Blast Protection Performance of Pre-Stressed High-Strength Steel Vehicle Underbody Structures

Abstract

Conventional design paradigms for vehicle underbody armor face an inherent trade-off: enhancing blast protection invariably incurs a prohibitive weight penalty. Here, we investigate a mechanical pre-stressing strategy for high-strength steel V-shaped vehicle underbody structures. A conventional V-shaped baseline structure was first subjected to a 6 kg TNT blast test, and the measured response was used to validate the numerical model. Based on the validated numerical model, four mass-equivalent (100 kg) configurations were subsequently compared numerically under escalating threats (2~8 kg TNT): pre-stressed steel, homogeneous steel, and all-metallic honeycomb sandwich panels (comprising high-strength steel face sheets and an aluminum alloy core) with both positive and negative Poisson’s ratios. The numerical results predict that the pre-stressed steel configuration exhibits the smallest maximum permanent floor deformations among the four configurations, with values of 22 mm, 46 mm, 131 mm, and 208 mm under 2, 4, 6, and 8 kg loads, respectively. Mechanistically, we reveal that for V-shaped geometries, residual-stress-induced stiffening and geometric arching are profoundly more effective than core crushing in controlling global bending, while the auxetic steel-faced aluminum honeycomb offers only marginal improvements over its conventional counterpart. This study offers a potential pathway for overcoming the weight–protection trade-off in underbody armor design. While the numerical predictions are encouraging, direct experimental validation of the pre-stressed configuration remains necessary prior to practical application.

1. Introduction

Improvised explosive devices (IEDs) remain one of the most pervasive asymmetric threats to military tactical vehicles in contemporary and future battlefields [1]. The severe blast loads generated by IED detonations impose extreme demands on vehicle underbody survivability, spurring extensive research into protective structural designs [2]. However, many proposed protective measures inevitably conflict with the stringent weight and mobility constraints inherent to modern combat platforms. Consequently, the development of lightweight yet blast-resistant vehicle structures has emerged as a frontier interdisciplinary challenge [3].

Among various protective strategies, optimizing the geometry and configuration of underbody components has received considerable attention, as such approaches promise performance improvements without substantial weight penalties. With the advancement of computational techniques, numerous optimization-based designs have been proposed. Wei et al. [4] optimized deterministic design variables—including thickness and geometry—for sheet metal components in vehicle anti-blast structures, achieving significant gains through Pareto solutions. Nayak et al. [5] optimized the geometry of honeycomb sandwich panels, effectively reducing backplate deformation and transmitted acceleration under constant-mass constraints. Argod et al. [6,7] developed a nodal-coordinate shape optimization methodology defined by velocity fields, employing a non-gradient differential evolution algorithm to identify ideal panel geometries that minimize out-of-plane displacement and impulse. Nevertheless, most of these studies were conducted under specific loading scenarios or geometric constraints, and their optimal configurations may not generalize across different blast intensities—a limitation that motivates the multi-load-level comparison undertaken in the present work.

In recent years, increasing research effort has been directed toward composite sandwich structures for blast protection, as they introduce additional energy-absorption mechanisms beyond geometric optimization. Zhang et al. [8] experimentally and numerically investigated the dynamic response of metal foam-cored sandwich panels under blast loading. Shen et al. [9] examined the deformation and collapse modes of curved sandwich panels with various curvatures under blast impact. Hassan et al. [10] studied the influence of core density on the blast resistance of foam-filled sandwich structures. Whisler et al. [11] found that sandwich panels achieved up to a 37% reduction in initial-average transmitted acceleration and a 76% reduction in peak acceleration compared with steel armor panels, along with a 49% weight saving. Imbalzano et al. [12] compared the blast resistance of auxetic and conventional honeycomb-cored sandwich panels under impulsive loadings. Hause [13] investigated the response of anisotropic flat sandwich panels to explosive pressure pulses. Collectively, these studies demonstrate the considerable potential of sandwich configurations, yet they also reveal that the benefits are highly dependent on core geometry, material, and loading intensity, making direct cross-design comparisons difficult without a unified numerical framework.

The performance of high-strength steel under extreme loading has also been extensively characterized, providing a necessary baseline for the present study. McDonald et al. [14] comprehensively characterized the deformation and rupture thresholds of high-strength steel panels, with detailed fractographic analysis of failure initiation and progression. Xu et al. [15] investigated shear failure behavior over a broad range of strain rates. Woo et al. [16] correlated fracture processes and damage mechanisms under high strain rates with acoustic emission characteristics. Zhou et al. [17] investigated the numerical modeling of a scaled vehicle underbody structure subjected to landmine loading, providing relevant methodological background for the blast-response modeling adopted in the present study. While these studies confirm that high-strength steel offers favorable strength-to-weight characteristics, its blast resistance remains governed by the conventional design trade-off: increasing plate thickness improves protection but adds weight—a limitation that alternative approaches such as preloading may help to overcome.

