With the rapid expansion of the electric vehicle market and the continuous advancement of intelligent transportation systems, the safety of EV battery pack systems has become a critical concern for both manufacturers and end users. The EV battery pack is the most valuable and fragile subsystem of an electric vehicle, and its integrity directly determines the overall crash safety of the vehicle. Over the past decade, numerous fire accidents involving electric vehicles have been attributed to mechanical abuse of the EV battery pack during bottom impacts. These events highlight the urgent need for a comprehensive understanding of the coupled mechanical, electrical, and thermal responses of lithium-ion cells under collision loading. Traditional design approaches rely heavily on experimental testing, which is both costly and time-consuming. Therefore, this study aims to establish a systematic simulation-driven design framework for the bottom impact protection structure of the EV battery pack, based on a high-fidelity mechanical-electrical-thermal coupled model. The research covers four main aspects: model construction, failure prediction, innovative structural design, and application verification.
1. The Coupled Simulation Model of the EV Battery Pack
The first and most fundamental step in this research was the development of a mechanical-electrical-thermal coupled simulation model for the EV battery pack cell module. This model was built using the LS-DYNA finite element software, which provides a robust platform for multi-physics coupling analysis. The mechanical sub-model describes the deformation behavior of the battery cells under external loading, the electrical sub-model simulates the current and voltage distribution, the thermal sub-model captures the heat generation and dissipation, and the short-circuit sub-model triggers when the distance between the positive and negative current collectors falls below a critical threshold. The interaction among these physical fields is illustrated by the following coupled relationships:
$$ \dot{q} = \dot{q}_p + \dot{q}_B + \dot{q}_I + \dot{q}_E \tag{1} $$
where \(\dot{q}_p\) is the heat generated by plastic deformation, \(\dot{q}_B\) is the heat produced during normal battery operation, \(\dot{q}_I\) is the heat released by internal short-circuit, and \(\dot{q}_E\) is the heat generated by thermal runaway reactions.
The electrical model is based on the distributed Randles circuit model, in which the cell terminal voltage is expressed as the superposition of the open-circuit voltage, the ohmic polarization drop, and the dynamic overpotential. The governing equation of the dynamic overpotential is given by:
$$ \frac{dV_c}{dt} = \frac{I}{C_{10}} – \frac{V_c(t)}{R_{10} C_{10}} \tag{2} $$
where \(V_c\) is the polarization voltage, \(I\) is the current, \(C_{10}\) is the double-layer capacitance, and \(R_{10}\) is the charge-transfer resistance. The state of charge (SOC) is defined as:
$$ SOC(t) = SOC(t_0) – \frac{c_q}{Q} \int_{t_0}^{t} I(t) dt \tag{3} $$
where \(c_q\) is the SOC conversion coefficient and \(Q\) is the nominal capacity of the cell.
The thermal sub-model solves the three-dimensional transient heat conduction equation:
$$ \rho c_p \frac{\partial \theta}{\partial t} =
abla \cdot (k
abla \theta) + \dot{q} \tag{4} $$
in which \(\rho\) is the density, \(c_p\) is the specific heat capacity, \(k\) is the thermal conductivity, and \(\theta\) is the temperature. During the simulation, the thermal runaway reaction is triggered when the temperature exceeds a threshold of 70°C, and an additional heat generation power of 30 mW is applied until the temperature reaches 300°C, representing the sequential decomposition reactions of the SEI film, the anode, the cathode, and the electrolyte.
