Introduction of a Novel Sunflower-Inspired Honeycomb Structure with Enhanced Energy Absorption Capacity under In-Plane Loading

Introduction of a Novel Sunflower-Inspired Honeycomb Structure with Enhanced Energy Absorption Capacity under In-Plane Loading | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Introduction of a Novel Sunflower-Inspired Honeycomb Structure with Enhanced Energy Absorption Capacity under In-Plane Loading Reza Sarkhosh This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5317681/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 20 May, 2025 Read the published version in Journal of the Brazilian Society of Mechanical Sciences and Engineering → Version 1 posted 4 You are reading this latest preprint version Abstract This study introduces a novel sunflower-inspired gradient structure where the size of hexagonal cells changes with a specific gradient in the radial direction. Subsequently, the crashworthiness and deformation performance of this structure were compared and analyzed with conventional honeycomb structures in both hollow and PU foam-filled states. In this research, specimens were first fabricated using additive manufacturing with PLA + material. After injecting polyurethane foam into the void spaces between cells, the specimens were subjected to quasi-static compressive loading in the in-plane direction at a 5 mm/min rate. The results showed that the sunflower-inspired honeycomb structure has significantly better crashworthiness and specific energy absorption properties than the conventional one. Based on these findings, it is concluded that the gradient design of cell sizes in the radial direction can lead to a 35% increase in specific energy absorption and a 20% increase in mean crushing force, along with a 143% improvement in crushing force efficiency, indicating enhanced performance in protective applications. Furthermore, it was demonstrated that the presence of foam can improve the performance of honeycomb structures. According to the results, foam-filled conventional honeycomb and sunflower-inspired honeycomb structures show increases of 43% and 41% in specific energy absorption, 82% and 89% in energy absorption and mean crushing force, and 23% and 10% in crushing force efficiency, respectively. The results indicate that the gradient design of cell sizes in the radial direction and the injection of PU foam into lattice structures can serve as a reference for designing energy absorbers with high-crashworthiness properties for various industries. Sunflower Honeycomb Energy absorption 3D printing PU foam Graded structure Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 Figure 16 Figure 17 Figure 18 Figure 19 Figure 20 Figure 21 1. Introduction Lattice structures have attracted attention due to their outstanding properties, such as high strength, low density, energy absorption capacity, and wide applications in automotive, medical, aerospace, and other industrial fields. The hexagonal honeycomb structure is the essential lattice structure, widely used as the core of sandwich panels in various industries due to its low weight, high strength, high energy absorption capacity, and ease of manufacture. With the advancement of manufacturing technology, particularly additive manufacturing, and the availability of 3D printers capable of producing complex geometries, extensive research has been conducted on new geometries [ 1 ] to enhance mechanical properties and energy absorption. Among these, gradient structures, where parameters such as size, angle [ 2 ], density [ 3 – 5 ], and cell thickness [ 6 ] vary with a specific gradient in the structure, have demonstrated improved mechanical properties and energy absorption compared to conventional structures due to their structural characteristics. Hybrid combinations [ 7 ] of different cells such as re-entrant and honeycomb [ 8 – 9 ], re-entrant and star-shaped [ 10 ], star-shaped and triangular [ 11 ], and star-shaped and arrowhead [ 12 ] also result in improved mechanical performance of structures. Hanfeng Yin et al. [ 13 ] classified and analyzed lattice structures used as energy absorbers from cell geometry, loading type, materials, and manufacturing methods. Amir Din et al. [ 14 ] suggested a two-dimensional honeycomb lattice structure that is filled using the Voronoi equation and fabricated this structure using a 3D printer with PLA material. Tensile and compressive tests were conducted on the Voronoi honeycomb structure, and the energy absorption results were compared with other honeycomb structures; the Voronoi honeycomb structure demonstrates superior energy absorption. In the aviation industry, Li et al. [ 15 ] created a novel pyramidal honeycomb structure that absorbs microwave radiation and has superior specific energy absorption compared to conventional structures. Three new two-dimensional hierarchical structures were proposed by Wenzheng Huang et al. [ 16 ] to increase energy absorption and mechanical strength and fabricated through laser-assisted additive manufacturing. Mechanical impact tests were conducted and compared with numerical simulation results, demonstrating increased energy absorption properties compared to conventional structures. Qiuyang He et al. [ 17 ] conducted an experimental and numerical study on a new 2D hierarchical honeycomb structure inspired by spider webs, fabricated through laser-assisted additive manufacturing. The experimental test results under out-of-plane loading were compared with the numerical solution results and presented a good consistency. In addition, the proposed hierarchical structures were found to have better energy absorption compared to conventional structures. Yingtao Tian et al. [ 18 ] conducted experimental and numerical investigations on a new bio-inspired honeycomb structure fabricated with a 3D printer. They evaluated this structure's mechanical properties and energy absorption by performing impact tests under out-of-plane loading and using numerical analysis. They demonstrated that the proposed structure offers better energy absorption characteristics than conventional honeycomb structures. Zhang Wen et al. [ 19 ] introduced a new 2D hierarchical honeycomb structure inspired by pomelo peel. After examining analytical and experimental results, they showed that the specific energy absorption property of this structure in out-of-plane loading has increased by 2.5 times compared to conventional honeycomb structures. Chung Ki et al. [ 20 ] reviewed research on the design of 2D honeycomb structures, examining them in terms of geometry, material, and loading methods. They compared their energy absorption properties and mechanical strength using charts. Danny Hidayat et al. [ 21 ] investigated the effect of manufacturing parameters through FDM 3D printing, such as plastic type, layer height, nozzle temperature, etc., on the mechanical strength and energy absorption of tubes filled with lattice structures. Habib et al. [ 22 ] conducted experimental and numerical studies on the cell thickness of nylon polymer honeycomb structures manufactured by 3D printing, studying their energy absorption characteristics. Nava Raj et al. [ 23 ] experimentally demonstrated that honeycomb and square structures made by 3D printing with a composite of TPU and ABS exhibit more desirable energy absorption in both in-plane and out-of-plane loading directions compared to their initial state. Zhang et al. [ 24 ] proposed a new structure by incorporating a triangular network into the honeycomb structure, showing through numerical simulation that the proposed structure has more desirable specific energy absorption in out-of-plane and in-plane directions compared to the conventional structure. Simon Bates et al. [ 25 ] studied the effect of density gradient on honeycomb structures' mechanical properties and energy absorption. They printed honeycombs with different density gradients using TPU material and 3D printing. Subsequently, they tested the compression and found that gradient structures have higher energy absorption in impact and quasi-static loading compared to uniform-density structures. Inspired by the internal structure of beetle elytra, Wang et al. [ 26 ] introduced modified triangular, square, and hexagonal structures. Finally, they demonstrated that the modified structures perform better than the original structure in terms of average crushing force and energy absorption. Niknam et al. [ 27 ] examined specific energy absorption of structures fabricated by stereolithography 3D printing as a function of density change. Experimental tests and numerical simulation results indicated that structures with varying densities exhibited a higher specific energy absorption compared to structures with uniform density. Kovalouglu et al. [ 28 ] conducted experimental and numerical studies on the size and thickness of honeycomb structure cells made by 3D printing with PLA and ABS materials, comparing the results related to maximum compressive force after uniaxial compression tests. Vazquez et al. [ 29 ] studied the effect of manufacturing parameters through 3D printing, such as density, printing direction, etc., on the energy absorption properties of honeycomb structures. Najafi et al. [ 30 ] proposed three new structures. After manufacturing the structures from ABS material using 3D printing and comparing the products with numerical simulation results, they demonstrated better energy absorption properties compared to conventional honeycombs. Cai et al. [ 31 ] introduced a new structure inspired by fish skin, manufactured by 3D printing, and compared the mechanical properties and energy absorption of the re-entrant structure with the original structure. After matching experimental results with numerical simulation results, they showed improved energy absorption characteristics in the new structure. Li et al. [ 32 ] improved energy absorption and mechanical properties compared to the original structure by designing a hierarchical combination of honeycomb structures. Yong Tao et al. [ 33 ] conducted an experimental and numerical investigation on a hierarchical square honeycomb structure. In this study, specimens were made by 3D printing with different cell sizes and numbers. After examining the results of compression tests and numerical simulations, they showed improved mechanical properties and energy absorption. Wang et al. [ 34 ] proposed a new Kagome honeycomb structure with triangular substructures. After construction and comparison of experimental and numerical results, they showed increased specific energy absorption compared to the original state. Furthermore, the structure's strength and specific energy absorption in concentrated and [ 35 ] distributed loadings can be improved by constructing structures with composite materials [ 36 ], especially by injecting PU foam into lattice structure cells [ 37 – 43 ], due to the foam's crushability properties and lightweight. Several industries, including aerospace, automotive, and construction, always seek lighter lattice structures with better energy absorption properties and more desirable crashworthiness. In this regard, researchers offer various solutions to increase specific energy absorption capability and crashworthiness properties. One of these solutions is to draw inspiration from structures that already exist in nature for designing new geometries. A new gradient honeycomb structure inspired by the structure of sunflowers is introduced in the present research. This structure is characterized by cell sizes decreasing radially towards the center. This new design is predicted to increase crashworthiness properties and energy absorption. 