As the global automotive industry transitions toward sustainable mobility, the safety of electric vehicle battery systems has become a critical engineering challenge. In particular, bottom impact events — caused by road debris, curbs, or uneven terrain — pose a significant threat to the structural integrity and thermal stability of lithium-ion battery packs. The resulting mechanical deformation can trigger internal short circuits, localized heating, and even thermal runaway, endangering both vehicle occupants and property. To address this issue, I have developed a comprehensive methodology that integrates mechanical-electrical-thermal coupling simulations, data-driven failure prediction models, and bio-inspired protective structures. The objective is to enhance the crashworthiness of electric vehicle battery packs under bottom impact scenarios through rigorous simulation, optimization, and application-oriented validation.
1. Multi-Physics Coupled Modeling of Electric Vehicle Batteries
The first step in my research was to establish a high-fidelity simulation framework that can accurately capture the coupled mechanical, electrical, and thermal responses of an electric vehicle battery module under external impact. Unlike traditional single-field analysis, this coupled approach allows simultaneous evaluation of structural deformation, short-circuit onset, heat generation, and potential thermal runaway. I implemented the model using LS-DYNA, which provides a robust environment for complex multi-physics interactions.
1.1 Mechanical Model
I modeled the battery module as a stack of ten pouch cells connected in parallel. Each cell was meshed using thick-shell elements (Tshell) to balance computational efficiency and accuracy. The overall module dimensions are 195 mm × 127 mm × 48.43 mm, with a cell thickness of 3.43 mm and an inter-cell gap of 1.57 mm. The mechanical behavior of the active material was represented by LS-DYNA material model 63 (MAT_CRUSHABLE_FOAM) with a density of 2223 kg/m³, Young’s modulus of 1 GPa, and Poisson’s ratio of 0.05. The stress-strain response, shown below, was calibrated from experimental data and used to capture the nonlinear compaction behavior during impact.
| Property | Value |
|———-|——-|
| Density | 2223 kg/m³ |
| Young’s modulus | 1 GPa |
| Poisson’s ratio | 0.05 |
| Cell length | 195 mm |
| Cell width | 127 mm |
| Cell thickness | 3.43 mm |
| Inter-cell gap | 1.57 mm |
| Number of cells | 10 |
$$ \sigma = f(\varepsilon, \dot{\varepsilon}) $$
where \(\sigma\) is the true stress, \(\varepsilon\) is the true strain, and \(\dot{\varepsilon}\) is the strain rate. I considered strain-rate effects through the available material model parameters to reflect dynamic loading conditions.
1.2 Electrical and Short-Circuit Model
For the electrical response, I adopted a distributed Randles equivalent circuit model within the electromagnetic solver of LS-DYNA. The circuit consists of an open-circuit voltage source, an ohmic resistance, and a parallel RC pair representing charge-transfer dynamics. Each cell layer is connected through isopotential surfaces, and the governing equation for the dynamic overpotential is:
$$ \frac{dV_c}{dt} = \frac{I}{C_{10}} – \frac{V_c}{R_{10} C_{10}} $$
Here, \(C_{10}\) is the double-layer capacitance, \(R_{10}\) is the charge-transfer resistance, and \(V_c\) is the polarization voltage. The state of charge (SOC) is updated via the Coulomb counting equation:
$$ \text{SOC}(t) = \text{SOC}(t_0) – \frac{c_q}{Q} \int_{t_0}^{t} I(t) dt $$
The distributed network enables simulation of spatially non-uniform currents across the electrode surfaces. The key aspect of the internal short-circuit model is that when the distance between a positive current collector node and a negative current collector node falls below a threshold \(d_s\), the Randles circuit in that region is replaced by a short resistance \(R_s\). In my model, I set \(d_s = 1.2 \times 10^{-5}\ \text{m}\) and \(R_s = 2 \times 10^{-4}\ \Omega\). This approach allows automatic detection of short-circuit onset as a function of mechanical deformation.
