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

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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.

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Authors and Affiliations

  1. Department of Engineering Mechanics, Tsinghua University, Beijing, 100084, China

    Haoyuan Guo & Yajun Yin

  2. School of Mechanical Engineering, University of Science and Technology Beijing, Beijing, 100083, China

    Liyuan Zhang

  3. Department of Mathematics, Tianjin University, Tianjin, 300072, China

    Yongxin Gao

Authors
  1. Haoyuan Guo
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  2. Liyuan Zhang
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  3. Yajun Yin
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  4. Yongxin Gao
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Corresponding author

Correspondence to Liyuan Zhang.

Additional information

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)

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Guo, H., Zhang, L., Yin, Y. et al. Relations between cubic equation, stress tensor decomposition, and von Mises yield criterion. Appl. Math. Mech.-Engl. Ed. 36, 1359–1370 (2015). https://doi.org/10.1007/s10483-015-1988-9

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  • DOI: https://doi.org/10.1007/s10483-015-1988-9

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Chinese Library Classification

2010 Mathematics Subject Classification

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