2. Empirical Study 2.1 Modeling the Geometry of Specimens In the sunflower-inspired honeycomb structure, the size of hexagonal cells decreases radially towards the center. In this pattern, as the cell size changes, the lengths of the sides and angles of the hexagon also change. The sides with index Y are aligned with the line from the center, and the connection points between two symmetrical X lines and symmetrical Y lines are located on the radial line from the center. Additionally, lines with similar labels are in symmetry with the red dotted line. The dimensions of the first-order cells are defined as shown in Fig. 1 . X 1 = 8.7mm Y 1 = 8.7mm α = 24˚ β = 120˚ Similarly, the first-order structure is formed by repeating hexagonal unit cells in the circumferential direction. In the gradient structure, a decrease in radius leads to an increase in order number. For the next order, the dimensions of the cells decrease according to formulas 1 and 2 until they reach the center. $$\:{x}_{n}={x}_{n-1}\times\:0.7\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:n\ge\:2$$ 1 $$\:{y}_{n}={y}_{n-1}\times\:0.7\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:n\ge\:2$$ 2 For the quasi-static compression test, specimens were designed as squares with dimensions of 70×70×70 mm, as shown in the geometry in Fig. 2 . Also, a plate with a wall thickness of 0.8 mm was added to distribute pressure uniformly at the contact point between the specimen and the compression machine jaws and to connect the cut cells at the top and bottom of the structure. A conventional honeycomb structure with geometric specifications and dimensions is introduced to compare the performance of the sunflower-inspired honeycomb structure, as shown in Fig. 3 . 2.2 Fabricating the Specimens In this stage, the conventional honeycomb and the sunflower-inspired honeycomb structures were modeled in CATIA software, as seen in Figs. 4 -a and 4 -b, respectively. Subsequently, models were initially prepared in the specialized 3D Simplify software with identical settings for each sample according to Table 1 , and then the 3D models were manufactured using a Hypercube 3D printer with PLA + material, as shown in Fig. 4 -c. Additive manufacturing using the FDM method is considered a new technology in manufacturing and production. In this method, thermoplastic polylactic acid is melted through heating. Then, the molten material is placed layer by layer through the nozzle on a defined path to produce the desired part. As shown in Fig. 4 -c, the parts were built horizontally to prevent the construction of supports. Moreover, to examine the mechanical properties of PLA + materials, three dumbbell-shaped specimens were made according to ASTM D368 standard with the geometry shown in Fig. 5 -a, using identical settings on the 3D printer, as shown in Fig. 5 -b. Subsequently, the specimens were subjected to uniaxial tension with a Zwick Roll-Z100 machine, as shown in Fig. 5 -c, and the results were presented in Fig. 6 and Table 2 . Table 1 3D printer parameters 3D printer Parameters quantity Layer height (mm) 0.3 Nozzle temperature (c) 210 Bed temperature (c) 50 Print speed (mm/s) 33.4 Nozzle diameter (mm) 0.4 Filament diameter (mm) 1.75 Table 2 Mechanical properties of PLA+ Material Density (g/cm 3 ) Young’s Modulus (GPa) Yield stress (MPa) Ultimate stress (MPa) Pla+ 1.2 2.71 33.4 37 2.3 Manufacturing and Injection of Foam Two-component polyurethane foam is injected into the hollow space of the honeycomb structure to increase energy absorption. Given the foam’s low density and properties, it is predicted that by injecting it into the honeycomb structure, the specific energy absorption and compressive tolerance will increase in the uniaxial quasi-static compression test results. In this section, after manufacturing the honeycomb structures using a 3D printer, it is time to prepare the two-component polyurethane foam. First, two components produced by the Pars Chemical Company, namely Polyol R and F 4109 and ISO PM 200, were mixed in a 1:1 ratio and injected into the hollow space of the lattice structure. After a few seconds, these two components react, and the volume expansion process and foaming begin, filling the hollow space between the cells. After final drying, excess foam is removed, and the foam-filled cubic specimen is prepared. Additionally, as shown in Fig. 7 , two cubic foam-bearing specimens were made to examine mechanical properties along with other specimens. They were subjected to quasi-static compression, and the results are presented in Fig. 8 and Table 3 . Table 3 Mechanical properties of polyurethane foam Material Density (Kg/m 3 ) EA (J) SEA (KJ/Kg) PU Foam 57.2 53 2.7 Three specimens of each structure (12 specimens in total) were made, as shown in Fig. 9 . Also, the weights of the specimens were measured using a scale with a 1-gram accuracy, and the specimens were coded with unique abbreviations, as shown in Table 4 . Table 4 Specimen coding Specimens code Description Loading Weight (g) HHEI H exagon H oneycomb E mpty I n plane 92 HHFI H exagon H oneycomb F oam Filled I n plane 117 SHEI S unflower H oneycomb E mpty I n plane 82 SHFI S unflower H oneycomb F oam Filled I n plane 110 2.4 Quasi-Static compression Test Quasi-static compression tests were conducted on 12 honeycomb specimens in the in-plane direction using the Zwick Roll-Z100 testing machine at room temperature, as shown in Fig. 10 -a. As seen in Figs. 10 -b and 10 -c, each specimen was placed on the machine's fixed platform. At this stage, the movable jaw moves downward at a constant speed of 5 mm/min to satisfy quasi-static conditions, compressing and crushing the honeycomb specimen until full compaction. This machine is connected to a computer that outputs the results through force-displacement curves. 3. Results and Discussion 3.1 In-Plane Crashworthiness Evaluation When structures are subjected to quasi-static compression, they initially experience reversible, elastic deformation [ 44 ]. As more force is applied, the structure enters the plastic and irreversible phase, and structural collapse and failure begin to occur [ 13 ]. This leads to a significant drop in the force-displacement curve. In the plastic phase, the collapse of the cells occurs gradually, and the force-displacement curve continues to fluctuate due to the crushing of the structure until full compaction is achieved. After complete compaction, the slope of the curve tends toward infinity, indicating that the structure's energy absorption capacity is exhausted. The area under the force-displacement curve before the final compaction is referred to as the absorbed energy by the honeycomb structure and is calculated using Eq. 3 . $$\:EA={\int\:}_{0}^{d}f\left(x\right)dx$$ 3 In industrial applications such as the aviation industry, the weight of the lattice structure is important. The specific energy absorption parameter [ 45 ] is defined in Eq. 4 based on the force-displacement curve, where the weight factor is dimensionless and can be considered a correct criterion for evaluating the energy absorption of the structure per unit mass. $$\:SEA=\frac{EA}{m}$$ 4 Where in Eq. 4 , EA is the amount of energy absorption, and \(\:m\) is the weight of the honeycomb structure. Additionally, the parameter defining the crushing force efficiency (CFE) is a critical feature for comparing and assessing energy-absorbing structures through crushing, expressed by the formula 5. $$\:CFE=\frac{MCF}{PCF}$$ 5 In Formula 5, the crushing force efficiency (CFE) has a direct relationship with the mean crushing force (MCF) and an inverse relationship with the first peak force (PCF). Eq. 6 is used to get MCF from the force-displacement curve. The force-displacement curve is used to obtain the PCF directly. $$\:MCF=\frac{1}{d}{\int\:}_{0}^{d}f\left(x\right)dx=\frac{EA}{d}$$ 6 Compressive loading was applied to specimens up to approximately 80% of their initial height. The curves show that the structures could absorb energy up to an average compression of 46 mm, after which the curve tends toward infinity with a sharp slope. In the calculations, this value is considered as the effective length. Curves 11 to 14 indicate that the force in SH structures increases with displacement due to the structure's gradient nature. The specific energy absorption and crushing force efficiency depend on the size of the hexagonal cells and their resistance to crushing [ 46 , 47 ]. These structures have the cells arranged radially from large to small. The first-order largest cells collapse first and experience a lower peak force than those in a uniform and conventional structure. After the first-order cells collapse, the remaining order cells also collapse, producing a stepwise increase in force in the force-displacement curve. The first peak force is