Optimizing energy absorption and peak force in metal/glass fiber sandwich panels with trapezoidal cores | Scientific Reports

Scientific Reports volume 14, Article number: 25371 (2024) Cite this article

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Sandwich panels with trapezoidal metal/glass fiber cores are increasingly popular due to their lightweight and energy-absorption properties. This study employs response surface methodology (RSM) and Box-Behnken design to investigate the effects of core angle, fiber orientation, and MCM-48 nanoparticles on the panels’ energy absorption and peak force, developing regression models with high R2 values of 0.9027 and 0.9228, respectively. Experimental tests were conducted to validate these models, showing minimal deviation from predicted values. Results indicate that increasing the fiber orientation angle from 30° to 90° enhances energy absorption and peak force by 72.18 and 46.9%, respectively, and adding MCM-48 nanoparticles up to 0.25% weight improves energy absorption by 60.8%. A core angle of 52° balances energy absorption and peak force, while integrating a metal wire mesh within the panels significantly enhances energy absorption and reduces core brittleness. The optimal parameters for maximum energy absorption and minimum peak force include a core angle of 58°, fiber orientation of 73.5°, and no nanoparticles. These findings provide valuable insights into the design and optimization of sandwich panels for various applications.

Sandwich panels have gained popularity in recent years due to their lightweight and energy-absorption properties, making them a popular choice in various industries1,2. These panels consist of two outer layers and a core material sandwiched in between, with metal and glass fiber trapezoidal cores being an ideal choice. Understanding the behavior of these sandwich panels under axial loading is crucial for their successful application3. Sandwich panels have become increasingly popular in various industries due to their lightweight and high-strength properties. These panels consist of two outer layers and a core material sandwiched in between, with metal and glass fiber trapezoidal cores being a common choice4,5.

Awd Allah et al.6, examined the effect of adding montmorillonite clay (MC) on the energy absorption of glass fiber reinforced polymer (GFRP) tubes under lateral loading. Tubes with 0–4 wt% MC were fabricated using hand lay-up techniques and tested for crushing load and energy absorption. Regression models predicted energy absorption indicators, and COPRAS identified 4 wt% MC as optimal for superior energy absorption capabilities. Abd El-baky et al.7, explored the crashworthiness of metal-composite hybrid cylinders for automotive applications. The study focused on jute/glass fiber reinforced epoxy composites overwrapped on aluminum cylinders under quasi-static axial loading. Key performance metrics, including peak crushing load, specific energy absorption, and crush force efficiency, were assessed. Results showed that Al-3G-2J-3G cylinders had the highest energy absorption and crush force efficiency, highlighting their potential as effective energy-absorbing structures in automotive applications. Awd Allah et al.8, studied the energy absorption and collapse behavior of 3D-printed PLA tubes with different infill patterns under axial compression. The square infill pattern showed superior performance in peak force, mean crush force, total absorbed energy, and specific absorbed energy, making it the most effective energy-absorbing structure as determined by the COPRAS method. Abd El-baky et al.9, studied the crashworthiness of jute/glass fiber reinforced epoxy overwrapped aluminum pipes under axial compression. The Al/2J/4G/2J configuration showed the highest specific energy absorption and crush force efficiency, indicating its potential for automotive energy absorption applications. Hegazy et al.10, studied the crashworthiness of glass fiber reinforced epoxy (GFRE) tubes with nano-alumina (Al2O3) under lateral compression. The optimal 3 wt% nano-Al2O3 significantly improved energy absorption. Using the COPRAS method, the study highlighted the potential of these tubes for energy absorption applications. Awd Allah et al.11, optimized the crashworthiness of glass-reinforced epoxy composites over PVC tubes using the Taguchi method. They found that hole number and diameter significantly affect specific energy absorption (SEA) and crush force efficiency (CFE), with the optimized configuration improving SEA by 74.72% and CFE by 48% compared to intact PVC tubes.

