A Unified Characteristic Theory for Plastic Plane Stress and Strain Problems

Abstract

Based on the unified strength criterion, a characteristic theory for solving the plastic plane stress and plane strain problems of an ideal rigid-plastic body is established in this paper, which can be adapted for a wide variety of materials. Through this new theory, a suitable characteristic method for material of interest can be obtained and the relations among different sorts of characteristic methods can be revealed. Those characteristic methods on the basis of different strength criteria, such as Tresca, von Mises, Mohr-Coulomb, twin shear (TS) and generalized twin shear (GTS), are the special cases (Tresca, Mohr-Coulomb, TS, and GTS) or linear approximation (von Mises) of the proposed theory. Moreover, a series of new characteristic methods can be easily derived from it. Using the proposed theory, the influence of yield criterion on the limit analysis is analyzed. Two examples are given to illustrate the application of this theory.