# A Study on Shock Absorption Characteristics of Honeycomb-Inserted Bollards
## 3 Numerical Simulations
### Simulation Result  
Table 2 summarizes the simulated maximum accelerations of the front bumper frame and the B-pillar, the vertical roof support structure of a vehicle, when collided with the varied yield strengths of both steel and in-plane honeycomb bollards. It was reported that the acceleration on the drivers (and passengers) during the collision is similar to the acceleration on the B-pillar [28]. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Item** & **Unit** & **PLA** & **Steel** \\ \hline Density & kg/m\({}^{3}\) & 1252 & 7830 \\ Young’s Modulus & Pa & \(3.5\times 10^{+09}\) & \(2.07\times 10^{+11}\) \\ Poisson’s Ratio & - & 0.36 & 0.33 \\ Bulk Modulus & Pa & \(4.17\times 10^{+09}\) & - \\ Shear Modulus & Pa & \(1.287\times 10^{+09}\) & - \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Specification of polylactic acid (PLA) and Steel. Figure 6: LS-DYNA simulation settings. Therefore, B-pillar acceleration data were used to analyze the accelerations felt by drivers. Since simulations with the honeycomb unit with 20 MPa yield strength exhibited the lowest B-pillar maximum acceleration, 20 MPa honeycomb unit was chosen for the simulations to compare its results with the conventional bollards. Figure 7a shows the qualitative deformation results with the conventional bollards, while Figure 7b with the 20 MPa in-plane honeycomb bollard. Figure 8 shows the time evolutions of maximum accelerations at the front bumper frame with the calculated maximum accelerations: \(1.037\times 10^{3}\) m/s\({}^{2}\) at 0.042 s for the steel bollard and 0.388 m/s\({}^{2}\) at 0.059 s for the in-plane honeycomb bollard. Compared to the steel bollard, the maximum acceleration of the honeycomb bollard was delayed by 0.017 s, with its value decreased to 64% of the former. In addition, the acceleration peaks occur only once for the steel bollard but three times for the honeycomb bollard, including the third one at 0.38 s, with its peak much lower than others. Figure 9 presents the simulated time history of the B-pillar accelerations. B-pillar maximum accelerations are \(3.44\times 10^{3}\) m/s\({}^{2}\) for the steel bollard and \(2.99\times 10^{3}\) m/s\({}^{2}\) for the honeycomb bollard, approximately 13% lower than the former. The simulated time evolutions of the front bumper and the B-pillar displacements due to the collision are graphed in Figure 10. Simulations showed that there is negligible deformation on the B-pillars. Thus, the front bumper frame displacements in Figure 10 were calculated using the physical distance between the bumper frame and the B-pillar, which was named the \"displacement gap\" in this paper, as inputs to the calculated strain values. It is shown in Figure 10 that there were no displacement gaps for the first 0.05 s after the start of the simulation since the bumper frame is not in contact with the bollards but the gap increases after the initial impact. Compared to the steel bollard, the maximum displacement time of the honeycomb bollard was delayed by 0.083 s and the maximum deformation value decreased by 26%. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Yield Stress (MPa)** & \
\begin{tabular}{c} **Front Bumper Frame Maximum** \\ **Acceleration (m/s\({}^{2}\))** \\ \end{tabular} &
\begin{tabular}{c} **B-Pillar Maximum** \\ **Acceleration (m/s\({}^{2}\))** \\ \end{tabular} \\ \hline
**Steel Bollard** & 215 & \(1.037\times 10^{+3}\) & \(3.44\times 10^{+1}\) \\  & 10 & \(0.701\times 10^{+3}\) & \(3.16\times 10^{+1}\) \\
**Honeycomb** & 20 & \(0.388\times 10^{+3}\) & \(2.99\times 10^{+1}\) \\
**Bollard** & 30 & \(0.481\times 10^{+3}\) & \(3.19\times 10^{+1}\) \\  & 40 & \(0.550\times 10^{+3}\) & \(3.25\times 10^{+1}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Maximum accelerations of the front bumper and the B-pillar for the simulated vehicle-bollard collisions. Figure 7: Maximum deformation of collision between vehicle and bollard; (**a**) steel bollard; (**b**) honeycomb 20 MPa bollard.