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General Description of Elastoplastic Deformation/Sliding Phenomena of Solids in High Accuracy and Numerical Efficiency: Subloading Surface Concept

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Abstract

The hypoelastic-based plastic constitutive model has been developed to describe the wide class of elastoplastic deformation behavior of solids. The physical and mathematical backgrounds of the hypoelastic-based plasticity, i.e. (i) the transformation of the material-time derivative of general scalar-valued tensor function to the corotational-time derivative required for the derivation of the consistency condition fulfilling the objectivity, (ii) the requirement for the derivation of the additive decomposition of the strain rate and the continuum spin into the elastic and the plastic parts from the multiplicative decomposition of the deformation gradient, (iii) the mechanical requirements for elastoplastic constitutive equations, i.e. the continuity and the smoothness conditions and (iv) the derivation of the general loading criterion are deliberated first. Then, the subloading surface model is formulated in the framework of the hypoelastic-based plasticity. It materializes the pertinent descriptions of wide classes of deformations, i.e. the monotonic, the non-proportional and the cyclic loadings, the rate-dependent deformation behavior in a general rate up to the impact load for wide classes of materials, e.g. metals and soils and the friction phenomena between solids and further the deformation behavior of metallic materials within the framework of the crystal plasticity. In addition, it possesses the distinctive advantage in numerical analysis such that the judgment of yielding is not required in the loading criterion and the stress is automatically attracted to the yield surface in the plastic loading process, engendering a high efficiency in numerical calculations.

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Acknowledgements

The author would like to express his sincere gratitude to Professor Genki Yagawa (Emeritus Professor, University of Tokyo and Toyo University) for inviting the author to present this monograph. He is indebted to his former students at Kyushu University, who have discussed and collaborated for a long time during work undertaken until retirement: Prof. M. Ueno (currently Prof., Univ. Ryukyus), Dr. T. Okayasu (currently Assoc. Prof., Kyushu Univ.), Dr. S. Tsutsumi (currently Assoc. Prof., Osaka Univ.), and Dr. S. Ozaki (currently Assoc. Prof., Yokohama Natl. Univ.), Dr. T. Ozaki (Kyushu Electric Eng. Consult. Inc.) and to the engineers: Dr. T. Mase (Tokyo Electric Power Services Co., Ltd) and Dr. K. Okamura, Dr. N. Suzuki and Mr. T. Kuwayama (Nippon Steel & Sumitomo Metal Corporation) for the collaborations. The particular gratitude is dedicated to Prof. Y. Yamakawa (Tohoku Univ.) for the close collaborations and the valuable discussions and advices.

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  1. Joining and Welding Research Institute, Osaka University, Mihogaoka 11-1, Ibaragi-shi, 567-0047, Osaka, Japan

    Koichi Hashiguchi

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K. Hashiguchi is Emeritus professor of Kyushu University.

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Hashiguchi, K. General Description of Elastoplastic Deformation/Sliding Phenomena of Solids in High Accuracy and Numerical Efficiency: Subloading Surface Concept. Arch Computat Methods Eng 20, 361–417 (2013). https://doi.org/10.1007/s11831-013-9089-1

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