A constitutive equation for filled rubber under cyclic loading

This paper describes experiments and the development of constitutive equations to predict the steady-state response of filled rubber under cyclic loading. An MTS servo-hydraulic machine was used to obtain the dynamic hysteresis curves for a filled rubber compound in uniaxial tension-compression. The material tests were performed with mean strains from −0.1 to 0.1, strain amplitudes ranging from 0.02 to 0.1, and strain rates between 0.01 and 10 s⁻¹. Temporary material set, the Payne effect and rate-dependence were observed from the experimental results. A hyper-viscoelastic constitutive model was developed to characterize the dynamic response of the rubber. A cornerstone of this constitutive modeling was to devise a scheme to evaluate material set and a finite strain, non-linear viscoelastic law from the test data. Predictions of the dynamic hysteresis curves using the proposed constitutive equation were found to be in good agreement with the uniaxial test results.