# Improving the Impact Resistance of Anti-Ram Bollards Using Auxetic and Honeycomb Cellular Cores
## 3 Results and Discussion  
This section shows the crashworthiness performance of the hollow-steel, honeycomb-core, and auxetic-core bollards against a single M1-class vehicle impact with varying speeds of 16, 32, 48, 64, and 80 km/h. Table 3 shows the maximum deformation in the impact direction (Z) for the 15 cases considered. The table only considers the deformation of the bollards, while vehicle maximum movement/penetration is represented by the rigid 'grey' model. In parallel, Figure 4 compares the maximum displacement in the top center reference point of the bollards for all the cases in one bar graph. At lower velocities of 16 and 32 km/h (the 1 st and 2 nd rows of Table 3), the hollow-steel bollard was successful in preventing the vehicle from penetrating the barrier/bollard. In other words, the inclusion of cellular cores might not be necessary for such low vehicular impact speeds. However, at 48 km/h (3 rd row of Table 3), the hollow-steel bollard noticeably bends, and the role of cellular cores is visible. At 48 km/h, the maximum displacement in the top center reference point (Figure 4) was reduced from 643.1 mm (for the hollow bollard) to 509.2 (for the honeycomb-core) and 466 mm (for the auxetic-core). In other words, a reduction in the maximum displacement of 20.8% and 27.5% occurred when with the addition of the honeycomb-core and auxetic-core bollards, respectively. At 64 km/h, the vehicle fully penetrated the hollow-steel bollard, and the cellular cores played a vital role in preventing full penetration of the vehicle, reducing the maximum displacement of the bollard's top center reference point (Figure 4) from 688 mm (for the hollow bollard) to 669.1 (for the honeycomb-core) and 618.2 mm (for the auxetic-core). At a high speed of 80 km/h (5 th row of Table 3), it appears that none of the models were successful in preventing the vehicle from penetrating the barrier. The maximum displacements of the bollard's top center reference point (Figure 4) were almost the same for the hollow-steel, honeycomb-core, and auxetic-core bollards when subjected to an M1-class vehicle impact of 80 km/h. It is also important to look at the velocity-time history of the impacting vehicle to check the effectiveness of the bollards in stopping vehicle penetration. Figure 5 shows the velocity (km/h) vs. time (s) of the vehicle before and after crashing the hollow-steel, honeycomb-core, and auxetic-core bollards. When the vehicle had initial impact velocities of 16 and 32 km/h (Figure 5a,b), the hollow-steel, honeycomb-core, and auxetic-core bollards were not only successful in stopping the vehicle but also in reversing the vehicle back, showing negative velocity values. At 48 km/h (Figure 5c), honeycomb-core and auxetic-core bollards were able to stop the vehicle (~zero velocity) compared to the hollow-steel bollard (~10 km/h). The difference is more dominant at 64 km/h, where the auxetic-core bollard outperformed the other two in terms of reducing the velocity of the vehicle to only 6.5 km/h (~90% reduction). At a low velocity of 6.5 km/h, the vehicle is not expected  
Figure 3: The considered cases in this study (15 numerical models in total) for the hollow-steel, honeycomb-core, and auxetic-core bollards when subjected to the M1-class vehicle impact velocities of 16, 32, 48, 64, and 80 km/h. As the aim of this study was to design a new energy-absorbing anti-ram bollard, the plastic dissipation energy (PDE) of the whole numerical model (steel pipe + core) is an important factor to assess. According to the findings of [PERSON] et al. [5], due to local deformations, the energy absorption of hollow-steel bollards can be increased by decreasing its width-to-thickness ratio, i.e., by reducing the diameter or increasing the thickness. In this paper, the inclusion of a cellular core may change the behavior. Figure 6 compares the plastic dissipation energy (PDE) in (k) of the hollow-steel, honeycomb-core, and auxetic-core bollards when subjected to M1-class vehicle impact velocities of 16, 32, 48, 64, and 80 km/h.