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

Jing Li and Li Ma

Chaos, Solitons & Fractals, 2023, vol. 177, issue C

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.

Keywords: Time-varying viscosity; ψ-fractional calculus; Constitutive equation; Creep and relaxation (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:177:y:2023:i:c:s0960077923011323

DOI: 10.1016/j.chaos.2023.114230

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