The role of the weight function in the generalised distributed-order Maxwell model: The case of a distributed-springpot and a dashpot

Abstract

In this work, our focus is on investigating the significance of the weighting function (c(α)) in the Generalised Distributed-Order Maxwell (GDOM) model. The GDOM model comprises a distributed springpot and a dashpot in series, rendering it more intricate than the Fractional Viscoelastic Fluid - FVF model (consisting of only one springpot and one dashpot in series). However, the GDOM model remains simple enough to facilitate a better comprehension of its behaviour in various flow scenarios, such as relaxation, creep compliance, steady shear viscosity, and small amplitude oscillatory shear. To validate our findings, we conduct fitting analyses using experimental data, which affirm that the single-element model demonstrates solid-like viscoelastic behaviour at low frequencies, while the GDOM model exhibits fluid-like viscoelastic behaviour, accurately capturing the rubbery plateau and transition region observed in polymer systems.