Fluid based sandwich panel core structure for blast load mitigation

Abstract

Researchers have extensively explored various approaches to enhance the blast resistance of structures, concentrating on optimizing structural designs and employing a wide range of materials. This research investigates the impact of incorporating water as a fluid within the core of tubular sandwich panels on blast mitigation effectiveness. The study systematically analyzes various panel configurations by altering key design parameters: the thickness of the face sheets, spacing between the core elements, and proportion of fluid within the core. These variables are scrutinized through metrics such as elastic strain energy, the amount of work applied externally, and the movement of the panel. Utilizing finite element analysis, 27 distinct numerical experiments were conducted to gather data. The findings demonstrate that panels with a water-filled core exhibit superior blast resistance compared to their non-fluid counterparts. Specifically, panels with completely filled cores showed the lowest levels of panel displacement and external work, whereas those with half-filled cores recorded the highest elastic strain energy. Furthermore, regression analysis revealed that plate thickness predominantly influences panel displacement and external work, whereas the fluid volume fraction within the core most significantly affects elastic strain energy. This study contributes to the understanding of fluid-structure interactions in blast-resistant design, offering valuable insights for optimizing structural defenses against blast impacts.

1. Introduction and literature review

Sandwich panels are made up of two strong and rigid exterior sheets that surround a thick, yet lightweight and economical, inner core [1]. This unique composition endows the panel with enhanced properties, surpassing those of its individual constituents, such as being lightweight yet robust, and economically efficient [1]. These panels have found extensive applications across diverse sectors, including aerospace, marine, transportation, and defense, owing to their advantageous characteristics [[1], [2], [3]]. Despite their widespread usage, sandwich panels are vulnerable to damage from external impacts [[4], [5], [6]]. Such damage can significantly diminish their service lifespan, load-bearing capacity, and overall functionality [[7], [8], [9]]. Consequently, there has been a significant research emphasis on augmenting the resilience of sandwich panels, particularly in mitigating the effects of explosive loading.

In parallel to enhancing the intrinsic blast resistance of sandwich panels, there has been notable research in the development of external protective measures. Specifically, studies have explored the efficacy of deploying barriers to shield structures from direct blast impacts.

Numerous studies have delved into the field of blast mitigation by strategically placing barriers between the blast source and the targeted structure. These investigations have primarily concentrated on enhancing barrier performance through the utilization of various materials. Xu et al. [10] and Tamba et al. [11] have shed light on the effectiveness of gabion walls and supplementary protection walls in withstanding blast loads. Their research revealed that such barriers significantly attenuate the impact of blasts, primarily by reducing the resultant impulse transmitted beyond the wall. Key findings also highlighted that the proximity of the explosive charge and the wall's dimensions, particularly its height, are crucial in optimizing the wall's capability to mitigate blast effects. Moreover, Tamba et al. [11] discovered that the incorporation of an additional C-shaped wall further amplifies the blast mitigation efficacy.

Zhang et al. [12], Chen et al. [13], and Chen et al. [14] conducted both computational and experimental studies on the blast mitigation performance of water walls. They carried out 21 in-situ experiments using plastic bags and polyethylene containers filled with water and 0.2 kg of TNT, aiming to analyze the performance and calibrate their numerical models. Their findings indicate that water walls can significantly reduce peak reflected overpressure, especially when the walls are higher. Zhang et al.[12] and Chen et al.[13] focused on water walls housed in polyethylene containers. Zhang et al.[12] noted that improved mitigation performance was achieved with smaller distances between the water and the charge, as well as with greater water wall heights and reduced distances between the water and the structure. Chen et al.[13] examined the impact of the water wall's height, width, and proximity to the explosive charge. They found that decreasing the distance between the water barrier and the charge increased the duration of rising overpressure while reducing the impulse. Additionally, they observed that increasing the thickness of the water barrier wall diminished the impulse and peak overpressure. However, this reduction became less significant beyond a certain thickness threshold. Chen et al. [14] further investigated the blast mitigation performance of water walls made from water filled plastic bags and incorporated within a steel structure. Their study varied the water wall's height and thickness, revealing that optimal performance was achieved by minimizing the distance from the charge, increasing the water wall's thickness and height, and allowing the water mist to absorb and convert the blast energy into internal water energy.

The impact of utilizing various water barrier shapes has also been investigated. Huang et al. [15] and Zhou et al. [16] studied the blast shielding of hollow cylindrical barriers, while Bornstein et al. [17,18] examined how water barriers with various novel shapes perform. Huang et al. [15] explored the effect of hollow cylindrical water barriers on blast mitigation performance by varying its heights, thickness and inner diameters experimentally and numerically. The barriers were made of soft polyvinyl chloride. The authors observed that the barriers effectively reduced the peak overpressure and impulse of the blast wave, particularly along the sides and base of the cylindrical barriers, by reflecting and diffracting the shock wave. The best performance was achieved by increasing the barrier thickness, reducing the inner diameter, and increasing the height. However, they noted that this type of blast mitigation barrier cannot be used indoor. Similarly, Zhou et al. [16] examined the effect of hollow cylindrical barriers with different combinations of water and polyurethane (PU) foam through both numerical and experimental methods. They conducted six field tests to evaluate the effect of different material properties and arrangements on blast mitigation performance. Five different property arrangements were tested by varying the wall material between a single layer (water or PU) and a double layer (polyurea with varying inner and outer layers of water, PU foam, and PU foam sprayed with polyurea). The authors discovered that the hollow cylindrical barriers reduced the impact of the blast load by deflecting the blast wave. They concluded that the barrier with PU foam as the inner layer and water as the outer layer was the most effective due to the material arrangement and the PU foam high capacity for energy absorption.

