## 5 Discussion  
For its nature, the ski works in the elastic field only. Plastic deformations should be avoided. Therefore, during the experimental measurements, the constitutive law was characterized up to the yielding only. Most of the tested materials showed a good repeatability in the results. In some cases, due to low availability of materials, only one specimen was tested. Repetitions were possible for material 207 (both directions), 290 (both directions), 139 (X direction), and 9 (X direction). The discrepancies between repetition were very small, confirming the correct configuration of the testing setup and  
Figure 21: Von [PERSON] stress in the cross-section of the ski for different roll angles and loads.  
Figure 20: Turning radius vs. roll angle.  
adequacy of the measuring devices. Materials #207 and #9 showed the same behavior in both directions. The tests performed on material #135 and #31, in which the single fibers were easily visible, were performed with a special sample with a rectangular geometry instead of a dog-bone-shaped one. After measuring the thickness and width of a single fiber, the resistant area was computed by multiplying the area of a single fiber by the total number of fibers of each specimen.  
FEM results were fully validated by the experimental data for both modeling approaches (shell and solid). The 2D analysis presented a maximum displacement (in the three-point-bending) of 41 mm, showing a 2.5% difference with respect to the experimental data, while the 3D model predicted a maximum displacement of 44 mm (10% difference vs experiments). In the torsion-bending analysis, the 2D model predicted a rotation of 4.60\({}^{\circ}\), and the 3D model a rotation of 4.86\({}^{\circ}\). The difference with respect to the experimental data result was 3% and 9.5%, respectively.  
For the shell model, discrepancies in the predicted displacement/rotation with respect to the measured one could be attributed to the following reasons:  
* The ski was modeled with multiple sections having different heights; thus, the perfect curved shape of the ski was not correctly replicated;
* The steel edges and the lateral layers (cage) were not modeled. On the other side, the simplification in the 3D models are:
* The longitudinal curvature of the ski was not considered;
* The assumption on the material properties taken during material characterization affected results.  
Both the 2D and the 3D models had the same maximum width, but the lateral layers were modeled in the 3D model only. The second order (area) moment of these vertical layers was lower with respect to the horizontal ones; therefore, it is reasonable that the 2D models resulted in a stiffer quality compared to the 3D one. From Figure 7 to Figure 13, it can be observed that not all layers had structural purposes. The lower and the upper layers were not significantly loaded despite the maximum strain. This was due to their low elastic modulus. The material of the bottom layer, for example, was aimed to reduce friction with snow and to insulate the ski from humidity. FEA allowed for an accurate evaluation on how each layer contributed to the total stiffness of the ski.  
The discrepancies observed in the torsion-bending analysis can be explained with the geometrical and material simplifications already explained, but also considering that the shear module G plays a fundamental role. The fact that it was approximated with the Campbell simplification may affects results.  
The simulations of the real behavior of the ski in contact with the snow showed that the rolling angle played a much more significant role with respect to the applied load in terms of turning radius. This was equal to about 22 m for a roll angle equal to 45\({}^{\circ}\), 34 m for a roll angle equal to 30\({}^{\circ}\), and 111 m for a roll angle of 10\({}^{\circ}\). The geometrical rounding radius of the ski was 40 m. The turning radius decreased to 14 m when the roll angle was increased to 60\({}^{\circ}\).