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Rheological analysis of the general fractional-order viscoelastic model involving the Miller–Ross kernel

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Abstract

The present work is mainly stimulated by the definition of the general fractional-order derivative operator (GFODO) involving the Miller–Ross kernel in the sense of the Liouville–Sonine type. The novel emphasis is the introduction of the GFODO within the Miller–Ross kernel into the Maxwell model and Kelvin–Voigt model, thereby constructing viscoelastic constitutive models with the property of inheritance and memorability. It is noteworthy that the fractional viscoelasticity can capture the strain response within a wide range of strain rates. The procedure used in our paper to calculate the creep compliance of the proposed model is the Laplace transform, and then comparisons between the general fractional-order models and the classical integer-order models are presented. In summing up, it may be stated that the general fractional-order Kelvin–Voigt model exhibits a very different behavior compared to the classical Kelvin–Voigt model and it can describe the whole creep process including the accelerated creep stage.

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Acknowledgements

This work was supported by the Yue-Qi Scholar of the China University of Mining and Technology (Grant No. 102504180004).

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Authors and Affiliations

  1. School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou, 221116, Jiangsu, China

    Yi-Ying Feng, Xiao-Jun Yang, Jian-Gen Liu & Zhan-Qing Chen

  2. State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou, 221116, Jiangsu, China

    Yi-Ying Feng, Xiao-Jun Yang, Jian-Gen Liu & Zhan-Qing Chen

  3. School of Mathematics, China University of Mining and Technology, Xuzhou, 221116, Jiangsu, China

    Xiao-Jun Yang & Jian-Gen Liu

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  1. Yi-Ying Feng
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Feng, YY., Yang, XJ., Liu, JG. et al. Rheological analysis of the general fractional-order viscoelastic model involving the Miller–Ross kernel. Acta Mech 232, 3141–3148 (2021). https://doi.org/10.1007/s00707-021-02994-7

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