The behavior of sandwich panels under axial loading is crucial for their successful application, and understanding their mechanical properties is essential for the design and optimization of these panels for different applications12. Several studies have investigated the mechanical behavior of sandwich panels under axial loading, with varying results depending on the type of core material and loading conditions13. Hou et al.14 investigated a commercial corrugated sandwich panel’s mechanical behavior under combined compressive loading. They identified stress-displacement variations with loading angle and categorized three deformation patterns. Their findings included a positive loading rate effect in initial collapse and a negative effect post-collapse, attributed to material strain softening. Zhang et al.15 investigated the out-of-plane compression behavior and energy absorption capabilities of modified sinusoidal corrugated (MSC) sandwich panels with gradient designs, fabricated using additive manufacturing. Their results showed that the gradient design enhances energy absorption and reduces the undulation of load-carrying capacity, with the analytical model accurately predicting compressive modulus and strength with a maximum deviation of less than 25%.

Several studies conducted by Awd Allah and colleagues have investigated the crashworthiness of composite and hybrid structures under various loading conditions. In one study, the performance of glass/nano-silica/epoxy composite cylinders under lateral loading was examined, revealing that the inclusion of SiO2 significantly reduced the absorbed energy (AE) and specific absorbed energy (SEA). Another study tested hybrid metal/composite structures under axial compression loads, showing that Al6063/4G/4C tubes exhibited the highest AE and SEA values. Additionally, research on the effect of adding nanocarbon powder to composite tubes demonstrated that 0.5 wt% nanocarbon significantly improved SEA, but higher concentrations led to a decline in performance. Finally, a study on the lateral crashing response of nanocarbon-filled composite tubes confirmed similar findings, with 0.5 wt% nanocarbon offering the best performance16,17,18,19.

Awd Allah et al.20 investigated the crashworthiness of glass-reinforced epoxy composites (GFRE) over wrapped PVC circular tubes with cutouts. Another study focused on the crashworthiness of 3D-printed gyroid structure tubes with cutouts, finding that holes significantly influence performance21. Research on jute fiber-reinforced epoxy/aluminum hybrid pipes under axial compression highlighted the impact of design parameters like hole diameter and number of J-plies on crash indicators22. Lastly, an analysis of hybrid glass/nano-silica/epoxy composite cylinders under lateral loading showed that SiO2 inclusion reduced energy absorption19. Hatami et al.23 investigated the impact behavior of self-compacting cementitious composites reinforced with steel fibers and expanded steel sheets. Their study demonstrated improved energy absorption and reduced deformation in composite panels under dynamic loading. The materials also exhibited enhanced tensile, compressive, and flexural strengths, making them suitable for high-energy applications. Hatami and Hosseini24, investigated the interaction between bending moment and axial force (M-P) in mild steel beams using elastic–plastic idealizations. Their study derived kinematic admissible interaction relations that can predict strains, surpassing rigid perfectly plastic models. By examining a commercial rolled steel T-section, they identified key cases for neutral axis positioning, essential for establishing accurate M-P interaction relations. Hatami et al.25 analyzed the perforation behavior of thin aluminum targets under hypervelocity impact from spherical aluminum projectiles. Their study utilized extensive data from MSFC and SDIF to investigate the effects of projectile diameter, plate thickness, and velocity on hole formation. The results show that hole diameter generally exceeds projectile size, and the angle of impact has minimal influence. They developed a nondimensional model that accurately predicts hole diameter across a wide velocity range, addressing gaps and inconsistencies in previous empirical models.

Integrating metal wire mesh and glass-fiber reinforced epoxy laminates markedly improves composite sandwich panels’ compressive strength and energy absorption properties. Metal wire mesh, known for its strong mechanical attributes, provides extra reinforcement and support, thereby boosting the compressive strength of these panels. Meanwhile, with their excellent strength-to-weight ratio and durability, metal wire mesh and glass-fiber epoxy laminates enhance the structural integrity and energy absorption capacity of the panels upon impact. Many studies have been conducted on metal meshes under impact loading19,23,24. This blend of materials creates a synergistic effect, enhancing both the mechanical performance and energy absorption capabilities of composite sandwich panels. Wan et al.29, investigated the low-velocity impact behavior of glass fabric reinforced epoxy panels with embedded wire nets (WN-GF/epoxy). They found that embedding wire nets significantly improved tensile strength, impact resistance, and energy absorption, with perforation threshold velocity increasing bi-linearly. Scanning electron microscopy revealed increased delamination as a key factor in energy absorption. Finite element models validated these findings, highlighting fiber and wire breaking and delamination during impacts. Cengiz et al.30 developed stainless-steel wire mesh/carbon-fiber reinforced epoxy laminates, enhancing their flexural and low-velocity impact behavior. The study found that steel wire mesh significantly improved impact resistance by dissipating energy and reducing damage like fragmentation and delamination. Micro-CT and SEM analyses confirmed a strong reinforcement-epoxy matrix interface. However, the steel mesh had minimal effect on flexural strength.

