Enhanced Side Pole Impact Protection: Crashworthiness Optimization for Electric Micro Commercial Vehicles

Abstract

This study presents a novel optimization framework applying the multi-objective response surface method to enhance the safety of electric micro commercial vehicles (E-MCVs) during side pole impacts. By focusing on seven critical load-bearing components, including the B-pillar and door frame beam, we achieved a 2% reduction in component weight while significantly improving energy absorption by 22.2%. The optimization led to a substantial decrease in intrusion, with B-pillar abdominal intrusions reduced by 22.5% and lower threshold intrusions down by 26.3%. Despite these improvements, challenges remained regarding battery pack deformation. To address this, we proposed two innovative solutions: strengthening the side longitudinal beams and integrating a bionic thin-walled energy-absorbing structure. These approaches effectively reduced side intrusions of the battery pack by 43.5% to 43.8%, with the bionic structure showing superior performance in weight management. However, the manufacturing feasibility and cost implications of the bionic design necessitate further exploration. The innovation in this study lies in the dual application of a response surface optimization method for load-bearing components and the integration of biomimetic design principles, significantly advancing collision safety for E-MCVs while providing new insights into the weight-efficient safety design.

1. Introduction

With the advancement of the global energy transition and the implementation of low-carbon development strategies, electric vehicles have become a crucial component of modern transportation systems [1]. In particular, electric micro commercial vehicles have experienced rapid market growth due to their cost-effectiveness, environmental benefits, flexibility, and maneuverability. With the increasing number of electric vehicles, their safety has become a growing concern for both industry stakeholders and society. Automotive safety performance remains a key determinant of market competitiveness, and new vehicle models must undergo rigorous crash safety testing before market entry. According to statistics, in 2021, side impact accidents caused 21.9% of passenger car occupant deaths and 11.3% of light truck occupant deaths [2].

Side impact tests primarily comprise two categories: side moving deformable barrier (MDB) collisions [3,4] and side rigid pole collisions. Researchers worldwide have extensively studied these collisions and identified a critical issue: when a vehicle’s side lacks sufficient buffer space and energy-absorbing structures, the impact force transfers directly to the body components, significantly compromising occupant safety. Recent research has increasingly focused on side pole impacts, as these incidents often result in more severe body damage. This severity stems from the highly concentrated impact area, limited energy-absorbing space, and the likelihood of secondary collisions between vehicle components, presenting substantial risks to occupant safety [5].

Electric vehicles (EVs) introduce unique challenges in side structure design owing to their distinct power system architecture—such as floor-mounted battery packs and centralized electric drivetrains—which fundamentally differ from the engine-front and fuel-tank-rear layouts of conventional vehicles [6]. These differences necessitate innovative approaches to crash energy management and structural integration. Researchers have made significant contributions to addressing these challenges. For instance, Xia et al. conducted a simulation study on side pole impact for a two-seat small electric passenger car based on the earlier E-NCAP evaluation standard [7]. Their research employed multi-objective and multidisciplinary optimization techniques to enhance door stiffness. This optimization significantly improved overall side pole impact performance. By incorporating floor-mounted collision beams and reinforcing door sill beams with aluminum alloy profiles, they achieved notable reductions in B-pillar intrusion. These findings provide valuable insights for improving the crashworthiness of electric vehicle side impact structures.

With the rapid advancement of new energy vehicle (NEV) technologies, side pole impact safety has emerged as a critical research frontier in electric vehicle (EV) development [8,9]. While early-stage studies primarily focused on isolated component analysis, contemporary methodologies continue to face two systemic limitations. First, body structure analyses predominantly rely on body-in-white (BIW)-only simulations, which fail to capture the critical interactions between the battery pack and load-bearing structures [10,11]. Second, battery safety evaluations often assess enclosure integrity in isolation, neglecting its synergistic role within the vehicle’s crash energy management system [12,13,14]. Although emerging efforts—such as integrated BIW-battery simulations for passenger EVs [15,16,17,18]—have shown promise, they remain constrained by two significant gaps: (1) existing integrated models are primarily validated for passenger vehicles, despite fundamental design divergences in electric micro commercial vehicles (E-MCVs); and (2) current frameworks inadequately address the conflicting demands of battery protection and cargo-oriented structural rigidity in E-MCVs.

The urgency of addressing these gaps is underscored by the unique crash dynamics of E-MCVs. To meet cargo-carrying requirements, E-MCVs employ high-tensile-strength steel in load-bearing components (e.g., longitudinal rails and B-pillars), prioritizing bending and torsional stiffness over mass reduction. This design approach, combined with compact dimensions that place battery packs close to lateral body panels, creates a cascading failure risk: collision forces bypass conventional energy absorption pathways, directly compromising battery integrity. These distinct failure mechanisms necessitate safety solutions that extend beyond traditional passenger vehicle design conventions.