Preloading technology offers a fundamentally different mechanism for enhancing structural impact resistance. Rather than adding material or altering geometry, it harnesses residual stresses to modify the stiffness distribution and deformation response of the structure itself. This technique has been primarily applied to large-scale concrete structures. Abdalla [18] studied the influence of utility duct size and position on the dynamic performance of prestressed concrete beams. Iqbal et al. [19] experimentally and numerically compared the drop-impact resistance and energy-absorption capacity of prestressed versus non-prestressed concrete plates. Other studies [20] demonstrated that post-tensioning and fiber layers increased the impact resistance of slab strips while reducing peak displacements and damage. In the context of composite panels, Moallemzadeh et al. [21] compared the dynamic responses of pre-stressed and non-pre-stressed panels under high-velocity impact, while Saghafi et al. [22] investigated the effect of compression preloads on plate buckling. Eric Kerr-Anderson et al. [23] provided a comprehensive review of pre-stressed composite laminates and sandwich structures under ballistic impact. More recently, Darrock et al. [24] subjected curved pre-stressed plates to buried charges of 100–250 g in dried sand and found that this technology substantially improved blast resistance, outperforming other passive armor solutions. Despite these encouraging results, previous studies on pre-stressing or preloading have mainly focused on concrete members, composite panels, or isolated plates. Meanwhile, separate studies on blast-loaded welded steel structures have demonstrated that weld geometry, heat-affected-zone properties, and welding-induced residual stresses can significantly influence permanent deformation and failure behavior [25]. However, the combined effects of mechanical pre-forming, the associated residual stress field, and welded high-strength steel V-shaped vehicle underbody geometry under buried blast loading remain insufficiently understood. In particular, it is still unclear whether a residual stress state deliberately introduced through pre-forming can improve deformation resistance when acting together with geometric arching in a welded V-shaped underbody structure. This specific gap motivates the present study. This study aims to assess the blast protection performance of pre-stressed high-strength steel when applied to vehicle underbody structures. In contrast to prior works that typically optimize a single design under a fixed blast scenario, the present work systematically compares four mass-equivalent configurations—namely, a pre-stressed steel, a homogeneous steel, a positive Poisson’s ratio honeycomb sandwich panel, and a negative Poisson’s ratio honeycomb sandwich panel—under TNT-equivalent charges ranging from 2 kg to 8 kg. The investigation follows a combined experimental–numerical methodology. A scaled V-shaped benchmark model is first subjected to a 6 kg TNT blast to record the structural deformation. These experimental data serve to calibrate and validate a high-fidelity finite-element model developed in LS-DYNA. The validated model is then used to evaluate the four candidate designs in terms of maximum permanent deformation and energy dissipation. By covering multiple load levels and design typologies, this comparative framework is specifically designed to (i) benchmark the effectiveness of preloading against state-of-the-art sandwich structures, and (ii) elucidate the dominant physical mechanisms that govern protective performance across different threat intensities.

The primary objective of this study is to determine whether mechanical pre-forming can improve the blast resistance of a V-shaped high-strength steel vehicle underbody without increasing structural mass. To this end, a scaled V-shaped benchmark structure was first subjected to a 6 kg TNT blast test, and the measured structural response was used to validate an LS-DYNA finite-element model. Based on the validated baseline model, four mass-equivalent protective configurations—a pre-stressed high-strength steel plate, a conventional homogeneous steel plate, steel-faced aluminum-honeycomb sandwich panel with a positive Poisson’s ratio, and a steel-faced aluminum-honeycomb sandwich panel with a negative Poisson’s ratio—were comparatively evaluated under 2, 4, 6, and 8 kg TNT-equivalent blast loads. The study specifically aims to (1) quantify the deformation-control benefit provided by mechanical pre-forming relative to conventional steel and honeycomb sandwich solutions under an equal-mass constraint, and (2) clarify the roles of pre-forming-induced residual stress, geometric arching, face-sheet stiffness, and core energy absorption in governing the blast response of V-shaped underbody structures.

2. Experimental and Numerical Methodology

This section describes the experimental setup and numerical modeling employed in this study. A scaled V-shaped underbody model was first subjected to a controlled explosion test to provide baseline deformation data. A corresponding finite-element model was then developed in LS-DYNA and calibrated against the experimental results. The validated model served as the basis for subsequent comparative analyses of different protective configurations.

2.1. Bench Model and Experimental Setup

Full-scale blast tests provide the most reliable assessment of structural anti-explosion performance, but their high cost and complexity often limit their feasibility. In this study, a scaled bench model was designed to represent a typical V-shaped vehicle underbody structure. The model geometry is shown in Figure 1. The overall height of the bench model was 870 mm, with the lowest point positioned 450 mm above the ground. The design area of the anti-explosion component was 1910 mm × 649 mm, and the floor plate thickness was 10 mm.

The bench model was fabricated from commercially available 700E high-strength steel. The mechanical properties and constitutive parameters directly relevant to the numerical analysis are provided in Section 2.2 and

Table 1. Johnson–Cook material parameters for the high-strength steel plate.

A (MPa)	B (MPa)	C	n	m	D1	D2	D3	D4	D5
765	584.0	0.01	0.65	0.940	0.20	2.00	−5.00	−0.007	2.86

Note: D1–D5 are the Johnson–Cook damage parameters.