The internal short-circuit model is activated when the distance between the positive and negative current collectors decreases below the threshold \(d = 1.2 \times 10^{-5}\) m. At that moment, the Randles circuit is replaced by a short-circuit resistance \(R_s = 2 \times 10^{-4}\,\Omega\), and the short-circuit heat is calculated as:
$$ \dot{q}_I = \frac{I^2 R_s}{V_e} \tag{5} $$
where \(V_e\) is the element volume. The multi-physics coupling relationship is summarized in Table 1.
| Model | Output | Transferred parameter | Received parameter |
|---|---|---|---|
| Mechanical | Deformation, stress | Displacement d, plastic power P | Temperature \(\theta\) |
| Electrical | Potential, current | Joule heat \(\dot{q}_j, \dot{q}_r, \dot{q}_c\) | Temperature \(\theta\) |
| Internal short-circuit | Short-circuit resistance | Short-circuit heat \(\dot{q}_I\) | Displacement d, voltage |
| Thermal | Temperature field | Temperature \(\theta\) | Heat sources |
| Thermal runaway | Runaway heat | Additional heat \(\dot{q}_E\) | Temperature \(\theta\) |
The mechanical model was constructed using the LS-DYNA material model 63 with a density of 2223 kg/m³, Young‘s modulus of 1 GPa, and Poisson’s ratio of 0.05. The cell geometry in the module was 195 mm in length, 127 mm in width, and 3.43 mm in thickness, while the spacing between cells was 1.57 mm. The entire module consisted of 10 cells connected in parallel, leading to an overall dimension of 195 mm × 127 mm × 48.43 mm. The accuracy of this coupled model was validated against experimental results from the literature, and the stress and temperature contours obtained from a spherical impact simulation demonstrated close agreement with published reference data. This validation confirmed that the model is capable of reproducing the mechanical response, stress concentration, and temperature rise of an EV battery pack under impact loading.
2. Parametric Study of the Impact Process
To investigate the influence of impact parameters on the failure behavior of the EV battery pack, I conducted a series of ball impact simulations on the coupled cell model. Four key design variables were identified: the radius of the impact ball \(R\), the mass \(M\), the impact velocity \(V\), and the impact angle \(\theta\). A full-factorial sampling method was adopted to generate 500 simulation cases covering a comprehensive parameter space. The variable ranges are listed in Table 2.
| Level | \(R\) (mm) | \(V\) (m/s) | \(M\) (kg) | \(\theta\) (°) |
|---|---|---|---|---|
| 1 | 10 | 8 | 0.2 | 30 |
| 2 | 20 | 11 | 0.4 | 45 |
| 3 | 30 | 14 | 0.6 | 60 |
| 4 | 40 | 17 | 0.8 | 90 |
| 5 | 50 | 20 | 1.0 | — |
The failure criteria for the EV battery pack cells were established as follows: (1) the maximum temperature exceeds 70°C, indicating the onset of SEI decomposition and potential thermal runaway; (2) the maximum von Mises stress exceeds the yield strength of the material, representing structural failure. Based on these criteria, the results of the 500 simulations were statistically analyzed. Table 3 summarizes the number of failure and safe cases at each impact angle.
| Impact angle | 30° | 45° | 60° | 90° |
|---|---|---|---|---|
| Failure count | 49 | 54 | 57 | 22 |
| Safe count | 76 | 71 | 68 | 103 |
From the statistical results, it was observed that smaller balls with higher mass and higher impact velocity tend to induce cell failure more easily. A smaller contact area leads to higher stress concentration, while a larger kinetic energy directly increases the deformation and heat generation. In addition, the impact angle significantly influences the failure probability. At a 30° impact angle, the vertical velocity component is relatively small, so the projectile tends to rebound rather than penetrate the cells, resulting in fewer failure cases. As the impact angle increases toward 90°, the perpendicular velocity component becomes larger, making it more likely for the ball to penetrate the module and cause severe damage. These observations are consistent with the physical understanding of impact mechanics and confirm the reliability of the coupled simulation model.
3. Failure Prediction Based on Machine Learning
Although finite element simulation provides detailed physical insights into the failure mechanisms of the EV battery pack, the computational cost is high and it is difficult to use in real-time applications. To address this issue, I developed a rapid failure prediction model using machine learning methods. Five individual classifiers were selected as base learners: Support Vector Machine (SVM), K-Nearest Neighbors (KNN), Artificial Neural Network (ANN), LightGBM, and XGBoost. In addition, a Stacking ensemble learning framework was constructed to combine the predictions of multiple base learners and improve overall accuracy.