Bornstein et al. [17] also studied the blast mitigation performance of various novel shapes of water barriers. They examined the shadowing, Fluid-Structure Interaction (FSI), and spreading mitigation mechanisms of five container shapes: mushroom, quadrangular, diamond cone and inverted cone, diamond, and mushroom shapes. They also investigated the blast mitigation performance of a kinetic energy defeat device consisting of 1.5-L water-filled bottles arranged in two rows. The results showed that the quadrangular container performed best, reducing peak dynamic deformation by 70%. The container with a mushroom-shaped was the second-best performer, resulting in a 62% reduction in peak dynamic deformation. The mushroom-shaped container had the best blast mitigation performance with the highest mass efficiency, despite having less than half the mass of the quadrangular container. In a separate study, Bornstein et al. [18] explored the blast mitigation effect of different fluid containers through both experimental and numerical methods, using six high-density polyethylene containers filled with bulk water, aerated water, shear thickening fluid, expanded polystyrene, sand, and a combination of EPS and water. They examined different heights for the water container. The results showed that sand was the best-performing fluid container in terms of volume, reducing dynamic deformation by about 60%. Water was the best performer in terms of mass. The authors concluded that mass is an important factor in the performance of a mitigant in reducing momentum transferred to the target, acting as a mitigation mechanism.

Other researchers have investigated various mechanisms for mitigating the effects of blasts, such as studying the impact of different sandwich panel structures or the use of different materials as blast mitigants. Sandwich panels can mitigate impact loading through plastically deforming the core structure and the front plate, dissipating the impact energy [19]. Al-Rifaie et al. [20], Liu et al. [21], Alberdi et al. [19], and Kumar and Patel [22] examined the blast resistance of sandwich panels with various corrugated core structures. While Cheng et al. [23] and Lu et al. [24] studied how tubular core structure assist in mitigating the blast. Al-Rifaie et al. [20] examined low-cost aluminum sandwich panels with various unconnected corrugated core layers and topologies, finding the trapezoidal topology most effective in minimizing core deformation. Liu et al. [21] studied laser-welded corrugated sandwich panels, noting better blast resistance and lower deformation in the longitudinal direction of the core. Alberdi et al. [19] compared different core shapes under blast loads, discovering that diamond-folded cores excelled with smaller blasts, while hexagonal and square honeycomb cores were superior with larger blasts, and orthogonal folded cores showed the least backplate deflection. Kumar and Patel [22] found that octagonal honeycomb cores outperformed square ones in blast resistance.

Cheng et al. [23] examined the efficacy of cladding structures subjected to blast loading, specifically focusing on composite panels featuring tubular cores. Their investigation delved into the impact of variables such as the quantity of core tubes, the spacing between tubes, the material properties of the tubes, and the thickness of the tube walls on the overall performance of the panels. The results indicated that sandwich panels with core tubes effectively reduced the blast impact on the backplate and that there is a negative correlation between the deflection of the top plate and the interaction between the core tubes. In a separate study, Lu et al. [24] investigated numerically and experimentally the behavior of sandwich panels with empty and foam-filled cores. The tubular cores were subjected to impact loads. The loads were applied using cylindrical and hemispherical heads from different positions. The results revealed that filling the tubular core with aluminum foam and increasing its density reduced the maximum displacement and increased energy absorption.

Recent studies on honeycomb core sandwich panels, particularly for maritime, military, and vehicle protection, have revealed significant advancements in blast resistance. Li et al. [25] found that ultralight all-metallic honeycomb panels outperform traditional metallic plates in blast resistance, thanks to their energy absorption capabilities. Ghate and Goel [26] enhanced this efficiency by exploring different aluminum core topologies (square, circular, hexagonal), with multi-layered cores showing superior strength and energy dissipation. Patel and Patel [27] demonstrated that increased core height in honeycomb panels improves blast resistance by enhancing energy absorption and reducing back face deflection, especially with 71 mm cores. Similarly, their subsequent study [28] indicated that smaller cell sizes in these panels offer better resistance in low-intensity blasts. Lizheng Li et al. [29] discovered that polyurea-coated auxetic honeycomb panels significantly boost blast resistance, with back side coatings being particularly effective. Ul Haq et al. [30] introduced novel cores combining auxetic and hexagonal cells, resulting in improved energy absorption and minimized deflection under blast loads. Wei et al. [31] showed that additive manufactured Ti–6Al–4V panels with auxetic structures exhibit enhanced blast resistance, influenced by face sheet thickness and core layers. Finally, Yaqoub et al. [32] found that tubular core designs in sandwich panels show minimal deformation and high kinetic energy dissipation under blast loads, highlighting the role of facade plate thickness in blast resistance and the need for further research in this area. The recent reviewed studies on honeycomb sandwich panels for blast resistance demonstrate significant advancements in this field. They reveal that factors like core design, material properties, and structural optimizations greatly enhance blast mitigation. Innovations in metallic honeycomb panels, varied core topologies, and coating methods have shown improved energy absorption and reduced deformation under blast loads.

Recent research in the field of foam-filled core sandwich panels has focused on enhancing their blast resistance, exploring core gradients, damage mechanisms, and deformation under various blast conditions. Li et al. [33] conducted evaluations on sandwich panels featuring foam cores with varying densities when exposed to blasts and fragment impacts. Their findings indicated that panels with a low-density foam positioned at the front exhibited reduced deflection at the back face. Additionally, the variation in core density had a minimal effect on the panels’ capacity to prevent perforation. Xu et al. [34] investigated foam-nickel sandwich structure subjected to near-field blast loading, demonstrating significant deformation and potential as protective structures. Another study by Xu et al. [35] examined foam-aluminum core panels in response to near-field blasts, particularly for tandem-shaped-charge warhead structures, noting that lower density and larger cell diameter increased deformation and affected fuze acceleration. Kazemi et al. [36] simulated cylindrical aluminum foam cores sandwich structures, discovering that laminated foam cores enhanced energy absorption and reduced displacement, especially with decreased core density and increased curvature and face-sheet thickness. Lastly, Zhang et al. [37] evaluated the how kirigami corrugated (KC) panels filled with polyurethane foam mitigates the blast, finding that foam-filled KC panels outperformed aluminum foam panels in energy absorption and blast load mitigation, with higher foam density improving performance. The summarized findings of the studies on foam-filled sandwich panels for blast resistance demonstrate significant advancements in enhancing protective capabilities. Key observations include the importance of front face sheet in energy absorption, effectiveness of low-density foam in reducing deflection, and the impact of core density and cell diameter on deformation under blast loads.

