It is widely known that rubber components in tire structures exhibit their inelastic behavior, like rate dependency and hysteresis, during rolling operations. The resulting internal dissipation is well recognized as the main cause of temperature rise, which changes mechanical properties and eventually the performance of car tires. Despite the fact that a variety of computational techniques for thermomechanical analysis of tires in stationary rolling contact have been suggested over the last three decades, most of them are extracted from the same modeling concept originally presented by Whicker et al.¹ A partition of the overall simulation process into three major steps (mechanical, dissipation and thermal module) is well accepted. Unfortunately, within this modeling concept the authors inevitably encounter the same problem with the calculation of energy loss in the second module since the behavior of rolling tires is only assumed to be nonlinear elastic in the first mechanical step. To this point a number of empirical solutions have been suggested. The application of linear viscoelastic constitutive relations is only found in a few publications, which is, however, not an appropriate choice if large deformations are concerned.

To avoid the problems with conventional approaches mentioned above, a new simulation technique is developed and presented in this contribution. Different from the existing approaches, the dissipative behavior of rolling tires is directly characterized by a finite-strain thermoviscoelastic constitutive model with options for specific rubber phenomena like frequency and temperature-dependent response. The simulation is performed within the Arbitrary-Lagrangian-Eulerian (ALE) kinematic framework, which allows for an efficient finite element implementation, such as a local mesh refinement of the contact region and time-independent formulation of the weak presentation of momentum balance. For the computation a three-phase staggered scheme is suggested. First the mechanical subproblem is solved using the developed thermoviscoelastic constitutive equations. Deformations and dissipation rates are then transferred to the subsequent thermal phase for the solution of heat equations. Finally, in the third step material history is treated by solving the advection equations using Time-Discontinuous Galerkin method within the spatially fixed finite element mesh.