The incorporation of nanoparticles into epoxy resins has been shown to improve their mechanical properties, such as strength and toughness. Among the various types of nanoparticles, MCM-48 nanoparticles have attracted attention due to their unique mesoporous structure and high surface area31. Several studies have investigated the effects of MCM-48 nanoparticles on the mechanical properties of epoxy resins. For instance, Li synthesized MCM-48 nanoparticles and incorporated them into an epoxy resin system. They found that the addition of MCM-48 nanoparticles improved the tensile strength and modulus of the epoxy resin, as well as its fracture toughness. The comprehensive properties of the composites with 2% MCM-48 were the best, with a flexural strength of 82.15 MPa, a flexural elastic modulus of 2.45 GPa, and an impact strength of 21.75 kJ/m231. In addition to improving mechanical properties, MCM-48 nanoparticles have also been shown to enhance other properties of epoxy resins, such as thermal stability and flame retardancy32. Overall, the incorporation of MCM-48 nanoparticles into epoxy resins has shown promise for improving their mechanical properties and other important characteristics. Further research is needed to optimize the nanoparticle loading and processing conditions for different applications.

The crashworthiness behavior of sandwich panels with metal/glass fiber trapezoidal cores under axial loading are influenced by various factors such as the thickness and height of the core material, the angle of the cells, and the loading conditions. Understanding these factors is essential for the design and optimization of sandwich panels for different applications, contributing to the development of lightweight and high-strength materials for various industries. Integrating metal wire mesh and glass-fiber reinforced epoxy laminates markedly improves the compressive strength and energy absorption properties of composite sandwich panels. Meanwhile, glass-fiber reinforced epoxy laminates, with their excellent strength-to-weight ratio and durability, enhance the structural integrity and energy absorption capacity of the panels upon impact. This technique effectively solves issues related to structural failure under compressive loads, inadequate energy dissipation during impacts, and the need for lightweight yet robust materials. As a result, these improved panels are particularly suitable for high-strength, impact-resistant applications in the aerospace, automotive, and marine industries. This work introduces a novel approach to enhancing the mechanical performance of sandwich panels with trapezoidal metal/glass fiber cores by systematically optimizing core angle, fiber orientation, and the incorporation of MCM-48 nanoparticles. The innovation lies in the use of response surface methodology (RSM) and Box-Behnken design to develop precise regression models for predicting and optimizing energy absorption and peak force, validated through experimental tests. The study’s findings highlight the significant impact of fiber orientation and nanoparticle content on the panels’ performance, and demonstrate the efficacy of integrating a metal wire mesh to further enhance energy absorption and reduce brittleness.

In the construction of sandwich panels with trapezoidal cores, glass fibers and metal reinforced with epoxy resin and nanoparticles were used. The resin used, marketed under the name "Epoxy Resin 209" by Iran Composite Kavian Company, and the hardener with a resin-to-hardener ratio of 100 to 55 by weight were selected. The gel time of this resin is about 120 min, and the final curing time is 24 h at ambient temperature. Unidirectional glass fibers, 350 g per square meter, of class E with two types of weaves, Plain and Twill, made by AMP China, were used to produce the composite sandwich samples. For the top and bottom face sheet of the composite sandwich structures, four layers of glass fibers with fixed angles were used. For the trapezoidal core, a combination of glass fibers and metal mesh was used. AISI 304 metal mesh with a mesh density of 160 (i.e., mesh spacing of 0.094 mm) and a wire thickness of 0.065 mm was used to reinforce the composite. To enhance the properties of the resin, porous silica nanoparticles MCM-48 with pore sizes of 5 nm, synthesized by the hydrothermal method, were used. The selection of materials for this study was driven by their unique properties and potential to enhance the performance of sandwich panels. Glass fibers were chosen due to their high tensile strength, lightweight nature, and cost-effectiveness, making them an ideal reinforcement material for improving the structural integrity of the panels. The inclusion of MCM-48 nanoparticles was based on their ability to enhance the mechanical properties and energy absorption capacity of the composite materials, even at low concentrations. Metal components were incorporated to leverage their high strength and stiffness, which, when combined with glass fibers, create a synergistic effect that enhances the overall performance of the sandwich panels. The combination of these materials aims to create a composite with optimized energy absorption and peak force characteristics, suitable for applications requiring high strength-to-weight ratios and improved impact resistance.

