## 2 Materials and Methods
### Simulation Phase  
The two types were modelled using finite elements after having obtained their geometries experimentally in the laboratory. All cross-section dimensions of the two tyres were measured and drawn in AutoCAD (by Autodesk, San Rafael, CA, USA). In particular, the cross-section of each tyre was measured at regular intervals of the tyre profile, thus allowing a careful 2D reconstruction of the shapes and of the thicknesses (Figure 3a). In addition, the lug sections of the tyres were also measured with respect to both the front view and the top view. Subsequently, the section drawn in AutoCAD was imported into SpaceClaim 2019 R3 (by Ansys, Canonsburg, Pennsylvania, USA). All tyre segments were chamfered with interpolation splines. The 3D models of the tyres were created from a revolution of each cross-section around the related tyre axis of rotation and the lug geometries were 3D-modelled separately and added as a matrix of objects (Figure 3b). As shown, the graphical comparison of the two images is very precise and the geometric model is very detailed and close to reality. Figure 3: Example of a cross section of a tyre (here: a 420/85 R24 tyre); (**a**) exported by AutoCAD and (**b**) modelled in Ansys SpaceClaim 2019 R3. Figure 2: Experimental setup for the measurement of the elastic properties of the tyres: (**1**) Tested tyre (in this case: 460/85 R34); (**2**) transducer; (**3**) weighing platform; (**4**) crane rope; (**5**) hydraulic cylinder; (**6**) acquisition system (connected to the laptop on the right side of the photograph, used to store the data collected). Figure 4 shows an example of one of the two types in section (Figure 4a), and the whole tyre (Figure 4b) as well. The model that is proposed is _all-inclusive of all the components that make up a tyre_, from the solid part of the rubber to the carcass, without modelling them separately. In the performed geometrical modelling, the smallest parts have not been considered and the level of detail, although quite high, has not dropped beneath geometries smaller than one centimetre, all this in order to simplify the subsequent calculation of deformations and stresses. However, the chosen geometric approximation does not generate any significant change in the tyre deformation characteristics compared to the actual geometry. The tyre deformation configurations were simulated with Ansys Mechanical 2019 R3 software (Ansys, Inc., Canonsburg, PA, USA) using two models composed respectively of 21,130 nodes and 9381 tetrahedral elements for the 420/85 R24 tyre and 28,617 nodes and 8921 tetrahedral elements for the 460/85 R34 tyre. The strength of this work is the definition of a simplified model that can show the same deformations of the real physical system under the same loading conditions. To this end, the model of the tyre has been modelled as a homogeneous spatial continuum. Since the tyre internal belts and piles have not been modelled, a new material was defined in the FE software. The stress-strain curve was approximated with a linear trend similar to the low-strain Neo-Hookean model [43], and so it represents the simplest model that can be implemented. A quasi-static test was conducted [44]. Subsequently, the characteristics of the rubber were iteratively changed by trying to mediate the real conditions; thus, the texture and the metallic filaments, which are generally present in the tyre carcass, were also included in the elasticity parameters of the selected material. In particular, an average Poisson's ratio of 0.48 was selected for all the tests [43] with different pressures and for both the tyres, in order to compensate for the presence of some metallic elements within the tyre mesh. Instead, the values of Young's modulus were calculated for all the tests through a convergent iteration process so that the strain curve calculated with the FEM method coincided with the experimental one.