During the training process, the dataset was split into training and testing subsets with a ratio of 8:2, and Bayesian optimization was performed to tune the hyperparameters of each model using accuracy as the objective metric. The optimal parameters and corresponding accuracies are listed in Table 4.
| Model | Optimal parameters | Accuracy |
|---|---|---|
| SVM | degree=3, kernel=rbf | 0.77 |
| KNN | n_neighbors=15, p=2, weights=uniform | 0.77 |
| ANN | hidden_layer_sizes=100, activation=relu | 0.78 |
| LightGBM | learning_rate=0.3, num_leaves=116 | 0.80 |
| XGBoost | learning_rate=0.2, max_depth=3 | 0.77 |
The evaluation of these models was based on several statistical metrics defined as follows:
$$ \text{Accuracy} = \frac{TP+TN}{TP+TN+FP+FN} \tag{6} $$
$$ \text{Recall} = \frac{TP}{TP+FP} \tag{7} $$
$$ \text{Precision} = \frac{TP}{TP+FP} \tag{8} $$
$$ F1 = \frac{2 \cdot \text{Precision} \cdot \text{Recall}}{\text{Precision} + \text{Recall}} \tag{9} $$
where TP, TN, FP, and FN represent the numbers of true positives, true negatives, false positives, and false negatives, respectively. The ROC curve and the area under the curve (AUC) were also used to compare the classification performance across models.
For the Stacking framework, I used 5-fold cross-validation to generate the meta-features from the base learners. Four different combinations of base learners and meta-learners were tested, and the results are shown in Table 5.
| 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 |
Among these combinations, the Stacking model using LightGBM, XGBoost, ANN, and SVM as base learners with ANN as the meta-learner achieved the highest accuracy of 0.82. The AUC value of this Stacking model reached 0.86, which was higher than any of the individual base learners. This demonstrates the advantage of ensemble learning in improving the prediction of EV battery pack cell failure under impact conditions.
To evaluate the generalization ability of the best-performing Stacking model, an additional set of 27 samples outside the original design domain was generated. The prediction accuracy on these out-of-domain samples was 0.78, with an F1 score of 0.694. Although there was a slight degradation compared to the in-domain performance (F1 = 0.75), the model still exhibited satisfactory prediction accuracy and stability. This result confirms that the Stacking model is capable of providing reliable predictions for unseen impact scenarios, which makes it suitable for real-time safety assessment of the EV battery pack.
| Dataset | Accuracy | Precision | Recall | F1 Score |
|---|---|---|---|---|
| In-domain | 0.82 | 0.818 | 0.692 | 0.750 |
| Out-of-domain | 0.78 | 0.758 | 0.641 | 0.694 |
4. Design of the Lotus-Root-Inspired Protective Plate
Based on the failure prediction results, it is clear that the EV battery pack is highly vulnerable to bottom impacts. Therefore, I proposed an innovative lotus-root-inspired multi-cell protective plate to enhance the crashworthiness of the EV battery pack under-ground impact conditions. The design is inspired by the natural geometry of lotus roots, which exhibit a unique two-end-wide and middle-narrow configuration. This shape provides excellent energy absorption and impact resistance properties. The basic unit cell of the lotus-root structure is composed of two positive hexagonal frustum shapes connected by a small platform face, as shown conceptually in the parametric diagram.