Research on side pole crash safety in EVs has largely focused on optimizing body structures through multi-objective optimization techniques, which aim to enhance both lightweight design and crash safety by modifying component dimensions [19,20,21]. However, there remains a notable gap in the integration of bionic structural technology. Recent years have seen growing interest in applying bionic principles to structural design, particularly in developing energy-absorbing structures that offer efficient energy dissipation and distribution. Numerous studies have demonstrated the significant advantages of bionic structures in energy absorption [22,23,24]. Nevertheless, further research is needed to validate their practical applications and systematically integrate them into vehicle body structures.

Based on the above considerations, this study investigates an electric micro commercial vehicle designed for the European market, with a specific focus on side pole impact protection. Detailed collision simulation tests are conducted at a 75° inclination in accordance with E-NCAP protocols to identify structural vulnerabilities. The research objectives are threefold: (1) to improve the safety of the vehicle in the side pole crash test by optimizing the structural parameters of the body so that the intrusion depth L1 of the B-pillar abdomen should be less than 310 mm (the buffer space between the driver and the side structure of the vehicle is approximately 320 mm); (2) to limit plastic deformation of the battery packs to less than 10% of their original size under severe collision conditions; and (3) to implement a multi-objective optimization framework using response surface methodology and second-generation genetic algorithms to balance mass efficiency and load path controllability. Two battery pack protection schemes are proposed and compared: increasing the thickness of the side longitudinal beams and embedding a bionic thin-walled energy-absorbing structure within the side longitudinal beams. The effectiveness of these approaches is systematically evaluated through comprehensive numerical analysis and experimental validation.

2. Side Pole Impact Simulation Analysis

2.1. Vehicle Model Development and Validation

This research focuses on an electric micro commercial vehicle designed for the European market, with key specifications listed in

Table 1. Vehicle-related parameters.

Name	Parameters
Curb weight/kg	1130
Front and rear wheelbase/mm	2430
Front axle load/kg	530
Rear axle load/kg	575
Position of the drive motor	Rear-motor rear-drive
Steering wheel layout	Right-hand drive

. The battery pack is mounted directly beneath the vehicle’s chassis, and the body frame is constructed of cold-rolled and high-strength steel. The vehicle model was developed using HyperMesh 2019 software. Vehicle components were modeled with MAT_024 for metal parts, the rigid body was defined using MAT_20, and weld points were characterized by MAT_100, as shown in Figure 1.

To validate the effectiveness of the finite element simulation model, this study compares the simulation results with data from a full-scale 100% frontal crash test conducted on an actual vehicle. In accordance with the EU regulations, the frontal impact of the vehicle on the rigid wall was carried out at a speed of 50 km/h. The model validation focuses on comparing the acceleration–time curves measured at the lower B-pillar between the simulation and the physical test. As shown in Figure 2, the peak acceleration recorded in the physical test is 51.9 g, while the simulation predicts 51.2 g, representing a minor difference of only 1.3%. Furthermore, Figure 3 illustrates the comparison of front-end deformation patterns between the physical test and simulation results, demonstrating excellent agreement. These correlations in both acceleration response and deformation pattern verify the reliability of the finite element model for subsequent detailed analyses.

Although the frontal impact verification achieved a 1.3% acceleration correlation, it is important to note that the numerical model has inherent uncertainties, including (1) simplification of the material model in terms of dynamic load characterization; (2) grid sensitivity of fault prediction; (3) contact interface modeling during component interaction; (4) idealization of boundary conditions; and (5) algorithm approximation error. These limitations need to be verified by multi-scenario experiments to ensure the reliability of the model under different collision conditions.

2.2. Side Pole Impact Analysis of the Original Vehicle Model

According to European side pole impact test regulations, the test involves a vehicle impacting a stationary rigid pole at a speed of 32 km/h. The pole, with a diameter of 254 mm, was positioned such that its central axis aligned with the center of gravity of the driver’s head. During the side pole impact test configuration, a 75° angle was maintained between the vehicle’s longitudinal centerline and the prescribed impact direction vector, as shown in Figure 4. Based on these regulations, a finite element model for the side pole impact was established. The contact between the rigid pole and the full-vehicle finite element model was defined as automatic surface-to-surface contact, with a friction coefficient of 0.3 to accurately simulate component interactions during collision. The material failure criterion was strain-based, as illustrated in Figure 5, and a series of simulation tests were conducted.

Traditional side pole impact tests for vehicles primarily focus on B-pillar intrusion. However, for electric vehicles, the battery pack mounted at the vehicle’s bottom is equally critical. This study specifically examines both lower sill intrusion and battery pack deformation. As shown in Figure 6, the side pole impact simulation of the original vehicle indicates that the deformation is concentrated within the narrow space around the B-pillar. The small collision contact area and resulting impact force cause significant intrusion on the vehicle’s right side, resulting in a V-shaped deformation of the body, B-pillar twisting, and severe deformation of the lower sill beam.