reduced, the average crushing force is increased, the crushing force efficiency is significantly improved, and the crashworthiness is greatly enhanced. The gradient nature of the cell sizes and this stepwise collapse leads to a positive slope in the force-displacement curve, thus increasing the absorbed energy. As shown in Table 5 , the superiority of the gradient structure in specific energy absorption is confirmed due to the gradient structure’s lower weight and higher energy absorption compared to the conventional structure. The comparison of crashworthiness parameters indicates that the in-plane loading of the SHEI structure has 35% more specific energy absorption than the HHEI structure, and the SHFI structure has 32% more specific energy absorption than the HHFI structure. In addition, the 143% and 118% increase in crushing force efficiency of the SHEI and SHFI structures, respectively, compared to the corresponding conventional honeycomb structures, demonstrate the excellent performance of the proposed structure. Furthermore, a 20% increase in SHEI structure and a 25% increase in the SHFI structure in terms of energy absorption, and a 20% increase in the SHEI and a 25% increase in the SHFI in terms of mean crushing force compared to their corresponding counterparts in conventional honeycomb, completes the excellent performance of the proposed structure in crashworthiness and energy absorption. Moreover, the presence of foam in the structures causes an increase in crashworthiness parameters. SHFI and HHFI structures exhibit 41% and 43% increase in specific energy absorption, 89% and 82% increase in energy absorption and mean crushing force, and 10% and 23% increase in crushing force efficiency compared to SHEI and HHEI structures. Figures 15 and 16 illustrate the crushing behavior of SHEI and SHFI structures. As expected, in these structures, the first order of cells experiences collapse from top or bottom, with region I indicating the resistance of the first order. Subsequently, the walls aligned with the displacement direction apply pressure to the next order, causing the cells of the second order to begin collapsing, as shown by Region II. This process then repeats at the other side of the structure, and after the collapse of orders 1 and 2 from top and bottom, orders 3 and 4 also collapse following the same pattern, as shown in curves III and IV. The last region corresponds to the resistance of the 5th order and the central cell of the structure, which has the highest resistance among the gradient structures and is marked as curve V. According to previous studies [ 48 – 49 ], the crushing pattern of conventional honeycomb cells under compressive loading varies at different speeds. In quasi-static loading, as shown in Figs. 15 and 17 , in HHEI and HHFI structures, the row of hexagonal cells first collapses diagonally [ 50 – 52 ]. Then, as expected [ 53 ], an X-shaped collapse pattern forms and progresses until complete compression of the cells. Notably, the peaks and troughs in Fig. 17 , separated by dashed lines, correspond to the collapse of a diagonal row of cells in the conventional honeycomb structure during compressive loading. This indicates the compressive resistance of each row against crushing and plastic deformation. As shown in Figs. 16 and 17 , HHFI and SHFI structures have higher strength SHEI and HHEI structures, increasing the area under the curve, average crushing force, and energy absorption. This can be attributed to the presence of rigid polyurethane foam that increases the compressive resistance of cells against crushing by filling the hollow space between hexagonal cells. Considering the light weight of PU foam, it will also increase the specific energy absorption. Additionally, the curves of foam-filled structures exhibit less fluctuation than those without foam. As shown in Table 5 and Figs. 18 to 21 , the SHFI structure exhibits the best performance in crashworthiness properties, particularly specific energy absorption. The HHEI structure offers the weakest performance. This highlights the beneficial effect of gradient design of cell sizes and polyurethane foam injection on the performance and efficiency of honeycomb structures. Furthermore, the polyurethane foam-filled gradient sunflower-inspired honeycomb structure has a special appeal for industries such as aerospace and marine, where the structure's weight is critical. It can be a good substitute for conventional honeycomb structures. Table 5 Parameters of crashworthiness Specimens code W (g) EA (J) MCF (KN) CFE (%) SEA (KJ/Kg) HHEI 92 216.3 4.69 83 2.35 HHFI 117 394 8.56 102 3.37 SHEI 82 260.3 5.65 202 3.17 SHFI 110 491 10.67 222 4.46 4. Conclusion This research proposes a new gradient sunflower-inspired honeycomb structure where the size of hexagonal cells gradually decreases in the radial direction according to a certain gradient. The performance of this novel structure was analyzed and compared with the conventional honeycomb structure under in-plane loading conditions. An investigation was conducted on filling the hollow space between cells with rigid polyurethane foam in conventional honeycomb and sunflower-inspired honeycomb structures. The production of 12 specimens made from PLA + using an FDM 3D printer was carried out, followed by quasi-static loading tests. Similar behavior of sunflower-inspired and conventional honeycomb structures was observed under hollow and foam-filled conditions. Thanks to stepwise and controlled collapse mechanisms, the results demonstrated that the sunflower-inspired honeycomb structure exhibits a much higher influence on crashworthiness parameters compared to the conventional structure. The findings are highlighted below: The sunflower-inspired honeycomb structure with a hollow core has a 35% higher SEA, a 20% higher EA, a 20% higher MCF, and a 143% higher CFE compared to the conventional honeycomb structure with a hollow core. The PU foam-filled sunflower-inspired honeycomb structure has 32% SEA, 24% EA, 118% CFE, and 25% MCF higher than the PU foam-filled conventional honeycomb structure. Rigid PU foam injection in the conventional honeycomb structure gives a 43% increase in SEA, 82% in EA, 82% in MCF, and 23% in CFE. Rigid PU foam injection in the sunflower-shaped honeycomb structure results in a 41% increase in SEA, an 89% increase in EA, MCF, and a 10% increase in CFE. The findings revealed that the gradient design of hexagonal cell sizes and the application of PU foam in the hollow space of honeycomb structures are effective strategies for enhancing the crashworthiness properties of honeycomb structures. This study can serve as a reference for developing high-performance energy absorbers and provide high-capacity energy absorber solutions for various industries such as aerospace, automotive, and others. Declarations 5. 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. 6. Consent to participate All authors participated in the research work reported in this paper. 7. Consent to publication All authors agreed to publish the findings of this research. References Habib, F. N., Iovenitti, P., Masood, S. H., & Nikzad, M. (2018). 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Materials , 16 (4), 1571. https://doi.org/10.3390/ma16041571 Safikhani Nasim, M., Yaghootian, A., & Mosalmani, R. (2023). Energy absorption of the additively manufactured novel re-entrant auxetic structure in comparison with honeycomb structure: experimental and numerical analysis. Journal of the Brazilian Society of Mechanical Sciences and Engineering , 45 (5), 275. https://doi.org/10.1007/s40430-023-04178-x Kucewicz, M., Baranowski, P., & Małachowski, J. (2019). A method of failure modeling for 3D printed cellular structures. Materials & Design , 174 , 107802. https://doi.org/10.1016/j.matdes.2019.107802 Lin, H., Han, C., Yang, L., Karampour, H., Luan, H., Han, P., ... & Zhang, S. (2022). Dynamic Performance and Crashworthiness Assessment of Honeycomb Reinforced Tubular Pipe in the Jacket Platform under Ship Collision. Journal of Marine Science and Engineering , 10 (9), 1194. https://doi.org/10.3390/jmse10091194 Cite Share Download PDF Status: Published Journal Publication published 20 May, 2025 Read the published version in Journal of the Brazilian Society of Mechanical Sciences and Engineering → Version 1 posted Reviewers agreed at journal 12 Nov, 2024 Reviewers invited by journal 12 Nov, 2024 Editor assigned by journal 01 Nov, 2024 First submitted to journal 27 Oct, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-5317681","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":377374613,"identity":"db6c322e-b813-4399-bd10-8bcfdd46018e","order_by":0,"name":"Reza Sarkhosh","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA7UlEQVRIie3OsWvCQBTH8Z8EdDlxTRCSf+EkECgF/VcShHaxu0OHN9VFnIUO/gudnE8emOXcT3Apgc4NQrGLWEEyFDl1c7jv8OAd94EHuFx3WI+OUynA91T1qs7+PSVVRerpzUTI6w6TqvG5HepNGL2Pt+XuldEaqRoPLaRHIg60+YrlZjVviyXD1ykW2kK6EAjom7MP/2Xuoc6AARZkITEaxe+RzKaDotztGdEl0iEkARnOyAzgN98Y8hKRLJIH0hxL85S0m5Nn0dEZ2Uk+Kta05DCa9v8O+3kMw5y5tBF4/3YB1KzA5XK5XFd0ACjhWJsISOaRAAAAAElFTkSuQmCC","orcid":"","institution":"Aeronautical University of Science and Technology: Shahid Sattari University of Aeronautical Engineering","correspondingAuthor":true,"prefix":"","firstName":"Reza","middleName":"","lastName":"Sarkhosh","suffix":""}],"badges":[],"createdAt":"2024-10-23 09:36:40","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5317681/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5317681/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s40430-025-05634-6","type":"published","date":"2025-05-20T15:57:27+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":70216520,"identity":"a959cfef-2d3c-4c4e-b88a-159dd5d37356","added_by":"auto","created_at":"2024-11-29 15:43:52","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":103985,"visible":true,"origin":"","legend":"\u003cp\u003eThe first-order unit cells of the gradient sunflower-inspired honeycomb structure\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-5317681/v1/0aacdd40023607cdd9983a0d.png"},{"id":70214843,"identity":"32b5d5d7-5468-49d3-9a9b-f852fb298e64","added_by":"auto","created_at":"2024-11-29 