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Polymers 2018, 10(9), 988;

Limitations of Viscoelastic Constitutive Models for Carbon-Black Reinforced Rubber in Medium Dynamic Strains and Medium Strain Rates

School of Engineering and Materials Science, Queen Mary University of London, Mile End Rd, London E1 4NS, UK
Japan Agency for Marine-Earth Science and Technology, Department of Mathematical Science and Advanced Technology (MAT), Yokohama Institute for Earth Sciences (YES) 3173-25, Showa-Machi, Kanazawa-Ku, Yokohama, Kanagawa 236-0001, Japan
Jaguar Land Rover, Banbury Road, Gaydon CV35 0RR, UK
Author to whom correspondence should be addressed.
Received: 26 July 2018 / Revised: 29 August 2018 / Accepted: 30 August 2018 / Published: 4 September 2018
(This article belongs to the Special Issue Elastomers)


Modelling the viscoelastic behavior of rubber for use in component design remains a challenge. Most of the literature does not consider the typical regimes encountered by anti-vibration devices that are deformed to medium dynamic strains (0.5 to 3.5) at medium strain rates (0.5/s to 10/s). Previous studies have either focused on the behaviour at small strains and small strain rates or in fast loading conditions that result in low cycle fatigue or tearing phenomena. There is a lack of understanding of the dynamic response of natural rubber suspension components when used in real vehicle applications. This paper presents a review of popular viscoelastic nonlinear constitutive models and their ability to model the mechanical behaviour of typical elastomer materials such as Natural Rubber (NR) incorporating different PHR (Parts per Hundred Rubber, XX) of carbon black. The range of strain and strain rate are typical for the materials used in rubber suspensions when operating in severe service operating conditions, such as over rough terrain or over pot-holes. The cyclic strain is applied at different amplitudes and different strain rates in this medium strain range. Despite the availability of many models in the literature, our study reports that none of the existing models can fit the data satisfactorily over a wide range of conditions. View Full-Text
Keywords: viscoelastic behaviour; filled rubber; hysteresis; stress softening; review viscoelastic behaviour; filled rubber; hysteresis; stress softening; review

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Carleo, F.; Barbieri, E.; Whear, R.; Busfield, J.J.C. Limitations of Viscoelastic Constitutive Models for Carbon-Black Reinforced Rubber in Medium Dynamic Strains and Medium Strain Rates. Polymers 2018, 10, 988.

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