Niet-lineaire totale Lagrangiaanse eindige-elementenmodellering van banden: Een modelreductieaanpak voor efficiënt virtueel ontwerp

Pneumatic tires are essential components in road vehicles, transmitting dynamic forces between the road and the vehicle. Consequently, tires significantly influence overall vehicle performance. Due to the impact of tire behavior on numerous factors, including noise, emissions, safety and comfort, tire design is inherently complex. The coupling of tire performance metrics arises from the use of diverse materials and intricate geometries that form a composite structure, resulting in highly nonlinear behavior governed by numerous design parameters. Optimizing tire performance is thus a challenging, multi-objective problem. The conventional tire design process relies heavily on prototyping and experimental testing, which is costly, time-consuming and limited in its exploration of the design space. This dissertation proposes a virtual design analysis approach using high-fidelity, predictive, first-principle models to overcome these limitations. The nonlinear Finite Element Method (FEM) is employed to account for the geometric and material nonlinearity of the tire. By using the Total Lagrangian formulation instead of the state-of-the-art Arbitrary Lagrangian Eulerian (ALE) formulation, modeling arbitrary geometries including complex tread patterns is enabled and treating inelastic material behavior is largely facilitated. The hyper-viscoelasticity of the rubber is described by a Neo-Hookean material law in combination with a Prony series approach and rubber incompressibility is addressed through a mixed displacement-pressure FE formulation. The composite structures of the tire belts and the carcass are modeled by rebar elements. Through the exact representation of the geometry and the use of constitutive material laws, a direct link between model and tire design parameters is established, from which the methodology derives its predictive capabilities. To enforce the contact conditions with the road, a geometrical constraint-based approach, enforced by a Node-to-Surface contact element in combination with the penalty method, is selected due to the good trade-off between accuracy and efficiency. Robustness is added to the contact algorithm by employing a variable penalty function that limits the contact forces. Numerical damping introduced by the generalized-alpha solver further increases the stability of the dynamic simulations. Comparative studies confirm the equivalence of the Total Lagrangian and ALE formulations with respect to dynamic hub and contact forces for smooth and rough road rolling. Although the developed Total Lagrangian tire model requires more computational effort in both cases, the difference is less pronounced on smooth roads due to the increased numerical cost associated with changes in the active contact set in the ALE model. To reduce computational costs and enable larger design space exploration, a novel parametric Model Order Reduction (pMOR) method for rough road rolling contact problems is introduced. The approach combines the Multi Expansion Modal (MEM) method with a Generalized Component Mode Synthesis (GCMS) framework. While the a-priori generated MEM basis consisting of dynamic modes and nonlinear static solutions simultaneously addresses distributed and local nonlinearities, rotational invariance is added by the GCMS framework within the ME-GCMS method. To further reduce the computational load, an Energy Conserving Sampling and Weighting (ECSW) hyper reduction is employed. Additional efficiency is achieved by exploiting the cyclic symmetry within a linear interpolation, which adjusts the basis and the hyper reduction weights according to the rotational angle of the structure. The good approximation quality of the developed ME-GCMS method was validated by low errors of the global displacement field and hub forces for tire rough road rolling. Significant speedups of up to 20 underline the efficiency of the method. Further investigations confirm the predictive capability, accuracy and efficiency of both the full-order model (FOM) and reduced-order model (ROM) by achieving a good match between reported tire design trends in literature and the FOM as well as strong agreement between FOM and ROM outputs for a range of operational and design parameters. In addition, the influence of viscoelasticity and tread pattern geometry was demonstrated, while numerical time domain integration parameters are shown to have a negligible impact on tire KPIs in comparison to the observed design trends. In conclusion, the combination of a Total Lagrangian nonlinear FE tire and the dedicated parametric MOR scheme ME-GCMS offers a predictive, accurate and efficient simulation framework for virtual tire design analysis. This work addresses critical modeling and computational challenges and lays the groundwork for more advanced, cost-effective, and scalable virtual tire development.