Based on ES-2 side impact dummy data, three observation points were established near the B-pillar (Figure 7), corresponding to the head, chest, and abdomen regions, with an additional point on the lower sill beam. Analysis of the measurement data (Figure 8) reveals that the intrusion values at principal monitoring locations exceeded the maximum permissible threshold of 350 mm. Notably, the peak intrusion recorded in the chest region reached a critical level of 396 mm, posing a significant threat to occupant safety.

By observing the deformation of the battery pack at the bottom of the vehicle in Figure 9, it was found that the original design results in significant deformation of the bottom. This is primarily due to the side impact on the vehicle, which causes severe compression of the right longitudinal beam of the battery pack, leading to significant deformation of both the battery pack bracket and the battery pack itself. The measurement results show that the maximum intrusion of the battery pack’s sidewall reaches 107.7 mm, approximately 16.3% of the overall dimension. The degree of deformation presents a clear safety hazard [25].

3. Multi-Objective Optimization of the Body-in-White Structure

3.1. Optimization Parameters Selection and Design Objectives

The side pole impact simulation reveals severe structural vulnerabilities: significant B-pillar deformation, extensive body frame and foundational beam collapse, and weak lateral body resistance to deformation. The root causes stem from low steel strength in critical load transfer components and insufficient reinforcement structures along energy transmission paths.

Through detailed analysis of load transfer paths, seven key components were identified as closely related to collision deformation. Therefore, this study proposes to optimize the vehicle body structure by selecting high-strength steel and increasing the thickness of specific components.

This study optimizes seven key components shown in Figure 10 based on the original design to improve crashworthiness while minimizing overall vehicle mass. The optimization targets include B-pillar abdominal intrusion (L₁), lower sill intrusion (L₂), total absorbed energy (E) of the optimized components; and total mass (M) of the optimized components. The design variables are the thicknesses of the seven components, with the value ranges provided in

Table 2. Range of design variables.

Design Variables	Corresponding Components	Lower Limit/mm	Initial Value/mm	Upper Limit/mm
t1	B-pillar outer panel	0.5	0.65	2.0
t2	B-pillar reinforcement plate	1.0	1.2	2.0
t3	B-pillar inner plate	0.8	1.0	2.0
t4	Lower sill inner plate	0.8	1.0	1.5
t5	Sill reinforcement beam	1.0	1.5	2.5
t6	Sill outer plate	0.5	0.65	1.2
t7	Upper beam inner plate	0.6	0.7	1.5

. Its range is determined by material properties, manufacturing process capabilities and existing material specifications.

The optimal Latin hypercube experimental method was used for data sampling within the design variable range, resulting in 75 sample points. These sample points were imported into LS-DYNA 2022 software for calculation and the experimental samples and simulation results are recorded in

Table 3. Test samples and simulation results.

Title 1	t1/mm	t2/mm	t3/mm	t4/mm	t5/mm	t6/mm	t7/mm	M/kg	L1/mm	L2/mm	E/J
1	1.80	1.89	1.32	1.07	1.16	1.01	1.37	39.47	304.09	262.45	11,766.6
2	1.96	1.80	1.40	1.24	1.41	0.57	1.03	38.00	305.56	256.29	12,202.0
3	1.21	1.46	1.95	1.19	1.55	1.16	1.44	38.29	314.94	269.53	12,060.6
4	1.03	1.08	1.01	0.80	1.47	0.86	0.93	32.02	329.68	285.61	10,852.2
…	…	…	…	…	…	…	…	…	…	…	…
75	0.87	1.72	1.82	0.98	2.10	1.15	0.81	36.67	316.42	265.37	10,847.9

(detailed data are shown in Appendix A,

Table A1. Test samples and simulation results.

