## 1 Introduction  
Vinyl nitrile (VN) foams are polymeric closed-cell foams, commonly used for energy absorption in helmets [1; 2; 3; 4]. These foams are often chosen for their capacity to sustain several impacts without compromising their energy absorption capability. Additionally, it was shown that a helmet with a VN foam liner was better at reducing rotational acceleration than a helmet with an expanded polypropylene (EPP) foam, the most commonly used foam [3]. However, the stress vs. strain behavior of VN foam during impact has never been described.  
The mechanical characterization of foam for impact protection is usually performed in pure compression [5; 6; 7; 8]. However, typical impacts sustained by helmets are oblique [9; 10; 11; 12], loading the -liner material in combined compression and shear. Methods have been developed to test material for energy absorption in combined compression-shear loading [13; 14; 15; 16; 17; 18]. For instance, [PERSON] et al. [18] tested the effect of the anisotropy of polymer foam on the energy absorption in quasi-static loading with two independent displacement actuators, applying, respectively, shear and compression to the sample. However, few studies have characterized impact protective material during high-speed combined compression-shear loading. Among these studies, two methods were used. [PERSON] et al. [19] modified the Split Hopkinson pressure bar to apply high-speed compression and shear loading to honeycombs. This method provided the overall behavior of a structure at a high constant strain rate under combined shear-compression, but the normal and shear behaviors of the structure could not be isolated [19]. To get the normal and shear behaviors separately, [PERSON] [20], [PERSON] et al. [21], and later [PERSON] et al. [22] used a multiaxial load cell. They developed drop test rigs [20; 22] and a linear impactor [21] for impacting foam material in both compression and shear to study polypropylene, expanded polystyrene foam, and aluminum honeycomb.  
The mechanical behavior of polymeric foams typically varies with strain rate [23; 24]. In a helmet, the foam must deform to absorb impacts of various speeds and energies [23]. Hence, the strain rate dependency of protective foams must be characterized. This is often performed with the Split Hopkinson pressure bar, enabling materials testing at a high constant strain rate [24]. When the Split Hopkinson pressure bar is not applicable (i.e., large samples, or study of compression and shear behaviors in combined loading), researchers have used drop test rigs, where the deformation of the sample is induced by the impact of a falling mass [5; 20; 22]. During the impact, the impactor decelerates, and the strain rate varies. Impactor deceleration depends on its mass and initial speed, as well as on foam geometrical and mechanical properties [5]. The varying strain rate during the impact not only makes foam behavior difficult to compare, but also to model, as most finite element analysis solvers use material laws with constant strain rates. To alleviate such limitations, [PERSON] et al. [8] combined multiple impact test results to define stress vs. strain curves at constant strain rates. However, this method has never been applied to foam characterization in combined compression and shear.  
The objective of this study was to characterize the strain rate dependent behavior of three VN foams in both compression and combined compression and shear. This characterization was performed under quasi-static (compression-only) and impact loading conditions (compression and combined compression and shear). For impacts, a drop test rig was used to study the normal and shear behaviors of the foam separately, and a method was developed based on [PERSON] et al. [8] to account for strain rate variation during the impactor deceleration.