Modelling the Time-Dependent Behavior of Elastomers Using Fractional Viscoelastic Material Formulations

Elastomer materials are often used for components such as tire treads or hydraulic sealings, when deformable and damping behavior of components are desired and high dynamic loads appear. Such elastomers show time- and frequency-dependent characteristics, called viscoelasticity. The modelling of viscoelastic material is mainly implemented in simulations by rheological models, which often consists of elastic and damping elements. A viscoelastic model can be parametrized to experimental data to describe a specific elastomer with high accuracy. The most common model is the Prony-series. This model uses several Maxwell-branches (connection of one elastic and one damping element in series). Every branch is only able to fit the experimental behavior at one single excitation frequency. This fact makes it necessary to use a lot of parameters for adapting the frequency- and temperature-dependent characteristics over decades of the excitation frequency. To overcome this need for a huge amount of parameters we formulate a fractional viscoelastic model approach that gets along with a much smaller set of parameters, using finite elements. In order to reduce the numerical effort, a similarly formulated model is set up on force-displacement level additionally. In this way, the complexity of the simulation can be reduced with mapping of the material behavior.