Structural response and failure modes of armor steel plates under dynamic underwater explosions

Abstract

In this research, we examine the dynamic deformation and blast-tolerance of all-metal plates and sandwich panels under underwater explosive (UNDEX) loading. The blast performance of four alloys, Mild Steel (MS), SS304, AL6XN, and AISI 4340, was based on the Johnson–Cook (JC) plasticity model as the shock factors increased from 0.42 to 0.73. The Fluid-Structure Interaction (FSI) model and nonlinear finite-element simulations were employed in the present computational analysis to yield measurable results for the deformation and equivalent plastic strain (PEEQ) of the target plates and the plastic dissipation energy of the sandwich panels. AISI 4340 consistently showed the most stability after each blast series, indicating that the material undergoes the least deformation and exhibits the lowest PEEQ due to its extremely high yield strength and resistance to plastic deformation. AL6XN exhibited appreciable performance under moderate shock and stress levels due to its pronounced strain-hardening behaviour; however, higher load levels reduced performance due to thermal softening. The SS304 exhibited reasonable deformation in addition to exhibiting a generous energy absorption capacity. Mild Steel deformed the most and had the highest PEEQ, while also having the most plastic energy dissipation. The sandwich panels subjected to underwater shock conditions demonstrate that at lower blast intensities, most of the blast energy is absorbed by the front face sheet. However, at higher blast intensities, the core’s contribution to energy absorption increases, thereby aiding energy distribution and enhancing overall stability. The blast-mitigation properties of AISI 4340 were outstanding, whereas SS304 and AL6XN improved the suitability of moderate designs for blast-tolerant applications. These analyses will help select the steels that optimize performance in marine, defense, and subsea applications for blast-resistant protective structures.

Keywords

dynamic energy absorption fluid-structure interaction sandwich panel sustainable structures underwater blast mitigation

Introduction

Civil infrastructure and defense applications have focused on how materials behave under extreme dynamic loading conditions, such as those from surface and underwater explosions. Underwater explosions generate intense, short-duration pressure pulses that impose both global and local loads on structural elements. Global loads govern the overall structural response, such as large-scale bending and membrane deformation driven by the transmitted shock impulse. Local loads arise from highly concentrated pressure effects associated with shock reflection, cavitation, and bubble pulsation near the structural surface, leading to localized stress concentrations, plastic strain accumulation, and potential damage initiation. Unlike air blasts, underwater loading generates lower-amplitude, long-duration, and repetitive bubble-collapse pulses that play a crucial role in structural damage and pose a higher risk of blasting-related issues [Rajeev et al., 2024; Lazar et al., 2024; Rajeev et al., 2025; Ramajeyathilagam et al., 2004]. Hence, material behavior under this sort of loading must be correctly characterized to formulate designs of marine structures [Vishnu Vijay Kumar., 2023].

Mild steel is readily available and easy to fabricate for ship hulls and offshore platforms. However, one reason they often exhibit large permanent deformation is that the material has low yield strength and insufficient strain hardening [Ramajeyathilagam et al., 2004]. Based on earlier studies, materials with a larger initial strength-to-density ratio and greater strain-rate sensitivity can provide significantly improved resistance to blast loading by reducing global deflection and local accumulation of plastic strain [Ramajeyathilagam et al., 2004]. In this context, materials such as stainless steels (e.g., SS304) exhibit high ductility and an excellent strain-hardening exponent. They have shown promising results for applications in toughness and distributed plasticity [Vishnu Vijaya Kumar et al., 2023]. Several researchers examined sophisticated alloys such as AL6XN (super-austenitic stainless steel) and AISI 4340 (high-strength, low-alloy steel) for their strength, ductility, and durability under demanding underwater conditions. [Thai et al., 2018].

The selection of materials for dynamic blast resistance is based on several factors, such as (1) strain-rate sensitivity, (2) thermal softening, and (3) ability to fail without perforation and enhanced energy dissipation. The Johnson-Cook (J-C) constitutive model [Talaat et al., 2022] provides a robust framework for linking these material properties, including deflection, plastic strain, failure modes, and plastic energy dissipation. The flow of a material under high strain rates from elastic resistance and plastic flow is affected by parameters such as the initial yield stress (A), strain hardening (B, n), strain-rate sensitivity (c), and thermal softening (m) [Rizwanullah et al., 2020]. AISI 4340 is a high-yield steel. Materials with larger strain-hardening exponents (SS304, etc.), on the other hand, are more favorable for dispersing plastic strain and absorbing blast energy. [Bendarma et al., 2023; Yadav et al., 2020; Köhnen et al., 2018] Alloys such as AL6XN can have a moderate yield strength with exceptionally high hardening coefficients. This provides an additional mechanism of blast resistance by gradually counteracting deformation as strain accumulates [Thai et al., 2018]. Steels subjected to air and underwater blasts have been considered, with yield strength and ductility affecting global deflection and failure [Imbalzano et al., 2017; Wadley et al., 2007]. Research on various grades of stainless steel shows that strain-rate sensitivity and work-hardening techniques reduce localized strain and fracture [Boonkong et al., 2016]. AL6XN is demonstrated to be a corrosion-resistant alloy, primarily tested in marine environments; its properties are also being considered for blast applications [Wadley et al., 2007]. AISI 4340 is an alloy that has been extensively studied in the aerospace and defense industries due to its exceptional strength and toughness. However, little characterization of its material response to underwater blast loading has been undertaken [Pardo et al., 2007].

