yield criterion and the associated flow rule, the quasi-linear differential equation systems of stress and velocity fields in the plane stress problem of an ideal rigid-plastic body are established in this paper. Judgements on the types of these differential equation systems are made by using the theory of characteristics. They may be elliptic or hyperbolic, depending on the considered stress state. In the hyperbolic case, equations of two families of characteristics and relations connecting the stress or velocity components along characteristics are derived. Three examples are given to illustrate the application of the aforementioned method of characteristics derived. As a conclusion, the effectiveness and advantages of this method compared with those based on the von Mises and Tresca yield criteria are expounded in the last section of this paper.