. All connections in the bench model were welded, and the integrity of the welded joints is important for maintaining the overall structural response under blast loading. Based on preliminary weldability investigations, an HCr20Ni10Mn7Mo welding consumable was selected. The selection was intended to provide the welded joints with sufficient ductility and crack resistance, thereby reducing the risk of premature weld failure during the large transient deformation induced by blast loading. Preheating and post-weld thermal control were applied during fabrication to reduce the risk of welding-induced cracking. Detailed thermal-cycle parameters were not retained during fabrication and therefore cannot be reported quantitatively in the present study. The mechanical properties assigned to the weld material in the numerical model are provided in Section 2.2 and

Table 2. Material parameters of the weld joints.

Yield Strength (MPa)	Tensile Strength (MPa)	Engineering Elongation (%)	Young’s Modulus (GPa)	Poisson’s Ratio
510	730	3.7	206	0.30

.

To reproduce the support and inertial conditions of an actual vehicle as closely as possible within the scaled bench test, the experimental apparatus was freely placed on the ground without additional bolted or fixed constraints. A total counterweight of 3000 kg was placed on the upper part of the bench model. The distribution and position of the counterweight were adjusted according to the mass distribution and loading condition of the corresponding vehicle configuration, so that the scaled test apparatus could reasonably reproduce the inertial constraint imposed by the vehicle body on the underbody structure during the blast event. The final experimental setup is shown in Figure 2.

The explosion tests were conducted in accordance with the NATO AEP-55 standard [26], which specifies the placement of a cylindrical mine charge beneath the vehicle. A representative location directly under the bench model was selected for the experiment. The explosive charge consisted of 6 kg of TNT, manufactured without a cavity. The charge was configured with a height-to-diameter ratio of 0.33 to approximate standard density. The soil bed (wet density 2200 ± 100 kg/m³) was prepared in a test area of at least 2 m × 2 m around the charge, which was saturated with water prior to testing. Soil humidity was maintained within 1.5% below the optimum level, with the typical optimum humidity for sandy–gravelly soils ranging between 5% and 7% [27].

2.2. Finite Element Modeling

To accurately capture the dynamic deformation of high-strength steel under blast loading, an appropriate material constitutive model is essential. The finite-element model was developed using LS-DYNA, with the Johnson–Cook constitutive model [28] employed for the high-strength steel,

$$\sigma =(A+B{\epsilon }^n)\left(1+Cln {\dot{\epsilon }}^{\ast }\right)(1-{T^{\ast }}^m)$$

(1)

where A is the initial yield-stress parameter of the Johnson–Cook model at the reference strain-rate and reference temperature; B is the strain-hardening coefficient; n is the strain-hardening exponent; $C$ is strain-rate hardening constant; ${\dot{\epsilon }}^{\ast }=\dot{\epsilon }/{\dot{\epsilon }}_0$ is the dimensionless strain-rate and ${\dot{\epsilon }}_0$ is the reference strain-rate; $T^{\ast }=(T-T_0)/(T_M-T_0)$ is the homologous temperature where $T$ is absolute temperature; $T_0$ is reference temperature and $T_M$ is material’s melting temperature; and $m$ is thermal softening constant. The Johnson–Cook parameters adopted for the 700E high-strength steel were obtained through inverse identification based on previous material test data from our research. The reference strain rate was ${\dot{\epsilon }}_0=0.0001/\mathrm{s}$, the reference temperature was $T_0=298.15 \mathrm{K}$, and the melting temperature was $T_M=1800 \mathrm{K}$. The material model parameters for the high-strength steel used in the tests are listed in Table 1.

Since the primary weld joints in the bench model were T-shaped, the welding parameters were determined based on standard T-joint crack testing procedures. The material model *MAT_PLASTIC_KINEMATIC was selected to define the weld joints [29], with the corresponding mechanical properties summarized in Table 2. The elongation value listed in Table 2 was used as an engineering-level failure parameter in the weld-joint model. It should be noted that this value does not represent a fully calibrated local fracture strain accounting explicitly for necking, stress triaxiality, and mesh dependence.

For the explosive, the *MAT_HIGH_EXPLOSIVE_BURN model was used, and the detonation products formed after initiation are described by the Jones–Wilkins–Lee (JWL) equation of state [30]:

$$P=A_J\left(1-{\displaystyle \frac{\omega }{R_{1}V}}\right)e^{-R_{1}V}+B_J\left(1-{\displaystyle \frac{\omega }{R_{2}V}}\right)e^{-R_{2}V}+{\displaystyle \frac{\omega E_0}{V}}$$

(2)

where $A_J$, $B_J$, $R_1$, $R_2$, and $\omega$ are explosive material constants, $V$ is the relative volume, and $E_0$ is the internal energy per unit volume, which depends on the explosive type, as shown in

Table 3. Material parameters of TNT.