15:19:52","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":148076,"visible":true,"origin":"","legend":"\u003cp\u003eSquare specimen of the gradient honeycomb structure\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-5317681/v1/dd4274451114505d3e520494.png"},{"id":70215570,"identity":"f46b1573-4cce-48d4-afa4-15d3b71c9c25","added_by":"auto","created_at":"2024-11-29 15:27:52","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":99965,"visible":true,"origin":"","legend":"\u003cp\u003eGeometry of conventional honeycomb cell\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-5317681/v1/679cb22195b5e924e5b5fd19.png"},{"id":70214851,"identity":"b49fd525-ce40-4d63-bd39-a36684d10d4e","added_by":"auto","created_at":"2024-11-29 15:19:52","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":856105,"visible":true,"origin":"","legend":"\u003cp\u003ea) Isometric view of the 3D model of conventional honeycomb structure b) Isometric view of the 3D model of sunflower-inspired honeycomb structure c) Manufacturing of specimens by 3D printer\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-5317681/v1/3b062a58ef2d3433a5c16dcd.png"},{"id":70215805,"identity":"36395ccf-a373-4f4e-af58-50146d9b94a0","added_by":"auto","created_at":"2024-11-29 15:35:52","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":314907,"visible":true,"origin":"","legend":"\u003cp\u003ea) Geometry of tensile test specimens b) PLA+ specimens c) Specimen placement in the machine\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-5317681/v1/3d82a79a8f6e9330254f36a7.png"},{"id":70214844,"identity":"4b87c976-8fbf-4f2d-96bd-4a83eadc94c5","added_by":"auto","created_at":"2024-11-29 15:19:52","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":74768,"visible":true,"origin":"","legend":"\u003cp\u003eStress-strain curve of tensile test\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-5317681/v1/9f795e26337fc29cc96188f1.png"},{"id":70214850,"identity":"f58396cd-1485-43ac-ad70-554ba6a7b0f3","added_by":"auto","created_at":"2024-11-29 15:19:52","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":221109,"visible":true,"origin":"","legend":"\u003cp\u003eCubic specimens of polyurethane foam\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-5317681/v1/edfb31abfd40703dba1c3e97.png"},{"id":70214845,"identity":"55da5635-33ed-46cb-8ed9-aa068d53a6dd","added_by":"auto","created_at":"2024-11-29 15:19:52","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":58090,"visible":true,"origin":"","legend":"\u003cp\u003eThe force-displacement curve of the compression test of PU foam\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-5317681/v1/91ac1901c8f872637a1a0730.png"},{"id":70215809,"identity":"47036021-0a7c-4507-a496-c0c841aa187d","added_by":"auto","created_at":"2024-11-29 15:35:52","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":849191,"visible":true,"origin":"","legend":"\u003cp\u003ePrepared specimens for quasi-static compression test\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-5317681/v1/9dcddd0cfb4e732918d823d8.png"},{"id":70215578,"identity":"6f6546b7-0260-4fa9-a9da-cfe423f1d0f3","added_by":"auto","created_at":"2024-11-29 15:27:52","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":464371,"visible":true,"origin":"","legend":"\u003cp\u003ea) Image of the Zwick Roll-Z100 pressure machine, b) Specimen placement jaws c) How the specimen is placed in the machine\u003c/p\u003e","description":"","filename":"10.png","url":"https://assets-eu.researchsquare.com/files/rs-5317681/v1/3c6bb12574fb3dbdd5b78433.png"},{"id":70215574,"identity":"3c8eb25d-78ff-4b78-b30b-eb8462376515","added_by":"auto","created_at":"2024-11-29 15:27:52","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":73679,"visible":true,"origin":"","legend":"\u003cp\u003eThe force-displacement curve of the HHEI structure\u003c/p\u003e","description":"","filename":"11.png","url":"https://assets-eu.researchsquare.com/files/rs-5317681/v1/0485a2a2ee0e6ffe35d56b45.png"},{"id":70215580,"identity":"c245c14d-b8ca-4444-8742-042e25c5310f","added_by":"auto","created_at":"2024-11-29 15:27:52","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":68510,"visible":true,"origin":"","legend":"\u003cp\u003eThe force-displacement curve of the HHFI structure\u003c/p\u003e","description":"","filename":"12.png","url":"https://assets-eu.researchsquare.com/files/rs-5317681/v1/eeac0c7d78f41df824dd691f.png"},{"id":70215808,"identity":"caa04ba3-2d90-4f57-b45c-2cff1aa06f30","added_by":"auto","created_at":"2024-11-29 15:35:52","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":70217,"visible":true,"origin":"","legend":"\u003cp\u003eThe force-displacement curve of the SHEI structure\u003c/p\u003e","description":"","filename":"13.png","url":"https://assets-eu.researchsquare.com/files/rs-5317681/v1/e522354b49371f7e4d057282.png"},{"id":70214853,"identity":"bffce576-5ad6-4d0d-8738-afbeb14c2770","added_by":"auto","created_at":"2024-11-29 15:19:52","extension":"png","order_by":14,"title":"Figure 14","display":"","copyAsset":false,"role":"figure","size":69626,"visible":true,"origin":"","legend":"\u003cp\u003eThe force-displacement curve of the SHFI structure\u003c/p\u003e","description":"","filename":"14.png","url":"https://assets-eu.researchsquare.com/files/rs-5317681/v1/764614d074c2883a025ecc23.png"},{"id":70214860,"identity":"b194f566-d302-42f8-97e5-2543eb666960","added_by":"auto","created_at":"2024-11-29 15:19:52","extension":"png","order_by":15,"title":"Figure 15","display":"","copyAsset":false,"role":"figure","size":884185,"visible":true,"origin":"","legend":"\u003cp\u003eDeformation pattern of structures a) HHEI b) HHFI c) SHEI d) SHFI\u003c/p\u003e","description":"","filename":"15.png","url":"https://assets-eu.researchsquare.com/files/rs-5317681/v1/3a55b04a2793c2499cc676f7.png"},{"id":70214862,"identity":"134cbd31-ee5a-425c-b6bb-174595b661bd","added_by":"auto","created_at":"2024-11-29 15:19:52","extension":"png","order_by":16,"title":"Figure 16","display":"","copyAsset":false,"role":"figure","size":104275,"visible":true,"origin":"","legend":"\u003cp\u003eMagnified force-displacement curves of SHEI and SHFI structures\u003c/p\u003e","description":"","filename":"16.png","url":"https://assets-eu.researchsquare.com/files/rs-5317681/v1/068b3e322817330c23d0d9d4.png"},{"id":70214863,"identity":"c6cff647-d367-49a3-9e15-8fa454628581","added_by":"auto","created_at":"2024-11-29 15:19:52","extension":"png","order_by":17,"title":"Figure 17","display":"","copyAsset":false,"role":"figure","size":107782,"visible":true,"origin":"","legend":"\u003cp\u003eThe magnified force-displacement curves of HHEI and HHFI structures.\u003c/p\u003e","description":"","filename":"17.png","url":"https://assets-eu.researchsquare.com/files/rs-5317681/v1/b53a82b34bc920ef5330fc89.png"},{"id":70215811,"identity":"7b788496-ee23-42f9-9f52-c915ddf98d44","added_by":"auto","created_at":"2024-11-29 15:35:54","extension":"png","order_by":18,"title":"Figure 18","display":"","copyAsset":false,"role":"figure","size":15424,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of the MCF of structures as a bar chart\u003c/p\u003e","description":"","filename":"18.png","url":"https://assets-eu.researchsquare.com/files/rs-5317681/v1/9970a779b263f250c4d19a55.png"},{"id":70215579,"identity":"9f072b5c-68bd-4625-b759-0568abe74c14","added_by":"auto","created_at":"2024-11-29 15:27:52","extension":"png","order_by":19,"title":"Figure 19","display":"","copyAsset":false,"role":"figure","size":15616,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of the MCF of structures as a bar chart\u003c/p\u003e","description":"","filename":"19.png","url":"https://assets-eu.researchsquare.com/files/rs-5317681/v1/6b8f92ee25d5cbf69f98ecff.png"},{"id":70214856,"identity":"e93f8635-1b82-4728-ab41-f4ea7912b45d","added_by":"auto","created_at":"2024-11-29 15:19:52","extension":"png","order_by":20,"title":"Figure 20","display":"","copyAsset":false,"role":"figure","size":16683,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of the EA of structures in a bar chart\u003c/p\u003e","description":"","filename":"20.png","url":"https://assets-eu.researchsquare.com/files/rs-5317681/v1/fe4e4a374371998ce0aff465.png"},{"id":70215807,"identity":"b0456aa6-cf77-4fc4-8fb4-4d57c2452dda","added_by":"auto","created_at":"2024-11-29 15:35:52","extension":"png","order_by":21,"title":"Figure 21","display":"","copyAsset":false,"role":"figure","size":16862,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of the CFE of structures in a bar chart\u003c/p\u003e","description":"","filename":"21.png","url":"https://assets-eu.researchsquare.com/files/rs-5317681/v1/73607a2d8d4d7f7614ea99b9.png"},{"id":83460171,"identity":"34710acb-019f-4f34-9c58-bf76699350d0","added_by":"auto","created_at":"2025-05-26 16:11:31","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":6237374,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5317681/v1/25cdce41-ef3c-4138-9089-5a309e2b8fdb.pdf"}],"financialInterests":"","formattedTitle":"Introduction of a Novel Sunflower-Inspired Honeycomb Structure with Enhanced Energy Absorption Capacity under In-Plane Loading","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eLattice structures have attracted attention due to their outstanding properties, such as high strength, low density, energy absorption capacity, and wide applications in automotive, medical, aerospace, and other industrial fields. The hexagonal honeycomb structure is the essential lattice structure, widely used as the core of sandwich panels in various industries due to its low weight, high strength, high energy absorption capacity, and ease of manufacture. With the advancement of manufacturing technology, particularly additive manufacturing, and the availability of 3D printers capable of producing complex geometries, extensive research has been conducted on new geometries [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e] to enhance mechanical properties and energy absorption. Among these, gradient structures, where parameters such as size, angle [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e], density [\u003cspan additionalcitationids=\"CR4\" citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e], and cell thickness [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e] vary with a specific