# Improving the Impact Resistance of Anti-Ram Bollards Using Auxetic and Honeycomb Cellular Cores
## 3 Results and Discussion
The differences start to appear when the bollard is more deformed  
Figure 4: Maximum displacement in the impact direction (Z), for the top center reference point 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. Figure 5: Velocity (km/h) vs. time (s) of the M1-class vehicle with initial impact velocities of 16, 32, 48, 64, and 80 km/h before and after crashing into the hollow-steel, honeycomb-core, and auxetic-core bollards. when subjected to impact speeds of 48, 64, and 80 km. As 64 km/h is the highest speed that was successfully suppressed by the auxetic-core ballard, more results will be discussed here. The records (Figure 6, at 64 km/h) show PDE values of 116.7, 164.7, and 177.5 kJ for the hollow-steel, honeycomb-core, and auxetic-core ballards, respectively. Keeping the hollow-steel ballard as a benchmark, it is clear that the PDE sharply increased by 52% when adding the re-entrant auxetic core. This is linked to the auxetic lateral shrinkage due to the negative Poisson's ratio that condenses the structure and causes increased plastic strain. The findings agree with the conclusions of [30] that the addition of cellular cores (in their case, honeycomb topology) improved the shock-absorption capability compared to conventional steel ballards. Figure 7 shows the energy components of the auxetic-core ballard when subjected to the M1-class vehicle impact speed of 64 km/h. The kinetic energy is dramatically reduced with a negative slope at the end, indicating that it could go closer to zero if the analysis total time were conducted for more than 0.3 s. Moreover, the internal energy (yellow curve) is mainly composed of plastic dissipation energy and frictional dissipation energy, which reflects the superior performance of the proposed auxetic-core ballard. The strain energy and damage dissipation energy are small due to the relatively small deformed and damaged area compared to the whole mass of the model. Figure 6: Comparison between plastic dissipation energy (PDE) in (kJ) of the hollow-steel, honeycomb-core, and auxetic-core ballards when subjected to M1-class vehicle impact velocities of 16, 32, 48, 64, and 80 km/h. Figure 7: The energy components of auxetic-core ballard when subjected to an M1-class vehicle impact speed of 64 km/h. Figure 8 shows the maximum equivalent plastic strain among all section points (denoted in Abaqus as PEEQMAX) of the auxetic-core boldar when subjected to an M1-class vehicle impact speed of 64 km/h. The values are higher for the steel pipe (1.72) compared to 0.5 for the inserted auxetic core. This reflects that the auxetic material could have been more effectively used if it covered the steel pipe rather than being inserted in. In such a design, the'sacrificial' cellular material may plastically deform more than the'more rigid' supporting steel pipe. Hence, in future research, authors suggest checking the performance of anti-ram steel bollards that are 'covered' with protective cellular materials. Lastly, Figure 9 presents the JC-Damage Initiation Criterion of the auxetic-core boldar when subjected to an M1-class vehicle impact speed of 64 km/h. As the auxetic core is aluminum, more damage is seen there than in the steel pipe. The location of damage is either that in contact with the vehicle or the yielding/bending zone near the ground surface (assumed boundary condition). The results agree with the findings of [5], where tested bollards showed local plastic failure. [PERSON] et al. [5] stated that _\"Steel sections are economical and provide valuable mechanical properties for use in industry, however, they are prone to local failure due to their thin-walled elements\"_. The authors also believe that if the vehicle was modeled as a non-rigid body with deformable front bumpers, the auxetic-core boldar would have shown further protection capacity.