Title 1	t1/mm	t2/mm	t3/mm	t4/mm	t5/mm	t6/mm	t7/mm	M/kg	L1/mm	L2/mm	E/J
1	1.80	1.89	1.32	1.07	1.16	1.01	1.37	39.47	304.09	262.45	11,766.6
2	1.96	1.80	1.40	1.24	1.41	0.57	1.03	38.00	305.56	256.29	12,202.0
3	1.21	1.46	1.95	1.19	1.55	1.16	1.44	38.29	314.94	269.53	12,060.6
4	1.03	1.08	1.01	0.80	1.47	0.86	0.93	32.02	329.68	285.61	10,852.2
5	0.66	1.65	1.87	1.32	1.26	1.06	0.90	35.73	280.54	323.51	10,327.8
6	1.94	1.81	1.89	1.26	1.95	0.83	1.39	40.49	246.59	296.24	11,923.8
7	1.51	1.50	1.74	0.96	1.28	0.64	1.46	36.23	270.10	316.64	11,822.2
8	1.47	1.88	1.90	1.34	1.85	0.82	0.67	38.15	256.79	310.00	11,716.1
9	0.93	1.35	1.14	0.87	2.46	0.66	0.89	31.03	264.10	318.57	9445.7
10	0.76	1.42	1.97	1.29	1.67	0.58	1.35	34.09	276.36	311.31	11,303.2
11	1.39	1.73	0.83	1.37	1.51	0.73	1.42	40.76	265.83	304.68	12,135.2
12	1.90	1.22	1.34	1.49	1.73	0.72	0.87	36.57	252.98	307.87	11,905.6
13	1.92	1.57	0.96	0.89	1.99	0.67	0.76	35.83	252.79	305.48	11,197.9
14	0.64	1.91	1.30	1.39	2.07	0.98	0.77	35.46	263.91	313.96	10,569.4
15	0.95	1.04	1.48	1.50	1.35	0.94	1.06	34.11	279.67	323.46	10,495.2
16	1.09	1.11	0.85	1.04	2.14	0.85	1.40	33.40	269.83	316.13	10,744.1
17	0.70	1.07	1.53	1.20	2.20	0.88	0.70	32.49	272.05	322.37	10,088.9
18	1.07	1.77	1.85	1.05	1.14	0.60	0.83	34.77	279.60	324.85	10,950.2
19	0.62	1.74	1.76	1.11	2.28	0.63	0.84	33.73	263.55	316.82	10,360.6
20	0.54	1.82	1.25	1.30	1.22	0.61	1.16	36.09	284.87	324.50	9943.9
21	0.56	1.69	1.24	0.93	1.53	0.84	0.66	32.54	281.67	325.39	10,427.4
22	1.33	1.54	1.21	1.36	2.48	0.69	0.65	35.08	251.88	310.64	10,064.3
23	1.70	1.32	1.08	1.40	1.32	1.13	1.25	37.88	264.73	310.24	11,999.4
24	1.41	1.62	1.16	1.12	2.18	1.18	1.45	35.55	274.29	316.76	11,341.6
25	1.49	1.10	2.00	1.24	1.30	0.70	0.94	35.29	270.61	321.64	11,560.7
26	1.23	1.12	1.47	0.89	2.40	1.12	1.06	35.56	260.67	313.37	10,059.4
27	1.82	1.76	0.82	1.33	1.89	0.96	0.88	38.08	253.02	299.87	11,630.2
28	0.72	1.49	1.22	0.91	1.71	0.51	1.34	31.94	279.45	325.04	10,790.9
29	1.68	1.03	0.93	1.14	2.16	0.92	0.80	34.9	256.79	308.99	11,369.8
30	1.11	1.14	1.77	1.00	1.37	1.08	0.64	34.66	279.07	326.55	10,734.2
31	1.74	1.38	1.72	0.99	2.22	0.90	0.62	37.00	249.80	307.35	10,779.8
32	0.91	1.31	1.12	1.09	1.10	0.93	1.48	34.00	287.12	325.22	10,143.5
33	1.53	1.85	1.69	0.88	2.05	0.53	1.05	36.44	255.31	309.07	11,262.9
34	1.05	1.64	0.90	1.01	2.30	1.11	0.73	35.29	260.85	310.60	9905.4
35	0.78	1.34	0.80	1.31	1.63	0.75	0.82	31.92	277.96	321.90	10,771.7
36	1.72	1.05	1.45	0.92	2.03	0.59	1.17	34.59	260.44	313.88	11,619.6
37	1.35	1.68	1.71	1.45	1.06	0.81	1.32	37.57	271.85	315.47	11,476.2
38	1.15	1.99	1.00	1.16	1.81	0.55	0.78	34.49	266.22	313.53	11,251.3
39	2.00	1.30	0.88	1.02	1.45	0.78	1.31	36.39	258.39	302.85	12,242.5
40	1.66	1.00	1.58	0.97	1.39	1.03	1.26	36.40	267.82	315.23	11,952.3
41	0.68	1.23	1.11	1.16	1.57	1.20	0.97	33.75	281.23	324.82	10,555.4
42	1.19	1.92	1.48	1.47	2.12	0.62	1.21	36.83	257.45	306.24	11,526.6
43	1.55	1.97	1.38	0.95	1.49	0.97	0.69	37.73	262.35	310.86	11,867.9
44	1.27	1.24	1.37	1.06	1.65	0.52	0.60	32.44	272.68	327.44	11,372.4
45	1.25	1.84	1.19	1.42	1.08	0.89	0.75	36.31	274.63	318.72	10,893.8
46	0.52	1.16	1.56	1.08	1.12	0.71	0.98	31.73	293.13	334.20	9301.0
47	0.85	1.93	0.91	1.13	1.43	1.09	1.15	35.92	276.02	313.66	11,067.3
48	1.78	1.43	1.04	0.90	1.61	1.19	0.95	37.55	260.15	307.56	11,707.4
49	0.80	1.45	1.64	1.48	1.59	0.59	0.72	33.16	275.64	325.72	10,973.8
50	1.13	1.26	1.03	1.46	2.36	1.04	1.11	35.58	258.00	310.05	10,617.8
51	1.86	1.55	1.84	1.22	1.18	1.10	0.92	39.47	260.72	308.49	11,834.0
52	1.31	1.18	1.17	1.25	1.20	0.50	1.20	32.96	279.38	324.90	10,878.6
53	0.89	2.00	1.79	1.06	1.69	0.86	1.29	36.93	269.32	312.44	11,708.8
54	1.98	1.27	1.61	1.27	2.24	1.11	1.11	39.46	243.30	298.10	11,591.9
55	1.76	1.66	1.81	0.81	1.91	1.05	1.22	39.27	253.04	303.08	11,738.4
56	0.99	1.47	1.94	1.41	2.34	0.99	1.09	36.98	256.76	310.30	10,968.2
57	1.84	1.51	1.06	1.23	2.42	0.65	1.27	37.14	244.74	299.55	10,562.3
58	1.27	1.70	0.95	0.94	1.00	0.68	1.01	34.08	281.29	320.68	10,832.2
59	1.17	1.51	1.66	1.03	2.44	0.76	1.49	36.18	255.69	308.06	10,316.7
60	1.43	1.87	0.98	0.83	1.93	0.80	1.33	36.47	262.02	306.74	11,589.0
61	1.88	1.41	1.63	0.82	1.24	0.74	0.86	36.33	264.09	313.70	11,659.5
62	0.97	1.28	1.98	0.84	1.85	0.76	1.04	34.05	275.12	322.59	11,078.0
63	0.82	1.19	1.27	1.35	2.26	0.54	1.18	32.28	267.89	319.32	10,464.4
64	0.58	1.60	1.35	1.43	1.75	1.00	1.43	35.32	273.47	317.19	10,829.8
65	1.62	1.37	1.92	1.28	2.32	0.56	1.00	36.44	248.90	307.56	11,285.5
66	0.50	1.57	1.29	0.86	2.01	1.02	1.28	33.86	275.48	320.31	10,076.4
67	1.01	1.61	1.60	0.85	1.04	1.07	1.10	35.78	284.52	324.66	10,597.3
68	1.64	1.20	1.09	1.18	1.02	0.90	0.71	34.93	272.24	319.19	10,845.4
69	0.60	1.01	1.68	1.15	1.97	0.95	1.38	33.35	278.95	322.47	10,248.5
70	0.74	1.78	0.87	1.20	2.38	0.77	1.23	34.17	260.87	307.63	10,039.7
71	1.60	1.96	1.42	1.10	2.50	0.94	0.99	38.94	244.94	298.56	10,245.7
72	1.57	1.15	1.55	1.38	1.83	0.79	1.50	36.67	259.64	311.28	11,919.5
73	1.35	1.39	1.42	1.41	1.77	1.14	0.61	36.80	262.90	316.76	11,443.4
74	1.45	1.95	1.51	1.44	1.77	1.17	1.14	40.09	257.59	303.28	11,991.5
75	0.87	1.72	1.82	0.98	2.10	1.15	0.81	36.67	316.42	265.37	10,847.9