The hand lay-up method was specifically chosen for fabricating the sandwich panels due to its simplicity, cost-effectiveness, and ability to control the layer configuration and fiber orientation with precision. In the first stage, based on the experimental design and specifying the core angle parameter at three levels (46, 52, and 58°) six Teflon molds were made using a CNC machine, with three molds for the upper jaw and three for the lower jaw. For the synthesis of MCM-48 nanoparticles, following the method outlined in Shao’s article33, first, 10 ml of tetraethyl orthosilicate are mixed with 50 ml of deionized distilled water. This solution is vigorously stirred for one hour at 40 °C using a magnetic stirrer. Next, 0.9 g of sodium hydroxide and 0.19 g of potassium bromide (KBr) are added to the mixture. The solution is stirred again for another hour. Afterward, 10.61 g of cetyltrimethylammonium bromide surfactant is added, and stirring continues for an additional hour. Finally, the resulting mixture is placed in an autoclave at 120 °C for 24 h. During this stage, it is crucial to ensure that the sample container is not shaken. The final product is first filtered and washed with distilled water five times, then dried at 100 °C. The surfactant is removed by heating to 550 °C in air at a rate of 1 °C per minute for 4 h. The synthesized nanoparticles have a high surface area, providing a large surface for the resin to interact and bond strongly with the fibers in fiber-reinforced composites. Subsequently, the resin and hardener were mixed at a weight ratio of 100 to 55. For the samples containing MCM-48 silica nanoparticles, a specified weight ratio of the nanoparticles was first added to the resin. To ensure complete mixing and uniform distribution of the nanoparticles in the resin, the mixture was placed in an ultrasonic probe at 400 rpm for 15 min. Then, the hardener was added to the resulting mixture and stirred again for 10 min using the ultrasonic device. As shown in Fig. 1, after cutting the glass fabric and wire meshes to the desired dimensions and angles, the mold surfaces were prepared by coating them with release wax. Next, the layers were placed in the following order: one layer of Dacron for surface uniformity, one layer of glass fiber, two layers of wire mesh, another layer of glass fiber, and finally a layer of Dacron on the mold, with each layer being fully impregnated with the resin and hardener mixture. In the next step, after layering, the mold cover was placed on the layers and positioned under two 2-ton hydraulic jacks. At this stage, the molds were subjected to this press for 24 h to achieve complete resin curing. After this period, the mold was opened, and the core was separated. The facing sheets were similarly produced, but for attachment to the core, the final resin-impregnated glass fiber layer was placed on the core prepared in the previous step using a mold to ensure complete bonding between the core and the facing. The assembly was then subjected to a 40-kg weight for 24 h, ensuring that the load was concentrated only on the grooves. Finally, the opposite facing was similarly placed on the core.

Schematic illustration of the steps for constructing panels with hybrid glass/metal sheets.

In this study, quasi-static compression tests were performed on the sandwich panel samples using a 40-ton capacity STM-400 compression testing machine manufactured by Santam34. In this machine, the lower jaw is fixed, and the upper jaw applies a distributed load on the surface of the sandwich panels at a displacement rate of 0.5 mm per minute. A slower speed minimizes the effects of inertia and dynamic forces, allowing us to closely examine the material’s true energy absorption and mechanical response under axial loading. Additionally, this speed aligns with established standards in material testing, ensuring consistency and comparability with previous studies in the field. By using 0.5 mm/min, we were able to obtain reliable data on the deformation behavior of the sandwich panels, contributing to a more precise understanding of their crashworthiness. The testing machine and the loading jaws are shown in Fig. 2.