1.3 Thermal Model and Thermal Runaway
The temperature field is computed by solving the three-dimensional transient heat conduction equation:
$$ \rho c_p \frac{\partial T}{\partial t} = \nabla \cdot (k \nabla T) + \dot{q} $$
where \(\rho\) is density, \(c_p\) is specific heat capacity, \(k\) is thermal conductivity, and \(\dot{q}\) is the total heat generation rate, which includes contributions from plastic deformation, Joule heating, short-circuit heating, and exothermic side reactions:
$$ \dot{q} = \dot{q}_p + \dot{q}_B + \dot{q}_I + \dot{q}_E $$
The individual terms are:
$$ \dot{q}_p = \frac{P}{V_e}, \quad \dot{q}_B = \frac{j^2}{\sigma} + \frac{I^2 R_0}{V_e} + \frac{I T}{V_e} \frac{\partial U}{\partial T}, \quad \dot{q}_I = \frac{I^2 R_s}{V_e}, \quad \dot{q}_E = \frac{\dot{Q}_E}{V_e} $$
where \(P\) is plastic dissipation power, \(R_0\) is ohmic resistance, \(R_s\) is short-circuit resistance, and \(\dot{Q}_E\) is the heat generation from thermal runaway side reactions. In my simulations, I set the onset temperature for thermal runaway side reactions at 70°C and the termination temperature at 300°C, with an exothermic power of 30 mW. The coupling between the mechanical, electrical, and thermal domains is summarized in the following table:
| Coupling Type | Transferred Quantities | Direction |
|---|---|---|
| Mechanical → Electrical | Current collector distance | Unidirectional |
| Mechanical → Thermal | Plastic dissipation power | Unidirectional |
| Electrical ↔ Thermal | Heat generation and temperature | Bidirectional |
| Thermal → Thermal runaway | Temperature threshold | Unidirectional |
| Thermal runaway → Thermal | Exothermic power | Unidirectional |
1.4 Model Validation
To verify the reliability of my coupled model, I simulated a spherical impact scenario and compared the resulting stress and temperature distributions with published experimental observations. The finite element model of a 30 mm radius sphere impacting the battery module at 10 m/s is shown in the simulation setup. The stress contours exhibit a concentrated region near the impact point, consistent with the expected local yielding. The temperature contours show a distinct hot spot caused by mechanical energy dissipation and potential short-circuit heating. These qualitative agreements confirm that the coupled model can reproduce primary failure features under impact loading.
2. Failure Prediction of Electric Vehicle Battery Packs based on Coupled Simulations
With the validated coupled model, I conducted a systematic parametric study to investigate how the impactor characteristics affect the failure behavior of an electric vehicle battery module. I selected four key design variables: sphere radius \(R\), sphere mass \(M\), impact velocity \(V\), and impact angle \(\theta\). The variables were varied over the following ranges:
| Variable | Levels |
|---|---|
| R (mm) | 10, 20, 30, 40, 50 |
| V (m/s) | 8, 11, 14, 17, 20 |
| M (kg) | 0.2, 0.4, 0.6, 0.8, 1.0 |
| θ (°) | 30, 45, 60, 90 |
Using a full factorial sampling approach, I performed 500 independent simulations covering a wide envelope of impact conditions. For each simulation, I recorded whether the battery module fails, defined by two failure criteria: (1) the maximum stress exceeds the material yield stress, or (2) the maximum temperature exceeds the SEI decomposition temperature (70°C). The failure status was encoded as \(S=1\) for failure and \(S=0\) for safety.
2.1 Statistical Analysis of Simulation Results
The simulation results revealed a clear trend: smaller and heavier spheres impacting at higher velocities are more likely to induce failure. The impact angle also plays a crucial role. For example, at 30° incidence, the vertical velocity component is smaller, and the sphere tends to rebound, reducing the risk of penetration. As the impact angle increases to 90°, the impact energy is fully directed into the battery, leading to a higher failure probability. The distribution of failure cases across different angles is summarized below:
| Impact Angle | Failure Cases | Safe Cases |
|---|---|---|
| 30° | 49 | 76 |
| 45° | 54 | 71 |
| 60° | 57 | 68 |
| 90° | 22 | 103 |
The relatively lower number of failures at 90° seems counterintuitive, but it can be explained by the fact that many large-radius, low-mass spheres at moderate velocities simply rebound without causing critical deformation. The critical failure mechanisms are dominated by local stress concentration and internal short-circuit induced heating.