Recent research in blast-resistant sandwich panels extends beyond honeycomb and foam-filled cores, incorporating diverse and innovative approaches. This expansion in the field embraces a wide array of materials and designs, reflecting the evolving needs for enhanced protection in various environments. Rolfe et al. [38] examined a hybrid composite-skinned sandwich panels subjected to an air blast loading, aiming to increase energy absorption by promoting delamination under blast loads. Image correlation using aa high-speed camera and micro-CT scanning, they found that Hybrid-3B skinned panels outperformed glass-fiber reinforced polymer and matched carbon-fiber reinforced polymer panels in damage resistance under single blasts, while Hybrid-4 panels excelled under repeated blasts due to unique damage patterns and stress relief features. Jiang et al. [39] studied the blast response of sandwich panels with graded re-entrant circular auxetic cores for explosion protection in buildings and vehicles. The study considered various geometric and thickness factors, with multi-objective optimizations significantly enhancing panel performance, demonstrating the promise of auxetic cored structures in blast protection applications.

Finally, a recent paper [40] reviewed the impact of various geometrical parameters on the resistance of sandwich panels to blast loads, a crucial aspect in engineering structures, especially in defense applications. The review highlighted the significance of parameters such as material and thickness of the core, front and back plates, core density and grading, types of core and face sheets, core filling and stiffening strategies, panel curvature, explosive charge mass, and standoff distance. This comprehensive analysis aimed to provide insights into the current state of sandwich panel applications in mitigating blast load effects.

The current research represents a significant advancement in the field of blast mitigation, distinguishing itself from existing literature through its innovative approach. While previous studies have independently explored the efficacy of water barriers in large-scale applications and the benefits of structural design alterations, this study uniquely combines these two strategies in the design of sandwich panels. The novel aspect of this research lies in its holistic integration of fluid dynamics and structural engineering principles, thereby improving the blast mitigation capabilities of these panels. Through rigorous numerical investigations, the study thoroughly evaluates the blast mitigation performance of these sandwich panels, marking a substantial contribution to the field of protective structural design. This approach not only broadens the scope of traditional blast mitigation methods but also opens new avenues for the development of more resilient and efficient protective structures.

Following the comprehensive introduction and the in-depth literature review that set the stage for this study, the paper is structured as follows: the methodology section details the numerical modeling and analytical techniques employed, laying a solid foundation for the experimental approach. This is followed by the results and discussion sections, where data obtained from the experiments are meticulously presented and analyzed. These findings are then interpreted, highlighting the novel contributions of the study. The paper ends with the conclusion section, which synthesizes key insights, reflects on the implications of the work, and proposes directions for future research.

2. Methodology

Dharmasena et al. [41] conducted explosive laboratory tests on steel alloy sandwich structure with square honeycomb structural core to examine panel's behavior. In their experimental setup, a cylindrical TNT charge was detonated 100 mm away from the panel's center. The current study employs numerical modeling to simulate Dharmasena et al.'s [41] experiment using a 3 kg TNT charge, but with a different core structure. A tubular core was selected for this research instead of a honeycomb structure, based on Yaqoub et al.'s [32] findings that this core shape exhibits minimal deformation and superior kinetic energy dissipation compared to other examined structural shapes. In addition, this study will explore the impact of water filling within the core structure. The selection of a tubular core is strategic, as it simplifies the process of water filling and ensures effective integration of the fluid into the structure. The Finite Element Analysis (FEA) software, Abaqus/CAE, was utilized to create the numerical models and to obtain responses, which were subsequently analyzed using regression techniques.

Fig. 1a provides a schematic view of the problem setup illustrating the position of the TNT charge at 100 mm from the center of the all-steel sandwich panel. The sandwich panel comprises three layers: a 50-mm-thick tubular core flanked by two 650 × 650-mm faceplates as shown in Fig. 1b. This study's goal is to identify the ideal configuration and fluid quantity needed to improve the panel's resistance to impacts. It examines three key design elements: the thickness of the face plates, the spacing between the core tubes, and the volume fraction of fluid within the tubular core.

Fig. 1.

Numerical Model a) Schematic b) using Abaqus Software.

2.1. Design of experiments (DOE)

Experimental Design approach was employed to create a plan aimed at evaluating the influence of three design variables that affect the panels' ability to mitigate blast effects. A full factorial design was selected, featuring three levels per variable to thoroughly examine non-linear responses. Thicknesses of the panel plates (P) were varied either as 5 or 10 mm, and the core spacing distances (D) were established at 75, 112.5, and 150 mm to study their impact. This setup was intended to establish three distinct spacings within the core structure while ensuring consistent spacing across the panel area. The fluid volume fraction (V) within the core was altered to encompass scenarios of empty, half-filled, and fully filled cores corresponding to a 0, 50 and 100 % volume fraction respectively.

A series of 27 numerical experiments, as delineated in the DOE, are conducted to gather information about the deformation behavior and energy dissipation in each of those cases. Key response metrics measured included the external forces work done; the internal energy including elastic strain energy, energy dissipated by viscoelasticity, inelastic dissipated energy and energy dissipated by damage; in addition to kinetic energy, and the panel's maximum vertical displacement (U3).

