## 3 Results and Discussion
### Influence of the Physical Parameters on the Tyre Global Coefficient of Elasticity
#### 3.1.2 FE Simulation  
From the analysis of the experimental data of the tests on both tyres at the two pressures of 1.0 bar and 1.6 bar, three linear stretches with different slope of the load-deflection curves were identified; for this reason, three stretch phases were implemented in the FE model in terms of extremal points. Under the hypothesis of linearity of the tyre deflections with the inflating pressure values, the load-deflection curve was calculated and plotted at the intermediate pressure of 1.3 bar between the two values used in the experiments. The experimental deflections at each phase and at the pressures of 1.0 bar, 1.3 bar, and 1.6 bar were then applied to the FE models and the resulting forces on the anchorages of the internal circular crown of the tyres were calculated. The contact that occurs during the flattening of the tyres on a plane was simulated by taking into consideration _four lugs for the 420/85 R24 tyre_ and _six lugs for the 460/85 R34 tyre_. For both the tyres, differential displacements were given to the lugs in order to simulate the contact that gradually affects different areas of the tyres. The final coefficients (Young's modulus, Poisson's ratio) resulting from the iterative tuning process of the FE models at 1.0 bar and 1.6 bar are shown in Table 4. Instead, [PERSON]'s modulus and Poisson's ratio corresponding to the pressure of 1.3 bar were calculated by averaging the value of those coefficients at 1.0 bar and 1.6 bar, thus hypothesizing that a linear variation of elastic coefficients produces a linear variations of deflections. The load-deflection curves with different [PERSON]'s moduli, Poisson's ratios and inflation pressures (1.0 bar, 1.3 bar, 1.6 bar) resulting from the FEM simulations are represented in Figure 7. In the same figure, the experimental curves for both the tyres at 1.0 bar and 1.6 bar and the calculated curve at 1.3 bar are also reported for proper comparison with the FEM outputs. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Type**} & \multicolumn{2}{c}{_p = 1.0 bar (ref.)_} & \multicolumn{2}{c}{_p = 1.3 bar (+30\%)_} & \multicolumn{2}{c}{_p = 1.6 bar (+60\%)_} \\ \cline{2-5}  & **E (MPa)** & _\(\
u\) (-)_ & _E (MPa)_ & _\(\
u\) (-)_ \\ \hline
420/85 R24 & 7.6 (ref.) & 0.48 & 8.3 (+9.2\%) & 0.48 & 9.0 (+18.4\%) & 0.48 \\
460/85 R34 & 14.0 (ref.) & 0.48 & 16.5 (+17.9\%) & 0.48 & 19.0 (+35.7\%) & 0.48 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Values of Young’s moduli and Poisson’s ratios for the finite elements method (FEM) simulations. The coefficients related to 1.0 bar and 1.6 bar were obtained by converging experimental and FEM results; the coefficients at 1.3 bar are the average between the coefficients at the other pressures. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Type**} & \multirow{2}{*}{**Unit**} & \multicolumn{2}{c}{**Stretch 1**} & \multicolumn{2}{c}{**Stretch 2**} & \multicolumn{2}{c}{**Stretch 3**} \\ \cline{3-5}  & & **Ave. Values** & **Ave. Values** & **Ave. Values** \\ \hline
420/85 R24 & N\(\cdot\)mm\({}^{-1}\) & 55 & 81 & 107 \\
460/85 R34 & N\(\cdot\)mm\({}^{-1}\) & 51 & 86 & 160 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Differences between the elastic coefficients at 1.0 bar and 1.6 bar in the three stretches of a loading curve in the two experimental trials for the two tyres (in N\(\cdot\)mm\({}^{-1}\)), according to Equation (1). The curve in blue is the experimental curve, whilst the curve in red is the curve calculated through the FE model. As can be seen, except for the initial section, the two curves are superimposed. From the analysis carried out through the FE modelling, it can be seen that an increase of 0.3 bar (i.e., 0.03 MPa) in the type inflation pressure corresponds to an increase in [PERSON]'s modulus of 0.7 MPa and 2.5 MPa for the 420/85 R24 and 460/85 R34 types, respectively.