$\mathit{\rho }$ (kg/m3)	$\mathit{D}$ (m/s)	${\mathit{P}}_{\mathit{C}\mathit{J}}$ (GPa)	${\mathit{Q}}_0$ (J/kg)	${\mathit{A}}_{\mathit{J}}$ (GPa)	${\mathit{B}}_{\mathit{J}}$ (GPa)	${\mathit{R}}_1$	${\mathit{R}}_2$	$\mathit{\omega }$	${\mathit{E}}_0$ (GPa)
1570	6930	21	4.52 × 106	371.20	3.23	4.15	0.95	0.30	7.0

Note: $\mathsf{\rho }$ is the explosive density; $\mathrm{D}$ is the detonation velocity; ${\mathrm{P}}_{\mathrm{C}\mathrm{J}}$ is the Chapman–Jouguet pressure.

.

The air domain was modeled using the *MAT_NULL material model with the *EOS_LINEAR_POLYNOMIAL equation of state, which defines pressure as:

$$P=C_0+C_1\mu +C_2{\mu }^2+C_3{\mu }^3+(C_4+C_5\mu +C_6{\mu }^2)E$$

(3)

where $\mu$ is the relative volume and $E$ is the internal energy per unit volume. The coefficients for air were set as $C_0$ = 0.1 MPa, $C_1$ = $C_2$ = $C_3$ = $C_6$ = 0, and $C_4$ = $C_5$ = 0.4 MPa [31]. The soil medium was modeled by *MAT_SOIL_AND_FOAM_FAILURE [32], with a pressure–volume strain curve that conforms to the soil conditions of the tests in this study [33].

The finite element model was developed in LS-DYNA to replicate the experimental setup. The steel plates and weld joints were modeled using Belytschko–Tsay shell elements [34] with five integration points through the thickness. A 10 mm element size was adopted for the main steel structure to balance computational accuracy and computational efficiency in capturing the global deformation response. The explosive, air, and soil domains were modeled using the ALE formulation and coupled with the Lagrangian structure using the *CONSTRAINED_LAGRANGE_IN_SOLID keyword, as shown in Figure 3. A penalty-based coupling formulation was adopted (CTYPE = 4). The ALE domain was discretized using a nominal element size of 15 mm. The penalty stiffness scale factor was set to PFAC = 0.1, consistent with the standard LS-DYNA penalty-coupling formulation [35]. The coupling was applied in the normal direction (DIREC = 2), and an NQUAD value of 3 was adopted for the coupling calculation. The bench model was not rigidly constrained to the ground, thereby reproducing the free-standing condition adopted in the blast test. A total counterweight of 3000 kg was applied to the upper part of the structure, with its position and distribution corresponding to those used in the experiment, to reproduce the inertial effect of the vehicle body on the underbody structure. Gravitational acceleration was applied to the entire numerical model to reproduce the initial gravitational loading state of the experimental setup, including the self-weight of the bench structure and the applied counterweight. Owing to the extremely short duration and high intensity of the blast loading, the contribution of gravity to the transient structural deformation is negligible compared with that of the blast-induced loading. Welded joints between plates were modeled as tied contacts with failure criteria based on the weld material properties. For the subsequent analysis of sandwich structures, the bonding between steel face sheets and aluminum core was also modeled as tied contact.

To validate the numerical model, the simulation results were compared against the experimental measurements. The primary experimental data recorded included high-speed images of the blast event, plastic deformation of the hull floor, and acceleration histories at selected locations on the floor.

The floor deformation was measured using a pre-marked grid system. Prior to the experiment, a coordinate grid was drawn on the floor surface, with point A1 designated as the coordinate origin (Figure 4a). After the explosion, the deformed coordinates of each grid point were recorded relative to this origin. The labels A–E denote the grid rows, while P1 and P2 indicate the acceleration measurement locations and F1 and F2 indicate the weld-failure locations observed after the blast test. Some grid lines became less visible after the explosion because of the severe structural deformation and surface damage. For the acceleration measurements, sensors were mounted on the floor at the positions shown in Figure 4b. Prior to integration, the initial offset of each acceleration signal was removed using the mean value of the pre-blast signal. A fourth-order Butterworth low-pass filter with a cutoff frequency of 1 kHz was then applied to suppress high-frequency measurement noise. Zero-phase forward–backward filtering was employed to avoid phase distortion. The filtered acceleration signals were first integrated to obtain velocity histories, followed by baseline correction to reduce integration drift. The corrected velocity histories were subsequently integrated to obtain displacement histories, which were compared with the corresponding numerical results in Figure 4c.

Figure 5 compares the explosion flow field observed in the experiment with the corresponding numerical simulation. In the experiment, the blast shock wave interacted with the soil particles to generate a coupled flow field above the bench model. In the numerical results, the two simulation image sequences are obtained from the same simulation but use different visualization settings: one displays both the explosive flow field and soil, whereas the other displays only the soil to more clearly illustrate the soil ejecta and dispersion process. The overall evolution and dispersion characteristics show good agreement with the experimental observations.

