Abstract
Atangana–Baleanu (AB) fractional derivative solves some outstanding problems in the field of fractional differentiation because of its nonsingular and nonlocal kernel characteristics. It also provides a new research direction for the application of fractional derivatives in the constitutive modeling of rock and soil materials. In this paper, we propose a new AB fractional-order dashpot and use it in a comparative study. We find that the new dashpot has the capability to capture the memory effect of the traditional Riemann–Liouville (RL) fractional-order dashpot. It can also describe the viscoelastic behavior of materials as a function of time. By replacing the Newtonian dashpot with the AB fractional-order dashpot in the Nishihara model, we establish a new AB fractional-derivative (ABFD) creep model. We analytically solve the ABFD creep model by the Laplace transform. The fitting results for the experimental data obtained for rock salt creep show that the ABFD creep model provides a better fitting capability than the Nishihara model and Riemann–Liouville (RL) fractional-derivative model.
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Acknowledgements
This work is supported by the National Natural Science Foundation of China (51827901, 52121003, 52142302), the 111 Project (B14006), and the Yueqi Outstanding Scholar Program of CUMTB (2017A03). The financial supports from the Guizhou Department of Education Youth Talent Growth Project of China ([2019]161) and the Bijie Science and Technology Bureau Joint Fund project of China (G[2019]26) are also gratefully acknowledged. The authors would like to express his heartfelt thanks to the anonymous reviewers for their valuable and constructive comments. The reviewer’s suggestions contributed greatly to the improvement of this work.
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Deng, H., Zhou, H., Wei, Q. et al. A creep constitutive model based on Atangana–Baleanu fractional derivative. Mech Time-Depend Mater 27, 1171–1186 (2023). https://doi.org/10.1007/s11043-022-09560-1
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DOI: https://doi.org/10.1007/s11043-022-09560-1