## 1 Introduction  
Ski mountaineering is a niche sector of winter sports in which the equipment, namely the skis, is determinant for the performances of the athletes. Most of the races foresee the climbing of a hill; in this condition having a light ski is fundamental. Moreover, during the downhills, the lightweight is not as important as the stiffness of the ski. Finding the best compromise between these 2 main properties meansdesigning a good ski. However, the optimization process requires several attempts and, considering that the current design approaches of ski-mountaineering (skimo or skialp) are characterized by a relevant testing activity, the whole development of a new model could be very expensive and time consuming. A preliminary screening of the multifarious designs is made by simplified laboratory tests, such as three-point-bending or torsional tests. Only the most promising prototypes are tested by skilled professional skiers, like mountain guides, or athletes that can give a more accurate evaluation of the properties of the ski in real conditions which characterize their practical use. This trial and error approach has significant economical disadvantages and requires long times for assembling and testing all the ski variants. Having the possibility to reduce the number of physical prototypes with a virtual preliminary screening could represent a significant improvement of the whole design and manufacturing process.  
Finite element analysis (FEA) is already used for the development and design phases of alpine downhill skis [1; 2; 3; 4]. In literature, several works in which the mechanical behavior of alpine or carving skis is analyzed are present [5; 6; 7]. However, the adoption of these modeling techniques for the development of mountaineering skis seem to be not yet widespread. It must be highlighted that for ski-mountaineering the necessity to find a balance between performances and lightweight design represents an additional issue which complicates the design [8]. The aim of the present study is to develop a reliable numerical model of an existing mountaineering ski. The model is based on the geometrical data of the ski and the results of material characterization tests of the different layers of the ski obtained combining tensile tests on flat dog-bone-shaped samples with digital image correlation (DIC) measurements. The dog-bone-shaped specimens were produced by laser cutting. Each material was tested in two different directions. For the materials for which it was possible, the tensile test was repeated twice. Digital image correlation [9; 10; 11; 12; 13; 14; 15; 16] combined with the [PERSON] [17] hypothesis allowed the estimation of the four in-plane elastic properties.  
Moreover, a real prototype (ski available on the market) was also tested in three-point-bending and bending-torsional tests. Simulations of these two conditions were performed with different levels of simplifications. The numerical results were compared with those obtained from three-point bending and torsion-bending tests on the real ski [18].  
Once the numerical model of the ski was validated, its behavior in different working conditions was studied. In particular, the ski-snow interaction was simulated. The snow was modeled according to Lintzen [19]. Different roll angles and loads were simulated to better understand the behavior of the ski under operation.