2.2 Development of a Stacking Ensemble Learning Model
Since the high-fidelity coupled simulations are computationally expensive, I developed a machine-learning-based surrogate model to predict battery failure in real-time. I compared the performance of five individual classifiers — Support Vector Machine (SVM), K-Nearest Neighbors (KNN), Artificial Neural Network (ANN), LightGBM, and XGBoost — against a Stacking ensemble model that combines these classifiers. The Stacking model uses a two-layer architecture: the base-level learners generate predictions, which are then used as features by a meta-learner to produce the final output.
To prevent overfitting, I applied a 5-fold cross-validation strategy. The training set was divided into five folds; each base model was trained on four folds and validated on the remaining fold. This process was repeated five times, so every sample received an out-of-fold prediction. The meta-learner was then trained on these out-of-fold predictions. For the test set, the predictions from all folds were averaged to generate the input features for the meta-learner.
2.3 Hyperparameter Optimization and Performance Comparison
I used Bayesian optimization to tune the hyperparameters of each learner, using accuracy as the evaluation metric. The optimized parameters and resulting accuracies are reported in the table below:
| Model | Optimal Hyperparameters | Accuracy |
|---|---|---|
| SVM | kernel=rbf, degree=3 | 0.77 |
| KNN | n_neighbors=15, p=2, weights=uniform | 0.77 |
| ANN | activation=relu, alpha=0.007, hidden_layer_sizes=100 | 0.78 |
| LightGBM | learning_rate=0.3, max_depth=3, n_estimators=500 | 0.80 |
| XGBoost | learning_rate=0.2, max_depth=3, n_estimators=50 | 0.77 |
The ROC curves of the base models exhibited an average AUC of approximately 0.78. Then, I constructed a Stacking ensemble with different combinations of base learners and meta-learners. The best configuration used XGBoost, ANN, SVM, and LightGBM as base learners, with ANN as the meta-learner. This achieved an accuracy of 0.82 and an AUC of 0.86, significantly outperforming every individual model. The detailed comparison is shown below:
| Meta-learner | Base Learners | Accuracy |
|---|---|---|
| SVM | XGBoost, ANN, SVM, KNN | 0.79 |
| ANN | LightGBM, XGBoost, ANN, SVM | 0.82 |
| SVM | XGBoost, ANN, SVM, LightGBM | 0.80 |
| KNN | XGBoost, KNN, SVM, LightGBM | 0.81 |
| ANN | KNN, ANN, SVM, LightGBM | 0.81 |
I further evaluated the generalization ability of the best Stacking model on 27 out-of-domain samples with parameter combinations lying outside the original design space. The model achieved an accuracy of 0.78, with a precision of 0.758 and a recall of 0.641. Although slightly lower than the in-domain performance, this result confirms the model’s robustness and its practical value for real-time safety assessment of electric vehicle battery packs.
3. Design of a Lotus-Root-Inspired Multi-Cell Protective Plate
Having established a reliable failure prediction framework, I focused on designing a protective structure that can mitigate the impact-induced damage to the bottom of an electric vehicle battery pack. I drew inspiration from the lotus root, a natural structure that exhibits excellent energy absorption and impact resistance due to its porous, gradient geometry. My proposed design consists of an array of unit cells, each formed by two truncated hexagonal prisms joined at their smaller faces, creating a waist-like profile. This shape promotes progressive crushing and efficient energy dissipation.
