## 3 Finite Element Model  
The finite element model is set up using a commercial nonlinear finite element code. A dynamic explicit analysis is used for simulating the crushing of the cellular structure. The model assembly consists of a planar rigid striker, a planar rigid base, and a 3D deformable shell cellular structure as shown in Figure 9a. The striker is assigned an inertial mass of 275 kg with a velocity of 15 m/s [22; 44]. \begin{table}
\begin{tabular}{c c} \hline
**Parameters** & **Values** \\ \hline Strut thickness & 0.2, 0.4, or 0.6 mm \\ Wall thickness & 0.2, 0.4, or 0.6 mm \\ Gradient(s) & (\(T_{2}\)\(-\)\(T_{1}\))/\(L\) \\ Length(\(L\)) & 50, 100, or 150 mm \\ \hline \end{tabular}
\end{table} 
Table 1: Geometric parameters. \begin{table}
\begin{tabular}{c c c} \hline
**Type** & **Assortment** & **Simulations** \\ \hline UT & Struts = \(T_{1}\), Walls = \(T_{2}\), Length = \(L\) & 9 \\ SWT & Struts = \(T_{1}\), Walls = \(T_{2}\), Length = \(L\) & 18 \\ AT & (Struts, Walls)i = \(T_{1}\), (Struts, Walls)i+1 = \(T_{2}\), Length = \(L\) & 9 \\ GT & Stacks = \(T_{1}\)\(\rightarrow\)\(T_{2}\) with s increments, Length = \(L\) & 9 \\ \hline \end{tabular}
\end{table} 
Table 2: Assortment and number of simulations. \begin{table}
\begin{tabular}{c c} \hline
**Parameters** & **Values** \\ \hline \(E\) & 73.1 GPa \\ \(v\) & 0.33 \\ \(A\) & 276 MPa \\ \(B\) & 700 MPa \\ \(C\) & 0.0001726 \\ \(n\) & 0.421 \\ \(m\) & 1.37 \\ \(Tm\) & 502 \({}^{\circ}\)C \\ \(Tt\) & 413 \({}^{\circ}\)C \\ \(\dot{\epsilon_{0}}\) & 1 s\({}^{-1}\) \\ \(\rho\) & 2780 kg/m\({}^{3}\) \\ \hline \end{tabular}
\end{table} 
Table 3: Aluminum AA2024 Johnson-Cook Material Properties [41; 42]. During head-on collisions, the two frontal tubes are expected to absorb less than 50% of the mass kinetic energy of the vehicle to protect the passengers [44; 45]. Since batteries are either located at the back, the sides, or the center of the vehicle, they are not a primary concern during a frontal collision. However, assuming that the cellular structures need to absorb an equivalent amount of kinetic energy during a side or a rear impact, the inertial mass is set at 275 kg, which is 25% of the mass of a compact electric vehicle of 1100 kg [22]. While the striker is free to move along [\(\pm\)Y], it cannot rotate or translate along any other axes. The base is fixed and assigned a tie-constrain with the cellular structure. The cellular structure was meshed using the S4R shell continuum element with a mesh size of 0.8. The mesh size is selected after a mesh sensitivity analysis as shown in Table 4. \(F_{P}\), \(F_{\mu}\), \(E_{A}\), and \(E_{SEA}\) all start converging at a mesh size of 0.8 within a reasonable computation time. The general model (boundary condition, material model, and constraints) is validated using the model described by [23]. We managed to obtain good accuracy. After which, we used this model and replaced the tubular geometry with our cellular structure geometry. The material model used in both cases are Johnson-Cook which is well established in the literature and is commonly used with aluminum alloy materials. To validate further our FE model used in this paper, a cellular structure geometry from the literature [46], as shown in Figure 9b, and Johnson-Cook AA3003 material properties [47] was used. We simulated the work in [46] using the FE model presented in this paper with slight changes to the material properties [47] and inertia values to meet the requirements of [46]. The specific energy absorption values reported in [46] are compared to our FE model simulations as depicted in Table 5. It is demonstrated that the error between [46] and our FE approach is small.