## 2 Materials and Methods
### Methods  
To give a general validity to the adopted approach, the mechanical properties of the different materials were obtained with dedicated tensile tests combined with DIC techniques. These allow the characterization of the 4 in-plane elastic properties of each material used in the ski successively tested. The materials used in the ski manufacturing are composited themselves. They have two major constituents, fibers and matrix. Fibers ensure the resistance and stiffness, while matrix plays the role of keeping the fibers together and protecting them from external agents. The theory of orthotropic laminas and laminated structures could be used for describing these materials. The assumption of having (for each material) just one principal direction was made. Orthotropic materials can be described in the space with 9 independent elastic parameters (for a completely non-isotropic material the constants are 21). For a lamina of small thickness and with longitudinal continuous fibers, the elastic behavior can be described with 4 elastic constants only: The 2 in-plane elastic modules, the in-plane shear module, and one of the two in-plane Poisson ratios. The 2 elastic modules can be obtained directly from unidirectional tensile tests while the Poisson's ratio can be extrapolated from digital image correlation (DIC) measurements. The shear module was evaluated by means of the approximated Campbell formula [17].  
The tested materials are identified with a code number. Specifically, 9, 24, 139, 207, 290, 135, 31, 86, and 217.  
Tensile tests were performed on the STEPLab UD04 (Figure 1) testing machine available in the labs of the Free University of Bolzano/Bozen. It is capable to apply static forces up to 4.5 kN. Each test was performed with a crosshead speed 0.1 mm/min.  
While the Young's modules can be directly derived from the monoaxial tests, the estimation of the Poisson's ratio requires the calculation of the strains in 2 perpendicular directions (Equation (1)).  
\[\
u_{xy}=-\frac{\varepsilon_{y}}{\varepsilon_{x}};\,\
u_{yx}=-\frac{ \varepsilon_{x}}{\varepsilon_{y}} \tag{1}\]  
Figure 1: STEPLab UD04 tensile machine and testing setup; (right) dog-bone sample geometry and dimensions.  
Digital image correlation (DIC) was used for this purpose. A reflex Nikon D750 camera with a 24-85 zoom, 32 MPixel resolution, and a stabilizer was placed perpendicularly to the specimen surfaces. It acquired pictures of the sample at each 0.5 s. External light sources were used for a better illumination of the specimen's surface.  
Two-dimensional digital image correlation is an advanced optical measurement technique allowing displacement and strain fields on a planar surface to be reconstructed.  
Firstly, a characteristic black and white \"speckle\" pattern was created on the specimen surface. Pictures were acquired at a fixed rate for the entire tensile test. The first picture acquired (undeformed sample) was used as reference. Cross correlation operations allowed the recognition of facets (subsets of the specimen's surface) across all the time steps (corresponding to different images and deformations) (Figure 2). Once all subsets were recognized for each timestep, the displacement field and successively the strain field of the tested component could be reconstructed. The software used was GOM-Correlate [20].  
Knowing the strains in 2 independent directions allowed the calculation of the Poisson's ratio according to Equation (1). The shear module could be finally obtained using the Campbell equation (Equation (2)).  
\[\frac{1}{G_{xy}}=\frac{(1+v_{xy})}{E_{x}}+\frac{(1+v_{yx})}{E_{y}} \tag{2}\]