gradient in the structure, have demonstrated improved mechanical properties and energy absorption compared to conventional structures due to their structural characteristics. Hybrid combinations [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e] of different cells such as re-entrant and honeycomb [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e], re-entrant and star-shaped [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e], star-shaped and triangular [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e], and star-shaped and arrowhead [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e] also result in improved mechanical performance of structures. Hanfeng Yin et al. [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e] classified and analyzed lattice structures used as energy absorbers from cell geometry, loading type, materials, and manufacturing methods. Amir Din et al. [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e] suggested a two-dimensional honeycomb lattice structure that is filled using the Voronoi equation and fabricated this structure using a 3D printer with PLA material. Tensile and compressive tests were conducted on the Voronoi honeycomb structure, and the energy absorption results were compared with other honeycomb structures; the Voronoi honeycomb structure demonstrates superior energy absorption. In the aviation industry, Li et al. [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e] created a novel pyramidal honeycomb structure that absorbs microwave radiation and has superior specific energy absorption compared to conventional structures. Three new two-dimensional hierarchical structures were proposed by Wenzheng Huang et al. [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e] to increase energy absorption and mechanical strength and fabricated through laser-assisted additive manufacturing. Mechanical impact tests were conducted and compared with numerical simulation results, demonstrating increased energy absorption properties compared to conventional structures. Qiuyang He et al. [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e] conducted an experimental and numerical study on a new 2D hierarchical honeycomb structure inspired by spider webs, fabricated through laser-assisted additive manufacturing. The experimental test results under out-of-plane loading were compared with the numerical solution results and presented a good consistency. In addition, the proposed hierarchical structures were found to have better energy absorption compared to conventional structures. Yingtao Tian et al. [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e] conducted experimental and numerical investigations on a new bio-inspired honeycomb structure fabricated with a 3D printer. They evaluated this structure's mechanical properties and energy absorption by performing impact tests under out-of-plane loading and using numerical analysis. They demonstrated that the proposed structure offers better energy absorption characteristics than conventional honeycomb structures.\u003c/p\u003e \u003cp\u003eZhang Wen et al. [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e] introduced a new 2D hierarchical honeycomb structure inspired by pomelo peel. After examining analytical and experimental results, they showed that the specific energy absorption property of this structure in out-of-plane loading has increased by 2.5 times compared to conventional honeycomb structures. Chung Ki et al. [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e] reviewed research on the design of 2D honeycomb structures, examining them in terms of geometry, material, and loading methods. They compared their energy absorption properties and mechanical strength using charts. Danny Hidayat et al. [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e] investigated the effect of manufacturing parameters through FDM 3D printing, such as plastic type, layer height, nozzle temperature, etc., on the mechanical strength and energy absorption of tubes filled with lattice structures. Habib et al. [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e] conducted experimental and numerical studies on the cell thickness of nylon polymer honeycomb structures manufactured by 3D printing, studying their energy absorption characteristics. Nava Raj et al. [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e] experimentally demonstrated that honeycomb and square structures made by 3D printing with a composite of TPU and ABS exhibit more desirable energy absorption in both in-plane and out-of-plane loading directions compared to their initial state. Zhang et al. [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e] proposed a new structure by incorporating a triangular network into the honeycomb structure, showing through numerical simulation that the proposed structure has more desirable specific energy absorption in out-of-plane and in-plane directions compared to the conventional structure. Simon Bates et al. [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e] studied the effect of density gradient on honeycomb structures' mechanical properties and energy absorption. They printed honeycombs with different density gradients using TPU material and 3D printing. Subsequently, they tested the compression and found that gradient structures have higher energy absorption in impact and quasi-static loading compared to uniform-density structures. Inspired by the internal structure of beetle elytra, Wang et al. [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e] introduced modified triangular, square, and hexagonal structures. Finally, they demonstrated that the modified structures perform better than the original structure in terms of average crushing force and energy absorption. Niknam et al. [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e] examined specific energy absorption of structures fabricated by stereolithography 3D printing as a function of density change. Experimental tests and numerical simulation results indicated that structures with varying densities exhibited a higher specific energy absorption compared to structures with uniform density. Kovalouglu et al. [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e] conducted experimental and numerical studies on the size and thickness of honeycomb structure cells made by 3D printing with PLA and ABS materials, comparing the results related to maximum compressive force after uniaxial compression tests. Vazquez et al. [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e] studied the effect of manufacturing parameters through 3D printing, such as density, printing direction, etc., on the energy absorption properties of honeycomb structures.\u003c/p\u003e \u003cp\u003eNajafi et al. [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e] proposed three new structures. After manufacturing the structures from ABS material using 3D printing and comparing the products with numerical simulation results, they demonstrated better energy absorption properties compared to conventional honeycombs. Cai et al. [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e] introduced a new structure inspired by fish skin, manufactured by 3D printing, and compared the mechanical properties and energy absorption of the re-entrant structure with the original structure. After matching experimental results with numerical simulation results, they showed improved energy absorption characteristics in the new structure. Li et al. [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e] improved energy absorption and mechanical properties compared to the original structure by designing a hierarchical combination of honeycomb structures. Yong Tao et al. [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e] conducted an experimental and numerical investigation on a hierarchical square honeycomb structure. In this study, specimens were made by 3D printing with different cell sizes and numbers. After examining the results of compression tests and numerical simulations, they showed improved mechanical properties and energy absorption. Wang et al. [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e] proposed a new Kagome honeycomb structure with triangular substructures. After construction and comparison of experimental and numerical results, they showed increased specific energy absorption compared to the original state.\u003c/p\u003e \u003cp\u003eFurthermore, the structure's strength and specific energy absorption in concentrated and [\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e] distributed loadings can be improved by constructing structures with composite materials [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e], especially by injecting PU foam into lattice structure cells [\u003cspan additionalcitationids=\"CR38 CR39 CR40 CR41 CR42\" citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e], due to the foam's crushability properties and lightweight. Several industries, including aerospace, automotive, and construction, always seek lighter lattice structures with better energy absorption properties and more desirable crashworthiness. In this regard, researchers offer various solutions to increase specific energy absorption capability and crashworthiness properties. One of these solutions is to draw inspiration from structures that already exist in nature for designing new geometries. A \u003cem\u003enew gradient honeycomb structure inspired by the structure of sunflowers\u003c/em\u003e is introduced in the present research. This structure is characterized by cell sizes decreasing radially towards the center. This new design is predicted to increase crashworthiness properties and energy absorption.