A. Becker’s research while affiliated with Continental AG and other places

When simulating the behaviour of a rolling tyre, it is important to model the friction between the rubber tyre tread and the road surface. Friction tests were carried out over a range of different loading conditions, velocities, and temperatures. From an analysis of the experimental results, a phenomenological law for the friction coefficient has been proposed. This is incorporated into a finite element program. Comparison of the experimental data with finite element computations demonstrates the validity of the model. The main applications of the friction model are in simulations of the rolling tyre during braking and/or cornering. The results obtained include global braking and side forces as well as local mechanical processes in the contact patch, for example, the distribution of contact pressure and sliding velocities. From this, criteria for important aspects of tyre performance such as wear can be computed. Thus the tyre engineer is helped to understand and optimise tyre design with the aid of simulation.

Based on the generalized Maxwell-model, a viscoelastic material approach for steady-state rolling structures has been developed. Unlike a transient finite element formulation the final state is attained in a few load increments and just one time step. The consistent linearization of the steady-state viscoelastic constitutive formulation leads to additional coupling matrices so that the number of non-zero entries in the global stiffness matrix is increased. The steady-state formulation of the viscoelastic material approach as well as the transient formulation allow the addition of so-called Prandtl-elements to consider elastoplastic effects, too. Numerical results confirm the robustness, reliability and capability of the steady-state viscoelastic material formulation.

The hysteretic behavior of tire rubber compounds was investigated by tension/compression tests at different strains and strain rates, dynamic tests with varying frequencies and amplitudes, and tests with small cycle loading and unloading. According to these effects, a material model was developed that considers the complex frequency dependent (viscoelastic) as well as the rate independent (elastoplastic) inelastic behavior of filled rubber. This model combines different rheological elements representing viscous and plastic effects. The approach is valid for large strains. The hysteretic model has been implemented in an in-house FE code to analyze tire behavior assuming a constant driving velocity. The numerical algorithm is robust and shows excellent convergence, making it suitable even for large tire models. In computations for rolling tires, the consideration of the hysteresis yields a direct calculation of rolling resistance and energy dissipation, thus the new material law should prove useful in simulations of wear and durability.