Figure 6 presents the plastic deformation of the bench model floor obtained from the experiment and the simulation. The deformation patterns—from the early weld-joint failure to the final hull deformation—were well captured by the numerical model. In particular, the experimentally observed weld-failure locations and the associated global deformation pattern were reproduced with reasonable agreement. The maximum residual floor deformation measured in the experiment was 260 mm, while the corresponding numerical prediction was 268 mm, corresponding to a relative error of approximately 3.1%. Overall, the agreement in the weld-failure locations, global deformation pattern, displacement response, and residual deformation magnitude provides a reasonable structural-level basis for the subsequent comparative analyses.

3. Design of Protective Configurations

This section describes the four protective configurations evaluated in this study. The pre-stressed high-strength steel plate is introduced as the proposed design, while three alternative configurations—a conventional steel plate, a positive Poisson’s ratio honeycomb sandwich panel, and a negative Poisson’s ratio honeycomb sandwich panel—are adopted as baselines for comparison. All four configurations were designed with an equivalent mass of 100 kg to ensure a fair assessment of their protective performances.

3.1. Pre-Formed High-Strength Steel with Forming-Induced Residual Stresses

As illustrated in Figure 7, a 10-mm-thick high-strength steel plate with an area of 600 mm × 1500 mm was subjected to a plastic pre-bending process. During the numerical forming analysis, the maximum equivalent stress reached approximately 1002 MPa at a forming radius of 547 mm and approximately 1544 MPa at a radius of 384 mm. These values represent local peak stresses developed during the corresponding plastic forming stages rather than nominal material-strength values. After unloading, the plate retained the prescribed curved geometry and the associated forming-induced residual stress field, which were subsequently transferred to the blast analysis.

It should be noted that the superior response of the pre-bent plate results from the combined effects of the residual stress field and geometric arching, rather than from residual stress alone. The higher pre-bending level is accompanied by increased local stress and plastic deformation and should therefore be carefully controlled to avoid excessive plastic deformation or possible material damage. In the present study, the pre-bending process was used to establish the prescribed residual stress state and initial curved geometry for the subsequent blast analysis. Further experimental characterization is required to quantitatively evaluate any potential material degradation induced by the pre-bending process.

The installation position of the pre-formed steel plate under the bench model is shown in Figure 8. In LS-DYNA, the plastic pre-forming process was first simulated using an implicit analysis. After the prescribed forming state was reached, the bending load was removed and the plate was allowed to spring back to obtain the unloaded pre-formed configuration. The resulting deformed geometry, forming-induced residual stress field, plastic-strain state, and associated material history variables were then transferred to the subsequent explicit blast analysis using the Full Deck Restart procedure [36]. The pre-formed plate was installed and constrained according to the underbody configuration shown in Figure 8. Therefore, the blast calculation was initialized from the unloaded pre-formed state rather than from a continuously loaded bending state.

3.2. Other Protective Configurations

Three reference configurations—all composed of steel face sheets and an aluminum honeycomb core, i.e., all-metallic sandwich structures—were selected to benchmark the performance of the pre-stressed steel plate, representing different design philosophies currently employed or explored in blast protection engineering.

Before detailing the individual configurations, it is essential to clarify the construction of AS2 (the conventional homogeneous steel plate), as its geometry and fabrication method directly affect the fairness of the comparison. AS2 shares the exact same macroscopic V-shaped profile as AS1. Importantly, AS2 is fabricated from a single monolithic 10-mm-thick high-strength steel plate that is cold-pressed into the V-shaped die form—rather than being welded together from two separate flat plates along the ridge. This avoids a vulnerable weld seam at the V-ridge, ensuring a continuous load path and preserving structural integrity under blast loading. AS2 contains no foam core, adhesive, or sandwich elements; it is simply a homogeneous steel plate, which is subsequently welded (via T-joint welds) onto the surrounding bench frame, as described in Section 2.1.

The four configurations follow a progressive design logic. AS1 and AS2 use the same high-strength steel material, plate thickness, in-plane dimensions, and installation position, while AS1 is additionally subjected to the plastic pre-forming process described in Section 3.1. As a result, AS1 differs from AS2 not only in residual stress but also in initial curvature and forming-induced material history. AS2 remains as a single flat steel plate without pre-forming or an intentionally introduced residual-stress field. AS2, AS3, and AS4 are subsequently compared as representative monolithic and sandwich protective concepts, with AS2 serving as the common baseline. These comparisons are intended as equal-mass structural-concept comparisons rather than strict single-variable isolations. All four configurations were designed with an equivalent total mass of 100 kg. Figure 9 illustrates the four configurations installed on the bench model:

• AS1: Pre-stressed high-strength steel plate (proposed design);
• AS2: Conventional homogeneous high-strength steel plate (10 mm thickness) without pre-bending;
• AS3: Positive Poisson’s ratio honeycomb sandwich panel (8 mm steel faces + aluminum honeycomb core);
• AS4: Negative Poisson’s ratio honeycomb sandwich panel (8 mm steel faces + aluminum honeycomb core).

AS2, a homogeneous steel plate of uniform thickness, serves as the baseline representing conventional armored vehicle practice. AS3 extends this concept by introducing a honeycomb core, a configuration widely studied for its energy absorption capacity through core crushing [37,38,39]. AS4 further modifies the core geometry to a negative Poisson’s ratio (auxetic) configuration, which has attracted recent interest for its unique deformation behavior under compression [40]. Including both AS3 and AS4 allows for a direct comparison between conventional and auxetic architectures, while their contrast with AS2 reveals the benefits of sandwich construction in general.