).

3.2. Development and Validation of Surrogate Model

The surrogate model offers high accuracy and low computational cost, making it widely used in multi-objective, multi-variable optimization design. Common response surface models include the Kriging model, radial basis function, and polynomial response surface model [26]. The response surface approximation model can accurately approximate functional relationships within a local range using a limited number of experiments, while expressing them in simple algebraic equations. This significantly reduces computational time.

Polynomial response surface models are commonly used to construct surrogate models in vehicle crashworthiness optimization because they can capture nonlinear relationships for complex crash dynamics, while being computationally more efficient than finite element analysis for optimization iterations [27,28,29,30]. At the same time, they strike a balance between accuracy and computational cost. Therefore, this study adopts the response surface method to establish the surrogate model and selects a third-order response surface model. Its mathematical expression is given in Equation (1).

$$y\left(x\right)={\beta }_0+{\displaystyle \sum _{i=1}^n{\alpha }_i{x}_i+{\displaystyle \sum _{i=1}^n{\beta }_i{x}_i^2+{\displaystyle \sum _{i=1}^n{\gamma }_i{x}_i^3+{\displaystyle \sum _{i\ne j}{\theta }_{ij}{x}_i{x}_j}}}}$$

(1)

In this equation, y(x) represents the response objective function, while x_i and x_j denote the i and j design variables, respectively. The term ${\beta }_0$ is a constant; ${\alpha }_i$, ${\beta }_i$, ${\gamma }_i$, and ${\theta }_i$ are the coefficients of the corresponding terms. The parameter n indicates the number of design variables.