Quasi-static compression testing machine by Santam.

In sandwich panels, due to significant deformation and panel destruction, the load and energy applied to the structure are absorbed. This amount of energy is equal to the area under the force–displacement curve. Additionally, the initial peak force is a critical characteristic examined in the study of energy absorbers because reducing the initial contact force prevents sudden load application to the structure, thereby reducing the damage incurred. The absorbed energy can be calculated using the integral of the applied force with respect to displacement. This value is obtained by integrating the area under the force–displacement curve using Eq. (1).

In these relationships, Ea represents the absorbed energy in joules, and δmax is the maximum displacement of the force F applied to the surface of the sandwich panel.

The energy absorption model for the sandwich panel reinforced with glass fiber and metal, along with the optimization of parameters, was performed using Response Surface Methodology (RSM) and the Design-Expert software. Three parameters were examined at three levels (low, center, and high, coded as − 1, 0, and 1) using this method to model and optimize energy absorption and peak force. A total of 17 runs were conducted to develop the energy absorption and peak force model, along with optimal points for the parameters of core rib angle, percentage of MCM-48 nanoparticles, and the angle of fibers used in the composite layers. Based on preliminary tests, previous studies3,21,24,25, and manufacturing constraints, the range of parameters investigated is presented in Table 1. The mix design and the parameter values for each sample are introduced in Table 2 along with the sample names. The sample names are a combination of letters and numbers. The symbol "C" and the number following it represent the core rib angle, the symbol "F" and the number following it indicate the fiber orientation angle in the lay-up, and the symbol "N" and the number following it signify the percentage of nanoparticles added to the resin to enhance its mechanical properties. For example, the sample C52-F60-N2.5 has a core rib angle of 52°, a fiber orientation angle of 60° in the hand lay-up, and a nanoparticle percentage of 2.5% by weight in the resin.

As seen in the force–displacement diagrams in Fig. 3, during the collapse of the core of the sandwich panels, the force initially increases linearly to its peak value. This point indicates the ultimate strength of the structure under compressive load and includes the elastic region. With the onset of plastic deformation, the force–displacement curve suddenly experiences a significant drop.

Comparison of force, energy-displacement diagrams for (a) varying fiber angles, (b) varying nanofiller percentages, and (c) varying core strut angles.

Energy displacement diagrams for several samples are shown in Fig. 3. In Fig. 3a, it is observed that with a constant core strut angle and nanofiller percentage, increasing the fiber angle from 30 to 90° increases the initial peak force and energy absorption by 46.9% and 72.18%, respectively. Figure 3b illustrates the effect of varying the nanofiller percentage on the collapse behavior of the sandwich panel. The results indicate that adding nanofillers up to 0.25% by weight improves the collapse behavior of the panel; with a 0.25% by weight addition of nanofillers, the energy absorption increases by 60.8%, but further addition of nanofillers leads to a decrease in energy absorption. In Fig. 3-c, it is seen that reducing the core strut angle from 52 to 46°, while maintaining approximately the same energy absorption, decreases the initial peak force by 5%, indicating the optimal behavior of the sandwich panel at a 52-degree strut angle.

This region, shown in section 2 of Fig. 4, corresponds to the initiation of buckling in the core struts of the sandwich panel. Figure 4 shows the progressive collapse of the C58-F60-N2.5 sample under compressive loading. The failure pattern of all the samples shows that initially, the sample experiences buckling in the core struts to one side. Then the core begins to collapse and gradually starts to crumble along the same strut. After some time, this strut itself forms a column, which leads to an increase in the structural resistance once again (section 4 in Fig. 4)4.

Progressive collapse of sandwich panel.

The primary failure mechanisms of the core struts include delamination29, and the formation of plastic hinges, as shown in Fig. 5. The presence of metal fibers reduces the brittleness of the glass fibers, and no fractures or tears were observed in the failure pattern of the samples. Additionally, the core’s separation from the face sheets, which is often cited in various sources as the main weakness of trapezoidal-core sandwich panels, was not observed in these samples. According to Fig. 4, in some of the sandwich panels, matrix cracking in the struts was also observed, leading to fluctuations in the force level at the peak of the force–displacement curve. However, due to the presence of wire mesh sheets, complete fracture did not occur, which contributed to the energy absorption capacity of these panels.