Both shock propagation, fluid-structure interaction, and cavitation require combined hydrodynamic theory and nonlinear material response for a complete understanding [Bendarma et al., 2023; Vo et al., 2021]. Codes involving Euler-Lagrange methodology have been extensively used by LS-DYNA and ABAQUS [Dassault Systèmes Simulia Corp., 2022] to model deformation and development of plastic strain and failure modes of a plate [Vishnu Vijaya Kumar et al., 2023; Karagiozova et al., 2009; Sun et al., 2017]. The Johnson-Cook plasticity models, developed from high-strain-rate studies, can yield reasonably accurate quantitative responses to blast loading. However, this depends on sound, comprehensive material data, which are somewhat limited for advanced steels such as AL6XN. The blast resistance mechanism does not focus solely on minimizing deflected motion but also on how materials absorb the energy of the loading. The plastic dissipation energy is an essential link between the load and the measured deformation. Higher shock factors will result in higher energy absorption. This will be reflected in higher equivalent plastic strain (PEEQ) and greater global deflections. Past research indicates that high-strength materials, such as AISI 4340, exhibit less deformation at a given load than ductile materials, such as SS304, which absorb a significant amount of energy before failure. Within this context, assessing the toughness and survivability of the target materials is essential [Zhu et al., 2007].

Many studies have either analyzed traditional ship steels or composite materials, as noted in several literature sources [Ramajeyathilagam et al., 2004; Miller et al., 2010]. Typically, when researchers examine stainless steels, they focus on corrosion resistance or general mechanical behaviour rather than on dynamic response, as in the case of UNDEX [Thai et al., 2018]. Only a few experiments compare different grades of steel under similar underwater blast conditions, ranging from mild steel to super-austenitic stainless steel and high-strength steel. Furthermore, previous studies have tended to assess only global deformation or localized strain, often omitting relevant evaluations of midpoint deflection, PEEQ, and J-integral. The present research investigates the underwater shock response of four alloys across a wide range, from 0.42 to 0.73. The alloys mild steel, SS304, AL6XN, and AISI 4340 are investigated. Employing an assessment and simulation approach based on the Johnson–Cook constitutive model and analyzing the blast mitigation performance of sandwich panels using four measures: (i) Front face midpoint deflection as a metric of global response, (ii) PEEQ as a measure of localized plastic strain, (iii) core energy absorption and, (iv) plastic energy dissipation of the front and back face sheet. This study is novel because it compares the dynamic responses of materials under laboratory-scale underwater blasts and links constitutive material properties to structural response. In the present work, controlled underwater blast conditions are achieved by varying the charge mass while maintaining a constant standoff distance, thereby generating a prescribed range of shock factors. The resulting pressure–time histories are defined using established empirical UNDEX relations, ensuring repeatable and physically consistent loading conditions across all simulations. The study will thus not only rank the performance of these steels but also identify trade-offs between minimizing deformation and maximizing energy absorption, while providing a means of utilizing these steels in real-world blast-tolerant marine and subsea applications.

Methodology

Problem formulation

To evaluate the fluid-structure interaction (FSI) of monolithic target plates under underwater explosive (UNDEX) loading, computational models were developed following established methodologies [Ramajeyathilagam et al., 2004]. The experimental framework (Refer Figure 1), designed to analyze plastic deformation and structural failure, utilized a box-shaped chamber configured to simulate an air-backed boundary condition. A top cover plate with a thickness of 0.025 m was employed to secure the specimens. The experimental specimens (monolithic target plates) were positioned between the top flange of the box chamber and the cover plate, secured via a zigzag bolting pattern to approximate fully constrained edge conditions. Physical trials utilized mild steel plates with external dimensions of 0.55 × 0.45 × 0.002 m³, providing a net exposed surface area of 0.30 × 0.25 m² within the shock environment. The loading was generated using PEK I explosives positioned at a standoff distance of 0.150 m, aligned with the central axis of the target plate. This entire assembly was submerged in a water shock tank to a depth of 2.0 m. The tank dimensions are 8.0 m at the base and 6.0 m at the side walls ensured that shock wave reflections from the boundaries and the free surface were negligible. Experimental variables included explosive charge weights ranging from 0.01 to 0.08 kg to capture a broad spectrum of dynamic responses.

