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.

Component design of rubber-based anti-vibration devices remains a challenge, since there is a lack of predictive models in 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). An approach is proposed that demonstrates all non-linear viscoelastic effects such as hysteresis and cyclic stress softening. As it is based on a free-energy, it is fast and easily implementable. The fitting parameters behave meaningfully when changing the filler volume fraction. The model was implemented for use in the commercial finite element software ABAQUS. Examples of how to fit experimental data and simulations for a variety of carbon black filled natural rubber compounds are presented.

Modelling the viscoelastic behaviour of rubber for use in component design remains a challenge. Previous reviews (Diani, Fayolle, & Gilormini 2009) and our studies presented in this paper highlight the issues of using of the most common viscoelastic non-linear constitutive models (Besdo & Ihlemann 2003;Bergström & Boyce 1998;Ogden & Roxburgh 1999). In detail, such models cannot reproduce or predict the experimental stress data for filled natural rubber loaded under the typical operating conditions. Examples of such conditions include cyclic strain history with constant strain rates and variable amplitude. This paper examines the behaviour of natural rubber elastomers filled with different percentages of carbon black. The elastomers chosen are typical of the materials used in vibration damping or automotive suspensions. We show that a constitutive model based on the fractional calculus can provide a good agreement for cyclic uniaxial tensile tests at a constant amplitude. The proposed model can capture, for example, the hysteresis and cyclic stress softening observed in the experimental data.