Fractional creep and relaxation models of viscoelastic materials via a non-Newtonian time-varying viscosity: physical interpretation

Non-water reactive polymer grouting technology is an important means to control water-induced engineering disaster emergency rescue. However, the time-varying viscosity of polymer slurry and the expansion force of slurry reaction are the main factors affecting the grouting treatment effect. Therefore, it is necessary to study the time-varying viscosity of polymer slurry and the expansion force of slurry reaction. Firstly, the expansion rate of polymer slurry with different expansion ratio is tested and checked by the self-made expansion rate measuring cylinder. Then, the reaction expansion force and viscosity of polymer slurry with different expansion ratio are tested and studied by the expansion force testing device and NDJ-5T digital rotational viscometer. The results show that the expansion rate of polymer slurry used in this paper is basically the same as the factory instructions At the same time, the viscosity of polymer slurry increases exponentially with time, and the curve is steeper, that is to say, the viscosity increases rapidly with time.

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A novel representation of time-varying viscosity with power-law and comparative study

International Journal of Non-Linear Mechanics ◽

10.1016/j.ijnonlinmec.2019.103372 ◽

2020 ◽

Vol 119 ◽

pp. 103372

Author(s):

Xu Yang ◽

Wei Cai ◽

Yingjie Liang ◽

Sverre Holm

Keyword(s):

Comparative Study ◽

Power Law ◽

Time Varying ◽

Varying Viscosity ◽

Representation Of Time

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Fractional derivative modeling of time-varying viscosity materials considering initial loading ramp in real experiments

Mathematics and Mechanics of Solids ◽

10.1177/1081286521995233 ◽

2021 ◽

pp. 108128652199523

Author(s):

Teng Su ◽

Hongwei Zhou ◽

Jiawei Zhao ◽

Daniel Dias

Keyword(s):

Fractional Derivative ◽

Superposition Principle ◽

Maxwell Model ◽

Step Function ◽

Parameter Determination ◽

Time Varying ◽

Loading Conditions ◽

Experimental Time ◽

Initial Loading ◽

Varying Viscosity

The fractional derivative models with time-varying viscosity have been used in characterizing creep or relaxation properties of different viscoelastic material, and many combination models were presented using the Boltzmann superposition principle. However, those models defined as initial ones in this manuscript usually ignored the initial loading ramp, and the ideal-loading condition is commonly assumed as a step function in modeling. The real-loading conditions of tested samples are usually a ramp load followed by constant stress or strain. The difference in loading conditions between the theoretical modeling and experimental procedure strongly influences the models’ rheological property characterization and parameter determination. It is especially the case for the fractional derivative model due to its memory or history-dependent characters, even though the ramp time is short compared with the total experimental time. An application example of the Maxwell model with time-varying viscosity Scott–Blair model (TVSM) shows that the initial loading ramp has a strong influence. To solve this problem, the authors propose modified models of TVSM based on real-loading conditions. The relative errors between initial and modified models are presented. In addition, a history-dependent optimization algorithm for parameter determination is proposed. Three sets of polymer experimental data are employed to suggest that the fitting results of models disregarding initial ramp loads are unreliable. The modified model should be used for characterizing rheological behavior, as this leads to obtaining the best fitting results even for a short experimental time.

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