Modelling of fluid-structure interaction and target plate

An extreme load case, similar to an underwater explosion, generates high-energy shock waves over a very short duration, typically lasting between 10^-5 and 10^-3 seconds. The decay of the shock can be approximated as a function of the mass of the explosive charge and the standoff distance of the explosive from the target plate. The pressure profile resulting from an underwater explosion event can be evaluated using the following empirical equations [1–5]. Dynamic underwater explosions (UNDEX) cause cavitation-induced nonlinearities. It is necessary to incorporate these nonlinearities into computational analyses to accurately capture the deformation response of targets. The total pressure load generated is based on Taylor’s theory and included in the study. Table 1 Lists the values of the constants represented in equations (2)–(5) for the trinitrotoluene (TNT) explosive, providing the necessary parameters related to the weight (W) of the explosive charge and the standoff distance (R) from the explosion source. The constants K₁ – K₄ and A₁ – A₄ define the polynomial acoustic equation of state used in Abaqus/Explicit[Dassault Systèmes Simulia Corp., 2022] to model the nonlinear compressibility of water under shock loading in underwater explosion simulations.

P (t) = P_{\max} \exp [- \frac{(t - t_{d})}{θ}]; 0 \leq t \leq θ

(1)

Peak Pressure

P_{\max}

is determined by,

P_{\max} = K_{1} {(\frac{W^{1 / 3}}{R})}^{A_{1}}

(2)

Table 1.

Constants for TNT explosives [Gupta et al., 2010].

Parameter	Constant	Value
Peak pressure $(P_{\max})$	K₁	52.4
Peak pressure $(P_{\max})$	A₁	1.13
Decay constant $(θ)$	K₂	0.084
Decay constant $(θ)$	A₂	−0.23
Impulse (Ι)	K₃	5.75
Impulse (Ι)	A₃	0.89
Total energy $(E)$	K₄	84.4
Total energy $(E)$	A₄	2.04

The decay constant $θ$ is determined by,

θ = W^{1 / 3} K_{2} {(\frac{W^{1 / 3}}{R})}^{A_{2}}

(3)

The impulse (I) and the total energy (E) are determined by

I = W^{1 / 3} K_{3} {(\frac{W^{1 / 3}}{R})}^{A_{3}}

(4)

E = W^{1 / 3} K_{4} {(\frac{W^{1 / 3}}{R})}^{A_{4}}

(5)

The degree of severity of an UNDEX event can be determined using the shock factor (SF), which is a function of the TNT weight (W), standoff distance (R), and the angle of the underwater explosion

(ϕ)

S F = \frac{(1 + \cos ϕ)}{2} \frac{\sqrt{w}}{R}

(6)

In the present computational analysis, a range of SFs, from 0.42 to 0.73, was investigated by varying the TNT mass while maintaining a constant standoff distance. The shock factor range considered in this study was selected to represent near-to intermediate-field underwater blast conditions that induce substantial plastic deformation without immediate catastrophic rupture of thin metallic plates. This range captures the transition from moderate to severe deformation, enabling meaningful comparisons of material-dependent blast resistance and energy-absorption characteristics. Lower shock factors typically result in predominantly elastic or limited plastic response, while significantly higher shock levels may lead to tearing or perforation. The values of SFs employed in the current computational analysis are presented in Table 2. Varying the shock factor enables the investigation of the structural response and deformation behaviour of targets for underwater blast mitigation.

Table 2.

Shock factors for underwater explosion (UNDEX) [Ramajeyathilagam et al., 2004].

Sl. No.	Standoff distance R	Charge weight W (kg)	Shock factor SF (kg^1/2/m)	Peak pressure (MPa)
1	0.150	0.020	0.42	202.0
2		0.040	0.6	268.0
3		0.050	0.67	302.6
4		0.060	0.73	313.0

As shown in Figure 2, the assembly consists of a water column and a target plate. Target plates of mild steel, measuring 300 × 250 × 2 mm, were modelled using the elasto-viscoplastic Johnson-Cook (J-C) model. The J-C model offers greater accuracy by accounting for thermo-elasticity, strain-rate hardening, and adiabatic softening. Table 3 lists the J-C material and damage parameters for mild steel, summarised from [Rajeev et al., 2025; Yadav et al., 2020]. The employed J-C plastic model is expressed as (equation (7)), where A, B, C, n, and m are material constants that represent the equivalent plastic strain rate and the reference strain rate, respectively. To account for temperature effects, the model incorporates parameters such as the normal temperature ( $T$ ), the melting temperature ( $T_{m}$ ), and the transition temperature ( $T_{t}$ ).

