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

doi:10.1007/s10483-015-1988-9

Applied Mathematics and Mechanics (English Edition) ›› 2015, Vol. 36 ›› Issue (10): 1359-1370.doi: https://doi.org/10.1007/s10483-015-1988-9

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

Haoyuan GUO¹, Liyuan ZHANG², YajunYIN¹, Yongxin GAO³

1. Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China;
2. School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083, China;
3. Department of Mathematics, Tianjin University, Tianjin 300072, China

Received:2014-10-08 Revised:2015-03-04 Online:2015-10-01 Published:2015-10-01
Contact: Liyuan ZHANG E-mail:zhangly@ustb.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 11072125 and 11272175), the Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 20130002110044), and the China Postdoctoral Science Foundation (No. 2015M570035)

Abstract

Abstract: Inspired by Cardano's method for solving cubic scalar equations, the additive decomposition of spherical/deviatoric tensor (DSDT) is revisited from a new viewpoint. This decomposition simplifies the cubic tensor equation, decouples the spherical/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.

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

2010 MSC Number:

Haoyuan GUO, Liyuan ZHANG, YajunYIN, Yongxin GAO. Relations between cubic equation, stress tensor decomposition, and von Mises yield criterion. Applied Mathematics and Mechanics (English Edition), 2015, 36(10): 1359-1370.

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

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