## 3 Materials and Methods
### The Simplified Finite Element Model of the Rubber Tyre
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \# &
\begin{tabular}{c} **Shell Element** \\ **Description** \\ \end{tabular} & **Ply** & **Thickness (mm)** & **Material Name** & **Angle (\({}^{\circ}\))** \\ \hline \multirow{8}{*}{1} & & 01 & 2.40 & 02—sidewall rubber & 0 \\  & & 02 & 0.61 & 07—carcass steel & 102 \\  & & 03 & 0.61 & 07—carcass steel & 78 \\  & SH-340 & 04 & 8.38 & 03/04—bead rubber & 0 \\  & tyre sidewall with strand & 05 & 10.0 & 11—wire steel & 0 \\  & & 06 & 8.38 & 03/04—bead rubber & 0 \\  & & 07 & 0.61 & 07—carcass steel & 102 \\  & & 08 & 0.61 & 07—carcass steel & 78 \\  & & 09 & 2.40 & 02—sidewall rubber & 0 \\ \hline \multirow{8}{*}{2} & & 01 & 5.00 & 02—sidewall rubber & 0 \\  & & 02 & 0.43 & 08/10—chrafer belt steel & 0 \\  & & 03 & 5.00 & 03/04—bead rubber & 0 \\  & & 04 & 0.43 & 08/10—chrafer belt steel & 0 \\  & SH-280 & 05 & 0.61 & 07—carcass steel & 102 \\  & tyre sidewall & 06 & 0.61 & 07—carcass steel & 78 \\  & & 07 & 11.7 & 03/04—bead rubber & 0 \\  & & 08 & 0.61 & 07—carcass steel & 102 \\  & & 09 & 0.61 & 07—carcass steel & 78 \\  & & 10 & 3.00 & 02—sidewall rubber & 0 \\ \hline \multirow{8}{*}{3} & & 01 & 5.00 & 02—sidewall rubber & 0 \\  & & 02 & 0.43 & 08/10—chrafer belt steel & 0 \\  & SH-200 & 03 & 8.69 & 03/04—bead rubber & 0 \\  & tyre sidewall & 04 & 0.61 & 07—carcass steel & 102 \\  & & 05 & 0.61 & 07—carcass steel & 78 \\  & & 06 & 4.66 & 02—sidewall rubber & 0 \\ \hline \multirow{8}{*}{4} & & 01 & 8.50 & 02—sidewall rubber & 0 \\  & SH-140 & 02 & 0.61 & 07—carcass steel & 102 \\  & tyre sidewall & 03 & 0.61 & 07—carcass steel & 78 \\  & & 04 & 4.28 & 02—sidewall rubber & 0 \\ \hline \multirow{8}{*}{5} & & 01 & 5.90 & 02—sidewall rubber & 0 \\  & SH-120 & 02 & 0.61 & 07—carcass steel & 102 \\  & tyre sidewall & 03 & 0.61 & 07—carcass steel & 78 \\  & & 04 & 4.88 & 02—sidewall rubber & 0 \\ \hline \multirow{8}{*}{6} & & 01 & 11.0 & 02—sidewall rubber & 0 \\  & SH-170 & 02 & 0.61 & 07—carcass steel & 102 \\  & tyre sidewall & 03 & 0.61 & 07—carcass steel & 78 \\  & & 04 & 4.78 & 02—sidewall rubber & 0 \\ \hline \multirow{8}{*}{7} & & 01 & 3.00 & 02—sidewall rubber & 0 \\  & & 02 & 0.25 & 06—belt steel & \(-\)12 \\  & & 03 & 0.25 & 06—belt steel & \(+\)12 \\  & SH-170 & 04 & 0.25 & 06—belt steel & \(-\)12 \\  & tyre belt & 05 & 4.80 & 02—sidewall rubber & 0 \\  & & 06 & 0.61 & 07—carcass steel & 102 \\  & & 07 & 0.61 & 07—carcass steel & 78 \\  & & 08 & 7.23 & 02—sidewall rubber & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Structural composition of the simplified tyre model. In Table 5, the isotropic materials that are reported had an angle of 0 degrees, since, in ABAQUS, it is obligatory to input the grainline for any composite shell element. The total  
Figure 5: Composite shell elements groups from 1 to 9 (transparent in the background, there is the complex tyre model). Figure 6: Example of a layered structure shell element: SH-120 element (#9) group with 9 layers. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \# &
\begin{tabular}{c} **Shell Element** \\ **Description** \\ \end{tabular} & **Ply** & **Thickness (mm)** & **Material Name** & **Angle (\({}^{\circ}\))** \\ \hline \multirow{8}{*}{8} & & 01 & 2.07 & 02—sidewall rubber & 0 \\  & & 02 & 0.25 & 06—belt steel & \(-\)12 \\  & & 03 & 0.25 & 06—belt steel & \(+\)12 \\  & SH-140 & 04 & 0.25 & 06—belt steel & \(-\)12 \\  & tyre belt & 05 & 3.90 & 02—sidewall rubber & 0 \\  & & 06 & 0.61 & 07—carass steel & 102 \\  & & 07 & 0.61 & 07—carass steel & 78 \\  & & 08 & 6.06 & 02—sidewall rubber & 0 \\ \hline \multirow{8}{*}{9} & & 01 & 0.92 & 02—sidewall rubber & 0 \\  & & 02 & 0.25 & 06—belt steel & \(-\)40 \\  & & 03 & 0.25 & 06—belt steel & \(-\)12 \\  & & 04 & 0.25 & 06—belt steel & \(+\)12 \\  & SH-120 & 05 & 0.25 & 06—belt steel & \(-\)12 \\  & tyre belt & 06 & 2.80 & 02—sidewall rubber & 0 \\  & & 07 & 0.61 & 07—carass steel & 102 \\  & & 08 & 0.61 & 07—carass steel & 78 \\  & & 09 & 6.06 & 02—sidewall rubber & 0 \\ \hline \hline \end{tabular}
\end{table}