σ_{y} = [A + B {({\bar{ε}}_{p l})}^{n}] [1 + C \ln (\frac{{\bar{ε}}_{p l}}{{\dot{ε}}_{0}})] [1 - {(\frac{T - T_{t}}{T_{m} - T_{t}})}^{m}]

(7)

Table 3.

Summary of the validated numerical results.

Sl. No.	Stand-off distance R (mm)	Shock factor SF (kg^1/2/m)	Front face midpoint deformation (mm)		Error (%)
Sl. No.	Stand-off distance R (mm)	Shock factor SF (kg^1/2/m)	Experimental [Ramajeyathilagam et al., 2004]	Numerical [present Work]	Error (%)
1	150	0.42	57.8	59.3	2.59
2		0.60	86.4	90.2	4.39
3		0.67	107.8	104.0	3.52
4		0.73	125.0	114.4	8.48

Abaqus Explicit finite element application was used to model the target and the explosive, in accordance with the dimensional parameters and experimental boundary conditions reported in the literature [Ramajeyathilagam et al., 2004]. The interaction between the surface of the target plate and the water column was defined using the UNDEX definition. The water column was modelled with tetrahedral 3D acoustic elements (AC3D4). Continuing the mesh sensitivity analysis, the target plates were discretised using 8,400 of 4 node linear quadrilateral elements with reduced-integration shell elements of type S4R, with an aspect ratio of 1. All the plate edges were fully constrained to mimic the experimental boundary conditions. The source of the underwater explosion was located 150 mm away from the midpoint of the target plate. The J-C material constants of AL6XN, SS304, and AISI 4340 are sourced from [Yadav et al., 2020; Wadley et al., 2007; Pardo et al., 2007].

Validation of the FSI model

The fluid-structure interaction established between the water column and the target plate in the present work is validated against the experimental results reported in [Ramajeyathilagam et al., 2004]. In Figure 3, the artificial strain energy remained below 5% of the total internal energy throughout the simulation, indicating numerical stability and negligible influence of non-physical deformation modes. The physical validity of the numerical model is established through direct comparison with experimental midpoint-deformation data reported in the literature, with a maximum deviation of 8.48% across the shock factors investigated in the current study. Together, these observations confirm that the predicted response is both numerically stable and physically representative of the underlying underwater blast behaviour. The midpoint plastic deformation of the target plates under UNDEX loading in the present FSI model is validated against experimental data in Figure 4. Deformation contours of the multi-view cuts presented in Figure 5 indicate the depth of plastic deformation in the target plates. Table 3 summarizes the validated results of the present simulation and compares them with the experimental values. The accuracy of the present numerical FSI scheme was demonstrated to be higher, with a maximum error of 8.48% for SF 0.73.

Results and discussion

Dynamic behaviour of target plates subjected to UNDEX loading

The peak deformation of various target plates for varying shock factors is summarised in Figure 6. The contours of the front face midpoint deformation of the target plates along the lateral edge is presented in Figure 7 and the contours of equivalent plastic strain (PEEQ) to evaluate the inelastic deformation behaviour of target plates are offered in Figure 8. The midpoint deflection of the target plate represents its global deformation response under impulsive loading. In underwater explosions, deflection captures the balance between the driving pressure pulse and the plate’s resisting stiffness and strength. The results of the midpoint deflections highlight a significantly varying structural response with increasing shock factors. Mild Steel exhibited the highest deformations, consistently exceeding 114 mm for the highest shock factor. The excessive deformation results from its low yield strength and limited hardenability under strain. Across all shock factors, the deflections of AISI 4340 were the lowest and never surpassed a value of 82 mm. The primary reason for limiting the plate’s displacement during shock loading is its high initial yield strength. Stainless steel, SS304, and AL6XN exhibited a moderate response to deformation, with AL6XN dominating at low shock factors due to its significantly higher strain hardening coefficient compared to SS304. Nonetheless, as the shock factor increased, effectiveness decreased, and overall performance remained similar. SS304 has the lowest yield strength among the three steels. Hence, it has some plastic flow. The hardening exponent of SS304 and strain-rate sensitivity is much higher than that of mild steel. Due to this, the deflections of SS304 are much less than those of mild steel. Understanding the deflection response is linked to the complexity of yield strength, hardenability, and dynamic sensitivity, which distinctly reflect the blast-deformed behaviour.

