A viscoelastic constitutive model of rubber under small oscillatory load superimposed on large static deformation considering the Payne effect

The viscoelastic behavior of carbon-black-filled rubber under small oscillatory loads superimposed on large static deformation is dealt with. In this class of problems, as the strain amplitudes of the load increase, the dynamic stiffness decreases, and this phenomenon is known as the Payne effect. Besides the effects of the static deformation and the frequencies of the superimposed dynamic load, the Payne effect is considered in this study. Influence factors are introduced in this model in order to consider the influence of static predeformation, the dynamic-strain-dependent properties, and frequency-dependent properties. For simplicity, separation of the three dominant variables, frequency, prestatic deformation, and dynamic amplitude of strain, is assumed. The Kraus model is used for describing the Payne effect. Dynamic tension tests are executed to obtain the model parameters and also for the verification of the proposed model. The suggested constitutive equation shows reasonable agreement with test data.