## 2 Materials and Methods
### Data Analysis  
For quasi-static and impact compressions, force (F), impactor displacement (disp.) and time (t) were converted into engineering strain (\(\varepsilon\)) (ratio of displacement to initial sample height), strain rate (\(\tau\)) and engineering stress (\(\sigma\)) (ratio of force to initial sample area). Two stress vs. strain curves were obtained under combined compression and shear: A compressive stress vs. strain curve and a shear stress vs. strain curve. The compressive strain and shear strain were calculated using Equation (1), and they were equal because the loading angle was 45\({}^{\circ}\). The compressive stress is the force obtained from the \(z\)-axis of the load cell (perpendicular to the impacted surface of the foam) divided by the sample area (Figure 1). The shear stress is the force obtained from the \(x\)-axis of the load cell (along the impacted surface of the foam) divided by the sample area. \[\varepsilon=\frac{\text{Disp.}\times\frac{\sqrt{2}}{2}}{\text{Sample height}} \tag{1}\]  
During the drop test, the impacting mass decelerated as it compressed the foam, so the strain rate was not constant. The objective of the following analysis, adapted from [PERSON] et al. [8], was to create engineering stress vs. strain curves at a constant strain rate simplify the comparison between foams. For each foam and testing condition, \(\varepsilon\), \(\tau\), and \(\sigma\)were plotted in a 3D space (Figure 2a). A polynomial surface was fitted with the least absolute residual method using the _fit_ function in Matlab R2018b (MatWorks, Natick, MA, USA) [29] (Figure 2b). A sensibility analysis of the quality of the fit (measure with R\({}^{2}\)) between experimental points and the fitted polynomial surface was performed to choose the degree of the polynomial surface (supplementary material Figure S2): The polynomial surface chosen was of degree 5 in strain and of degree 1 in strain rate (R\({}^{2}>0.97\)). To ensure that the surface crossed the 0 abscissa, the point of origin of each curve was weighted with the weighting of 10. Then, the stress vs. strain curves at four constant strain rates (50, 100, 150, and 200 s\({}^{-1}\)) were extracted from the polynomial surface (Figure 2c). The absorbed energy per unit volume and the efficiency diagrams of the VN foams were plotted to evaluate and compare their impact energy absorption. The absorbed energy per unit volume (W) corresponds to the area under stress vs. strain curve up to the point of interest (Equation (2)) [6]. The efficiency (Eff) is defined by [PERSON] [30] as the efficiency of energy absorption of a compressed foam compared with an ideal one that transmits the same but constant force when fully compressed. The efficiency of energy absorption is calculated as the ratio of absorbed energy up to the point of interest divided by the stress \(\sigma_{1}\) at this point (Equation (3)) [5; 31]. The energy per unit volume and the efficiency were plotted against the  
Figure 2: Method to obtain stress vs. strain curves at a constant strain rate: (**a**) Plotting the curves strain (\(\varepsilon\)), strain rate (\(\tau\)) and stress (\(\sigma\)) from different impact heights in a 3D space, (**b**) polynomial surface fitting, and (**c**) extraction of the four stress vs. strain curves. stress, to identify the optimum usage of the foam in terms of energy absorbed and transmitted stress [5; 30]. The stress, strain, and absorbed energy at maximum efficiency were calculated. \[\text{W}=\int\sigma\text{*d}\varepsilon \tag{2}\]  
\[\text{Eff}=\frac{\int_{0}^{\varepsilon 1}\sigma\text{*d}\varepsilon}{\sigma 1} \tag{3}\]  
The stress vs. strain curves of VN foams displayed three regions: Linear elasticity, plateau, and densification. The stress and the strain at yield and at the onset of densification were identified from the experimental results, as well as the Young's modulus. The Young's modulus was measured as the slope of the curve at 0 strain.