In the low-load case of SF−0.42, the maximum midpoint deformation of the mild steel is 59.3 mm, whereas that of AISI 4340 is 38.5 mm. The stainless steels are midway: SS304 at 53.3 mm and AL6XN at 45.2 mm. The deformation of AISI 4340 was minimal at the lowest loading and differed by approximately 35%. AL6XN experienced medium deformation at 24%, which is lower than that of Mild Steel. SS304 is most similar to Mild Steel, as it varies little and differs by only about 10%. With a shock factor of 0.73, materials again exhibited significant deformation. The maximum deflection of Mild Steel was 114.4 mm. Similarly, SS304, AL6XN, and AISI 4340 had deflection values of 96.7 mm, 84.0 mm, and 82.0 mm. The deflection of Mild Steel is 39.5% more than that of AISI 4340. Although Mild steel deforms the most, the relative difference for the high-strength alloy decreases as the severity of the load conditions increases. Further investigation reveals that the shock factor increases by 15.2% for Mild Steel, 81.6% for SS304, 85.8% for AL6XN, and 112.6% for AISI 4340. The higher-strength alloy exhibits better resistance to deformation in absolute terms, but it is more susceptible to shock loading in relative terms.

When examining equivalent plastic strain, it is apparent that the four alloys exhibit significant differences in the accumulation of permanent deformation under shock loading in an underwater environment. Mild Steel has the highest PEEQ value due to its high strain and effort, which increase plastic strain quite rapidly. This is due to the low yield stress and limited hardening of mild steel. SS304 exhibits a moderate to high accumulation of plastic strain, but the deformation is more evenly distributed in space. This is due to the material’s large hardening exponent and strain-rate sensitivity. Additionally, the material exhibits localised yielding, thereby enhancing its energy-absorption capacity. AL6XN shows a lower overall PEEQ. This is due to the high hardening coefficient, which increases the resistance to yielding. The drop in PEEQ of AL6XN is marked at high shock factors. It is also susceptible to thermal softening. AISI 4340 consistently exhibits a low overall PEEQ value due to its very high yield strength, which increases resistance to the initiation of plastic flow. The trend for PEEQ responses was in agreement with deflection results; AISI 4340 was most resistant to permanent strain, followed by AL6XN and SS304, while Mild Steel was the most susceptible to permanent strain.

The PEEQ data reveal a consistent ranking of the shock factors. AISI 4340, which exhibits the lowest equivalent plastic strain among other grades, provides excellent resistance to plastic deformation. AL6XN and SS304 develop intermediate levels of PEEQ, with AL6XN generally exhibiting lower levels at moderate shock factors due to its high strain hardening capacity, and SS304 displaying greater levels but more evenly distributed across the plate. Mild Steel again demonstrates the highest PEEQ values, indicating considerable plasticity and a tendency towards localised deformation. Mild Steel peak PEEQ values are approximately 20-100% higher than equivalent AISI 4340 values across the range of shock factors, while AL6XN PEEQ often measures 10-40% less at low loads than SS304.

The plastic dissipation energy curves in Figure 9 demonstrate that plates subjected to higher shock factors, SF−0.73, absorb a significant amount of energy, several times higher than 0.42. The majority of the plastic energy for all four materials is apparently absorbed within the first half of the blast duration, and when the curves plateau, plastic work occurs primarily within the initial shock front. The relationship between PEEQ and deflection is more direct: Mild Steel, which has the highest PEEQ and deflection, also exhibits the most significant total energy absorption. AISI 4340 absorbs the smallest amount of plastic energy, having the lowest PEEQ (plastic equivalent strain) and the smallest deflection. SS304 and AL6XN had plastic energy absorption between the two extremes, with dissipation derivatives consistent with their PEEQ values. The differences in total dissipation by material are significant. For example, in the highest-shock case, Mild Steel absorbed substantially more energy than AISI 4340, whereas SS304 and AL6XN dissipated 20–60% more plastic energy than AISI 4340. In the high-intensity regime (shock factors 0.67 and 0.73), the observed reduction in plastic dissipation energy for Mild Steel is directly attributable to the onset of structural rupture. Severe strain localization triggers plate tearing and a rapid loss of load-carrying capacity, which induces stress relaxation and terminates further plastic work accumulation. In contrast, higher-strength alloys specifically AISI 4340, AL6XN, and SS304 maintain their structural integrity at these load levels, continuing to absorb energy through sustained plastic deformation. Consequently, the diminished plastic dissipation energy in Mild Steel at higher shock factors signifies premature material failure and structural deficiency rather than a superior blast-mitigation characteristic.