\u003c/p\u003e"},{"header":"2. Empirical Study","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Modeling the Geometry of Specimens\u003c/h2\u003e \u003cp\u003eIn the sunflower-inspired honeycomb structure, the size of hexagonal cells decreases radially towards the center. In this pattern, as the cell size changes, the lengths of the sides and angles of the hexagon also change. The sides with index Y are aligned with the line from the center, and the connection points between two symmetrical X lines and symmetrical Y lines are located on the radial line from the center. Additionally, lines with similar labels are in symmetry with the red dotted line. The dimensions of the first-order cells are defined as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eX\u003csub\u003e1\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;8.7mm\u003c/p\u003e \u003cp\u003eY\u003csub\u003e1\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;8.7mm\u003c/p\u003e \u003cp\u003eα\u0026thinsp;=\u0026thinsp;24˚\u003c/p\u003e \u003cp\u003eβ\u0026thinsp;=\u0026thinsp;120˚\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eSimilarly, the first-order structure is formed by repeating hexagonal unit cells in the circumferential direction. In the gradient structure, a decrease in radius leads to an increase in order number. For the next order, the dimensions of the cells decrease according to formulas 1 and 2 until they reach the center.\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:{x}_{n}={x}_{n-1}\\times\\:0.7\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:n\\ge\\:2$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:{y}_{n}={y}_{n-1}\\times\\:0.7\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:n\\ge\\:2$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eFor the quasi-static compression test, specimens were designed as squares with dimensions of 70\u0026times;70\u0026times;70 mm, as shown in the geometry in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. Also, a plate with a wall thickness of 0.8 mm was added to distribute pressure uniformly at the contact point between the specimen and the compression machine jaws and to connect the cut cells at the top and bottom of the structure.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eA conventional honeycomb structure with geometric specifications and dimensions is introduced to compare the performance of the sunflower-inspired honeycomb structure, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Fabricating the Specimens\u003c/h2\u003e \u003cp\u003eIn this stage, the conventional honeycomb and the sunflower-inspired honeycomb structures were modeled in CATIA software, as seen in Figs.\u0026nbsp;\u0026lt;link rid=\"fig4\"\u0026gt;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u0026lt;/link\u0026gt;\u003c/span\u003e-a and \u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e-b, respectively. Subsequently, models were initially prepared in the specialized 3D Simplify software with identical settings for each sample according to Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, and then the 3D models were manufactured using a Hypercube 3D printer with PLA\u0026thinsp;+\u0026thinsp;material, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e-c. Additive manufacturing using the FDM method is considered a new technology in manufacturing and production. In this method, thermoplastic polylactic acid is melted through heating. Then, the molten material is placed layer by layer through the nozzle on a defined path to produce the desired part. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e-c, the parts were built horizontally to prevent the construction of supports. Moreover, to examine the mechanical properties of PLA\u0026thinsp;+\u0026thinsp;materials, three dumbbell-shaped specimens were made according to ASTM D368 standard with the geometry shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e-a, using identical settings on the 3D printer, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e-b. Subsequently, the specimens were subjected to uniaxial tension with a Zwick Roll-Z100 machine, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e-c, and the results were presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e and Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e3D printer parameters\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3D printer Parameters\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003equantity\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLayer height (mm)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNozzle temperature (c)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e210\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBed temperature (c)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e50\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePrint speed (mm/s)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e33.4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNozzle diameter (mm)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFilament diameter (mm)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.75\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eMechanical properties of PLA+\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMaterial\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDensity (g/cm\u003csup\u003e3\u003c/sup\u003e)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eYoung\u0026rsquo;s Modulus\u003c/p\u003e \u003cp\u003e(GPa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eYield stress (MPa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eUltimate stress (MPa)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePla+\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.71\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e33.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e37\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3 Manufacturing and Injection of Foam\u003c/h2\u003e \u003cp\u003eTwo-component polyurethane foam is injected into the hollow space of the honeycomb structure to increase energy absorption. Given the foam\u0026rsquo;s low density and properties, it is predicted that by injecting it into the honeycomb structure, the specific energy absorption and compressive tolerance will increase in the uniaxial quasi-static compression test results. In this section, after manufacturing the honeycomb structures using a 3D printer, it is time to prepare the two-component polyurethane foam. First, two components produced by the Pars Chemical Company, namely Polyol R and F 4109 and ISO PM 200, were mixed in a 1:1 ratio and injected into the hollow space of the lattice structure. After a few seconds, these two components react, and the volume expansion process and foaming begin, filling the hollow space between the cells. After final drying, excess foam is removed, and the foam-filled cubic specimen is prepared. Additionally, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e, two cubic foam-bearing specimens were made to examine mechanical properties along with other specimens. They were subjected to quasi-static compression, and the results are presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e and Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eMechanical properties of polyurethane foam\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMaterial\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDensity (Kg/m\u003csup\u003e3\u003c/sup\u003e)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eEA (J)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSEA (KJ/Kg)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePU Foam\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e57.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e53\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.7\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThree specimens of each structure (12 specimens in total) were made, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e. Also, the weights of the specimens were measured using a scale with a 1-gram accuracy, and the specimens were coded with unique abbreviations, as shown in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eSpecimen coding\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSpecimens code\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDescription\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eLoading\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eWeight (g)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHHEI\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eH\u003c/span\u003eexagon \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eH\u003c/span\u003eoneycomb \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eE\u003c/span\u003empty\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eI\u003c/span\u003en plane\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e92\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHHFI\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eH\u003c/span\u003eexagon \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eH\u003c/span\u003eoneycomb \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eF\u003c/span\u003eoam Filled\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eI\u003c/span\u003en plane\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e117\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSHEI\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eS\u003c/span\u003eunflower \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eH\u003c/span\u003eoneycomb \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eE\u003c/span\u003empty\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eI\u003c/span\u003en plane\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e82\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSHFI\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eS\u003c/span\u003eunflower \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eH\u003c/span\u003eoneycomb \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eF\u003c/span\u003eoam Filled\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eI\u003c/span\u003en plane\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e110\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e2.4 Quasi-Static compression Test\u003c/h2\u003e \u003cp\u003eQuasi-static compression tests were conducted on 12 honeycomb specimens in the in-plane direction using the Zwick Roll-Z100 testing machine at room temperature, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e-a. As seen in Figs.