Based on the large number of simulation results obtained from the experimental design plan, and using Equation (1), response surface approximate models for the total mass (M) of the optimized components, total energy absorption (E) of the optimized components, B-pillar abdominal intrusion (L₁), and lower threshold intrusion (L₂) were established. The corresponding third-order response surface approximate models are shown in Equations (2)–(5).

$$M\left(t\right)=26.467+2.133t_1{t}_2+0.934t_2{t}_6+1.694t_3{t}_6+1.685t_4{t}_7$$

(2)

$$\begin{array}{l}E\left(t\right)=3823.61+3862.316t_1+3291.686t_5\\ -663.432t_1^2-590.22t_4^2-632.877t_1{t}_5+313.528t_2{t}_7\\ +215.674t_3{t}_4+866.421t_4{t}_5-407.328t_5^3\end{array}$$

(3)

$$L_1\left(t\right)=354.13-8.777t_5-3.827t_1{t}_6-4.666t_2{t}_4-4.459t_2{t}_7-1.978t_1^3$$

(4)

$$L_2\left(t\right)=310.583-9.218t_1-4.032t_5^2-6.087t_2{t}_4-1.675t_3{t}_5-1.785t_1^3$$

(5)

To verify the accuracy of the third-order response surface approximate models constructed above, the R² value from variance analysis was used to assess the precision of the models. R² represents the similarity between the actual values and the model’s predicted values. The closer R² is to 1, the higher the similarity between the actual and predicted values, indicating better model fitting. Typically, an R² value greater than 0.9 is considered acceptable. The specific calculation methods are given in Equations (6)–(8).

$$R^2=1-{\displaystyle \frac{Q_r}{Q_t}}$$

(6)

$$Q_r={\displaystyle \sum _{i=1}^{n_1}{\left(y_i-{ŷ}_i\right)}^2}$$

(7)

$$Q_t={\displaystyle \sum _{i=1}^{n_1}{\left(y_i-{\overline{y}}_i\right)}^2}$$

(8)

In the equation, n_i is the number of samples; y_i is the actual simulation values; ${ŷ}_i$ is the response surface prediction values; ${\overline{y}}_i$ is the mean of actual simulation values.

We obtained an approximate model of component energy absorption with R² = 0.925; the R² of the quality approximation model is 0.965. The R² values of the B-pillar abdominal invasion approximation model and the lower threshold invasion approximation model are 0.954 and 0.983, respectively.

3.3. Multi-Objective Optimization Model and Results

The genetic algorithm follows the principle of natural selection. Recent years have witnessed the emergence of various novel optimization algorithms such as whale optimization algorithm (WOA), gradient-based Newton direction optimization (GNDO), and arithmetic optimization algorithm (AOA), which have been successfully applied in different fields including wireless communication systems [31] and fluid mechanics [32]. Among these optimization methods, the second-generation non-dominated sorting genetic algorithm (NSGA-II) is widely used due to its efficiency in solving multi-objective optimization problems. The NSGA-II algorithm offers strong robustness and excellent global search capabilities [33,34]. It enhances optimization accuracy through an elite strategy, ensuring a uniform distribution of Pareto optimal solutions.

In this study, the NSGA-II algorithm parameters are set as follows: population size of 40, 40 iterations, crossover probability of 0.9, crossover distribution index of 10, and mutation distribution index of 20. Multi-objective optimization is performed based on Equation (9), considering practical manufacturing precision. The final optimized thicknesses for the seven components are determined as 2.0 mm, 1.0 mm, 0.8 mm, 0.9 mm, 2.0 mm, 0.5 mm, and 0.6 mm.

$$\left\{\begin{array}{l}find t_{i\min }\le t_i\le t_{i\max }\left(i=1,2,\cdots ,7\right)\hfill \\ \begin{array}{l}\min M\left(t\right),\min L_1\left(t\right),\min L_2\left(t\right)\\ \max E\left(t\right)\end{array}\hfill \\ \begin{array}{l}s.t. M\left(t\right)\le 33.6\mathrm{kg}\\ L_1\left(t\right)\le 310\mathrm{mm}\end{array}\hfill \\ L_2\left(t\right)\le 270\mathrm{mm}\hfill \end{array}\right.$$

(9)

The optimized solution was re-submitted to LS-DYNA for validation. A comparison between the multi-objective optimization results and simulation data, as shown in

Table 4. Comparison of predicted results and simulation results.

Name	L1/mm	L2/mm	E/J	M/kg
Predicted value	309.3	252.3	11,032.0	32.9
Simulated value	313.0	257.0	11,126.6	33.2
Error/%	1.2	1.9	0.9	0.9

, reveals that the relative error does not exceed 2%, confirming the accuracy of both the surrogate model and the optimization method.

Table 5. Multi-objective optimization results.

Status	L1/mm	L2/mm	E/J	M/kg
Before optimization	397.5	343.5	8045.0	33.6
After optimization	313.0	257.0	11,126.6	33.2
Percentage change/%	−21.3	−25.2	+38.3	−1.2

presents a comparison between the original and optimized designs. The maximum intrusion of the belly of the B-pillar is reduced from 397.5 mm to 313.0 mm, a decrease of 21.3%. The maximum intrusion of the lower sill decreases from 343.5 mm to 257.0 mm, representing a 25.2% reduction. The absorbed energy of the optimized components increases from 8045.0 J to 11,126.6 J, an improvement of 38.3%, while the total mass is slightly reduced from 33.6 kg to 33.2 kg, a 1.2% decrease.