The honeycomb cores in AS3 and AS4 were designed with the same base geometry and equivalent relative density. The cell geometry is defined by wall thickness t = 1 mm, cell length a = 14 mm, cell hypotenuse b = 5.8 mm, cell height h = 10 mm, with cell angles $\alpha$ = 65°, and $\beta$ = 115°. For the negative Poisson’s ratio configuration, the cell geometry was modified by inverting the cell orientation to create the characteristic re-entrant structure. Both core configurations were modeled using Al-5005 H34 aluminum alloy, and the corresponding material properties adopted from Shen et al. [41] are listed in

Table 4. Material properties of Al-5005 H34 aluminum alloy [41].

Density (kg/mm3)	Elastic Modulus (MPa)	Poisson’s Ratio	Yield Stress (MPa)	Hardening Modulus (MPa)
2.76 × 10−6	69,000	0.33	105	27,000

. The honeycomb cores were explicitly discretized using Belytschko–Tsay shell elements (ELFORM = 2), with a wall thickness of 1 mm and five through-thickness integration points. Automatic single-surface contact was used to capture self-contact during cell-wall crushing, with static and dynamic friction coefficients of 0.20 and 0.15, respectively. A stiffness-based hourglass-control formulation with a coefficient of 0.03 was adopted, and no element erosion was applied. The aluminum honeycomb core was tied to the steel face sheets and assumed to remain perfectly bonded throughout the blast response; hence, no interface failure stress or fracture-energy parameter was introduced.

The honeycomb cores were modeled explicitly using shell elements—rather than homogenized as an equivalent continuum—to capture the local buckling and contact interactions of individual cell walls, which are essential for predicting the core crushing behavior under blast loading. The bonding between the aluminum core and the steel face sheets was modeled using tied contacts, allowing for debonding and subsequent sliding upon exceeding a defined failure stress. The steel face sheets were modeled as 8 mm thick plates—2 mm thinner than AS1 and AS2—to accommodate the mass of the honeycomb core while maintaining the overall mass constraint of 100 kg for all four configurations. This mass reallocation inevitably increases the total sectional thickness of AS3 and AS4 compared to the homogeneous plates, a geometric divergence that will be addressed in the discussion of the results.

4. Results and Discussion

In the present study, the protective performance is evaluated primarily from the perspective of structural integrity and deformation resistance. Maximum permanent floor deformation is therefore adopted as the principal performance indicator. Although acceleration signals were obtained in the benchmark experiment and double-integrated to derive displacement histories for numerical-model validation, acceleration was not adopted as an independent performance metric in the subsequent comparative analysis. Since occupant injury assessment is beyond the scope of the present study, the discussion focuses on the structural deformation response of the underbody configurations. The calculated energy response is used only as a supplementary quantity to assist in interpreting the deformation mechanisms and is not regarded as an independent measure of superior blast protection, because a higher energy response may also result from greater plastic deformation, core crushing, or structural damage.

The results reported for the four protective configurations are deterministic numerical predictions obtained using the nominal material parameters, mesh resolution, and loading conditions defined in Section 2 and Section 3. Accordingly, the values presented in Figure 10 and Figure 11 should be interpreted as comparative numerical trends under the adopted model assumptions rather than as statistically bounded performance measures. A comprehensive uncertainty quantification, including mesh-sensitivity ranges, material-parameter variability, and experimental repeatability, was not performed for all configurations.

This section presents the simulation results for the four protective configurations under 2 kg, 4 kg, 6 kg, and 8 kg TNT-equivalent blast loads. The deformation responses of the four configurations are compared first, followed by an examination of their energy absorption characteristics. The observed differences are then discussed from three complementary perspectives: synergistic stiffening via pre-forming and arching, mass allocation under the equal-mass constraint, and stress wave attenuation at material interfaces. Unless otherwise specified, all reported deformations refer to the permanent plastic deformation of the floor plate after the blast event.

4.1. Deformation Response

Figure 10 shows the maximum floor deformations of the four configurations under each blast load. The pre-stressed steel plate (AS1) consistently exhibits the smallest deformation across all four loading levels, with values of 22 mm, 46 mm, 131 mm, and 208 mm for the 2 kg, 4 kg, 6 kg, and 8 kg TNT equivalents, respectively.

The conventional steel plate (AS2) exhibits smaller deformations than both sandwich configurations (AS3 and AS4) under all loading conditions. Among the two sandwich structures, the negative Poisson’s ratio configuration (AS4) consistently outperforms the positive Poisson’s ratio counterpart (AS3), with AS4 exhibiting slightly smaller deformation than AS3 across the investigated load levels.

