The component of vehicle tires that contacts the road is the tire tread. It consists of several tread blocks with different shape and can be realized by siped structures to improve the traction on the pavement, in particular in wet, icy, or snowy conditions. The blocks are usually made of elastomer materials, which possess viscoelastic behavior. Viscoelasticity can be described by classical rheological models or, alternatively, as shown in this paper, by fractional viscoelastic models. Fractional models can fit the material properties better with fewer parameters.

Each single tire tread block shows periodically frictional impacts with the pavement. The contact configurations and transitions among stick and slip or impact and detaching can be formulated as a linear complementarity problem, whose solution estimates the local contact forces.

We simulate transient deformations of a tire tread block by developing a discretized fractional viscoelastic model. The focus is on the deformation process of a tread block with siped structure on different ice tracks with frictional contact. In particular the interlocking of the tread block lips with the edges on the ice surface and the self-contact of the lips are considered. The simulation results are compared to measurements on a high velocity linear testing bench. The contact forces of the frictional contact for plane and rough surfaces on ice and also the deformation process of siped tread blocks, where self-contact can occur, are investigated. The qualitative comparison between results out of simulations and experiments shows a good agreement.

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