## 1 Introduction  
Energy-absorbing components have become ever more important within the transport industries, as they can provide increased passenger protection while complying with lightweight and reduced emission requirements. These structures should dissipate as much energy as possible during impact scenarios by plastic deformation, while the loads transferred to passengers and close structures must be kept as low as possible. Thin-walled tubular structures have been studied since the 1960s [1] and are the epitome of such devices, as their axial loading may yield progressive collapse modes with high specific energy absorption despite their light weight [2]. Furthermore, their shape and thickness-to-weight ratios are similar independently of the scale difference between aircraft, automobile, and train structures, which increases the versatility of the components [3]. As a result, steel and aluminium crash boxes are found in automobile assemblies [4], trains [5], aircraft [6], and even helicopter sub-floor structures [7]. After the initial studies seeking a deeper knowledge on the tubes' crush behaviour with diverse cross-sections and loading conditions [8; 9; 10], a number of investigations were carried out on filled tubes. Earlier designs for these inner reinforcements were light and soft cellular materials such as foams, although the current state of the art features cores ranging from metals [11] to fiber-reinforced polymers [12], cork [13; 14], wood [15], or combinations of two or more materials [16]. The use of cores allows for higher energy dissipation by the tubular components with little increase in weight and maintaining the space taken up by the tube. Adhering to cores made of cellular materials, foams have been by far the most studied, as they enable homogeneous and stable forces during axial crushing [17]. The mechanical properties of foams are highly dependent of two factors: the inner cellular structure and the base material conforming the cell walls [18; 19]. The choice of different base materials has been thoroughly examined, with aluminium and polymeric foams being used the most [20]. In the particular case of specimens filled with aluminium foams, [PERSON] et al. [21; 22] studied how and why the behaviour of square cross-sections is altered by the presence of a core, both under static and dynamic loads. It was found that foam filling resulted in a higher number of tube folds, rooted in the stiffness effect of the aluminium foam on the tube walls which reduced their buckling length. They also proposed an equation to predict the average crushing force of foam-filled extrusions, considering the contributions from the tube, foam, and the interaction effect between both. The aforementioned equation has since been used by other authors to determine the strengthening effect of different fillings. [PERSON] and [PERSON] [23] found that the contribution from the foam-tube wall interaction accounts for around 80% of the foam strength in square sections filled with aluminium foams, which can be doubled if using adhesive in the interface between both materials. [PERSON] and [PERSON] [24] studied the effect of polystyrene foams filling circular tubes, finding an increased interaction effect with smaller tube cross-sections. Another investigation relying on the equation from [PERSON] et al. [21] is the study from [PERSON] and [PERSON] [25] on the effect of tube thickness and foam density on the component's energy absorption, showing that filled tubes were energetically more efficient than empty tubes only after reaching a certain foam relative density. Much attention has been drawn towards polymeric foams given their low weight, high specific energy absorption, and production ease [26]. However, little has been published studying the effect of polymeric foams on the collapse of thin-walled tubes following a similar approach as that from [21; 22]. Some research can be found studying the interaction between polystyrene foams and circular tubes as that from [PERSON] et al. [27].