## 2 Materials and Methods  
### Numerical Model of a Cell Pack with Spacers  
The proposed concept aims to enhance the crashworthiness of a lithium-ion cylindrical cell pack by strategically placing spacers between the cells. This approach is designed to convert the initial line contacts between adjacent cells into broader surface contacts, thereby increasing the overall stiffness of the pack and reducing radial deformation during compression. Given the complexity and novelty of this idea, it was initially tested using Finite Element Analysis (FEA) rather than physical experiments. This choice was made because a material model for compression had already been defined in a previous paper [13], making FEA an efficient method to evaluate the concept without consuming physical resources at this early stage. As illustrated in Figure 1, the simulation results confirmed that filling the gaps between the cells with various materials could indeed reduce the radial deformation and require a greater force to achieve deformation. These findings suggest that the implementation of spacers could significantly improve the structural integrity and safety of lithium-ion cell packs in crash scenarios, providing a strong rationale for further experimental validation. The arrangement of the cells within the battery pack is a critical factor in evaluating the robustness and effectiveness of the proposed crashworthiness enhancement. Three potential configurations were considered and are illustrated in Figure 2. The first two, configurations V1 (Figure 2a) and V2 (Figure 2b), depict an intercalated pattern of the cells with two perpendicular directions of loading, as the configuration is not symmetrical on the top-down and lateral axes. Lastly, the third configuration, V3 (Figure 2c), shows direct stacking, where the cells are positioned closely adjacent to one another in a parallel arrangement, symmetrically as on the loading directions mentioned above. These diverse configurations were selected to test the concept across all plausible high-density battery pack designs, ensuring that the enhancement strategy is effective regardless of the cell arrangement. The loading scenario for the study was designed to simulate quasi-static conditions, reflecting real-world forces that a battery pack might experience in the event of a compression or indentation scenario. This was achieved using virtual compression equipped with two distinct impactors, as seen in Figure 3. The first impactor head is a flat plate that covers the entire surface of the pack, applying uniform compression across the cells. The second head is a 20 mm diameter cylinder recommended by SAND2017 6925:2017 [28] for cells under 32 mm diameter, specifically chosen to introduce a localized indentation force. By employing both a flat plate and a cylinder in the simulation, the study ensures that the effects of both flat and indentation compression are thoroughly evaluated, providing a comprehensive understanding of the pack's behavior under different stress conditions. The boundaries of the test setup are defined by three rigid plates representing the fixed ground and the walls of the battery pack. The spacers placed between the batteries presented in Figure 4, not connected directly with the batteries or the walls with adhesive or anything else, were modeled using solid elements and were constructed from three different materials: aluminum, 3D-printed PLA, and PLA at 60 \({}^{\circ}\)C. These materials were chosen for their distinct stiffness properties, shown in Table 1, which allowed for a comprehensive analysis of the concept's effectiveness under various conditions. Aluminum was selected for its high stiffness and durability, making it suitable for real-world EV applications. PLA, a commonly used 3D-printing material, was chosen for its ease of fabrication, offering a practical option for prototyping and physical testing.