3.1 Geometric Parameterization
The key geometric parameters of the lotus-root-inspired unit cell are:
- \(H\): height of the unit cell
- \(L_1\): short edge length of the hexagonal opening
- \(L_2\): long edge length of the hexagonal opening
- \(T_1\): wall thickness of the cell
- \(L_3\): length of horizontal connecting plates
- \(L_4\): length of vertical connecting plates
The inclination angle of the cell wall satisfies:
$$ \tan\theta = \frac{\sqrt{3}(L_2 – L_1)}{2H} $$
which ensures geometric compatibility and manufacturability. The cells are arranged both horizontally and vertically, with connecting plates providing structural continuity. The complete protective plate includes top and bottom face sheets that sandwich the multi-cell core, forming a robust sandwich structure.
3.2 Finite Element Analysis of the Protective Plate
I performed a series of dynamic impact simulations to evaluate the mechanical response of different geometric configurations. The plate material was aluminum with a density of \(2.7\times10^3\ \text{kg/m}^3\), elastic modulus of 70 GPa, yield strength of 380 MPa, and Poisson’s ratio of 0.3. The impactor was a rigid sphere of radius 20 mm impacting the plate at 200 mm/s. The plate’s edges were fully constrained, and a rigid wall was placed beneath the plate to simulate the supporting structure. The simulation setup is illustrated in the previous section.
For a baseline configuration with \(L_1=3\ \text{mm}\), \(L_2=5\ \text{mm}\), \(H=10\ \text{mm}\), and \(T_1=0.6\ \text{mm}\), the maximum stress on the bottom face sheet reached 353.2 MPa, while the rigid wall reaction force peaked at 6491 N. The deformation pattern showed that the core cells absorbed significant energy through progressive buckling, as evidenced by the displacement contours. The force-displacement response was non-linear, typical of cellular structures.
3.3 Parametric Study
I varied \(L_1\), \(L_2\), and \(H\) over three levels each, generating 27 models. The results indicated that:
- Increasing \(L_2\) initially increases the maximum stress on the bottom plate, but beyond a certain threshold, the stress decreases due to improved load distribution.
- Increasing \(L_1\) from 3 to 4 mm shows a non-monotonic effect: the stress first decreases (as the cell becomes more deformable), then increases when the structure becomes too flexible.
- Increasing \(H\) reduces both the maximum stress and the peak reaction force, because taller cells provide a longer crush stroke and more energy absorption.
- However, all three parameters increase the total mass of the plate.
These trends are consistent with the energy absorption mechanisms of cellular structures, where a balance between stiffness and deformability is essential.
4. Multi-Objective Optimization of the Protective Plate
To obtain the optimal compromise between structural safety and lightweight, I formulated a multi-objective optimization problem. The design variables were \(L_1 \in [3,4]\ \text{mm}\), \(L_2 \in [4,6]\ \text{mm}\), and \(H \in [8,12]\ \text{mm}\). The two objectives were to minimize (1) the maximum stress on the bottom face sheet, and (2) the total mass of the protective plate. The mathematical formulation is:
$$ \min \left\{ \sigma_{\max}(L_1,L_2,H), \ M(L_1,L_2,H) \right\} $$
$$ \text{s.t.} \quad 3 \le L_1 \le 4, \quad 4 \le L_2 \le 6, \quad 8 \le H \le 12 $$
4.1 Surrogate Modeling
Because running hundreds of full-scale dynamic simulations is computationally prohibitive, I used an optimal Latin hypercube design to generate 64 sample points uniformly in the design space. For each sample, I ran a dynamic simulation and extracted the maximum stress and mass. I then trained three surrogate models — Radial Basis Function (RBF), Kriging, and Neural Network (NN) — and compared their prediction accuracy using the coefficient of determination \(R^2\), mean relative error (MRE), and mean normalized error (MNE):
$$ R^2 = 1 – \frac{\sum_{i=1}^{n} (y_i – \hat{y}_i)^2}{\sum_{i=1}^{n} (y_i – \bar{y})^2} $$
$$ \text{MRE} = \frac{1}{n} \sum_{i=1}^{n} \left| \frac{y_i – \hat{y}_i}{y_i} \right| $$
$$ \text{MNE} = \frac{1}{n} \sum_{i=1}^{n} \frac{|y_i – \hat{y}_i|}{\max(y) – \min(y)} $$
The performance of the three surrogate models is summarized below:
| Model | Response | \(R^2\) | MRE | MNE |
|---|---|---|---|---|
| RBF | Stress | 0.9306 | 0.0473 | 0.0660 |
| RBF | Mass | 0.9846 | 0.1085 | 0.0245 |
| Kriging | Stress | 0.9523 | 0.0310 | 0.0474 |
| Kriging | Mass | 0.9984 | 0.2475 | 0.0102 |
| Neural Network | Stress | 0.9996 | 0.0773 | 0.0050 |
| Neural Network | Mass | 0.9973 | 0.1507 | 0.0138 |
Although the Kriging model had the highest \(R^2\) for mass, its MRE was relatively large, indicating potential overfitting. The neural network showed the best overall accuracy for stress prediction and a good balance for mass prediction. Therefore, I selected the neural network as the final surrogate model.