The key geometric parameters of the unit cell include the short edge length \(L_1\), the long edge length \(L_2\), the height \(H\), and the wall thickness \(T_1\). The connection plates between adjacent cells have lengths \(L_3\) (horizontal) and \(L_4\) (vertical). The relationship between the geometric parameters satisfies:
$$ \tan\theta = \frac{2(L_2 – L_1)}{H} \tag{10} $$
The entire protective plate consists of multiple unit cells arranged in both horizontal and vertical directions, with top and bottom cover plates added to form a complete sandwich structure. The finite element model was constructed using the HyperMesh preprocessor and solved with LS-DYNA. The material used was aluminum alloy with the properties listed in Table 6.
| Property | Density (kg/m³) | Elastic modulus (GPa) | Yield strength (MPa) | Poisson‘s ratio |
|---|---|---|---|---|
| Value | 2.7 × 10³ | 70 | 380 | 0.3 |
The impact simulation was performed by dropping a rigid ball with a radius of 20 mm at a velocity of 200 mm/s onto the upper surface of the protective plate, while the plate was clamped at its boundaries and supported by a rigid wall at the bottom. The displacement and stress distributions of the plate were monitored during the impact process. The results showed that the lotus-root structure effectively absorbed the impact energy through progressive deformation of the unit cells, demonstrating excellent energy dissipation capability.
To further quantify the performance of the protective plate, I evaluated the maximum stress on the bottom cover plate and the maximum reaction force on the rigid wall. A baseline configuration with \(L_1 = 3\) mm, \(L_2 = 5\) mm, \(H = 10\) mm, and \(T_1 = 0.6\) mm produced a maximum stress of 353.2 MPa and a maximum rigid-wall force of 20722.1 N. To understand the influence of the geometric parameters, 27 simulation models with different combinations of \(L_1\), \(L_2\), and \(H\) were analyzed. The results are summarized in Table 7.
| \(L_1\) (mm) | \(L_2\) (mm) | \(H\) (mm) | Mass (g) | Max stress (MPa) | Max force (N) |
|---|---|---|---|---|---|
| 3 | 5 | 8 | 521.6 | 458.1 | 23403 |
| 3 | 5 | 10 | 575.9 | 353.2 | 20722 |
| 3 | 5 | 12 | 587.3 | 375.1 | 22199 |
| 4 | 6 | 8 | 559.7 | 424.5 | 30047 |
| 4 | 6 | 10 | 585.9 | 386.2 | 22502 |
| 4 | 6 | 12 | 612.6 | 378.0 | 23405 |
From the parametric study, I found that both the maximum stress and the maximum force decrease as the cell height increases. A taller cell structure provides more room for deformation, which helps to distribute stress more evenly and reduces local stress concentration. On the other hand, increasing the short edge length or the long edge length generally increases the structural stiffness, leading to a more direct force transmission and a higher peak force. However, when the dimension exceeds a certain threshold, the overall structural stability improves and the stress begins to decline. Therefore, it is important to balance these geometric parameters to achieve optimal energy absorption and impact resistance.
5. Multi-Objective Optimization of the Protective Structure
To systematically find the optimal combination of geometric parameters, I formulated a multi-objective optimization problem. The design variables were the short edge length \(L_1\), the long edge length \(L_2\), and the cell height \(H\), with the ranges listed in Table 8.
| Variable | Initial value (mm) | Lower bound (mm) | Upper bound (mm) |
|---|---|---|---|
| \(L_1\) | 3 | 3 | 4 |
| \(L_2\) | 5 | 4 | 6 |
| \(H\) | 10 | 8 | 12 |
The optimization was aimed at minimizing two conflicting objectives: the maximum stress on the bottom cover plate \(\sigma_{max}\) and the total mass \(M\). The mathematical formulation of the optimization problem is:
$$ \min \, f(\sigma_{max}, M) \quad s.t. \quad 3 \leq L_1 \leq 4, \; 4 \leq L_2 \leq 6, \; 8 \leq H \leq 12 \tag{11} $$
To reduce the computational burden, I constructed surrogate models for both response functions. Three surrogate modeling techniques were compared: Radial Basis Function (RBF), Kriging, and Neural Network (NN). The prediction accuracies of these surrogates were evaluated using the coefficient of determination \(R^2\), the mean relative error (MRE), and the mean normalized error (MNE), defined as:
$$ R^2 = 1 – \frac{\sum_{i=1}^{n} (y_i – \hat{y}_i)^2}{\sum_{i=1}^{n} (y_i – \bar{y})^2} \tag{12} $$
$$ \text{MRE} = \frac{1}{n} \sum_{i=1}^{n} \left| \frac{\hat{y}_i – y_i}{y_i} \right| \tag{13} $$
$$ \text{MNE} = \frac{1}{n} \sum_{i=1}^{n} \left| \frac{\hat{y}_i – y_i}{\max(y_i) – \min(y_i)} \right| \tag{14} $$
The comparison results of the three surrogate models are presented in Table 9.
