## 5 Summary  
A complex finite element model of the tyre-pavement interaction was developed in this research study using ABAQUS finite element software. The developed model was sophisticated enough for the detailed analysis of the contact interaction; moreover, by applying appropriate material parameters, the model was also deemed suitable for further research work. In preparing the finite element simulation, considerable help was provided by the ABAQUS software manual [29], including many useful examples and pieces of information. Our results from the finite element simulation are in good agreement with literature data; therefore, a connection among the average contact pressure \(q\), the wheel load \(F\), and the inflation pressure of the tyre p was established. The results of our analysis show that the empirical equation published by [11], based on laboratory tests, can be appropriately applied for the determination of the average contact pressure \(q\). Comparison calculations were performed using the average contact pressure \(q\) and the radius of the substituting circle of the tyre contact area on the pavement surface \(a\) in order to compare the performance of the finite element twin tyre simulation and the substituting circular plate model. The results of the finite element simulation are in good agreement with the results of WESLEA pavement structure design software, the only exception being the vertical \(u_{zz}\) displacements or deflections. Critical stresses and strains for the asphalt layer fatigue and the subgrade compression criteria could be accurately determined by substituting the twin circular plate model.  
Based on the complex rubber tyre model, a second, simplified tyre model was also developed in order to analyse the tyre-pavement interaction not only under static but also under dynamic conditions. The basic idea of keeping all material characteristics and only rebuilding the carcass applying composite shell elements did not prove to be a satisfactory direction. The results of the simplified model do not indicate the behaviour of the radial tyre, but rather of the diagonal tyre, regarding contact areas and stresses. It is possible that a better approximation of the layered structure of the complex radial tyre can be provided by using nominal material parameters, determined in an iterative way. Regarding the objective function, temporarily, the empirical model of [11] seems to be a good choice. Analysing stresses and strains in the flexible road pavement structure, the complex and the simplified models mainly provided similar results, concerning practical considerations. Therefore, the simplified model is also suitable for the design of a new or strengthened road pavement structure, as it has a considerably lower computational demand, which means that it is also suitable for analysing dynamic cases. The simplified tyre model makes it possible to further develop the finite element model of the road pavement structure, keeping its composition almost unaltered, incorporating viscoelastic or even viscoelastic-plastic material models and taking into account the displacement between layers.  
Finally, the example of the two finite element tyre models, developed by different modelling approaches, indicates that the stiffness of rubber tyre models can vary in a wide range, even starting from the same geometry and materials. Consequently, our recommendation is that the simplified contact pressure model of any finite element tyre model is always published, as this would help the reproduction of research results by other researchers, even in the absence of originally used software.  
**Author Contributions:** T.K., methodology, software, visualization, and review and editing; P.P. and C.T., conceptualization, methodology, formal analysis, and writing--original draft preparation. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research study received no external funding.  
**Conflicts of Interest:** The authors declare no conflict of interest.