4.2 Optimization with DE-NSGA-II
I combined the neural network surrogate model with the DE-NSGA-II hybrid algorithm, which merges the global search capability of Differential Evolution (DE) with the fast non-dominated sorting and diversity preservation of NSGA-II. The algorithm parameters were set to a population size of 500, 200 generations, crossover probability of 0.8, and mutation probability of 0.1. The optimization produced a Pareto front, illustrating the trade-off between mass and maximum stress. Each point on the front represents a non-dominated design solution.
To select the most balanced solution, I applied the TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) method, which calculates the relative closeness of each Pareto solution to the ideal and anti-ideal solutions. The solution with the highest closeness coefficient (0.671) corresponded to \(L_1 = 3.5\ \text{mm}\), \(L_2 = 5.1\ \text{mm}\), and \(H = 8.9\ \text{mm}\). This design produced a predicted mass of 563.4 g and a maximum stress of 350.3 MPa.
4.3 Validation of the Optimal Design
I applied the optimized parameters to a new finite element simulation. The actual maximum stress from the simulation was 348.7 MPa and the mass was 561.8 g, resulting in relative errors of less than 5% compared to the surrogate model predictions. The optimized design reduced the maximum stress from 353.2 MPa (baseline) to 348.7 MPa, while the mass decreased from 575.9 g to 561.8 g — a reduction of 14.1 g. The maximum deformation also decreased from the baseline, confirming that the optimized protective plate provides both enhanced safety and improved weight efficiency. The comparison between the baseline and optimized designs is provided below:
| Design | \(L_1\) (mm) | \(L_2\) (mm) | \(H\) (mm) | Mass (g) | Max Stress (MPa) |
|---|---|---|---|---|---|
| Baseline | 3.0 | 5.0 | 10.0 | 575.9 | 353.2 |
| Optimized | 3.5 | 5.1 | 8.9 | 561.8 | 348.7 |
5. Application of the Optimized Protective Plate in a Battery Pack Bottom Impact Scenario
To demonstrate the real-world applicability of the optimized lotus-root-inspired protective plate, I integrated it into the finite element model of a commercial electric vehicle battery pack. The pack consists of a lower housing, battery modules, a battery management unit (BDU), thermal management components, and various connectors. I simplified the model by neglecting non-structural parts. The finite element model comprised 299,352 elements, with 16.8% solid elements (for modules and busbars) and 83.2% shell elements (for housings and covers). The battery pack materials include aluminum alloy for the housing and steel for the module frames.
5.1 Modal Analysis
Before conducting impact simulations, I performed a modal analysis using the Lanczos method to verify the dynamic characteristics of the battery pack. The first four natural frequencies were:
| Mode | Frequency (Hz) | Mode Shape Description |
|---|---|---|
| 1 | 25.24 | Center resonance of the upper cover |
| 2 | 29.31 | Two resonance regions on the upper cover |
| 3 | 40.41 | Three resonance regions on the upper cover |
| 4 | 47.51 | Two resonance regions on the upper cover |
The first-order frequency exceeds the typical excitation frequency range of passenger vehicles (15-20 Hz), ensuring that the battery pack is not prone to resonance under normal driving conditions. Thus, the structural design satisfies the vibration safety requirements.
