Fractional viscoelastic models: master curve construction, interconversion, and numerical approximation

Consumer products, such as foods, contain numerous polymeric and particulate additives that play critical roles in maintaining their stability, quality and function. The resulting materials exhibit complex bulk and interfacial rheological responses, and often display a distinctive power-law response under standard rheometric deformations. These power laws are not conveniently described using conventional rheological models, without the introduction of a large number of relaxation modes. We present a constitutive framework using fractional derivatives to model the power-law responses often observed experimentally. We first revisit the concept of quasiproperties and their connection to the fractional Maxwell model (FMM). Using Scott-Blair's original data, we demonstrate the ability of the FMM to capture the power-law response of 'highly anomalous' materials. We extend the FMM to describe the viscoelastic interfaces formed by bovine serum albumin and solutions of a common food stabilizer, Acacia gum. Fractional calculus allows us to model and compactly describe the measured frequency response of these interfaces in terms of their quasiproperties. Finally, we demonstrate the predictive ability of the FMM to quantitatively capture the behaviour of complex viscoelastic interfaces by combining the measured quasi-properties with the equation of motion for a complex fluid interface to describe the damped inertio-elastic oscillations that are observed experimentally.

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“…In this paper, we use the Caputo derivative for fractional differentiation, which is defined as [32][33][34] …”

Section: Mathematical Preliminaries (A) Definitionsmentioning

confidence: 99%

Power-law rheology in the bulk and at the interface: quasi-properties and fractional constitutive equations

2013

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“…However, this function has proven not applicable to all the mixes [25]. Other pre-smoothing methods can be found elsewhere [23,[26][27][28]. Another critical issue is that the existing fitting methods mostly involve sophisticated rheological expertise and empirical operations, which significantly reduces the efficiency for analysis.…”

Section: Introductionmentioning

confidence: 96%

A unified procedure for rapidly determining asphalt concrete discrete relaxation and retardation spectra

Sun

Huang

Chen

2015

Construction and Building Materials

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“…Thus, time‐temperature superposition principle needs to be coupled with the fractional viscoelastic constitutive model. For thermorheologically simple materials, the shift factor for each branch follows the same rule, and in each branch the effect of changing temperature is simply to horizontally shift the viscoelastic response as a function of frequency, that is,

a true(T true) = \frac{τ (T)}{τ (T_{normalr})}

where τ ( T r ) is the reference relaxation time at the reference temperature T r , and a ( T ) is the time‐temperature shift factor. The shift factor is commonly used by empirical equations, among which the Williams–Landel–Ferry (WLF) equation shown in eq is the most commonly used.…”

Section: The Novel Constitutive Modelmentioning

confidence: 99%

A novel fractional viscoelastic constitutive model for shape memory polymers

Pan

2018

J Polym Sci B Polym Phys

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Shape memory polymers (SMPs) are a class of smart materials which can recover from a deformed shape to their original shape by a certain external stimulus. To predict the deformation behaviors of SMPs, different constitutive models have been developed in the last few years. However, most of the constitutive models need many parameters to be determined by specific experiments and complex calibration processes. This drawback has limited their application in promoting the development of SMPs. Thus, it is imperative to develop a new constitutive model which is not only accurate, but also relatively simple. In our work, a novel fractional viscoelastic constitutive model coupling with time‐temperature superposition principle is first proposed for SMPs. Then, frequency sweep and temperature sweep experiments are conducted to determine the parameters of the model. Finally, the shape memory free recovery experiments are carried out to validate the predictive capability of the developed model. By comparing the predicted results with experimental data, we find that though our model has only eleven parameters in total, it could capture the thermomechanical behaviors of SMPs in very good agreement with experimental results. We hope the proposed new model provide researchers with guidelines in designing and optimizing of SMP applications. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018, 56, 1125–1134

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Fractional viscoelastic models: master curve construction, interconversion, and numerical approximation

Cited by 38 publications

References 38 publications

Power-law rheology in the bulk and at the interface: quasi-properties and fractional constitutive equations

Power-law rheology in the bulk and at the interface: quasi-properties and fractional constitutive equations

A unified procedure for rapidly determining asphalt concrete discrete relaxation and retardation spectra

A novel fractional viscoelastic constitutive model for shape memory polymers

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