Strain-induced nonlinearities of filler-reinforced rubber under cyclic deformations:: Experiments and modelling

In order to enhance the essential material properties of rubber, it is compounded with active fillers in the majority of applications. Due to the high surface reactivity and an aggregation of a filler network, the material is significantly strengthened. While intact at low strains, the filler network is deteriorated with increasing strain amplitudes leading to a conspicious loss in stiffness, which is widely known as Payne-effect. Besides, a pronounced maximum in the loss modulus can be observed at intermediate strain amplitudes. Since filler aggregates are mobile in certain limits, the material shows distinct recovery processes, as was proven recently in several experiments. In the present paper, several experimental results of dynamical measurements are displayed in due consideration of amplitude dependencies as well as recovery processes. In order to describe the depicted phenomena, a phenomenological model of viscoelasticity for small strains is presented, which is thermodynamic consistent and takes into account the current state of the filler network. As this model is formulated in the time domain, a Finite-Element implementation is quite suggesting and gives the possibility to calculate arbitrary loading processes. Finally, corresponding numerical results of Matlab simulations are presented and compared with given experimental results.