4.2. Energy Absorption

Figure 11 presents the numerically calculated energy response of each configuration under the four blast loading levels. The reported values were determined from the increase in the internal energy of the corresponding protective structural components during the blast response. No direct experimental measurement of energy absorption was performed in the present study; therefore, the values shown in Figure 11 were obtained solely from the numerical simulations. These energy values are used as a supplementary indicator to interpret the structural deformation mechanisms rather than as an independent measure of superior blast protection, because a higher internal-energy increase may also be associated with greater plastic deformation, core crushing, or structural damage. For the sandwich structures, a distinct numerical trend is observed: under the 8 kg and 6 kg loads, AS4 exhibits a higher internal-energy response than AS2, while AS3 shows a comparable response to AS2. Under the 4 kg and 2 kg loads, the differences among the three configurations are smaller.

Notably, the energy absorption of the sandwich structures is achieved with face sheets 2 mm thinner than those of AS2 (8 mm versus 10 mm), meaning that a portion of the mass has been reallocated from the steel plates to the aluminum cores.

4.3. Mechanisms Governing Protective Performance

The results presented in Section 4.1 and Section 4.2 reveal two key patterns: (1) the pre-formed steel configuration (AS1) exhibits the smallest permanent deformation among the four configurations; and (2) the sandwich structures (AS3 and AS4) exhibit higher calculated internal-energy responses than the conventional steel plate (AS2) under higher blast loads, while also undergoing larger permanent deformation. These observations indicate that a higher energy response does not necessarily correspond to superior structural protection. The underlying differences are discussed below in terms of the coupled structural mechanisms governing the numerical response.

Combined effects of pre-forming, initial curvature, and residual stress. The pre-forming process introduces both a residual stress field and a permanent curvature within the steel plate. The superior performance of AS1 should therefore be interpreted as the combined effect of the initial curved geometry, forming-induced residual stress state, and associated material history, rather than as the isolated effect of residual stress alone. The initial curvature can modify the load-transfer path and promote an arching-type structural response under out-of-plane blast loading, thereby contributing to the reduced permanent deformation. Meanwhile, the forming-induced residual stress field alters the initial stress state of the plate and may influence the subsequent yielding and stress redistribution during blast loading. However, this influence depends on the residual-stress distribution, boundary conditions, geometric nonlinearity, and possible reverse yielding. Since moment–curvature relationships, through-thickness residual-stress distributions, and controlled stress-relieved simulations with otherwise identical geometry were not evaluated in the present study, the individual contribution of residual stress cannot be quantitatively isolated. Therefore, the reduced permanent deformation of AS1 should be attributed to the combined pre-formed state rather than to an independently demonstrated increase in flexural stiffness caused by residual stress.

Mass allocation, thickness variation, and the stiffness–energy trade-off. The equal-mass constraint (100 kg for all four configurations) forces a trade-off between stiffness and energy absorption. In the sandwich structures, a portion of the mass is allocated to the low-density aluminum core, reducing the steel face sheet thickness from 10 mm (AS2) to 8 mm. Furthermore, to accommodate the low-density core while maintaining 100 kg, AS3 and AS4 possess a significantly greater total sectional thickness than AS1 and AS2. This increased thickness not only reduces the effective slenderness ratio of the steel face sheets but also alters the blast impulse coupling area, as the outermost surface interacts with the shockwave at a different stand-off distance. This reduction in steel thickness decreases the flexural rigidity of the structure, making it more susceptible to bending deformation under blast loading. The core contributes energy absorption through cell wall buckling and plastic folding, as illustrated in Figure 12. However, for the V-shaped geometry examined here—where the structural response is dominated by global bending [42]—the loss of face sheet stiffness outweighs the benefit of core energy absorption. Therefore, the differences between AS2 and the sandwich configurations should be interpreted as the combined effects of face-sheet thickness, sectional depth, core deformation, and the associated change in effective stand-off distance, rather than as the isolated effect of the honeycomb core alone.

The deformation process of the sandwich structures can be conceptually divided into three phases: stress wave propagation through the structure, compaction of the honeycomb core, and subsequent bending of the floor plate. While these phases overlap in time, the core compaction phase is where the honeycomb contributes most significantly to energy dissipation. In the later bending phase, the core’s contribution diminishes relative to the bending resistance of the steel face sheets.

Energy transfer and dissipation in the sandwich structures. The impedance mismatch between the steel face sheets and the aluminum honeycomb core affects the reflection and transmission of stress waves across the material interfaces [43]. Wave reflection redistributes the incident energy within the sandwich structure rather than directly dissipating it. The irreversible energy dissipation is primarily associated with plastic deformation of the steel face sheets, progressive buckling and plastic folding of the aluminum honeycomb walls, and frictional contact during core crushing. Accordingly, the energy values presented in Figure 11 represent the overall structural energy response resulting from these coupled deformation mechanisms. Since the aluminum honeycomb core and steel face sheets were modeled with a perfectly tied interface, interface fracture was not considered in the present analysis.