Integrated discussion

In this section, the midpoint deformation, PEEQ, and dissipation of plastic energy will be integrated to provide a general picture of the underwater shock-loading response. AISI 4340 exhibits the best performance, with minimal deflection, minimal plastic strain, and the lowest energy absorption, owing to its very high yield strength. AL6XN’s high strain hardening makes it an excellent performer under moderate shock loading. However, under maximum shock loading, strain hardening no longer contributes due to thermal softening. SS304 exhibits moderate deflection, yet it has a higher PEEQ than AL6XN. However, because SS304 exhibits strong strain-rate sensitivity and high hardening exponents, it absorbs energy in a more stable, distributed manner, resulting in improved toughness. The weakest material across the board on the spectrum is mild steel, as it exhibits greater deflections. Furthermore, it exhibits the worst residual PEEQ and the best plastic energy absorption, attributable to its low yield strength and poor hardening properties. The findings reveal a trade-off between minimal deformation, in which AISI 4340 outperforms all other materials, and the highest energy absorption, which is tied between SS304 and AL6XN. In contrast, Mild Steel is the least favourable anti-blast material.

Application of the steel face plates on the development of blast-tolerant sandwich panels

A sandwich panel typically consists of three main components: a face sheet on the front side, a core, and a face sheet on the back side. In this numerical simulation of all-metal honeycomb sandwich panels, the core had dimensions of 300 × 250 × 15 mm, and the face sheets were both 300 × 250 × 2 mm, resulting in an overall height of 19 mm for the sandwich panel. The honeycomb core was square-shaped with cell walls spaced at 15 mm intervals. The design of the sandwich panel used in this study is illustrated in Figure 10. The face sheets and cores were discretised using S4R linear quadrilateral shell elements with reduced integration and hourglass control to minimise distortion. The face sheets contained 8,400 elements, while the core was meshed with 16,365 elements of the same type. Tie constraints were employed to ensure a permanent bond on the top and bottom surfaces of the core with the corresponding face sheets. The front and back face sheets were completely constrained at all edges. The underwater explosion (UNDEX) source was located at 150 mm from the midpoint of the front face sheet. The modelling of the fluid-structure interaction (FSI) at the panel’s front face due to a shock wave was performed using the UNDEX definition. The discretisation pathway, developed with FSI boundary conditions and modelling, enabled a comprehensive numerical study of the sandwich panel’s response to varying underwater explosion intensities.

Dynamic behaviour of sandwich panels subjected to UNDEX loading

The Front face midpoint plastic deformation contours of sandwich panels subjected to varying shock factors are presented in Figure 11. Peak deformation of various sandwich panels is summarised in Figure 12 and the stress contours over the front face sheet of the sandwich panels are presented in Figure 13. The contours of the midpoint plastic deformation observed in the sandwich panels exhibit distinct responses to increasing shock intensity, relative to the materials. All panels exhibit a relatively low surface deflection at the lowest shock factor, 0.42, indicating that the core and face sheets are sufficiently stiff to accommodate any substantial plastic deformation. At this shock-loading level, deformation is characterised by small, localised yielding at the centre of the front face. The impact of shock factor 0.6 on the progression into permanent deformation for the MS panel. Permanent deformation also occurs, albeit to a lesser extent, in the SS304 panel. Both panel types exhibit pronounced plastic deformation at the centre, resulting in a smooth, dome-like bulge. This is essentially the type of behaviour expected in a ductile metal under impulsive loading. Both AISI 4340 and AL6XN plates also maintain a relatively stiff profile and exhibit a more localised level of deflection due to their higher yield strength and better ability to absorb energy in elastic–plastic transition. At high shock factors of 0.67 and 0.73, deformation is more significant and permanent, while plastic strain builds up in the centre blast area on the front face. The contours of Mild Steel are expanding radially, indicating the presence of plastically deformed material within this area. This further suggests lower resistance to the effects of localized blast pressure. On the other hand, AISI 4340 also exhibits impressive structural strength and retains its strength under the most severe shock loading. The high strength-to-weight ratio and hardened microstructure can effectively absorb blast energy with only slight permanent deflection. The AL6XN is a balanced material in terms of ductility and strength, and it absorbs shock energy to resist brittle fracture.