The formulas for calculating external work, elastic strain energy, and kinetic energy are detailed in equations (1), (2), (3), respectively [42]. The evaluation of the numerical models will concentrate on periods after the external forces due to work stabilizes and kinetic energy of the system peaks.

$${\dot{E}}_W={\int }_{S}v.t^{l}dS+{\int }_{V}f.vdV$$ (1)

$$E_S={\int }_0^t\left({\int }_V\left(1-d\right){\sigma }^u:{\dot{\epsilon }}^{el}dV\right)d\tau$$ (2)

$$E_K={\int }_v\frac{1}{2}\rho v.vdV$$ (3)

where ${\dot{E}}_W$ represents the external work done rate, $v$ denotes the velocity field vector, $t^l$ signifies the surface distributed load, $f$ represents body force vector, $E_S$ stands for elastic strain energy, $d$ represents the continuum damage parameter, ${\sigma }^u$ denotes undamaged stress, ${\dot{\epsilon }}^{el}$ is the elastic strain rates, $E_K$ represents kinetic energy, and $\rho$ stands for the current mass density

2.2. Numerical analysis

Abaqus/CAE explicit software was utilized to create the numerical model for this study. In an effort to closely replicate the setup described by Dharmasena et al. [41], the model depicted a sandwich panel designed as a 650 × 650 mm square, featuring a core height of 50 mm and face plate with 0.76 mm thickness. The meshed structure is shown in Fig. 2a. The faceplates of the panel were meshed using 21,125C3D8R solid elements as shown in Fig. 2b, while the tubular core shapes were meshed by 19,650–33,360 elements using either S4R quadrilateral or S3 triangular shell elements with a size of 30 elements as given in Fig. 2a. The water in the core was partitioned horizontally and meshed using C3D8R elements with an approximate global size of 0.005 as illustrated in Fig. 2c and d. The mesh elements for the water varied between 35,934 and 11,780, as per the core shapes' spacing distance and the core's fluid volume fraction. A mesh sensitivity study was conducted to guarantee results convergence for the chosen mesh size.

Fig. 2.

(a) Tubular core between face plates (Y-axis half section cut view) mesh (b) face plate mesh (c) water mesh (fully Filled-100 %volume fraction) mesh (d) water (half-filled-50% volume fraction).

The numerical models developed in this study applied AISI 4340, a low alloy steel, for all components of the panel i.e. both the faceplates and the tubular core. The choice of AISI-4340 steel, known for its large tangent modulus, high strength, and elevated rate of strain hardening, makes it particularly suitable for countering blast impacts. AISI 4340 steel properties are presented in Table 1 and were sourced from studies by Guo and Yen [43], and Arriaga and Waisman [44]. To accurately simulate the material's plasticity and the panel's damage progression, the Johnson-Cook model was employed, detailed in equations (4), (5) [45,46].

$$\sigma =\left(A+B{\epsilon }^n\right)\left(1+C\ln {\dot{\epsilon }}^{*}\right)\left(1-T^m\right)$$ (4)

$${\bar{\epsilon }}_D^{pl}=\left[d_1+d_2\mathit{exp}\left({-d}_3\eta \right)\right]\left[1+d_4\mathit{ln}\left(\frac{{\dot{\bar{\epsilon }}}^{pl}}{{\dot{\epsilon }}_0}\right)\right]\left(1+d_5\hat{\theta }\right)$$ (5)

Table 1.

Material properties of AISI-4340 [43,44].

A	792 (MPa)	$d_1$	0.05	$T_{melt}$	1520 (°C)
B	510 (MPa)	$d_2$	3.44	Density	7830 ($kg/m^3$)
C	0.014	$d_3$	2.12	Young's modulus	208 (GPa)
m	1.03	$d_4$	0.002	Poisson ratio	0.3
n	0.26	$d_5$	0.61	Critical fracture energy	12.5 (kJ $/m^2$)
${\dot{\epsilon }}_0$	1 (s−1)

In this formulation, $\sigma$ represents the material's yield stress, $A$ denotes the yield stress under reference conditions. B signifies the constant associated with strain hardening, while C is the coefficient that accounts for strain rate strengthening. The parameter n represents the strain hardening coefficient, and m indicates the coefficient for thermal softening. $\epsilon$ refers to reference strain, ${\dot{\epsilon }}^{*}$ denotes the strain rate, and d₁ to d₅ are dimensionless parameters used to describe failure. The Johnson-Cook model was selected because it accounts for plastic deformation, strain hardening, and damage evolution. The plasticity aspect of the model describes how the material undergoes plastic deformation, while the damage component simulates the initiation and growth or evolution of internal damage. This initiation is defined using the Johnson-Cook failure parameters d1 to d5 and is associated with the material's critical fracture energy.

The water in the simulation was treated as a hydrodynamic material, with its volumetric strength defined by the Mie-Grüneisen state equations, indicating a linear relationship with energy. The constants $c_0$ and s, which outline the linear Hugoniot curve connecting linear shock velocity with particle velocity, are detailed in Table 2 [47,48]. In this formulation, both the Hugoniot pressure and the specific energy (measured per unit of mass) are determined solely by the density. Gravitational effects were assumed to be negligible and were omitted for simplification, which is a reasonable approximation in cases of short blast duration or when dynamic effects are dominant. However, this assumption should be further examined, especially if the blast load induces rapid and intense dynamic forces, resulting in pronounced sloshing effects that could significantly influence the structural response. A frictionless general contact definition was used to enforce contact between the water and the tubular core. The presence of water in the core contributes to hydrodynamic damping, where the movement of the water inside the core absorbs and dissipates some of the energy from the blast-induced vibrations. This damping effect can help reduce the amplitude and duration of the structural vibrations caused by the blast, potentially improving the overall structural response.

Table 2.

Water Properties [47,48].

