引用本文: 王秀锋, 赵颖涛. 坐标变换法描述主应力空间中π平面上的应力偏量1)[J]. 力学与实践, 2022, 44(1): 171-174.
WANG Xiufeng, ZHAO Yingtao. THE DESCRIPTION OF DEVIATORIC STRESS IN THE $\pi$ PLANE OF PRINCIPAL STRESS SPACE: A COORDINATE TRANSFORMATION METHOD1)[J]. MECHANICS IN ENGINEERING, 2022, 44(1): 171-174.
 Citation: WANG Xiufeng, ZHAO Yingtao. THE DESCRIPTION OF DEVIATORIC STRESS IN THE $\pi$ PLANE OF PRINCIPAL STRESS SPACE: A COORDINATE TRANSFORMATION METHOD1)[J]. MECHANICS IN ENGINEERING, 2022, 44(1): 171-174.

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

• 摘要: 主应力空间中\pi平面上应力偏量的描述是弹塑性力学课程的基本知识点,是学习屈服准则和塑性本构关系的理论基础。本文根据常用的坐标变换方法,建立了主应力空间中任意应力分量与\pi平面上应力偏量的对应关系,推导过程简洁且数学思路清晰,是对现有弹塑性力学教材中该知识点是一个有益的补充。

Abstract: 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.

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