Auxetic versus conventional honeycomb. Within the sandwich category, AS4 (negative Poisson’s ratio) absorbs more energy than AS3 (positive Poisson’s ratio) under higher blast loads. Under compression, the re-entrant honeycomb of AS4 contracts laterally and progressively draws material toward the locally loaded zone, thereby enhancing the local impact resistance, as reported by Imbalzano et al. [12]. This effect is most pronounced when the core undergoes significant compaction, which explains why the energy absorption difference between AS3 and AS4 is more evident at higher blast loads (8 kg and 6 kg) than at lower loads (4 kg and 2 kg). Despite this advantage, AS4’s deformation remains larger than that of AS2 and substantially larger than that of AS1, confirming that for the V-shaped geometry, stiffness enhancement is more effective than auxetic core design in controlling permanent deformation.

The three mechanisms above converge to a consistent picture. Pre-forming enhances the flexural stiffness of the steel plate without adding mass, giving AS1 a decisive advantage in deformation control. Sandwich structures dissipate energy through core crushing and stress wave attenuation, but achieve this by reallocating mass away from the steel face sheets, reducing the flexural rigidity essential for resisting the bending-dominated deformation of V-shaped structures. Among the sandwich types, the negative Poisson’s ratio core offers modest improvements over the conventional honeycomb, but these improvements are secondary to the primary effect of face sheet stiffness. This explains why AS1 exhibits the smallest deformation among the four configurations, despite AS3 and AS4 absorbing comparable or greater energy under higher blast loads.

It should be noted that the experimental validation in the present study was based on a single 6 kg TNT blast test of the baseline configuration, and no repeated blast tests were conducted because of the highly destructive nature of the experiment, as well as the substantial cost and safety requirements associated with repeated explosive testing. Nevertheless, the entire test procedure, including the explosive arrangement and test conditions, was conducted in accordance with the NATO AEP-55 standard to ensure consistency and reproducibility of the experimental setup. The purpose of this experiment was primarily to verify the overall response trend and deformation mode predicted by the numerical model rather than to establish statistical confidence intervals for the blast response. In the subsequent comparative analysis, all four protective configurations were evaluated within the same numerical framework using consistent material models, boundary conditions, and blast-loading conditions, thereby providing a unified basis for comparing their relative structural-response trends. More extensive experimental validation and systematic uncertainty and sensitivity analyses are still required in future work to further quantify the robustness of the predicted differences among the different configurations.

5. Conclusions

This study investigated the structural response of four mass-equivalent vehicle underbody protective configurations through a combined experimental and numerical approach. A scaled V-shaped benchmark structure was first tested under a 6 kg TNT explosion, and the experimental deformation response was used to assess the structural-level predictive capability of the LS-DYNA model. Based on this benchmarked model, four configurations—pre-formed steel plate (AS1), conventional steel plate (AS2), positive Poisson’s ratio honeycomb sandwich panel (AS3), and negative Poisson’s ratio honeycomb sandwich panel (AS4)—were numerically compared under 2 kg, 4 kg, 6 kg, and 8 kg TNT-equivalent blast loads. The main numerical findings are summarized as follows.

(1) Under the adopted numerical model and nominal parameter set, the pre-formed steel configuration (AS1) exhibits the smallest predicted permanent deformation among the four configurations, with values of 22 mm, 46 mm, 131 mm, and 208 mm under the 2 kg, 4 kg, 6 kg, and 8 kg TNT-equivalent loads, respectively. This response should be interpreted as the combined effect of the initial curved geometry, forming-induced residual stress state, and associated material history. The individual contribution of residual stress was not isolated in the present study.

(2) For the V-shaped underbody structures considered here, permanent deformation is more closely associated with the bending resistance of the load-carrying steel faces than with the magnitude of the calculated internal-energy response. AS2 exhibits smaller predicted permanent deformation than both sandwich configurations under the investigated loading conditions, although the sandwich structures show comparable or higher internal-energy responses in some cases. This result indicates that a higher calculated energy response does not necessarily correspond to superior deformation resistance.

(3) The equal-mass constraint introduces a trade-off in mass allocation and sectional configuration. In AS3 and AS4, part of the total mass is allocated to the aluminum honeycomb core, requiring a reduction in steel face-sheet thickness from 10 mm to 8 mm and an increase in total sectional depth. Although core crushing contributes to the calculated internal-energy response, the reduced steel face-sheet thickness is accompanied by larger predicted permanent deformation under the investigated conditions. The differences between AS2 and the sandwich configurations should therefore be interpreted as the combined effects of face-sheet thickness, sectional depth, core deformation, and effective stand-off distance rather than as the isolated effect of the honeycomb core.

(4) The negative Poisson’s ratio configuration (AS4) shows slightly smaller predicted deformation and a somewhat higher calculated internal-energy response than the positive Poisson’s ratio configuration (AS3) under some higher blast loads. These differences represent numerical trends under the adopted model assumptions and should not be interpreted as experimentally validated advantages of the auxetic configuration.

(5) The present findings should be regarded as preliminary numerical predictions. Only the conventional baseline structure was directly subjected to blast testing, whereas AS1, AS3, and AS4 were evaluated numerically. In addition, controlled simulations isolating the individual effects of residual stress, initial curvature, material history, face-sheet thickness, sectional depth, and effective stand-off distance were not performed. Further physical testing and systematic controlled numerical studies are therefore required before quantitative performance advantages or general design recommendations can be established.