The rapid advancement of battery EV car technology has brought the issue of battery pack safety to the forefront. The battery box, housing the energy source, is critically vulnerable to impacts from road debris, posing significant risks of thermal runaway and catastrophic failure. Therefore, developing robust yet lightweight protective structures is paramount for the safety and reliability of every battery EV car. This work proposes a novel protective design utilizing a Body-Centered Cubic (BCC) lattice sandwich structure for the underbody shield of an electric vehicle’s battery compartment. To overcome the prohibitive computational cost of simulating detailed lattice geometries in full-scale models, a homogenization-based constitutive modeling approach is implemented. This method allows for efficient numerical analysis while accurately capturing the macroscopic mechanical behavior of the complex lattice, facilitating a comprehensive study on the design’s crashworthiness and the influence of key geometric parameters.
The proliferation of the battery EV car is a direct response to global energy and environmental challenges. However, the concentrated energy density of lithium-ion batteries introduces a severe safety concern, particularly regarding mechanical integrity under impact. Road debris impact, often referred to as “bottom intrusion,” is a frequent and dangerous event for a battery EV car, potentially leading to cell short-circuiting, fire, or explosion. Traditional monolithic steel plates add excessive weight, counteracting the efficiency gains of the battery EV car. Consequently, lightweight sandwich structures with energy-absorbing cores have emerged as a promising solution. Among these, metallic lattice structures offer an exceptional combination of high specific strength, specific stiffness, and tunable energy absorption, making them ideal candidates for protective applications in a battery EV car.
Problem Statement and Protective Structure Concept
The primary objective is to shield the battery box of a battery EV car from high-velocity impacts by road debris. A simplified battery box model is constructed, consisting of a cover, a lower tray, side plates, and mounting brackets. The threat is modeled as a rigid truncated cone, representing common sharp road debris like rocks or curb stones. The protective system is conceived as a sandwich panel attached beneath the lower tray. The core of this panel is a periodic BCC lattice structure, chosen for its balanced mechanical properties. The facesheets and the lattice core are designated to be made from high-strength 7075-T6 aluminum alloy for optimal strength-to-weight ratio, while the battery box itself uses automotive-grade steel sheets.
The relative density ($\bar{\rho}$) of the BCC lattice core, a critical parameter governing its mass and mechanical properties, is derived from its unit cell geometry. For a BCC unit cell with strut length \(L\) and strut diameter \(d\), the relative density is given by:
$$ \bar{\rho} = \frac{\rho_{\text{lattice}}}{\rho_{\text{solid}}} = \frac{8 \cdot (\frac{\pi d^2}{4}) \cdot (\frac{\sqrt{3}}{2}L)}{L^3} = 2\sqrt{3}\pi \left(\frac{d}{L}\right)^2 $$
$$ \bar{\rho} \approx 10.88 \left(\frac{d}{L}\right)^2 $$
The material properties assigned for the finite element simulation are summarized in the table below.
| Component | Material | Density (g/cm³) | Young’s Modulus (GPa) | Poisson’s Ratio | Yield Strength (MPa) |
|---|---|---|---|---|---|
| Battery Box (Cover, Tray) | DC01 Steel | 7.90 | 210 | 0.30 | 210 |
| Side Plates, Brackets | DC03 Steel | 7.85 | 210 | 0.30 | 170 |
| Protective Structure (Facesheets & Core) | 7075-T6 Aluminium | 2.81 | 72 | 0.33 | 235 |
Homogenization Constitutive Model for the Lattice Core
Explicitly modeling every strut in a full-scale battery box shield for a battery EV car results in an intractable number of finite elements. The homogenization technique addresses this by representing the periodic lattice as an equivalent continuous material with effective properties. A user-defined material model (VUMAT) is developed based on an anisotropic constitutive model for metallic lattice cores.
