A new constitutive model for carbon-black reinforced rubber in medium dynamic strains and medium strain rates

© 2017 Taylor & Francis Group, London, UK. 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