After applying multi-objective optimization, the deformation of the vehicle’s bottom structure remains significant. Observation points were established on both sides of the battery pack, as shown in Figure 11. The maximum intrusion of the battery pack reached 81.9 mm, approximately 12.4% of its total size. This level of deformation could potentially threaten the safety and performance of the vehicle’s bottom-mounted battery pack [25]. Therefore, from the perspective of battery pack collision safety, the optimized body structure still has limitations. Further exploration of additional protective solutions is needed.

4. Battery Pack Protection Strategy Development

Despite the optimization of the vehicle body, significant bottom deformation persists, highlighting the necessity for further refinement of the vehicle bottom and the components surrounding the power battery pack. To mitigate battery pack deformation resulting from the collapse of the lower longitudinal beams, this study proposes two engineering-based optimization solutions for the side longitudinal beams.

4.1. Solution 1: Side Longitudinal Beam Reinforcement

Increasing the thickness of components is a common method to enhance vehicle crashworthiness [35]. In this study, the thickness of the side longitudinal beam adjacent to the battery pack was increased from 1.6 mm to 2.0 mm, followed by side column collision simulations. The results indicate that thickening reduced the maximum intrusion of the battery pack’s sidewall to 74.5 mm. Although the maximum intrusion of the battery pack reduced, the value remains relatively high and requires further optimization.

Considering that the minimum processing precision for steel components is generally 0.1 mm, the study incrementally thickened the side longitudinal beam in steps of 0.1 mm. Simulations were then conducted to observe the intrusion of the battery pack’s sidewall.

4.2. Solution 2: Integration of Bionic Thin-Walled Energy-Absorbing Structures

Preliminary side pole collision simulations reveal that the side impact beam and door sill beam primarily absorb energy through bending deformation. This finding necessitated the design of a structure relying mainly on bending deformation for energy dissipation. Studies on thin-walled energy-absorbing units [36,37,38,39] indicate that multi-porous structures effectively absorb energy through bending deformation. Inspired by natural structures such as cattail fluff and lotus root cross-sections [38,40], an innovative bionic energy-absorbing structure is proposed (Figure 12). This structure mimics the multi-porous nature of these biological models, aiming to convert kinetic energy into internal energy through structural deformation and cavity wall buckling upon impact. The proposed structure is designed for integration with the battery pack’s right longitudinal beam, with the goal of enhancing the overall safety performance of electric vehicle battery assemblies in side impact scenarios.

The geometric parameters of the thin-walled energy-absorbing structure are derived from the dimensions of the side longitudinal beam in an electric mini commercial vehicle. The structure has a length of 200 mm and a thickness of T = 1 mm. The outer tube diameter is D₁ = 72 mm, the inner tube diameters are D₂ = 40 mm and D₃ = 20 mm, and the reinforcement tube diameter is D₄ = 8 mm. The structure includes five ribs, each with a thickness of 1 mm. The angle between adjacent ribs is θ = 72°.

The material selected for this structure is B340/590DP steel, which has a density of 7900 kg/m³, a Young’s modulus of 213 GPa, and a Poisson’s ratio of 0.3. Since the front energy-absorbing box and side longitudinal beams of the vehicle under study are made of B340/590DP steel, which is known for its good energy-absorption performance, this steel was chosen as the raw material for the energy-absorbing structure. This selection not only ensures efficient energy absorption but also facilitates assembly and welding in actual production, as it is the same material as the side longitudinal beams.

As shown in Figure 13, the bionic lotus root-like thin-walled energy-absorbing structure is embedded in the middle section of the longitudinal beam adjacent to the battery pack.

4.3. Side Pole Impact Performance Analysis of Protection Solutions

(1)

Comparison of Maximum Intrusion of Battery Pack Side Wall

Table 6. Battery pack optimization results.

	Side Longitudinal Beam Thickness/mm	Battery Pack Side Intrusion/mm
Solution 1	2.0	74.5
	2.1	69.3
	2.2	65.4
	2.3	63.1
	2.4	61.8
	2.5	60.5
Solution 2	/	60.8

shows the optimization results for the thickened longitudinal beam next to the battery pack. With Solution 1, the maximum intrusion into the side wall of the battery pack decreases as the thickness of the side stringer is increased, and there is a clear non-linear relationship between the two (Figure 14). After increasing the thickness of the side longitudinal beam to 2.5 mm, the maximum intrusion into the side wall of the battery pack decreases to 60.5 mm. With Solution 2, the maximum intrusion into the side wall of the battery pack is directly reduced to 60.8 mm.