Failure mechanism in sandwich panels with core sheets made of glass fibers/wire mesh.

The bar chart in Fig. 6 compares the initial peak force values for all samples. Sample C58-F30-N5 has the lowest initial peak force, with a value of 11,644 N, among all samples. On the other hand, sample C46-F90-N0 shows the highest initial peak force at 26,742 N, representing an increase of approximately 130% compared to sample C58-F30-N5. Additionally, the energy absorption levels, as shown in the bar chart in Fig. 7, indicate that sample C46-F90-N0 has the highest energy absorption at 152.7J among all samples.

Bar chart of the initial peak force in sandwich panels.

Bar chart of energy absorption in sandwich panels.

In the following, using the design of experiments and statistical analysis, the sensitivity analysis of parameters and their interaction in the collapse behavior of sandwich panels for maximum force response and energy absorption will be discussed. Force–displacement diagrams for other samples are shown in Fig. 8a,b.

Force–displacement diagrams for samples with fixed core degrees (a) 46° and, (b) 58°.

In this study, analysis of variance (ANOVA) was used to examine the interactions and effects of parameters on the initial peak force and energy absorption in sandwich panels. In the ANOVA, for each response separately, the sum of squared deviations from the overall mean responses was measured to determine the contribution and error of each parameter. A lower P-value for the parameter coefficients in the mathematical models, shown in Tables 3 and 4, indicates a greater impact of that parameter on energy absorption and initial peak force. In these tables, components of the second-order model with very high P-values were removed from the final equations for initial peak force and energy absorption33,34. Additionally, the values of two other components, the coefficient of determination (R2) and the adjusted coefficient of determination (adj-R2), are provided in Tables 3 and 4 for the initial peak force and energy absorption of the sandwich panels, respectively.

The regression results for the initial peak force response yielded a second-order equation with dual interactions between the three parameters: core rib angle, nanoparticle percentage, and fiber angle. In this equation, shown in Eq. (2), a power function with an exponent of 1.1 was used, which increased the accuracy of the equation in predicting the behavior of the sandwich panel. This is indicated by the closeness of the \({R}^{2}\) and \({R}_{adj}^{2}\) values. The \({R}^{2}\) and \({R}_{adj}^{2}\) values were found to be 0.9027 and 0.8443, respectively, indicating the model’s capability to predict the response behavior.

A second-order equation with a three-way interaction between the parameters of rib angle in the core, percentage of MCM-48 nanoparticles, and fiber angle was obtained for the energy absorption response, as shown in Eq. (3). The \({R}^{2}\) and \({R}_{adj}^{2}\) values are 0.9228 and 0.8766, respectively, indicating the high accuracy of the equation for predicting the energy absorption behavior of the panel. Additionally, in the obtained equation, a power coefficient of 1.3 was used to improve accuracy.

As shown in the force–displacement graph in Fig. 9, three identical samples were tested to verify the accuracy of the test. The results show that the maximum difference in the initial peak force among the three samples is 5.1%. Additionally, comparing the energy absorption results among the samples revealed a maximum difference of 1.7%, which is acceptable given the manufacturing process and the nature of the loading in energy absorbers.

Force–displacement graph for three identical samples, C52-F60-N2.5.

Confirming the accuracy of the statistical analysis results is essential for conclusive determination of the impact of the introduced parameters on the responses. The graphs in Fig. 10a,b show the normal probability of energy absorption and initial peak force, respectively. It can be seen that the residuals appropriately lie on a diagonal line and the errors are normally distributed.

Normal probability plots of the residuals for (a) energy absorption and (b) initial peak force.

The distribution graphs of the actual values obtained from the experimental tests compared to the predicted values for energy absorption and initial peak force are shown in Fig. 11a,b, respectively. As can be seen from these graphs, the presented model can accurately predict the behavior of the sandwich panel under axial loading, as indicated by the distribution of values near the diagonal line. This is further supported by the high \({R}^{2}\) values previously discussed.

