## 4 Results and Discussion
### Comparison of the Behaviour of Finite Element Tyre Models  
Differences between the two finite element tyre models were analysed at various tyre pressures and axle loads according to Table 6. The results consist of stresses in structures as well as contact areas and contact stresses of the tyre on the pavement, reflecting closely the results in the literature [25; 26]. In the inflation process of the tyre models, it could be observed that the tight surface in the complex model first lay on and tightened to the rim of the body of wheel and, afterward, it tumbled over. The current, simple model was not able to describe this deformation process; consequently, the deformation of the sidewall was not the same during inflation. The treads of the two models show nearly the same deformation; however, looking at Figure 9, it can be observed that the tread rims of the simple model moved on a larger arc, which means that the middle of the tread received a higher part from the axle load. Figure 8: Comparison of the running time of simulation phases of complex and simple tyre models, where the top row shows the complex tyre model and the bottom row shows the simple tyre model. Based on the finite element simulation, the contact area of the complex tyre model could be well approximated by a rectangle (see Figure 10). This answers to the behaviour of real radial tyres because these can be deformed only in the longitudinal direction and not in the transversal direction [27]. At the operational tyre inflation pressure and the highest allowed axle load, the distribution of contact stresses could be considered as an ellipsoid. However, in the case of low tyre pressure, the tread contacted the road surface unevenly; therefore, the middle of the tyre rose slightly, and the loading concentrated to the two sides of the tyre because of its stiffness. Consequently, the load distribution was not uniform and, according to Table 8, stress peaks (\(q_{max}\)) may occur, reaching 2-3-fold of the average contact pressure. However, this did not cause a problem, if only the stresses in the wearing course or the rutting were analysed, because the surplus pressures were equalised at 5-8 cm below the road surface, according to the FEM model. Figure 10: Parts of interaction simulation results: the contact area and contact stress distribution of the complex FEM type model (**left panel**) and of the simplified FEM tyre model (**right panel**). Figure 9: Comparison of deformation in the two types of finite element tyre models at 730 kPa pressure. The simplified tyre model had a smaller contact area (that was because of smaller compression values; see Figure 10); moreover, it had a larger loading on the road pavement structure at the middle of the tread. The shape of the contact area was elliptical or circular, which is characteristic for diagonal tyres since it allows significant displacements in both directions to happen. Within the contact area of the simple tyre, three stress peaks could be observed, namely, in the middle, an elongated elliptical one and, next to it, on both sides, circular ones. The shape of the contact area confirmed the shape of the deformation, analysed during inflation. The difference in the behaviour of the simplified tyre model can be explained mainly by the fact that the applied thin orthotropic plate-like shell element did not adequately describe the rebar of the tyre. The mechanical behaviour of the tyre is determined mainly by the construction of the carcass. Moreover, the layered shell elements react on shear stresses with a stiffer behaviour. The next step of our research study was to establish a connection among the average contact pressure q, the wheel load F, and the inflation pressure of the tyre p. The empirical connection (5) of [11], based on laboratory tests, was applied (Figure 11a). The parameters of the function were determined by the least squares method using data from Table 6, as follows:  
1. In the case of the complex tyre model (R\({}^{2}\) = 0.973), \[q=7.154F+0.272p+152.38.\] (7)
2.