坐标变换法描述主应力空间中π平面上的应力偏量  

THE DESCRIPTION OF DEVIATORIC STRESS IN THEπPLANE OF PRINCIPAL STRESS SPACE:A COORDINATE TRANSFORMATION METHOD

作　　者：王秀锋 赵颖涛[2] WANG Xiufeng;ZHAO Yingtao(School of Materials Science and Engineering,Xiangtan University,Xiangtan 411105,Hunan,China;School of Aerospace Engineering,Beijing Institute of Technology,Beijing 100081,China)

机构地区：[1]湘潭大学材料科学与工程学院,湖南湘潭411105 [2]北京理工大学宇航学院,北京100081

出　　处：《力学与实践》2022年第1期171-174,共4页Mechanics in Engineering

基　　金：国家自然科学基金(11872326,12172319);教育部第二批新工科研究与实践项目(E-SXWLHXLX20202602);湖南省青年骨干教师项目(湘教通[2018]356号);湖南省普通高校教改项目(湘教通[2018]291号)资助。

摘　　要：主应力空间中π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π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。The description of deviatoric stress in theπplane 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 inπplane.Our appoach gives a simple and clear mathematical idea,and could be adopted in textbook for“elasticity and plasticity”in future.

关 键 词：π平面 主应力空间 坐标变换 应力偏量 

分 类 号：O344[理学—固体力学]