Coordinate Systems for Plastic Yield Surfaces Stress and Strain Space Theories

摘要

In stress space, the expressions for yield criteria are given as functions of the principal stresses sigma 1, sigma 2 and sigma 3, or alternatively the cartesian components sigma ij, and in strain space as functions of epsilon 1, epsilon 2 and epsilon 3 or epsilon ij. Because the yield surfaces are associated with components in the pi plane, these functions are not always easily obtained. In the paper, intermediate variables X1, X2, X3 associated with the pi plane are introduced (X3 being coincident with the deviatoric axis). It is found that the yield functions are easily expressed in the chosen coordinate system. These coordinate axes may be used to obtain the expressions for the elasto-plastic constitutive matrices used in the finite element analysis. The theory is developed for both stress space and strain space as it is anticipated that the later formulation has an important place in the application of elasto-plastic analysis.