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Time Integration Algorithms for Elasto-Viscoplastic Models with Multiple Hardening Laws for Geomaterials: Enhancement and Comparative Study

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Abstract

To describe the behaviours of geomaterials such as time-dependency, anisotropy and destructuration, multiple hardening parameters and laws are generally needed for application in advanced elasto-viscoplastic models. Time integration with stress updating is a key step in the application of elasto-viscoplastic models to engineering practice. However, the robustness of time integration algorithms for such complicated models has rarely been studied, creating difficulties in selecting and improving algorithms. This paper focuses on use of three typical implicit time integration algorithms—Katona, Stolle and cutting plane—for integration of an advanced elasto-viscoplastic model. First, all selected algorithms are improved to fit the characteristics of the advanced model with multiple hardening parameters and are combined with adaptive substepping procedures to enhance their performance. Then a step-changed undrained triaxial test is simulated at the integration point level, on the basis of which variations in iteration number and relative error of stresses with step size are investigated and compared. Furthermore, the advanced model using different algorithms is implemented into finite element code, with global convergence and calculation time investigated and compared for two boundary value problems: a biaxial test and an embankment. All comparisons demonstrate that the modified cutting plane algorithm with substepping is the most robust and efficient one, followed by the modified Stolle with substepping and the modified Katona with substepping, for an advanced model with multiple hardening parameters.

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Acknowledgements

The financial supports provided by the research project (Grant No. 15217220, N_PolyU534/20) of Research Grants Council of Hong Kong, the Fundamental Research Funds for the Central Universities (Grant No. 2019JBM083) and the National Natural Science Foundation of China (Grant No. U2034204) are gratefully acknowledged.

Funding

The financial supports provided by the research project (Grant No. 15217220, N_PolyU534/20) of Research Grants Council of Hong Kong, the Fundamental Research Funds for the Central Universities (Grant No. 2019JBM083) and the National Natural Science Foundation of China (Grant No. U2034204) are gratefully acknowledged.

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Authors and Affiliations

  1. Key Laboratory of Urban Underground Engineering of Ministry of Education, Beijing Jiaotong University, Beijing, 100044, China

    Jian Li

  2. School of Civil Engineering, Beijing Jiaotong University, Beijing, 100044, China

    Jian Li

  3. Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

    Zhen-Yu Yin

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  1. Jian Li
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Appendix: Model Parameters of Anicreep

Appendix: Model Parameters of Anicreep

State parameters and constants of ANICREEP model are summarised in Table 7 with their definitions and determination methods. Alternatively, these parameters can also be easily identified by optimization methods as demonstrated by Yin et al. [38] and Jin and Yin [41].

Table 7 State parameters and constants of ANICREEP model for intact natural soft clays
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Li, J., Yin, ZY. Time Integration Algorithms for Elasto-Viscoplastic Models with Multiple Hardening Laws for Geomaterials: Enhancement and Comparative Study. Arch Computat Methods Eng 28, 3869–3886 (2021). https://doi.org/10.1007/s11831-021-09527-4

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