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A unified Maxwell model with time-varying viscosity via ψ-Caputo fractional derivative coined

Author

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  • Li, Jing
  • Ma, Li

Abstract

In order to describe the mechanical behaviors of viscoelastic materials that couple memory effects and time-varying viscosity properties toggled between thixotropy and rheopexy, this paper explores and establishes the constitutive equation of a unified Maxwell model with a variable kernel in terms of the ψ-Caputo fractional derivative. By virtue of a Volterra integral equation of the second kind and the ψ-Laplace transform technique, the closed-form expressions of creep and relaxation responses for the proposed model are derived and compared in detail. Furthermore, to enhance practicality, the exponential and power-law time-varying viscosity candidates are embedded into the proposed model, along with exhibiting the corresponding creep and relaxation behaviors in light of illustration and reasoning, respectively. The results may provide a fresh perspective for detecting the relationship between the viscoelastic system with nonlinear time-varying viscosity and generalized fractional calculus.

Suggested Citation

  • Li, Jing & Ma, Li, 2023. "A unified Maxwell model with time-varying viscosity via ψ-Caputo fractional derivative coined," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    • Handle: RePEc:eee:chsofr:v:177:y:2023:i:c:s0960077923011323
    DOI: 10.1016/j.chaos.2023.114230
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    References listed on IDEAS

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    1. Garra, R. & Consiglio, A. & Mainardi, F., 2022. "A note on a modified fractional Maxwell model," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    2. Garra, Roberto & Mainardi, Francesco & Spada, Giorgio, 2017. "A generalization of the Lomnitz logarithmic creep law via Hadamard fractional calculus," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 333-338.
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