Beyond global deformation metrics, the spatial distribution of equivalent plastic strain (PEEQ) and the identification of stress-concentration zones provide critical insights into the latent failure mechanisms of the sandwich panels. At moderate shock intensities (SF ≤ 0.60), the structural response is characterized by predominantly ductile and distributed deformation with minimal strain localization. However, as the shock factor escalates (SF ≥ 0.67), distinct failure modes emerge, governed by the interaction between the core topology and the material’s constitutive behavior. Concentration of plastic strain near the panel midpoint and at cell-wall intersections may initiate ductile cracking, particularly in alloys with lower yield strength such as Mild Steel. Under severe loading, high strain accumulation coupled with membrane stretching can culminate in localized tearing. The square honeycomb core is susceptible to local buckling of the cell walls under compressive shock transmission. While progressive plastic hinging and wall folding serve as primary energy-absorption mechanisms, these deformations may evolve into structural instability at higher shock intensities. Although the core significantly attenuates the incident shock wave, the transmitted impulse can still induce localized plastic strain on the rear face sheet. In extreme-intensity scenarios, this localization may progress into rear-surface cracking. While computational models often utilize tie constraints to represent ideal bonding, the substantial interfacial shear stresses generated under severe shock loading may, in practice, lead to delamination or debonding between the core and face sheets. The susceptibility to these failure modes is fundamentally tied to the selected alloy’s properties. High-strength alloys, notably AISI 4340, effectively minimize global deformation and delay the onset of tearing, though they may exhibit more pronounced localized stress concentrations. Conversely, highly ductile materials like SS304 facilitate a more even distribution of plastic strain, which mitigates the risk of sudden crack initiation at the expense of allowing larger overall structural deflections.

Figure 14 illustrates the evolution of plastic dissipation energy over time as a function of the shock factor, representing the energy-absorbing capacity of metallic sandwich panels across varying blast intensities. At the lowest intensity (SF = 0.42), the PDE values for all materials exhibit a moderate, nearly uniform increase, reaching approximately 10 kJ. This indicates that plastic deformation begins to occur, although it is primarily confined to the front face sheet. The deformation energy plateaus fairly quickly, indicating limited plastic flow and good elastic recovery at this load level. When the shock intensity is increased to SF = 0.60, the panels can absorb almost twice as much energy as at SF = 0.42. The mild steel MS and stainless steel SS304 will require more energy than AL6XN and AISI 4340. This indicates differences in ductility and yield strength between these materials. These metals undergo substantially greater plastic deformation before saturation. On the other hand, AISI 4340 and AL6XN, which are high-strength alloys, yield overall smaller values that are more stable and characteristic in energy growth curves, implying that their energy-absorbing capacity is controlled by the elastic–plastic transition rather than large-scale yielding. As both SF = 0.67 and SF = 0.73 use the same material response metric, the difference is significantly greater than that of SF = 0.50. The almost always maximum PDE of the Mild Steel panel implies that most of the plastic work is done, and permanent deformation occurs. This is because of its low stiffness. SS304 has a similar energy-absorption capacity, but its saturation is reduced owing to its enhanced strain-hardening capacity. Conversely, AISI 4340 and AL6XN exhibit significantly smaller PDE values, indicating that these materials are less susceptible to shock-induced plasticity. After 0.6 ms, the slope of the lines is noticeably flat even under severe load, indicating structural integrity is generally not compromised.

As shown in Figure 15, all plastic energy absorption occurs in the front face sheet, core, and back face sheet across all sandwich panels, providing a clearer picture of how energy is dissipated. At SF = 0.42, energy dissipation is minimal and mostly confined to the front face sheet that interacts directly with the shock wave. Due to insufficient load transfer through the core at low shock pressures, the core and back face sheet offer a small contribution. Some redistribution of energy occurs at a shock factor of 0.60. The core begins to absorb considerable amounts of the plastic energy, indicating that it dissipates the transmitted shock forces more effectively. The Mild Steel panel exhibits a relatively uniform energy distribution across the three layers over this range. Each layer absorbs nearly the same amount of energy (front ≈9.9 kJ, core ≈7.1 kJ, and back ≈5.6 kJ). This indicates efficient energy transfer due to structural integrity and continuity. At SF = 0.67, the front face sheet continues to act as the primary energy absorber for all materials, but the core starts to make a significant contribution, especially for SS304 and AISI 4340. This suggests the initiation of plastic yielding in the core, which is the most efficient way of energy absorption. The less-engaged back face sheet, with increasing energy uptake, represents a transmitted component of the blast wave. The maximum shock factor (SF = 0.73) yields the peak total PDE for all components. The mild steel panel captures the highest energy at either level (≈ 36 kJ). The energy dissipation appears to be nearly equal across the three layers, indicating that under severe loading, the entire sandwich is involved in deformation. The AISI 4340 and AL6XN were still expected to concentrate energy in the front and core layers. This can be attributed to their higher reservation capacity and the containment of localised plastic propagation through the thickness.

Constitutive analysis of material response

The performance disparities in deformation and energy absorption among the investigated alloys are fundamentally dictated by their constitutive behavior, as defined by the Johnson–Cook (J-C) model. The interplay between strength and ductility under high-strain-rate conditions governs the balance between deformation control and energy dissipation.

Influence of yield strength on global response

• High yield resistance: Alloys with a high initial yield strength (A), such as AISI 4340, demonstrate a superior ability to resist the onset of plastic flow.