\u0026nbsp;\u0026lt;link rid=\"fig10\"\u0026gt;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u0026lt;/link\u0026gt;\u003c/span\u003e-b and \u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e-c, each specimen was placed on the machine's fixed platform. At this stage, the movable jaw moves downward at a constant speed of 5 mm/min to satisfy quasi-static conditions, compressing and crushing the honeycomb specimen until full compaction. This machine is connected to a computer that outputs the results through force-displacement curves.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"3. Results and Discussion","content":"\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e3.1 In-Plane Crashworthiness Evaluation\u003c/h2\u003e \u003cp\u003eWhen structures are subjected to quasi-static compression, they initially experience reversible, elastic deformation [\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e]. As more force is applied, the structure enters the plastic and irreversible phase, and structural collapse and failure begin to occur [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. This leads to a significant drop in the force-displacement curve. In the plastic phase, the collapse of the cells occurs gradually, and the force-displacement curve continues to fluctuate due to the crushing of the structure until full compaction is achieved. After complete compaction, the slope of the curve tends toward infinity, indicating that the structure's energy absorption capacity is exhausted. The area under the force-displacement curve before the final compaction is referred to as the absorbed energy by the honeycomb structure and is calculated using Eq.\u0026nbsp;\u003cspan refid=\"Equ3\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:EA={\\int\\:}_{0}^{d}f\\left(x\\right)dx$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn industrial applications such as the aviation industry, the weight of the lattice structure is important. The specific energy absorption parameter [\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e] is defined in Eq.\u0026nbsp;\u003cspan refid=\"Equ4\" class=\"InternalRef\"\u003e4\u003c/span\u003e based on the force-displacement curve, where the weight factor is dimensionless and can be considered a correct criterion for evaluating the energy absorption of the structure per unit mass.\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\:SEA=\\frac{EA}{m}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere in Eq.\u0026nbsp;\u003cspan refid=\"Equ4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, EA is the amount of energy absorption, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:m\\)\u003c/span\u003e\u003c/span\u003e is the weight of the honeycomb structure. Additionally, the parameter defining the crushing force efficiency (CFE) is a critical feature for comparing and assessing energy-absorbing structures through crushing, expressed by the formula 5.\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$$\\:CFE=\\frac{MCF}{PCF}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn Formula 5, the crushing force efficiency (CFE) has a direct relationship with the mean crushing force (MCF) and an inverse relationship with the first peak force (PCF). Eq.\u0026nbsp;\u003cspan refid=\"Equ6\" class=\"InternalRef\"\u003e6\u003c/span\u003e is used to get MCF from the force-displacement curve. The force-displacement curve is used to obtain the PCF directly.\u003cdiv id=\"Equ6\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ6\" name=\"EquationSource\"\u003e\n$$\\:MCF=\\frac{1}{d}{\\int\\:}_{0}^{d}f\\left(x\\right)dx=\\frac{EA}{d}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e6\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eCompressive loading was applied to specimens up to approximately 80% of their initial height. The curves show that the structures could absorb energy up to an average compression of 46 mm, after which the curve tends toward infinity with a sharp slope. In the calculations, this value is considered as the effective length.\u003c/p\u003e \u003cp\u003eCurves 11 to 14 indicate that the force in SH structures increases with displacement due to the structure's gradient nature. The specific energy absorption and crushing force efficiency depend on the size of the hexagonal cells and their resistance to crushing [\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e, \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e]. These structures have the cells arranged radially from large to small. The first-order largest cells collapse first and experience a lower peak force than those in a uniform and conventional structure. After the first-order cells collapse, the remaining order cells also collapse, producing a stepwise increase in force in the force-displacement curve. The first peak force is reduced, the average crushing force is increased, the crushing force efficiency is significantly improved, and the crashworthiness is greatly enhanced. The gradient nature of the cell sizes and this stepwise collapse leads to a positive slope in the force-displacement curve, thus increasing the absorbed energy. As shown in Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e, the superiority of the gradient structure in specific energy absorption is confirmed due to the gradient structure\u0026rsquo;s lower weight and higher energy absorption compared to the conventional structure.\u003c/p\u003e \u003cp\u003eThe comparison of crashworthiness parameters indicates that the in-plane loading of the SHEI structure has 35% more specific energy absorption than the HHEI structure, and the SHFI structure has 32% more specific energy absorption than the HHFI structure. In addition, the 143% and 118% increase in crushing force efficiency of the SHEI and SHFI structures, respectively, compared to the corresponding conventional honeycomb structures, demonstrate the excellent performance of the proposed structure. Furthermore, a 20% increase in SHEI structure and a 25% increase in the SHFI structure in terms of energy absorption, and a 20% increase in the SHEI and a 25% increase in the SHFI in terms of mean crushing force compared to their corresponding counterparts in conventional honeycomb, completes the excellent performance of the proposed structure in crashworthiness and energy absorption. Moreover, the presence of foam in the structures causes an increase in crashworthiness parameters. SHFI and HHFI structures exhibit 41% and 43% increase in specific energy absorption, 89% and 82% increase in energy absorption and mean crushing force, and 10% and 23% increase in crushing force efficiency compared to SHEI and HHEI structures.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigures \u003cspan refid=\"Fig15\" class=\"InternalRef\"\u003e15\u003c/span\u003e and \u003cspan refid=\"Fig16\" class=\"InternalRef\"\u003e16\u003c/span\u003e illustrate the crushing behavior of SHEI and SHFI structures. As expected, in these structures, the first order of cells experiences collapse from top or bottom, with region I indicating the resistance of the first order. Subsequently, the walls aligned with the displacement direction apply pressure to the next order, causing the cells of the second order to begin collapsing, as shown by Region II. This process then repeats at the other side of the structure, and after the collapse of orders 1 and 2 from top and bottom, orders 3 and 4 also collapse following the same pattern, as shown in curves III and IV. The last region corresponds to the resistance of the 5th order and the central cell of the structure, which has the highest resistance among the gradient structures and is marked as curve V.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAccording to previous studies [\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e], the crushing pattern of conventional honeycomb cells under compressive loading varies at different speeds. In quasi-static loading, as shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig15\" class=\"InternalRef\"\u003e15\u003c/span\u003e and \u003cspan refid=\"Fig17\" class=\"InternalRef\"\u003e17\u003c/span\u003e, in HHEI and HHFI structures, the row of hexagonal cells first collapses diagonally [\u003cspan additionalcitationids=\"CR51\" citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e52\u003c/span\u003e]. Then, as expected [\u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e53\u003c/span\u003e], an X-shaped collapse pattern forms and progresses until complete compression of the cells. Notably, the peaks and troughs in Fig.\u0026nbsp;\u003cspan refid=\"Fig17\" class=\"InternalRef\"\u003e17\u003c/span\u003e, separated by dashed lines, correspond to the collapse of a diagonal row of cells in the conventional honeycomb structure during compressive loading. This indicates the compressive resistance of each row against crushing and plastic deformation. As shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig16\" class=\"InternalRef\"\u003e16\u003c/span\u003e and \u003cspan refid=\"Fig17\" class=\"InternalRef\"\u003e17\u003c/span\u003e, HHFI and SHFI structures have higher strength SHEI and HHEI structures, increasing the area under the curve, average crushing force, and energy absorption. This can be attributed to the presence of rigid polyurethane foam that increases the compressive resistance of cells against crushing by filling the hollow space between hexagonal cells. Considering the light weight of PU foam, it will also increase the specific energy absorption. Additionally, the curves of foam-filled structures exhibit less fluctuation than those without foam.\u003c/p\u003e \u003cp\u003eAs shown in Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e and Figs.\u0026nbsp;\u003cspan refid=\"Fig18\" class=\"InternalRef\"\u003e18\u003c/span\u003e to \u003cspan refid=\"Fig21\" class=\"InternalRef\"\u003e21\u003c/span\u003e, the SHFI structure exhibits the best performance in crashworthiness properties, particularly specific energy absorption. The HHEI structure offers the weakest performance. This highlights the beneficial effect of gradient design of cell sizes and polyurethane foam injection on the performance and efficiency of honeycomb structures. Furthermore, the polyurethane foam-filled gradient sunflower-inspired honeycomb structure has a special appeal for industries such as aerospace and marine, where the structure's weight is critical. It can be a good substitute for conventional honeycomb structures.