Parameter	Value
Density (ρ)	1000 $\left(Kg/m^3\right)$
Viscosity (η)	0.001 (N s $/m^2$)
$c_0$	1500 $\left(m/s\right)$
s	0
Grüneisen ratio (${\mathrm{\Gamma }}_0$)	0

An air blast load was used to model the explosion of the TNT charge. According to the modified Friedlander equation (6), the detonation of the TNT charge causes a rapid expansion of the air surrounding the explosive charge, producing a shock wave that moves away with high velocity [41]. This results in a rapid increase in atmospheric pressure (P_atm) to a maximum value (P_max) at the time of the shock wave's arrival, followed by an exponential drop to negative pressure values before returning to P_atm [22,41]. A 3 kg of TNT positioned 100 mm away from the top plate's center was used to simulate the explosive load. The duration of the blast load in the simulation was set at 1.5 ms. The explosive's detonation was simulated using the CONWEP explosive charge model, which includes the Incident Wave Interaction Property, as referenced in the studies [22,41], and [49]. The modeling of the blast load was similar to the pressure loading modeled by Dharmasena et al. [41], as illustrated in Fig. 3.

$$P\left(t\right)=\left(P_{\mathit{max}}-P_{atm}\right)\left[1-\frac{t-t_a}{t_d}\right]e^{\frac{t-t_a}{ɵ}}$$ (6)

where the pressure at any time (t) is given by $P_t$ , $P_{\mathit{max}}$ the maximum pressure, $P_{atm}$ the atmospheric pressure, ɵ the time decay, $t_a$ the duration of the maximum shock wave, and $t_d$ the duration of positive pressure.

Fig. 3.

Air blast pressure-time response.

Moreover, the boundary conditions of the numerical model are set to have the four sides of the front and back plates fixed by setting the displacements and rotations to zero, as shown in Fig. 1b. In addition, the welding between the tubular core and the front and back plates is modeled by setting tie constraints.

3. Results & discussion

3.1. Validation of the numerical model

This study's numerical model was validated through a comparison of its deformation behavior with the experimental findings from Dharmasena et al. [41] and the numerical analysis by Kumar and Patel [22], focusing on a square honeycomb sandwich panel subjected to a 3 kg TNT explosion from 100 mm away. The present model exhibited behaviors consistent with both Kumar and Patel's [22] numerical outcomes and Dharmasena et al.'s [41] experimental observations, as depicted in Fig. 4, Fig. 5.

Fig. 4.

Comparison of top plate vertical displacement results.

Fig. 5.

Comparison of bottom plate vertical displacement results.

Fig. 6a and b also illustrate the deformation shape of the numerical model full model and a sliced cut respectively, which resembles the deformation obtained by Kumar and Patel [22]. However, their model only represented one quarter of the sandwich panel using symmetry boundary conditions, whereas the model developed in this research modeled the complete panel. After validating the numerical model, the core shape of the sandwich panel was changed to a tubular shape, and dimensions were varied according to the planned DOE.

Fig. 6.

Square honeycomb Panel's vertical displacement at the end of the simulation (step time = 1.5E-03 ms) (a) full model view (b) slice cut view.

3.2. Numerical experiments results

The study's experimental design was strategically developed to assess the impact of three key variables on the panels' ability to withstand blasts, as detailed in section 2.1. These 27 numerical experiments were conducted as per the DOE plan, as illustrated in Table 3, to gather essential data for comparing different panel designs. Key response parameters measured included the peak displacement of the panel in the vertical direction (U3), the kinetic energy, the elastic strain energy, the plastic dissipated energy, the energy dissipated by damage and the external work.

Table 3.

Experimental design and numerical results.

Run No.	Plate Thickness (mm)	Core-Core Distance (mm)	Volume Fraction of Fluid (%)	U3 Dis-placement (mm)	Kinetic Energy (J)	Elastic Strain Energy (J)	Plastic Dissipated Energy (J)	Energy Dissipated by Damage (J)	External Work (J)
1	5	75	0	0.1593	3.71E+05	1.54E+04	4.37E+05	3.72E-01	9.98E+05
2	5	75	50	0.1497	3.56E+05	5.05E+04	3.33E+05	6.80E+00	9.21E+05
3	5	75	100	0.1335	3.31E+05	3.86E+04	2.77E+05	3.89E+01	7.52E+05
4	5	112.5	0	0.1637	3.82E+05	1.61E+04	4.44E+05	3.90E+01	1.03E+06
5	5	112.5	50	0.1482	3.73E+05	4.60E+04	3.62E+05	8.63E+01	9.72E+05
6	5	112.5	100	0.1419	3.71E+05	3.93E+04	3.17E+05	8.78E+01	8.58E+05
7	5	150	0	0.1723	3.89E+05	1.53E+04	4.48E+05	2.92E+01	1.03E+06
8	5	150	50	0.1597	3.82E+05	4.00E+04	3.79E+05	2.38E+01	1.00E+06
9	5	150	100	0.1503	3.88E+05	3.76E+04	3.43E+05	8.11E+01	9.15E+05
10	7.5	75	0	0.1057	2.98E+05	1.76E+04	3.52E+05	3.15E-01	7.60E+05
11	7.5	75	50	0.1106	2.73E+05	4.71E+04	2.69E+05	8.13E+00	7.10E+05
12	7.5	75	100	0.1012	2.48E+05	3.90E+04	2.28E+05	3.79E+01	5.86E+05
13	7.5	112.5	0	0.1039	3.11E+05	1.75E+04	3.59E+05	1.02E+00	7.85E+05
14	7.5	112.5	50	0.1066	2.98E+05	4.04E+04	2.95E+05	4.87E+01	7.50E+05
15	7.5	112.5	100	0.1041	2.87E+05	3.74E+04	2.62E+05	8.54E+01	6.70E+05
16	7.5	150	0	0.099	3.16E+05	1.82E+04	3.63E+05	3.54E-02	7.89E+05
17	7.5	150	50	0.1081	3.04E+05	3.79E+04	3.15E+05	2.03E+01	7.73E+05
18	7.5	150	100	0.1144	3.06E+05	3.79E+04	2.77E+05	9.41E+01	7.09E+05
19	10	75	0	0.08922	2.47E+05	1.87E+04	2.90E+05	1.92E-01	6.09E+05
20	10	75	50	0.09023	2.25E+05	4.31E+04	2.22E+05	5.43E+00	5.73E+05
21	10	75	100	0.0826	2.01E+05	3.89E+04	1.89E+05	3.42E+01	4.81E+05
22	10	112.5	0	0.08919	2.58E+05	1.91E+04	2.94E+05	4.86E-02	6.25E+05
23	10	112.5	50	0.09403	2.46E+05	3.54E+04	2.42E+05	4.42E+01	6.01E+05
24	10	112.5	100	0.08279	2.33E+05	3.32E+04	2.18E+05	8.98E+01	5.42E+05
25	10	150	0	0.0885	2.64E+05	1.93E+04	2.99E+05	0.00E+00	6.30E+05
26	10	150	50	0.0933	2.52E+05	3.31E+04	2.60E+05	2.18E+01	6.17E+05
27	10	150	100	0.09949	2.50E+05	3.11E+04	2.31E+05	88.7801	5.70E+05