• Deformation limitation: This high threshold limits global midpoint deflection and ensures the lowest accumulation of equivalent plastic strain (PEEQ) across all shock factors.

• Energy metrics: Because the material maintains structural rigidity, it records the lowest plastic dissipation energy, as less permanent work is performed on the structure.

Strain hardening and distributed plasticity

• Progressive resistance: In contrast, materials with lower initial yield strength but exceptional strain-hardening capacity (n), such as SS304 and AL6XN, initiate plastic flow at lower stress levels but progressively enhance their resistance as deformation accumulates.

• Dynamic sensitivity: The high hardening exponents and strain-rate sensitivity (C) of these stainless steels promote distributed plasticity under impulsive loading.

• Stable Absorption: This mechanism enables stable energy absorption and improved toughness, preventing immediate strain localization even as shock intensity increases.

Ductility and failure in mild steel

• Rapid strain accumulation: mild steel, characterized by relatively low yield strength and limited hardening properties, yields prematurely and accumulates plastic strain rapidly.

• Maximum dissipation: Consequently, it consistently exhibits the largest midpoint deflections and the highest total plastic dissipation energy.

• Performance trade-off: While its ductile nature allows for high energy uptake, the resulting excessive global deformation and susceptibility to localized tearing renders the least favorable material for high-intensity protective applications.

The current research demonstrates that structural deformation is minimized when high yield strength delays the initiation of plastic flow, whereas energy absorption is maximized when strain-hardening and strain-rate sensitivity facilitate sustained plastic work.

Conclusion

This research provides a comprehensive evaluation of the dynamic response and blast mitigation performance of various metallic alloys and square-cell honeycomb sandwich panels under underwater explosive (UNDEX) loading. By employing a validated fluid-structure interaction (FSI) computational framework integrated with Johnson-Cook plasticity modeling, this study elucidates how fundamental material characteristics specifically yield strength, strain hardening, and strain-rate sensitivity govern structural integrity under extreme impulsive pressures.

The significant findings of this research are summarised as follows

• Among the materials investigated, AISI 4340 demonstrated the highest level of blast resistance, maintaining the lowest midpoint deflection and equivalent plastic strain (PEEQ) across all shock intensities. Its exceptional yield strength and strain-rate response make it an ideal candidate for high-stiffness applications where minimal global deformation is the primary objective.

• AL6XN exhibited remarkable performance under moderate shock factors due to its significant strain-hardening capacity, which effectively inhibited the rate of plastic flow. However, at elevated shock intensities, the benefits of hardening were diminished by the onset of thermal softening.

• SS304 proved to be an optimal selection for structures requiring a balance of strength and ductility, exhibiting generous energy absorption capacity despite moderate deformations. In contrast, while Mild Steel demonstrated high plastic energy dissipation, its low yield strength resulted in prohibitive levels of global deflection and localized strain, rendering it the least favorable material for intense UNDEX conditions.

• In sandwich configurations, the core was identified as a critical component for energy redistribution. As the shock factor increased, the honeycomb core transitioned into the primary contributor for energy absorption, significantly enhancing the blast-tolerant capability of the overall structure.

The results establish a clear trade-off between rigidity and energy dissipation. For applications requiring maximum structural stability, high-strength alloys like AISI 4340 are recommended. For designs prioritizing damage tolerance and energy uptake, SS304 and AL6XN offer superior utility. These findings provide a robust foundation for the selection and optimization of materials in marine, defense, and subsea protective structures.

Scope for future work

Based on the findings of the current research, several critical avenues for future investigation have been identified to further advance the design of blast-resistant protective structures:

• While this study focuses on initial shock wave interaction, explicit modeling of subsequent bubble pulsation and late-time hydrodynamic effects is essential. Capturing these phenomena will provide a more comprehensive understanding of long-duration fluid-structure interaction (FSI) and its cumulative impact on structural deformation.

• A systematic parametric optimization of core topologies should be undertaken. Investigating biomimetic geometries—such as auxetic or hexagonal cells—and varying relative densities could yield significant improvements in energy redistribution and overall blast mitigation performance.

• Future studies should incorporate high-fidelity fracture and damage models, alongside cohesive interface modeling, to enable the direct prediction of crack initiation, structural tearing, and face-sheet debonding. Additionally, the integration of corrosion-resistant composite materials would expand the applicability of these findings to more diverse marine environments.

• Extending the current FSI validation to full-scale marine and subsea components will bridge the gap between computational simulations and real-world defense applications.

Footnotes

ORCID iDs

Prince Jeya Lal Lazar

Vishnu Vijay Kumar

Anupoju Rajeev

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Data Availability Statement

Data will be made available by the authors upon request.*

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