Elastic Anisotropy
The BCC lattice exhibits cubic symmetry, reducing the independent elastic constants to three: Young’s modulus \(E\), shear modulus \(G\), and Poisson’s ratio \( u\). The elastic constitutive relationship in the material principal directions is:
$$
\begin{Bmatrix}
\epsilon_{11} \\
\epsilon_{22} \\
\epsilon_{33} \\
\epsilon_{12} \\
\epsilon_{23} \\
\epsilon_{31}
\end{Bmatrix}
=
\begin{bmatrix}
1/E & -\nu/E & -\nu/E & 0 & 0 & 0 \\
-\nu/E & 1/E & -\nu/E & 0 & 0 & 0 \\
-\nu/E & -\nu/E & 1/E & 0 & 0 & 0 \\
0 & 0 & 0 & 1/G & 0 & 0 \\
0 & 0 & 0 & 0 & 1/G & 0 \\
0 & 0 & 0 & 0 & 0 & 1/G
\end{bmatrix}
\begin{Bmatrix}
\sigma_{11} \\
\sigma_{22} \\
\sigma_{33} \\
\sigma_{12} \\
\sigma_{23} \\
\sigma_{31}
\end{Bmatrix}
$$
Yield Criterion and Plastic Flow
A modified Hill-type yield criterion is adopted to account for the compressibility of the lattice core. The yield function \(f\) is defined as:
$$ f = \sigma_{\text{eff}} – \sigma_Y(\bar{\epsilon}^p) $$
where \(\sigma_Y\) is the yield stress as a function of equivalent plastic strain \(\bar{\epsilon}^p\), and \(\sigma_{\text{eff}}\) is the effective stress. For a sandwich structure where in-plane loads are carried primarily by the facesheets, the effective stress is defined considering only the out-of-plane stress components relevant for transverse crushing:
$$ \sigma_{\text{eff}} = \sqrt{ \tilde{\sigma}_i P_{ij} \tilde{\sigma}_j } \quad (i, j \in \{3, 5\}) $$
Here, \(\tilde{\sigma}_i\) are the stress components, and \(P_{ij}\) is a plasticity matrix that encodes the anisotropic yield strengths obtained from unit cell simulations under uniaxial compression and shear. An associated flow rule is used:
$$ \dot{\epsilon}^p_{ij} = \dot{\lambda} \frac{\partial f}{\partial \sigma_{ij}} $$
where \(\dot{\lambda}\) is the plastic multiplier. The hardening behavior \(\sigma_Y(\bar{\epsilon}^p)\) is derived from the volume-averaged stress-strain response of a single BCC unit cell under compressive loading.
Determination of Homogenized Properties
To populate the constitutive model, finite element simulations are performed on a single BCC unit cell with periodic boundary conditions. The simulations provide the effective elastic moduli (\(E\), \(G\), \( u\)) and the complete compressive stress-strain curve up to densification, which serves as the hardening law \(\sigma_Y(\bar{\epsilon}^p)\) for the homogenized material. This process effectively translates the micro-mechanical behavior of the struts into a macroscopic, computationally efficient material model suitable for simulating the protection of a battery EV car.
Model Verification and Computational Efficiency
The accuracy and efficiency of the homogenization approach are validated by comparing the impact response of a fully detailed lattice-cored sandwich panel with its homogenized counterpart. A hemispherical impactor strikes the center of a clamped panel. The hybrid modeling strategy employs a detailed lattice mesh in the central impact zone and homogenized elements elsewhere, connected via coupling constraints.
The results demonstrate excellent agreement in key impact metrics, such as impactor acceleration and kinetic energy dissipation, with errors below 2%. The computational savings, however, are dramatic, as shown in the table below. This validates the homogenized model as a reliable and immensely efficient tool for optimizing the protective structure for a battery EV car.
| Model Type | Number of Elements | Calculation Time | Memory Usage |
|---|---|---|---|
| Full Detailed Lattice Model | ~677,000 | 777 min | 8.89 GB |
| Hybrid Homogenized Model | ~23,000 | 67 min | 0.24 GB |
| Efficiency Gain | ~29.4x fewer | ~11.6x faster | ~37x less memory |
Performance Evaluation of the Protective System
Using the verified homogenized model, the effectiveness of the BCC lattice shield is assessed for the full battery EV car battery box under a severe road debris impact (7.5 kg, 20 m/s, 45° cone angle). Two key performance indicators (KPIs) are defined:
- Maximum Intrusion (\(I_{max}\)): The peak displacement of the battery box lower tray into the battery compartment.
- Energy Absorption Share (\(E_{share}\)): The percentage of the total impact energy absorbed by the protective structure itself.
The simulation results confirm the shield’s outstanding performance. The presence of the lattice structure significantly reduces the area of high stress concentration on the battery box. More quantitatively, at 20 m/s impact, the maximum intrusion is reduced by 51.5% compared to the unprotected baseline. The protective structure absorbs approximately 46% of the total impact energy. The performance remains robust across different impact speeds, crucial for the varying operating conditions of a battery EV car.