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eParameters of crashworthiness\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSpecimens code\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eW (g)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eEA (J)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMCF (KN)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eCFE (%)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eSEA (KJ/Kg)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHHEI\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e92\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e216.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e4.69\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e83\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e2.35\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHHFI\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e117\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e394\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e8.56\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e102\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e3.37\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSHEI\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e82\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e260.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e5.65\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e202\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e3.17\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSHFI\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e110\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e491\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e10.67\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e222\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e4.46\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"4. Conclusion","content":"\u003cp\u003eThis research proposes a new gradient sunflower-inspired honeycomb structure where the size of hexagonal cells gradually decreases in the radial direction according to a certain gradient. The performance of this novel structure was analyzed and compared with the conventional honeycomb structure under in-plane loading conditions. An investigation was conducted on filling the hollow space between cells with rigid polyurethane foam in conventional honeycomb and sunflower-inspired honeycomb structures. The production of 12 specimens made from PLA\u0026thinsp;+\u0026thinsp;using an FDM 3D printer was carried out, followed by quasi-static loading tests. Similar behavior of sunflower-inspired and conventional honeycomb structures was observed under hollow and foam-filled conditions. Thanks to stepwise and controlled collapse mechanisms, the results demonstrated that the sunflower-inspired honeycomb structure exhibits a much higher influence on crashworthiness parameters compared to the conventional structure. The findings are highlighted below:\u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eThe sunflower-inspired honeycomb structure with a hollow core has a 35% higher SEA, a 20% higher EA, a 20% higher MCF, and a 143% higher CFE compared to the conventional honeycomb structure with a hollow core.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eThe PU foam-filled sunflower-inspired honeycomb structure has 32% SEA, 24% EA, 118% CFE, and 25% MCF higher than the PU foam-filled conventional honeycomb structure.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eRigid PU foam injection in the conventional honeycomb structure gives a 43% increase in SEA, 82% in EA, 82% in MCF, and 23% in CFE.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eRigid PU foam injection in the sunflower-shaped honeycomb structure results in a 41% increase in SEA, an 89% increase in EA, MCF, and a 10% increase in CFE.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e \u003cp\u003eThe findings revealed that the gradient design of hexagonal cell sizes and the application of PU foam in the hollow space of honeycomb structures are effective strategies for enhancing the crashworthiness properties of honeycomb structures. This study can serve as a reference for developing high-performance energy absorbers and provide high-capacity energy absorber solutions for various industries such as aerospace, automotive, and others.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003e5. Declaration of Competing Interest\u003c/h2\u003e \u003cp\u003eThe 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.\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003e6. Consent to participate\u003c/strong\u003e \u003cp\u003eAll authors participated in the research work reported in this paper.\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003e7. Consent to publication\u003c/strong\u003e \u003cp\u003eAll authors agreed to publish the findings of this research.\u003c/p\u003e \u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eHabib, F. 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Dynamic Performance and Crashworthiness Assessment of Honeycomb Reinforced Tubular Pipe in the Jacket Platform under Ship Collision. \u003cem\u003eJournal of Marine Science and Engineering\u003c/em\u003e, \u003cem\u003e10\u003c/em\u003e(9), 1194. https://doi.org/10.3390/jmse10091194\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":true,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"journal-of-the-brazilian-society-of-mechanical-sciences-and-engineering","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"bmse","sideBox":"Learn more about [Journal of the Brazilian Society of Mechanical Sciences and Engineering](http://link.springer.com/journal/40430)","snPcode":"40430","submissionUrl":"https://www.editorialmanager.com/bmse/default2.aspx","title":"Journal of the Brazilian Society of Mechanical Sciences and Engineering","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Sunflower, Honeycomb, Energy absorption, 3D printing, PU foam, Graded structure","lastPublishedDoi":"10.21203/rs.3.rs-5317681/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5317681/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study introduces a novel sunflower-inspired gradient structure where the size of hexagonal cells changes with a specific gradient in the radial direction. Subsequently, the crashworthiness and deformation performance of this structure were compared and analyzed with conventional honeycomb structures in both hollow and PU foam-filled states. In this research, specimens were first fabricated using additive manufacturing with PLA\u0026thinsp;+\u0026thinsp;material. After injecting polyurethane foam into the void spaces between cells, the specimens were subjected to quasi-static compressive loading in the in-plane direction at a 5 mm/min rate. The results showed that the sunflower-inspired honeycomb structure has significantly better crashworthiness and specific energy absorption properties than the conventional one. Based on these findings, it is concluded that the gradient design of cell sizes in the radial direction can lead to a 35% increase in specific energy absorption and a 20% increase in mean crushing force, along with a 143% improvement in crushing force efficiency, indicating enhanced performance in protective applications. Furthermore, it was demonstrated that the presence of foam can improve the performance of honeycomb structures. According to the results, foam-filled conventional honeycomb and sunflower-inspired honeycomb structures show increases of 43% and 41% in specific energy absorption, 82% and 89% in energy absorption and mean crushing force, and 23% and 10% in crushing force efficiency, respectively. The results indicate that the gradient design of cell sizes in the radial direction and the injection of PU foam into lattice structures can serve as a reference for designing energy absorbers with high-crashworthiness properties for various industries.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e","manuscriptTitle":"Introduction of a Novel Sunflower-Inspired Honeycomb Structure with Enhanced Energy Absorption Capacity under In-Plane Loading","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-11-29 15:19:47","doi":"10.21203/rs.3.rs-5317681/v1","editorialEvents":[{"type":"communityComments","content":1},{"type":"reviewerAgreed","content":"","date":"2024-11-13T04:59:20+00:00","index":0,"fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-11-12T21:46:07+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-11-01T10:53:44+00:00","index":"","fulltext":""},{"type":"submitted","content":"Journal of the Brazilian Society of Mechanical Sciences and Engineering","date":"2024-10-28T02:59:59+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"journal-of-the-brazilian-society-of-mechanical-sciences-and-engineering","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"bmse","sideBox":"Learn more about [Journal of the Brazilian Society of Mechanical Sciences and Engineering](http://link.springer.com/journal/40430)","snPcode":"40430","submissionUrl":"https://www.editorialmanager.com/bmse/default2.aspx","title":"Journal of the Brazilian Society of Mechanical Sciences and Engineering","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"fb6f3721-fb93-43ec-8980-de3b7952c0c3","owner":[],"postedDate":"November 29th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2025-05-26T16:05:29+00:00","versionOfRecord":{"articleIdentity":"rs-5317681","link":"https://doi.org/10.1007/s40430-025-05634-6","journal":{"identity":"journal-of-the-brazilian-society-of-mechanical-sciences-and-engineering","isVorOnly":false,"title":"Journal of the Brazilian Society of Mechanical Sciences and Engineering"},"publishedOn":"2025-05-20 15:57:27","publishedOnDateReadable":"May 20th, 2025"},"versionCreatedAt":"2024-11-29 15:19:47","video":"","vorDoi":"10.1007/s40430-025-05634-6","vorDoiUrl":"https://doi.org/10.1007/s40430-025-05634-6","workflowStages":[]},"version":"v1","identity":"rs-5317681","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5317681","identity":"rs-5317681","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}