The energy absorbed through plastic deformation, which includes both rate-independent and rate-dependent types, is referred to as plastic dissipated energy. Meanwhile, the energy absorbed due to material damage pertains to the initiation and progression of damage within the material. The energy dissipated in damage, as indicated in Tables 3 and is negligible compared to the energy dissipated in plastic deformation, and therefore it has been neglected in further analysis. The data from the numerical model was captured at the moment when the external work stabilized, and the kinetic energy reached its highest point. The greatest upward movement of the panel (termed U3 Displacement) was observed at the midpoint of the uppermost layer of the sandwich panel.

3.3. Influence of design variables

3.3.1. Plate thickness

The numerical findings showed that the smallest peak vertical displacement in the sandwich panel, recorded at 82.6 mm, was achieved using a configuration with a faceplate thickness (P) of 10 mm, a spacing distance (D) of 75 mm between the centers of the core shapes, and a core fluid volume fraction (V) of 100%. A comparison of sandwich panels with plate thicknesses of 10 mm, 7.5 and 5 mm, given by Fig. 7a, b, and 7c respectively, revealed that the panel with a thickness of 5 mm had a displacement value of 133.5 mm, an approximate increase of 62%. Similarly, a panel with thickness (P) 5 mm, spacing (D) 150 mm, and volume fraction (V) 0% was compared to a panel with the same characteristics but a thickness (P) of 10 mm. The panel with a thickness of 5 mm had the highest displacement value of 172.5 mm, while the value decreased to 88.5 mm when the thickness was changed to 10 mm. Statistical analysis, as depicted in Fig. 8, demonstrates a significantly strong negative correlation between the panel's displacement and its thickness (P), with a Pearson correlation coefficient of −0.926. Furthermore, Fig. 9 illustrates that as the thickness of the panel's plate increases, its displacement decreases. This phenomenon is attributed to the fact that a thicker plate enhances the panel's overall stiffness, thereby augmenting its rigidity and its ability to withstand deformation from blast impacts. Fig. 9 also shows that the empty panel outperforms the half-full and full panels in terms of displacement, particularly as the thickness of the plate increases. This can be attributed to the same reasoning. Sandwich panels with thinner plates have lower stiffness, natural frequencies, and damping, which results in larger deformation. In the absence of water, the structure might not possess sufficient stiffness to resist the applied load, whereas filling it with water provides additional support, thereby reducing deformation. The addition of water may also alter the natural frequency, leading to reduced deformation. Therefore, the effects of adding water to the core are more pronounced in structures with thinner plates than in those with thicker ones, resulting in this observed trend.

Fig. 7.

Sandwich Panel Displacement at the End of Simulation Time Step = 1.50E-03 ms for sandwich panel with D = 75 mm, V = 100 % (a) P = 10 mm (b) P = 7.5 mm (c) P = 5 mm.

Fig. 8.

Plate thickness and maximum vertical displacement correlation matrix plot.

Fig. 9.

Maximum vertical displacement (U3) categorized by plate thickness (P).

Additionally, the statistical analysis indicated a minimal correlation between the thickness of the plate and the elastic strain energy, as evidenced by a Pearson correlation coefficient of −0.110. On the other hand, a significant inverse correlation was observed between the plate thickness and the work done by external forces, marked by a coefficient of −0.905. The minimal energy absorption by external forces, amounting to 481,266 J, was noted in a panel configuration with a 10 mm thickness, a 75 mm core-to-core spacing, and a core entirely filled with water. Conversely, a panel of the same specifications but with a 5 mm thickness showed a higher absorption value of 752,446 J, marking an approximate 56% increase. The highest value for the work of external forces saw a notable decrease from 1,030,880 J to 630,336 J, a reduction of approximately 39%, when the panel's thickness was increased from 5 mm to 10 mm. This panel had a core-to-core spacing of 150 mm and lacked any water in its core. The observed reduction can likely be attributed to the increased thickness of the plate, which enhances the panel's stiffness and its capacity to resist external forces.

3.3.2. Spacing between core

The findings indicated that the space between the core structures only marginally impacted the tubular sandwich panel's ability to mitigate blasts. Fig. 10 illustrates a modest rise in the peak vertical shift of the sandwich panel corresponding to an increase of the spacing distance. Similarly, Fig. 11 shows a slight escalation in amplitude of the work done by external forces as the distance between the core increases. This may be caused by the fact that as the spacing distance increases, the core's support for the faceplates decreases. Moreover, the analysis of correlations revealed that the spacing between core structures is only slightly linked to the maximal vertical movement of the sandwich panel, evidenced by a Pearson correlation coefficient of −0.103. This spacing also showed minimal correlation with both the elastic strain energy and the work exerted by external forces, having correlation coefficients of −0.159 and −0.181, respectively.

Fig. 10.

Maximum vertical displacement categorized by core-to-core distances (D).

Fig. 11.