| Impact Speed (m/s) | Max Intrusion – Unprotected (mm) | Max Intrusion – Protected (mm) | Reduction in Intrusion | Energy Share of Protection Structure |
|---|---|---|---|---|
| 10 | 33.62 | 18.84 | 43.96% | 48.72% |
| 20 | 66.45 | 32.23 | 51.50% | 45.93% |
| 30 | 106.97 | 51.95 | 51.43% | 43.26% |
Parametric Study and Design Guidelines
The homogenized model enables a comprehensive parametric study to guide the optimal design of the shield for a battery EV car. Three key design parameters are investigated: strut diameter (\(d\)), strut length (\(L\)), and facesheet thickness (\(t\)). A full-factorial Design of Experiments (DOE) is conducted for an extreme 30 m/s impact.
| Parameter | Level 1 | Level 2 | Level 3 |
|---|---|---|---|
| Facesheet Thickness, \(t\) (mm) | 0.50 | 1.00 | 1.50 |
| Strut Diameter, \(d\) (mm) | 1.00 | 2.00 | 3.00 |
| Strut Length, \(L\) (mm) | 13.86 | 17.32 | 20.78 |
The analysis yields the following insights for designing a battery EV car shield:
1. Influence of Strut Diameter (\(d\))
Increasing \(d\) increases the relative density and mass linearly. However, its effect on performance is non-monotonic:
- Maximum Intrusion (\(I_{max}\)): Initially decreases as \(d\) increases from 1.0 mm to 2.0 mm due to higher bending stiffness, then slightly increases for \(d = 3.0\) mm due to a transition in failure mode from progressive plastic buckling to a more brittle global bending.
- Energy Absorption Share (\(E_{share}\)): Generally decreases with increasing \(d\) (by 31-52%). Thinner struts undergo more extensive plastic deformation, leading to more efficient energy dissipation per unit mass.
Design Insight: A moderate strut diameter (~2.0 mm) offers a good compromise between intrusion resistance and mass efficiency for a battery EV car.
2. Influence of Strut Length (\(L\))
Increasing \(L\) decreases relative density, promoting light weight—a critical attribute for a battery EV car.
- Maximum Intrusion (\(I_{max}\)): Decreases significantly (13-48%) as \(L\) increases. A taller core provides a longer stroke for controlled crushing and energy absorption.
- Energy Absorption Share (\(E_{share}\)): Increases substantially (18-43%) with longer struts, confirming improved energy management.
Design Insight: Longer struts are highly beneficial for both energy absorption and light weighting, though packaging constraints (ground clearance) for the battery EV car must be considered.
3. Influence of Facesheet Thickness (\(t\))
The effect of \(t\) is strongly coupled with the strut diameter \(d\).
- For slender struts (\(d = 1.0\) mm), increasing \(t\) is detrimental: it increases \(I_{max}\) and decreases \(E_{share}\). This is because the stiff facesheets attract more load, causing premature shear failure in the weak core.
- For robust struts (\(d \geq 2.0\) mm), increasing \(t\) is beneficial: it reduces \(I_{max}\) (by 8-13%) and increases \(E_{share}\) (by 18-25%). The stronger core can effectively collaborate with the facesheets, leading to superior global bending resistance.
Design Insight: Facesheet thickness must be tailored to the core’s strength. For a high-performance battery EV car shield with a robust lattice core, moderately thick facesheets synergize well. However, minimizing \(t\) is always advantageous for weight reduction.
The parametric trends can be summarized by the following empirical relationships for the design space considered, where performance is a function \(F\) of the non-dimensional parameters \(d/L\) and \(t/L\):
$$ I_{max} \approx F_1\left(\frac{d}{L}, \frac{t}{L}\right) $$
$$ E_{share} \approx F_2\left(\frac{d}{L}, \frac{t}{L}\right) $$
$$ \text{Mass} \propto \bar{\rho} + \text{constant} \cdot t \approx 10.88\left(\frac{d}{L}\right)^2 + k \cdot t $$
Conclusion
This study successfully demonstrates the integration of a BCC lattice core as a high-performance protective shield for a battery EV car battery box. The implementation of a advanced homogenized constitutive model proves to be a transformative approach, enabling high-fidelity, full-scale impact simulations with computational efficiency unmatched by traditional detailed modeling. The parametric analysis provides clear, actionable design guidelines: a protective structure for a battery EV car should utilize a lattice core with moderately long struts and a diameter tuned for optimal specific energy absorption, paired with facesheets whose thickness is calibrated to the core’s relative density to avoid detrimental stiffness mismatches. This methodology not only significantly enhances the safety of the battery EV car against bottom intrusion but also does so through a lightweight, optimized design, directly contributing to the vehicle’s overall efficiency and range. The homogenization framework presented is a powerful and generalizable tool for the rapid development and optimization of advanced metamaterial-based protection systems in automotive engineering.