# Improving the Impact Resistance of Anti-Ram Bollards Using Auxetic and Honeycomb Cellular Cores
## 2 Case Study and Modelling
Detailed material parameters of Weldox 460E Steel and AL7075-T651 Aluminum are listed in Table 1. Vehicle material was arbitrarily defined, as it is defined as an underformable/rigid body, as mentioned earlier. Dynamic explicit analysis was used with a total time of 0.3 s. Due to the expected large deformation, geometric nonlinearity was toggled on. Adiabatic heating effects were included to consider the heat resulting from plastic deformations. Contact definition was made by defining tangential behavior with the 'penalty' friction formulation (friction \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Category** & **Constant** & **Description** & **Unit** & **Weldox 460E** & **AL7075-T651** \\ \hline \multirow{2}{*}{Elastic constants} & \(E\) & Modulus of elasticity & GPa & 200 & 70 \\ \cline{2-6}  & \(\
u\) & Poisson’s ratio & - & 0.33 & 0.3 \\ \hline \multirow{2}{*}{Density} & \(\rho\) & Mass density & kg/m\({}^{3}\) & 7850 & 2700 \\ \cline{2-6}  & \(A\) & Yield strength & MPa & 490 & 520 \\ \cline{2-6}  & \(B\) & Ultimate strength & MPa & 807 & 477 \\ \cline{2-6}  & \(n\) & Work-hardening exponent & - & 0.73 & 0.52 \\ \hline \multirow{2}{*}{Strain-rate hardening} & \(\dot{\varepsilon}_{0}\) & Reference strain rate & S\({}^{-1}\) & \(5\times 10^{-4}\) & \(5\times 10^{-4}\) \\ \cline{2-6}  & \(C\) & Strain rate factor & - & 0.0114 & 0.001 \\ \hline \multirow{2}{*}{Damage evolution} & \(D_{c}\) & Critical damage & - & 0.3 & 0.3 \\ \cline{2-6}  & \(p_{d}\) & Damage threshold & - & 0 & 0 \\ \hline \multirow{4}{*}{Adiabatic heating and temperature softening} & \(C_{p}\) & Specific heat & mm\({}^{2}\).K/S\({}^{2}\) & \(452\times 10^{6}\) & \(910\times 10^{6}\) \\ \cline{2-6}  & \(\chi\) & Taylor–Quinney empirical constant/inelastic heat fraction & - & 0.9 & 0.9 \\ \cline{2-6}  & \(T_{m}\) & Melting temperature & K & 1800 & 893 \\ \cline{2-6}  & \(T_{0}\) & Room temperature & K & 293 & 293 \\ \cline{2-6}  & \(m\) & Thermal-softening exponent & - & 0.94 & 1.0 \\ \hline \multirow{4}{*}{Fracture strain constants} & \(d_{1}\) & - & - & 0.0705 & 0.096 \\ \cline{2-6}  & \(d_{2}\) & - & - & 1.732 & 0.049 \\ \cline{2-6}  & \(d_{3}\) & - & - & \(-0.54\) & \(-3.465\) \\ \cline{2-6}  & \(d_{4}\) & - & - & \(-0.015\) & 0.016 \\ \cline{2-6}  & \(d_{5}\) & - & - & 0 & 1.099 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Johnson-Cook material model parameters for Weldox 460E Steel (adopted from [54,55]) and AL7075-T651 Aluminum (adopted from [56]) used for the bollard and its cellular core, respectively. coefficient = 0.3) and normal behavior with \"Hard\" contact. Separation after contact was allowed. The interaction was created using built-in general contact (Explicit) in Abaqus. A value of \(-9810\) mm/s\({}^{2}\) was applied for gravity acceleration for the whole model, as shown in Figure 2a. The impact velocity of the vehicle was applied at 16, 32, 48, 64, and 80 km/h (as specified in PAS 68:2013 standard) with the equivalent in mm/s. This resulted in five sub-models for each main model assembly, meaning that the total number of simulations was 15 models. The application of impact velocity was simulated using \"predefined field\" feature applied to the reference point (RF) of the car rigid body (Figure 2b). In this model, only the V3 (velocity in 3 rd/\(Z\)-direction) component was set to the desired velocity as the analysis concerns the effect of one-directional impact of a speedy vehicle on a bollard (Figure 2c). A mesh study was performed using a hollow-steel bollard and one impact velocity of 64 km/h, comparing three element sizes (30, 20, and 10 mm). Based on the mesh study (Table 2), it was found that 10 mm is the most suitable finite element size for the bollard from both cost-effectiveness and accuracy point of views. Reducing the mesh size below 10 mm did not reveal a noticeable change in the results, although computational time increased dramatically. Figure 2d shows the meshed numerical model.