| Model | Response | \(R^2\) | MRE | MNE |
|---|---|---|---|---|
| RBF | Stress | 0.9306 | 0.0473 | 0.0660 |
| Mass | 0.9846 | 0.1085 | 0.0245 | |
| Kriging | Stress | 0.9523 | 0.0310 | 0.0474 |
| Mass | 0.9984 | 0.2475 | 0.0102 | |
| NN | Stress | 0.9996 | 0.0773 | 0.0050 |
| Mass | 0.9973 | 0.1507 | 0.0138 |
Based on these comparisons, the Neural Network model was chosen as the surrogate model for the optimization process, as it provided the best balance between accuracy and computational efficiency. The DE-NSGA-II hybrid algorithm was then employed to solve the multi-objective optimization problem. This algorithm integrates the global search capability of differential evolution with the fast non-dominated sorting and diversity preservation of NSGA-II. The algorithm parameters are listed in Table 10.
| Parameter | Value |
|---|---|
| Population size | 500 |
| Number of generations | 200 |
| Crossover probability | 0.8 |
| Mutation probability | 0.1 |
After 200 generations of evolution, a set of Pareto-optimal solutions was obtained, showing the trade-off between the maximum stress and the mass of the protective plate. To select the final compromise solution, I applied the TOPSIS method, which ranks the Pareto solutions based on their relative closeness to the ideal solution. The optimal compromise solution had a relative closeness coefficient of 0.671, corresponding to a maximum stress of 350.3 MPa and a mass of 563.4 g, with design parameters \(L_1 = 3.5\) mm, \(L_2 = 5.1\) mm, and \(H = 8.9\) mm.
The optimized design was then validated by reconstructing the finite element model with the optimized parameters and performing a new impact simulation. The comparison between the surrogate model prediction and the finite element result is shown in Table 11.
| Source | Max stress (MPa) | Mass (g) |
|---|---|---|
| Finite element model | 348.7 | 561.8 |
| Surrogate model | 350.3 | 563.4 |
The errors between the surrogate predictions and the finite element results were less than 5%, confirming the reliability of the surrogate-based optimization approach. Compared with the baseline design, the optimized protective plate achieved a reduction in the maximum stress from 353.2 MPa to 348.7 MPa, while the mass was reduced from 575.9 g to 561.8 g. In addition, the maximum deformation of the protective plate decreased from 10.09 mm to 7.35 mm, indicating a significant improvement in both safety and lightweight performance.
6. Application of the Protective Plate in a Full Battery Pack
To further demonstrate the practical value of the proposed design, I applied the optimized lotus-root multi-cell protective plate to a real EV battery pack model. The battery pack consisted of a lower housing, an upper cover, battery modules, busbars, and other auxiliary components. The finite element model of the entire EV battery pack was built in HyperMesh, with the main structural parameters listed in Table 12.
| Element type | Number | Proportion |
|---|---|---|
| Solid elements | 48,141 | 16.8% |
| Shell elements | 251,211 | 83.2% |
Before conducting the impact simulation, I performed a modal analysis of the EV battery pack to ensure that its natural frequencies do not coincide with the excitation frequencies from the vehicle body. The first four natural frequencies are listed in Table 13.
| 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 natural frequency of 25.24 Hz is above the commonly required threshold of 22 Hz for passenger vehicles, indicating that the EV battery pack will not experience resonance under typical driving conditions.
