Relations between cubic equation, stress tensor decomposition, and von Mises yield criterion  

作　　者：Haoyuan GUO Liyuan ZHANG Yajun YIN Yongxin GAO 

机构地区：[1]Department of Engineering Mechanics, Tsinghua University [2]School of Mechanical Engineering, University of Science and Technology Beijing [3]Department of Mathematics, Tianjin University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2015年第10期1359-1370,共12页应用数学和力学（英文版）

基　　金：supported by the National Natural Science Foundation of China(Nos.11072125 and11272175);the Specialized Research Fund for the Doctoral Program of Higher Education of China(No.20130002110044);the China Postdoctoral Science Foundation(No.2015M570035)

摘　　要：Inspired by Cardano＇s method for solving cubic scalar equations, the addi- tive decomposition of spherical/deviatoric tensor （DSDT） is revisited from a new view- point. This decomposition simplifies the cubic tensor equation, decouples the spher- ical/deviatoric strain energy density, and lays the foundation for the von Mises yield criterion. Besides, it is verified that under the precondition of energy decoupling and the simplest form, the DSDT is the only possible form of the additive decomposition with physical meanings.Inspired by Cardano＇s method for solving cubic scalar equations, the addi- tive decomposition of spherical/deviatoric tensor （DSDT） is revisited from a new view- point. This decomposition simplifies the cubic tensor equation, decouples the spher- ical/deviatoric strain energy density, and lays the foundation for the von Mises yield criterion. Besides, it is verified that under the precondition of energy decoupling and the simplest form, the DSDT is the only possible form of the additive decomposition with physical meanings.

关 键 词：Cardano＇s method Caylay-Hamilton theorem cubic tensor equation decomposition of spherical/deviatoric tensor （DSDT） von Mises yield criterion 

分 类 号：O344.1[理学—固体力学]