Extending the visco-frictional branched modeling of filled rubbers to include coupling effects between rate and amplitude dependence

The traditional way to capture rate and amplitude dependence of filled rubbers is by a branched model containing elastic, viscous, and frictional branches, leading to a decoupling of the rate and amplitude dependence. In order to capture the experimentally observed phenomena with a steeper increasing dynamic modulus with frequency, for small amplitudes, a model by Besseling (1958) is revisited. In it‘s general form several stress fractions are added and each fraction has elastic, viscous, and frictional contributions in series. In this work the potential of Bessling‘s constitutive model is investigated by extending the traditional three branches by a forth branch from this model to account for the coupling effects. The stress calculation algorithms and behavior of one-dimensional models are compared to harmonic experiments in double shear. A simple eight parameter model is studied and shown roughly to give the desired behavior, although no fitting routine has been implemented