Work of external forces categorized by core-to-core distances (D).

3.3.3. Volume fraction of fluid in the core

The analysis of the effect of adding fluid to the core structure of the tubular sandwich panel showed that it improved the panel's blast mitigation performance. The results indicated that adding water to the core increased the elastic strain energy. For instance, the highest value of 50470.8 J was recorded for a panel with a plate thickness (P) of 5 mm, a spacing distance (D) of 75 mm, and a 50% volume fraction of fluid in the core (V). In comparison, a similar panel without water in the core had an elastic strain energy that was reduced by about 69%–15433.1 J, while the value was reduced by about 24% with a volume fraction of fluid (V) at 100%. The lowest elastic strain energy values were recorded for panels without water in the core, while the highest values were recorded for panels with a volume fraction of fluid at 50%. This may be attributed to the fact that the partially water-filled tube core creates greater stiffness and damping than fully filled or empty core structures. The combination of air and water as mediums also causes the shock wave energy to be stored and redistributed differently between the two mediums [18]. Furthermore, the analysis presented in Fig. 12 demonstrated a substantial positive relationship, indicated by a Pearson correlation coefficient of 0.722, between the core's fluid volume fraction and the elastic strain energy.

Fig. 12.

Volume fraction and elastic strain energy correlation matrix plot.

As depicted in Fig. 13, the removal of fluid from the core negatively impacted the elastic strain energy. A partially filled tube exhibited higher elastic strain energy, benefiting from increased stiffness and damping effect, compared to a tube that is either empty or fully filled. The total energy from the shock wave was stored and redistributed differently between the air and water, as referenced in Ref. [30]. Water, being incompressible and constrained in a closed pipe, resists applied pressure and reduces panel deformation. In contrast, air compresses under load, storing the energy in a recoverable form.

Fig. 13.

Elastic Strain Energy Responses for Sandwich Panel with P = 5 mm, D = 75 mm and varying V (%).

Fig. 14 shows the elastic strain energy responses for similar sandwich panels but with different volume fraction of fluid and a larger core to core spacing. The sandwich panel with a 50% volume fraction of fluid in the core recorded an approximate increase of 160% to be 39965.9 J compared to the sandwich panel with no fluid in the core. While a similar structure but fully filled with water, recorded an increase in the strain energy around 145% to be 37586.9 J. This reflects the effect that adding water has on elastic strain energy.

Fig. 14.

Elastic Strain Energy Responses for Sandwich Panel with P = 5 mm, D = 150 mm and varying V (%).

With respect to panel displacement, as illustrated in Fig. 15, the correlation test revealed no correlation between the maximum vertical displacement in the sandwich panel and the volume fraction of fluid in the core. Nonetheless, Fig. 9 suggests that, in many instances, the panel's displacement tended to decrease as the fluid volume fraction within the core structure increased, particularly in panels with a 5 mm plate thickness.

Fig. 15.

Volume fraction of fluid and maximum vertical displacement correlation matrix plot.

Fig. 16 also compares the effect of filling the tubular core with water on the displacement of the sandwich panel. The panels have a plate thickness (P) of 5 mm and a core spacing (D) of 75 mm at different time steps. The panel with a volume fraction of fluid (V) of 0% had a displacement of 159.3 mm, while the panel with a volume fraction of fluid (V) of 100% had a displacement value of 136.5 mm, a reduction of about 14%. This decrease in displacement might well be attributable to the stiffening of the panel caused by the addition of fluid to its core. As seen in Fig. 16a, in the case of no fluid the top plate will keep moving downwards compressing the tubular core and closing it then pushing the bottom plate further down. On the other hand, in the case of partially filled tube illustrated in Fig. 16b, the downward displacement of the top plate deforms the pipe causing enough pressure to move the water in other sections of the pipe that were not deformed then resisting further deformation. In case of a fully filled pipe, as illustrated in Fig. 16c, the fluid resists the movement of the top plate recovering part of the deformation.

Fig. 16.

Maximum Vertical Displacement Development with time for a) 0 %, b) 50 %, c) 100 % Fluid Volume Fraction.

Moreover, the analysis assessing the relationship between the core's fluid volume fraction and the energy absorbed by external forces revealed a slight correlation, indicated by a Pearson correlation coefficient of −0.328. According to the findings depicted in Fig. 17, there was a noticeable increase in the energy absorbed by external forces as the fluid volume fraction within the core increased, likely due to the enhanced stiffness of the panel resulting from the addition of water to the tubular core.

Fig. 17.

Work of External Forces categorized by Volume Fraction of Fluid.

3.4. Regression analysis

Regression analysis was performed using Minitab® 20.2 software. Regression analyses were conducted for three different outcomes: the peak displacement of the panel in the vertical direction, the amount of elastic strain energy, and the work done by external forces, as detailed in equations (7), (8), (9). The regression analysis for the peak vertical movement demonstrated a high level of predictive accuracy, with an R-Squared value of 97.71% and an adjusted R-Squared of 96.49%, showcasing the regression model's strength. In a similar vein, the regression analysis focusing on the work done by external forces proved to be highly reliable, with R-Squared and adjusted R-Squared values of 99.83% and 99.73%, respectively. For the model evaluating elastic strain energy, the R-Squared and adjusted R-Squared were 95.13% and 92.54%, indicating substantial predictive capability. These regression models were used to create main effects plots for the three numerical responses under study.

