Universal properties in the dynamical deformation of filled rubbers

Starting from the observation that the filler particles in filled rubbers form fractal clusters which are connected to each other, a theoretical model is developed which establishes a connection between the amplitude dependence of the elastic deformation of filled rubbers and the structural properties of the filler. It is assumed that the elastic modulus is dominated by the rigid filler network at very low strain, whereas at higher strain the rubber matrix provides the main contribution because of cluster break-up. Within this model the exponent arising in an empirical description of the amplitude dependence is derived from the connectivity of the filler clusters.