## 4 Results and Discussion  
### The Required Running Time of Finite Element Models  
The complex and the simplified tyre models were significantly different, considering the applied element types and the numbers of elements. According to Table 7, the road pavement structure model shared about 90% of the summarised number of elements of the simplified tyre finite element model and of the road pavement structure finite element model, while this proportion, in the complex model, was only 50%. Consequently, the total running time depended on the elaboration of the road pavement structure model.  
Comparing the working of the two different tyre models and the running times required for each simulation step, the observations showed that the largest difference could be found in the preparation phase. The running time of the preparation phase of the simple tyre model was 15-fold quicker than that of the complex model. The running time for each simulation phase shown in Figure 8 was equal to the total processing time (CPU time). That means that, if the simulation ran on more processor cores, the running time would have  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Tyre Pressure (kPa)**} & \multicolumn{3}{c}{**F/2 Load on One Tyre (kN)**} \\ \cline{2-4}  & **Operation Load** & **Overload** & **Extreme Overload** \\ \hline
430 & 17.5 & 20.0 & 22.5 \\ \hline
530 & 20.0 & 22.5 & 25.0 \\ \hline
630 & 22.5 & 25.0 & 27.5 \\ \hline
730 & 25.0 & 27.5 & 30.0 \\ \hline \hline \end{tabular}
\end{table}
Table 6: The tyre–pavement interaction simulation matrix.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Element Type**} & \multicolumn{2}{c}{**Complex Model (Per Tyre)**} & \multicolumn{2}{c}{**Simple Model (Per Tyre)**} \\ \cline{2-4}  & **Number of Elements** & **Usage** & **Number of Elements** & **Usage** \\ \hline \multirow{2}{*}{Continuum element} & \multirow{2}{*}{92,904} & all tyre parts and the body of wheel & \multirow{2}{*}{6000} & \multirow{2}{*}{read} \\ \cline{1-1} \cline{5-5}  & & & \\ \cline{1-1} \cline{5-5}  & & & \\ \cline{1-1} \cline{5-5}  & & & \\ \cline{1-1} \cline{5-5}  & & & \\ \cline{1-1} \cline{5-5}  & & & \\ \hline \multirow{2}{*}{Membrane element} & \multirow{2}{*}{10,500} & strengthening of the tyre, carcass, belts etc. & \multirow{2}{*}{0} & not applied \\ \cline{1-1} \cline{5-5}  & & & \\ \cline{1-1} \cline{5-5}  & & & \\ \hline Total number of elements & \multirow{2}{*}{103,404} & \multirow{2}{*}{12,200} \\ \cline{1-1} \cline{5-5}  & & & \\ \end{tabular}
\end{table}
Table 7: Element types and the number of elements applied in the two types of finite element tyre models.  
decreased proportionally. According to Figure 8, the elaboration of one contact simulation, applying the complex model, requires, in total, about 107 CPU hours (at 22 threads, about 4.9 h). After the first preparation phase and interaction simulations, it was possible to alter the load and the tyre pressure, which means that the result of another experimental condition could be reached in 67.4 CPU hours (at 22 threads, about 3 h). In the case of the simple tyre model, the elaboration of the contact simulation required, in total, 35.4 CPU hours (at 22 threads, about 1.6 h). In the case of any further modification of the load and the tyre pressure, the simulation time decreased to 15.8 CPU hours (at 22 threads, about 3/4 of an hour). This means that the simulation time applying the simple model was less than 1/4 of that of the complex model.  
Further time could be saved by applying reduced integration elements for the calculation of the road pavement structure model. In that case, the time of the interaction simulation decreased to 13.9 CPU hours (at 22 threads, about 0.63 h), while the time of the load simulation decreased to 11.8 CPU hours (at 22 threads, about 1/2 an hour), resulting in a further 30% time savings.