THE DESCRIPTION OF DEVIATORIC STRESS IN THE \pi PLANE OF PRINCIPAL STRESS SPACE: A COORDINATE TRANSFORMATION METHOD¹⁾

The description of deviatoric stress in the \pi plane of principal stress space is an important teaching content of “elasticity and plasticity”, which is the theoretic foundation of the follow-up courses (e.g., yield criterion, plastic constitutive relation, etc.). The contents in current related textbooks tend to confuse the readers. In order to solve this problem, we present a coordinate transformation method, so as to obtain the relationship between components of stress in principal stress space and deviatoric stress in \pi plane. Our appoach gives a simple and clear mathematical idea, and could be adopted in textbook for “elasticity and plasticity” in future.