Graphs of predicted values versus experimental values for (a) energy absorbed and (b) initial peak force.

In the force–displacement graphs in Fig. 3, it was observed how single-parameter changes affect the responses’ behavior with two parameters held constant. The three-dimensional surfaces resulting from the design of experiments illustrate the impact of each parameter and their interactions on the energy absorption and initial peak force responses, shown in Figs. 12 and 13, respectively.

3D graph showing the simultaneous impact of parameters on energy absorption: (a) Percentage by weight of nanoparticles and core rib angle, (b) Core rib angle and fiber angle, (c) Percentage by weight of nanoparticles and fiber angle.

3D graph showing the simultaneous impact of parameters on initial peak force: (a) Percentage by weight of nanoparticles and core rib angle, (b) Core rib angle and fiber angle, (c) Percentage by weight of nanoparticles and fiber angle.

In Fig. 12c, it is seen that at a fiber angle of 30°, adding 0.25% by weight of nanoparticles increases energy absorption; however, at a fiber angle of 90° in the lay-up, samples with 0.5% and 0% by weight of MCM-48 nanoparticles have higher energy absorption. In Fig. 12b, it is shown that the highest energy absorption occurs in the panel with a core rib angle of 46° and a fiber lay-up angle of 90°. Additionally, Fig. 12a shows that the highest energy absorption surface is observed at a core rib angle of 46° without nanoparticles in the panel structure. The bar chart in Fig. 7 also showed that the sample C46-F90-N0 had the highest energy absorption.

Figure 13a shows that at a core rib angle of 46°, increasing the nanoparticle percentage up to 0.25% by weight leads to an increase in the peak force. However, it is seen that this increase in nanoparticles at higher angles (58°) reduces the initial peak force. The highest peak force is generated at a fiber angle of 90° and a core rib angle of 46°, as shown in Fig. 13b. Proper design to reduce the peak force, based on the surface in Fig. 13b, occurs at a high core rib angle and a low fiber angle in the lay-up, which includes samples C58-F30-N0, C58-F30-N2.5, and C58-F30-N5 shown in the bar chart in Fig. 6.

In the three-dimensional surface in Fig. 13c, it is seen that for a fiber angle of 30° in the lay-up, adding nanoparticles up to 0.25% by weight increases the initial peak force, but further increases in nanoparticles lead to a decrease in the peak force again; meanwhile, the behavior of the panel at a fiber angle of 90° is completely different. Additionally, at a fiber angle of 60° in the lay-up, sensitivity to the nanoparticle percentage decreases.

Considering the interactions among parameters and the scattered response to parameter changes in the overall problem space, understanding the optimal conditions is essential. In the following sections, solutions for achieving optimal responses and reaching the optimal point will be analyzed and discussed.

After examining the effects of the core rib angle, percentage by weight of nanoparticles, and fiber lay-up angle on the collapse behavior of the sandwich panel, the precise values of these parameters that lead to maximum energy absorption and minimum initial peak force of the sandwich panel are determined. Using the BBD approach, as shown in Table 5, the initial conditions, parameter ranges, and their weighting importance in the optimization process are indicated. Since in the design of sandwich panels as energy absorbers, the approach of increasing energy absorption and reducing the initial peak force are equally important, the weighting for both responses is set to 3.

The optimal sample features a core rib angle of 58°, a fiber orientation of 73.5°, and no nanoparticles. This sandwich panel sample, with a maximum energy absorption of 102.9 J and a minimum initial peak force of 18,252 N, shows the best performance according to the design objectives within the overall problem space. Figure 14 illustrates the optimal point in this space.

Optimal point for (a) initial peak force behavior and (b) energy absorption behavior in the overall problem space.

To validate the optimization method and the statistical approach, experiments were conducted at the optimal point. Two identical samples with the optimal parameters were experimentally tested, as shown in Fig. 15. The average absorbed energy and initial peak force were 98.64 J and 19,277 N, respectively. The error percentage between the measured and predicted values for absorbed energy and initial peak force is 4.3% and 5.6%, respectively. The good agreement between the predicted and experimental results demonstrates the high accuracy and validity of the statistical model and confirms the optimal point.

