The Bi-Potential Theory Applied to Non-Associated Constitutive Laws

ZHOU Yang-jing; FENG Zhi-qiang; NING Po

doi:10.3879/j.issn.1000-0887.2015.08.001

Volume 36 Issue 8

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ZHOU Yang-jing, FENG Zhi-qiang, NING Po. The Bi-Potential Theory Applied to Non-Associated Constitutive Laws[J]. Applied Mathematics and Mechanics, 2015, 36(8): 787-804. doi: 10.3879/j.issn.1000-0887.2015.08.001

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The Bi-Potential Theory Applied to Non-Associated Constitutive Laws

doi: 10.3879/j.issn.1000-0887.2015.08.001

School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, P.R.China

Funds: The National Natural Science Foundation of China（11372260）

Received Date: 2015-04-28
Rev Recd Date: 2015-07-06
Publish Date: 2015-08-15

Abstract

Abstract

The explicit integration algorithm based on the traditional plastic mechanics framework and the implicit integration algorithm proposed by Simo-Taylor were 2 classic constitutive integration algorithms widely used in solid mechanics. These 2 algorithms were reviewed respectively with the 2 corresponding classic non-associated constitutive models: the Drucker-Prager model and the Armstrong-Frederick model as the examples. Then, according to the bi-potential theory and with the bi-potential concept applied to the material free energy, solid materials were divided into explicit standard materials and implicit standard ones. It was verified that the 2 classic integration algorithms both can effectively deal with explicit standard materials. However, in dealing with implicit standard materials, the orthogonality cannot be guaranteed in a unified form with the classic methods. The bi-potential algorithm has its own advantage in dealing with both explicit and implicit standard materials. The solution existence of the bi-potential integration algorithm was derived based on the variational principle. Furthermore, the results of the bi-potential algorithm and the classic algorithms were compared through calculation of the Drucker-Prager and Armstrong-Frederick models, and the accuracy and stability of the bi-potential algorithm were proved.
- bi-potential integration algorithm,
- explicit/implicit integration algorithm,
- non-associated constitutive law,
- D-P model,
- A-F model

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References(32)

References

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