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Elastoplastic theory of finite deformation and its solution method for non-ordinary state-based peridynamics

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Abstract

The peridynamics is a new meshless method, which has developed rapidly in recent years because of its superiority in dealing with discontinuity problems. In this paper, we established elastoplastic constitutive relations of finite deformation using Jaumann stress rate, Almansi strain rate, von Mises yield criteria, associated flow and isotropic hardening rule under the framework of non-ordinary state-based peridynamics. Further, the updated Lagrange solution method to the constitutive relation has also been proposed. We applied the solution to simulate the large elastoplastic tensile deformation of a rod and necking of a cylindrical bar, and the results are consistent with the analytical solution and the experimental results, separately. Our findings prove that the theory and method proposed in this paper are applicable to the analysis of elastoplastic finite deformation.

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Acknowledgements

This study was funded by the NSAF of China (Grant No. U183010034).

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Authors and Affiliations

  1. School of Sciences, Nan**g University of Science and Technology, Nan**g, 210094, Jiangsu, China

    Hongxiang Li & Dingguo Zhang

  2. Institute of Systems Engineering, China Academy of Engineering Physics, Mianyang, 621999, Sichuan, China

    Hongxiang Li, Zhiming Hao, Pan Li & **aolong Li

  3. Shock and Vibration of Engineering Materials and Structures Key Laboratory of Sichuan Province, Mianyang, 621999, Sichuan, China

    Zhiming Hao

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  1. Hongxiang Li
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Correspondence to Zhiming Hao.

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Li, H., Hao, Z., Li, P. et al. Elastoplastic theory of finite deformation and its solution method for non-ordinary state-based peridynamics. Meccanica 57, 2809–2820 (2022). https://doi.org/10.1007/s11012-022-01600-x

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