Sandwich panel samples at optimal parameter settings for samples (a) with metal mesh and (b) without metal mesh.

The sandwich panel with the optimal design is compared in two conditions: with and without metal mesh. As shown in Fig. 16, the presence of a metal mesh layer in the lay-up increases the number of plastic hinges in the ribs, reducing brittleness in the core and increasing energy absorption. The presence of the metal mesh prevents rib failure at the connection to the facings, indicating improved performance and behavior of the sandwich panel.

Collapse shapes of the sandwich panel at optimal conditions for samples with and without metal mesh.

Optimization of sandwich panels with metal/glass fiber trapezoidal cores demonstrates significant improvements in energy absorption and peak force characteristics. This study’s results align well with those reported by Zhang et al.39, who investigated composite blast-resistant materials with flexible fiber core layers and found that such structures exhibit higher energy absorption performance. Specifically, Zhang’s work shows that incorporating a flexible core layer, similar to the integration of metal wire mesh in our study, enhances the overall energy dissipation capabilities of the composite material.

This study presents a comprehensive analysis of the quasi-static behavior of sandwich panels with metal/glass fiber trapezoidal cores under axial loading. Utilizing Response Surface Methodology (RSM) and Box-Behnken design, we investigated the influence of core angle, fiber orientation, and MCM-48 nanoparticle content on the panels’ energy absorption and peak force. Key findings from this research include:

Increasing the fiber orientation angle from 30 to 90° significantly enhances energy absorption by 72.18% and peak force by 46.9%.

Incorporating MCM-48 nanoparticles up to 0.25% by weight improves energy absorption by 60.8%. However, further additions beyond this threshold result in diminished benefits.

A core angle of 52° provides an optimal balance, reducing peak force by 5% while maintaining comparable energy absorption levels.

The regression models developed for predicting energy absorption (R2 = 0.9228) and peak force (R2 = 0.9027) demonstrate high accuracy, confirmed through experimental validation with minimal deviations.

Integrating a metal wire mesh within the sandwich panels significantly increases energy absorption and reduces core brittleness. This enhancement is attributed to the formation of additional plastic hinges and the prevention of core failure at the interface points.

Optimized parameters for achieving maximum energy absorption and minimum peak force involve a core angle of 58°, a fiber orientation of 73.5°, and the absence of nanoparticles. Experimental validation of these parameters showed an energy absorption of 102.9 J and a peak force of 18,252 N, closely aligning with predicted values and confirming the model’s reliability.

The findings of this study provide valuable insights into the design and optimization of sandwich panels for applications requiring high strength-to-weight ratios and enhanced impact resistance. Future research should explore the long-term durability and fatigue performance of these optimized sandwich panels in various environmental conditions to further validate their practical applications.

The data supporting the outcomes of this study are available based on the request from the corresponding author.

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Department of Mechanical Engineering, Islamic Azad University of Shahrood, Shahrood, Iran

Mojtaba Lashgaroo

Department of Mechanical Engineering, Technical and Vocational University, Tehran, Iran

Mojtaba Lashgaroo & Ali Dadrasi

Faculty of Mechanical Engineering, Hakim Sabzevari University, Sabzevar, Iran

Ali Dadrasi

Faculty of Mechanical Engineering, Islamic Azad University of Shahrood Branch, Shahrood, Iran

Vali Parvaneh

Faculty of Mechanical Engineering, Velayat University, P.O. Box 99111 − 31311, Iranshahr, Iran

Hossein Taghipoor

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Correspondence to Ali Dadrasi or Hossein Taghipoor.

For our article, entitled “Investigation of the Quasi-Static Behavior of Sandwich Panels with Metal/Glass Fiber Trapezoidal Cores under Axial Loading”, which has been submitted to your journal, there is no conflict of interest.

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Lashgaroo, M., Dadrasi, A., Parvaneh, V. et al. Optimizing energy absorption and peak force in metal/glass fiber sandwich panels with trapezoidal cores. Sci Rep 14, 25371 (2024). https://doi.org/10.1038/s41598-024-76235-x

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Received: 09 June 2024

Accepted: 11 October 2024

Published: 25 October 2024

DOI: https://doi.org/10.1038/s41598-024-76235-x

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