$$U_3\text{Displacement}=0.3629-0.05028\mathrm{P}-0.000202\mathrm{D}-0.000523\mathrm{V}+0.002496P^2+0.000002D^2-0.000001V^2-0.000018\mathrm{P}*\mathrm{D}+0.000045\mathrm{P}*\mathrm{V}+0.000002\mathrm{D}*\mathrm{V}$$ (7)

$$\text{ALLSE}=13747+2720\mathrm{P}-90\mathrm{D}+934.5\mathrm{V}-133P^2+0.422D^2-5.707V^2-4.99\mathrm{P}*\mathrm{D}-15.13\mathrm{P}*\mathrm{V}-0.493\mathrm{D}*\mathrm{V}$$ (8)

$$ALLWK=1478332-156376\mathrm{P}+3252\mathrm{D}-2950\mathrm{V}+5885P^2-9.40D^2-11.10V^2-110.1\mathrm{P}*\mathrm{D}+173.2\mathrm{P}*\mathrm{V}+12.96\mathrm{D}*\mathrm{V}$$ (9)

The impact of fluid volume fraction on elastic strain energy is most significant, as illustrated in Fig. 18. There is a noticeable increase in elastic strain energy with a rise in the fluid volume fraction within the core. In comparison, the thickness of the plate and the spacing between core structures exert a lesser influence on elastic strain energy. Specifically, elastic strain energy shows a marginal decrease as either the plate thickness or the spacing between core shapes is enlarged.

Fig. 18.

Effect of design variables on the elastic strain energy.

The main effects plot in Fig. 19 indicates that plate thickness significantly influences the work done by external forces, more so than the fluid volume fraction or the spacing between core shapes. A notable reduction in the work done by external forces is observed with an increase in plate thickness, and a minor decrease occurs as the fluid volume fraction within the core rises. Conversely, the external work done slightly grows with a broader spacing distance between core structures. Similarly, plate thickness stands out as the dominant factor affecting the peak vertical displacement of the sandwich panel, whereas the impact of the core spacing and fluid volume fraction on displacement is less pronounced. Enhancing plate thickness markedly diminishes the panel's maximum vertical displacement, attributing to increased stiffness of the sandwich panel, as detailed in Fig. 20.

Fig. 19.

Effect of design variables on the elastic strain energy.

Fig. 20.

Effect of design variables on maximum vertical displacement of sandwich panel.

4. Conclusion

Industries increasingly require materials that are not only reliable but also possess specific desirable properties. In this context, sandwich panels are emerging as a dominant alternative to traditional metals, primarily due to their advantageous characteristics such as being lightweight, and cost-effective. Despite these benefits, the inherent heterogeneity of the structure leads to complex stress and strain patterns under impact loads. Consequently, a significant body of research has focused on enhancing blast mitigation techniques. This includes detailed analyses of core designs in sandwich panel structures and investigations into the energy response and absorption capabilities. Particularly noteworthy is the use of fluid-filled containers, which have been studied for their potential to improve blast mitigation efficiency.

This research marks a notable advancement in blast mitigation, standing out with its innovative approach that combines the use of water barriers and structural design alterations in the development of an all-steel sandwich panel.

This study details a numerical analysis aimed at evaluating the effectiveness of tubular sandwich panels in blast protection, with a focus on various design parameters. The research explored three primary design variables: the thickness of the panels, the separation between core structures, and the volume fraction of fluid within the core. The analysis was based on a specific blast scenario involving a 3 kg TNT explosive positioned 100 mm away from the panel, drawing on field experiments by Dharmasena et al. [41] to establish a realistic context. Utilizing Minitab® software, a full factorial design comprising 27 experiments was executed. The findings for that specific loading scenario indicated that panels with a 10 mm plate thickness, 75 mm spacing distance, and 100% fluid volume fraction in the core achieved the lowest values in terms of panel displacement and external work. This can be attributed to the increased stiffness from the thicker plate and the combined support provided by the tubular core and the water within it. It was observed that water within the core helped reduce plate fractures by absorbing kinetic energy, thereby limiting deformation and damage. The thickness of the panel played a significant role in the structural plastic deformation, with thinner plates leading to reduced stiffness. The simulation revealed that material damage initiated with the deformation of the plate, followed by thinning, initial fracture, and ultimately tearing. Additionally, the structure's deformation was significantly lessened when the center of the plate was supported by the core structure, even in cases of large core-to-core spacing, due to the enhanced stiffness at the center where the load application was maximal. The research identified that enhancing the rigidity of the tubular sandwich panel led to a decrease in its maximum vertical displacement. Additionally, the work done by external forces was found to diminish as the panel's rigidity increased. Enhancements to the panel's stiffness could be achieved through narrowing the distance between core elements, thickening the panel's plates, or adding water to the core structure. The highest values of elastic strain energy were recorded for panels with partially water-filled tubular cores, as the shock energy is absorbed and stored differently in the presence of both air and water. The space between the core structures had a relatively small impact on the panel's displacement, the amount of elastic strain energy, and the work done by external forces, especially when compared to the influence of other design elements.

Building upon the conclusions of this study, future research could focus on several key areas to enhance the understanding and effectiveness of blast mitigation in sandwich panel designs. Exploring various blast load intensity and duration, material variations and hybrid combinations for the core and faceplates, could provide valuable insights into how material properties impact blast resistance. Additionally, optimizing core geometry through varied shapes, sizes, panel inclination and design configurations may reveal crucial information about stiffness and blast mitigation. Applying these findings in real-world scenarios, with varying blast intensities, would also be beneficial to assess practical applications. Further investigation into the fluid dynamics within the core, accounting for the gravitational effects of the fluid medium and examining the impact of fluid properties, as well as the use of different fluids or combinations, would deepen our understanding of fluid-structure interactions under blast loads. A thorough cost-benefit analysis, considering the economic viability, and an environmental impact assessment, examining the full lifecycle from production to disposal, are crucial to ensure that these blast mitigation solutions are not only effective but also economically and environmentally sustainable.

Data availability statement

All data utilized in this research is included in the paper.

CRediT authorship contribution statement

Yaqoub S. AlAhmed: Writing – original draft, Methodology, Investigation, Data curation. Zied Bahroun: Writing – review & editing, Supervision, Methodology, Investigation, Conceptualization. Noha M. Hassan: Writing – review & editing, Supervision, Methodology, Formal analysis, Conceptualization.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.