The bottom impact simulation was conducted according to the Chinese standard test protocol, using a hemispherical impact head with a diameter of 150 mm, an extrusion speed of 2 mm/s, and a target force of 20 kN. The original protective structure used a conventional single-cell filling, while the optimized design replaced it with the lotus-root multi-cell filling. The mass of the protective plate increased slightly from 26.27 kg to 28.85 kg, corresponding to a mass increase of 9.83%, which is acceptable for the substantial safety improvement achieved.
The simulation results were compared in terms of the maximum displacement of the EV battery pack and the maximum stress in the battery cells. With the original filling structure, the maximum displacement of the EV battery pack under the bottom impact was 24.65 mm, while the optimized lotus-root filling reduced this value to 19.65 mm, a reduction of 20.28%. Similarly, the maximum cell stress decreased from 369.2 MPa under the original structure to 332.2 MPa with the optimized structure, representing a reduction of 12.73%. These results are summarized in Table 14.
| Indicator | Original filling | Lotus-root filling | Reduction |
|---|---|---|---|
| Max displacement (mm) | 24.65 | 19.65 | 20.28% |
| Max cell stress (MPa) | 369.2 | 332.2 | 12.73% |
The deformation cloud maps clearly indicated that the lotus-root filling effectively distributes the impact energy through the progressive collapse of the multi-cell structure, avoiding severe local stress concentration. The improved energy dissipation mechanism not only reduces the displacement of the EV battery pack housing but also protects the battery cells from excessive mechanical loading, thereby reducing the risk of internal short-circuit and thermal runaway. The optimized protective plate therefore provides a reliable and efficient solution for the bottom impact protection of the EV battery pack.
7. Conclusion
In this thesis, I conducted a comprehensive study on the bottom collision protection of the EV battery pack based on a mechanical-electrical-thermal coupled simulation framework. The main conclusions of this research are summarized as follows:
(1) A high-fidelity mechanical-electrical-thermal coupled simulation model was successfully established and validated. This model is capable of simultaneously capturing the mechanical deformation, electrical response, temperature rise, and short-circuit behavior of the EV battery pack under impact loading, providing a solid foundation for subsequent safety analysis.
(2) The parametric impact study revealed that the radius, mass, velocity, and impact angle of the intruder significantly influence the failure behavior of the cells. Smaller and heavier projectiles with high impact velocity are more likely to cause failure, and the impact angle affects the failure probability through its effect on the vertical velocity component.
(3) The Stacking ensemble learning model was found to outperform all individual classifiers in predicting the failure state of the EV battery pack cells, achieving an accuracy of 0.82 in the design domain and 0.78 outside the design domain. The model demonstrates excellent prediction accuracy and generalization ability, making it suitable for real-time safety assessment applications.
(4) An innovative lotus-root-inspired multi-cell protective plate was designed and optimized through a multi-objective optimization framework. The optimized design achieved a simultaneous reduction in the maximum stress, maximum deformation, and mass compared to the baseline design, demonstrating a good balance between crashworthiness and lightweight performance.
(5) The application of the optimized protective plate to a full EV battery pack under bottom impact confirmed its superior protective performance. The optimized plate reduced the maximum displacement of the battery pack by 20.28% and the maximum cell stress by 12.73%, significantly lowering the risk of battery failure and thermal runaway.
This research provides a systematic methodology for the safety design of the EV battery pack under bottom impact conditions. The integration of multi-physics simulation, machine learning prediction, and structural optimization offers a new pathway for the development of safer and more reliable electric vehicles. Future work will focus on extending the proposed methods to other impact scenarios, such as side impacts and torsional loads, as well as incorporating more advanced materials and manufacturing processes into the protective structure design.