A consistent implementation for inelastic materials in an ALE formulation for steady state rolling contact

The numerical analysis of rolling contact for rubber materials is a challenging task, especially due to the many nonlinearities inherent to the material, large deformations, friction, and energy dissipation, among others. Industrial applications can be found in ball bearings, rollers, and most commonly in tires of vehicles, applications where reliable numerical simulations lead to the improvement of durability, performance and safety. While a transient analysis stands as a practical and powerful tool for the simulation of rotating bodies, the large amount of computational resources required represents its biggest disadvantage. An alternative frequently used lays in a steady state simulation by means of an Arbitrary Lagrangian Eulerian (ALE) formulation, where the rotational velocity and axial loads are assumed to remain constant. Within this framework, the reference configuration is neither attached to the material particles nor fixed in space and special attention should be paid to the history variables of inelastic materials. In this work, a viscoelastic material model is implemented in an in-house finite element code, based on a generalized Maxwell model. The implementation takes into consideration the contribution of all elements connected in circumferential direction and a consistent linearization is made for each of them, leading to an assembled stiffness matrix with more non-zero values than a standard one. This approach is combined with smeared reinforcement embedded in base elements. The reinforcing layers are described by a hyperelastic material model, providing additional advantages for the modeling and simulation of reinforced rollers and tires. Numerical results for different examples show the capabilities of this implementation and the efficiency of the numerical algorithms is discussed. Important remarks and an outlook for further research concludes this presentation. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)