Advanced Rebar Formulation within a Thermo‐Mechanically Coupled Tire Simulation

Abstract

AbstractAs shown in various experiments, coupling between the thermal and the mechanical field of a rolling tire in contact with a rigid surface can be observed. An increase of its temperature over time when rolling with a constant velocity can be seen. This phenomenon is caused by the viscoelastic material properties, where the dissipated energy will lead to a heating of the rubber. Also the constitutive behaviour will change, when the temperature increases. A nonlinear viscoelastic material model is chosen to model an amplitude dependency of the time dependent behaviour of the rubber, proposed by Bergström and Boyce [1].Another important part of a tire are the reinforcements, which are embedded inside the rubber. These consist mostly of steel or polyester. These materials are not known for a dissipative behaviour and will not contribute to the heating of the tire. However, they also change their properties with increasing temperature and have a significant influence on the overall tire properties. Even without a contribution to the heating, the reinforcements will change its conductivity and have to be taken into account.For an accurate and efficient way to model the thermo‐mechanical coupling, an in‐house framework [2] will be presented, by use of the Arbitrary Langrangian Eulerian formulation and a commercial code. It is assumed, that the temperature in circumferential direction will stay constant and instant coupling effects are negligibly small. Therefore, the problem is split into a thermal and a mechanical part, and the coupling quantities (dissipated energy and temperature) are updated in a sequential manner.A common practise to model the reinforcements in tires is to use smeared layers, which leads to some difficulties. First of all, the modelling is only valid for a really small spacing between the bars. Another problem is, that the smeared layers have to fit with the nodes of the rubber matrix. Because of that, the mesh has to be refined, which leads to an increasing computation time and can cause numerical difficulties, due to too small elements.In this contribution, a different way of modelling the rebars within a thermo‐mechanical coupled algorithm is presented without the assumption of a smeared layer and treat them as single rebars. In numerical examples, the advantages of the proposed method are presented and the difference to the classical approach is shown. Also, the influence of the reinforcements on the stiffness, heat generation and rolling resistance of the tire, will be discussed. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)