5.2 Bottom Impact Simulation Setup
I simulated a bottom spherical impact scenario using a rigid sphere of 150 mm diameter moving upward at 2 mm/s with a target force of 20 kN. The simulation was terminated when either the force reached 20 kN or the deformation exceeded 10% of the pack height. Two configurations were compared: (1) the original protective plate with a conventional hollow filling, and (2) the optimized plate with the lotus-root-inspired multi-cell core. The mass of the optimized plate increased from 26.27 kg to 28.85 kg, a modest increase of 9.83%, which is acceptable for the significant safety improvement obtained.
5.3 Results and Discussion
The displacement contours of the battery pack under bottom impact are displayed for both configurations. The original configuration exhibited a maximum displacement of 24.65 mm, while the optimized lotus-root-filled configuration reduced the maximum displacement to 19.65 mm — a reduction of 20.28%. This indicates that the lotus-root structure effectively stiffens the bottom protective plate and distributes the impact load over a larger area.
More crucial is the stress response of the battery cells, which directly correlates with the risk of internal short circuits. The maximum cell stress was 369.2 MPa in the original configuration, whereas the optimized configuration reduced it to 332.2 MPa, corresponding to a 12.73% reduction. This significant decrease in cell stress implies a much lower probability of mechanical failure and subsequent thermal runaway in the electric vehicle battery.
The improved performance is attributed to two mechanisms: (1) the lotus-root core provides multi-level progressive crushing, absorbing more impact energy through plastic deformation; (2) the interconnected cell geometry creates a three-dimensional stress transmission network, avoiding stress concentration at a single point. The optimized protective plate thus demonstrates clear superiority in enhancing the crashworthiness of electric vehicle battery packs.
6. Concluding Remarks and Future Directions
In this research, I have presented a comprehensive framework for the safety design of electric vehicle battery packs under bottom collision. The study integrates high-fidelity multi-physics simulation, machine-learning-based failure prediction, and bio-inspired structural optimization. The key contributions are summarized as follows:
- I established a robust mechanical-electrical-thermal coupled simulation model for a battery module, capable of predicting deformation, short-circuit onset, temperature rise, and thermal runaway under impact loading.
- I conducted an extensive parametric study to understand how impactor size, mass, velocity, and angle influence battery failure. The results highlight the critical role of impact angle and the synergistic effects of multiple parameters.
- I developed a Stacking ensemble learning model that outperforms all individual classifiers, achieving 82% accuracy and 0.86 AUC on in-domain tests, and 78% accuracy on out-of-domain tests, demonstrating excellent generalization.
- I proposed a novel lotus-root-inspired multi-cell protective plate, systematically evaluated its mechanical response, and optimized its geometric parameters using a combination of optimal Latin hypercube sampling, neural network surrogate modeling, and the DE-NSGA-II multi-objective algorithm.
- I applied the optimized protective plate to a real battery pack and demonstrated substantial improvements in crashworthiness: a 20.28% reduction in maximum displacement and a 12.73% reduction in maximum cell stress, with only a modest mass increase.
These outcomes provide valuable theoretical and practical guidance for the collision safety design of electric vehicle battery systems. Future research could extend this work in several directions:
- Expanding the simulation framework to capture more complex loading scenarios, such as multiple impacts, oblique drops, and torsional loads.
- Incorporating more detailed electrochemical-thermal-mechanical coupling, including degradation effects and aging, to improve long-term safety predictions.
- Exploring other bio-inspired structures, hybrid materials, and topological optimization techniques to further enhance energy absorption while reducing weight.
- Validating the proposed protective structure through physical drop tower tests and real-vehicle bottom impact tests.
- Developing a real-time on-board safety monitoring system that uses the prediction model to alert drivers immediately after a bottom impact event.
In summary, the proposed methodology not only deepens the understanding of impact-induced failure in electric vehicle battery packs but also offers actionable design solutions that can be readily implemented in next-generation electric vehicles. The fusion of multi-physics simulation, data-driven modeling, and bio-inspired optimization holds great promise for improving the safety, reliability, and market acceptance of electric vehicles.