(2)

Analysis of Mass Variation

In Solution 1, the thickness of the side longitudinal beam is increased to 2.5 mm. This modification results in an increase in the mass of the side longitudinal beam from 6.9 kg to 11.3 kg, representing a 63.7% increase in weight. Consequently, the overall vehicle mass increases by 3.9‰.

In Solution 2, a thin-walled energy-absorbing structure is added to the side longitudinal beams. This addition increases the total mass of the side longitudinal beams by 1.6 kg, corresponding to a 23.2% increase in mass compared to the original design. As a result, the overall vehicle mass increases by 1.4‰.

(3)

Overall Analysis

It can be clearly seen from Figure 15a,b that the multi-objective optimization has significantly reduced the side intrusion of the battery pack. However, the side longitudinal beam is still severely squeezed. Combining with Figure 16, it can be known that the maximum intrusion amount of the optimized battery pack is 81.9 mm. As can be seen from Figure 15c,d, increasing the thickness of the side longitudinal beam to 2.5 mm or adding the thin-walled energy-absorbing structure has remarkably reduced the squeezing of the longitudinal beam, resulting in less deformation of the battery pack. Further, by referring to Figure 16, it is found that the maximum lateral intrusion amount of Solution 1 is 60.5 mm, while that of Solution 2 is 60.8 mm. The optimization effects of the two solutions are quite comparable. Compared to the original design, both Solution 1 and Solution 2 significantly reduce the maximum side intrusion of the battery pack, by 43.8% and 43.5%, respectively. From a lightweight perspective, the thin-walled energy-absorbing structure (Solution 2) offers a more significant advantage, though its manufacturing process is more complex, and its mechanical properties still need to be further verified.

Both protective solutions for the battery pack have their unique advantages; however, they differ significantly in terms of implementation feasibility and mass production considerations. On one hand, the thin-walled energy-absorbing structure offers a clear advantage in lightweight design, with the total mass of the side longitudinal beams increasing by only 23.2%—significantly lower than the 63.7% increase observed in the thickened side longitudinal beam solution. From a technical performance perspective, both solutions provide comparable protection for the battery pack, reducing the maximum side intrusion by approximately 43.5% to 43.8%. Nevertheless, when considering engineering feasibility, the two solutions present markedly different challenges.

Although the thin-walled energy-absorbing structure demonstrates excellent theoretical performance, it faces significant limitations in industrial production. Specifically, these include complex manufacturing processes, high difficulty in mass production, and the need for further research to verify its mechanical properties. In contrast, increasing the side longitudinal beam thickness offers several practical advantages: a mature manufacturing process, easier mass production, and relatively controllable technical risks.

Among these solutions, Solution 2—which involves filling the thin-walled energy-absorbing structure—demonstrates significant potential for widespread adoption due to its balanced approach between technical performance and production feasibility. While further optimization of the manufacturing process is necessary to facilitate large-scale application, the inherent advantages of this solution, such as a mature manufacturing process and controllable technical risks, make it a particularly promising choice for battery pack protection.

However, it is important to note that manufacturing bionic thin-wall structures presents three key challenges: (1) material–process compatibility for high-strength steel; (2) scalability of precision forming techniques (e.g., laser/hydro-forming); and (3) cost management in mass production. Although advanced hybrid manufacturing shows potential for addressing these challenges, its implementation requires significant tooling investments and process optimization to achieve economic viability. Therefore, while the technical merits of these solutions are clear, their practical implementation must carefully balance performance requirements with manufacturing constraints.

5. Conclusions

(1)

Side pole impact simulations of an electric micro commercial vehicle designed for the European market reveal critical safety concerns, including severe body deformation and battery pack compression that could lead to fire risks. These findings underscore the critical need for enhanced structural protection in electric vehicle design.

(2)

Multi-objective optimization of seven key components yielded dual benefits: a 2.0% weight reduction and 22.2% improved energy absorption. The optimization significantly enhanced safety performance, reducing B-pillar midsection and lower threshold intrusions by 22.5% and 26.3% respectively. These results demonstrate the effectiveness of response surface methodology in achieving both lightweight design and safety objectives.

(3)

Two solutions addressed battery pack deformation: traditional beam reinforcement and bio-inspired design. The conventional approach achieved a 43.8% intrusion reduction but required a 63.7% weight increase. The bio-inspired solution provided comparable protection (43.5% intrusion reduction) with only a 23.2% weight increase, highlighting the potential of biomimetic structures in automotive safety design.

(4)

Future research should prioritize (a) experimental verification through E-NCAP standard crash tests incorporating manufacturing tolerance analysis; (b) development of cost-effective production processes for mass manufacturing viability; (c) integrated durability–fatigue–thermal assessments under operational conditions; and (d) establishment of EV-specific design standards for side-impact protection that reconcile crashworthiness requirements with lightweighting constraints. These efforts will bridge the gap between theoretical optimization and practical implementation.