In-plane mechanical properties and energy absorption of non-uniform variable-thickness honeycomb structures

Abstract

To address the high energy demands in aerospace protective systems, this study proposes a bioinspired nonuniform variable-thickness honeycomb (NVTH) structure derived from human femur morphology, aiming to enhance energy absorption beyond conventional hexagonal honeycombs. A mechanical model integrating the upper bound theorem of plastic mechanics and virtual work principle was developed to analyze NVTH’s structural behavior. Finite element simulations systematically evaluated deformation modes, stress-strain responses, load-bearing capacity, and energy absorption characteristics. Key findings reveal that NVTH achieves 26.26% greater energy absorption than standard hexagonal honeycombs and 25.04% improvement over traditional negative Poisson’s ratio (NPR) configurations. The thickness-gradient design enhances buckling resistance by 23.33% compared to uniform counterparts, while exhibiting NPR properties and multi-stage collapse mechanisms under quasi-static compression. Experimental validation confirms the structure’s synergistic performance enhancements through controlled material redistribution. The proposed methodology demonstrates extensibility to diverse metamaterial architectures, including NPR variants, offering a generalized framework for optimizing energy-absorbing structures in advanced engineering applications. This biomimetic approach bridges anatomical efficiency with engineered material systems, establishing new pathways for lightweight, high-performance protective solutions in aerospace and related fields.

Keywords

honeycomb structure / variable-thickness design / mechanical property / energy absorption performance / quasi-static compression

References

[1] Zhang Q-c, Yang X-h, Li P, et al.. Bioinspired engineering of honeycomb structure – Using nature to inspire human innovation. Progress in Materials Science, 2015, 74: 332-400 J]

[2] Qi C, Jiang F, Yang S. Advanced honeycomb designs for improving mechanical properties: A review. Composites Part B: Engineering, 2021, 227: 109393 J]

[3] Yang W-z, Dong S-c, Zhu X-d, et al.. Superior energy absorption performance of layered aux-hex honeycomb filled tubes. International Journal of Mechanical Sciences, 2022, 234: 107702 J]

[4] Mohammadi H, Ahmad Z, Petrů M, et al.. An insight from nature: Honeycomb pattern in advanced structural design for impact energy absorption. Journal of Materials Research and Technology, 2023, 22: 2862-2887 J]

[5] Sang L, Han S-f, Peng X-s, et al.. Development of 3D-printed basalt fiber reinforced thermoplastic honeycombs with enhanced compressive mechanical properties. Composites Part A: Applied Science and Manufacturing, 2019, 125: 105518 J]

[6] Wei X-y, Jiao Y-h, Wang Y, et al.. Surface matching design of carbon fiber composite honeycomb. Journal of the Mechanics and Physics of Solids, 2024, 193: 105890 J]

[7] Brodeur S, Dastous J B. Design and testing of an arc resistant power transformer tank. IEEE Transactions on Power Delivery, 2020, 35(2): 699-706 J]

[8] Zeng C-j, Liu L-w, Bian W-f, et al.. Compression behavior and energy absorption of 3D printed continuous fiber reinforced composite honeycomb structures with shape memory effects. Additive Manufacturing, 2021, 38: 101842 J]

[9] Andrew J J, Alhashmi H, Schiffer A, et al.. Energy absorption and self-sensing performance of 3D printed CF/PEEK cellular composites. Materials & Design, 2021, 208: 109863 J]

[10] Hosen A, Hossain M F, Rana M S, et al.. Investigation of flexural strength of jute fiber based circular type honeycomb sandwich panel: An experimental and numerical approach. Results in Materials, 2023, 19: 100423 J]

[11] Hu L L, He X L, Wu G P, et al.. Dynamic crushing of the circular-celled honeycombs under out-of-plane impact. International Journal of Impact Engineering, 2015, 75: 150-161 J]

[12] Zhang Y, Xu X, Fang J-g, et al.. Load characteristics of triangular honeycomb structures with self-similar hierarchical features. Engineering Structures, 2022, 257: 114114 J]

[13] Liu Y, Zhang X-c. The influence of cell microtopology on the in-plane dynamic crushing of honeycombs. International Journal of Impact Engineering, 2009, 36(1): 98-109 J]

[14] Li M, Deng Z-q, Guo H-w, et al.. Optimizing crashworthiness design of square honeycomb structure. Journal of Central South University, 2014, 21(3): 912-919 J]

[15] Wang Z-g, Deng J-j, Liu K, et al.. Hybrid hierarchical square honeycomb with widely tailorable effective in-plane elastic modulus. Thin-Walled Structures, 2022, 171: 108816 J]

[16] Shahverdi Moghaddam H, Keshavanarayana S R, Yang C, et al.. Anisotropic hyperelastic constitutive modeling of in-plane finite deformation responses of commercial composite hexagonal honeycombs. Journal of Sandwich Structures & Materials, 2022, 24(1): 5-34 J]

[17] Wang Y-l, Yu Y, Wang C-y, et al.. On the out-of-plane ballistic performances of hexagonal, reentrant, square, triangular and circular honeycomb panels. International Journal of Mechanical Sciences, 2020, 173: 105402 J]

[18] Wang Z-g, Lei Z-p, Li Z-d, et al.. Mechanical reinforcement mechanism of a hierarchical Kagome honeycomb. Thin-Walled Structures, 2021, 167: 108235 J]

[19] Yan X-n, Wang R, Chen Y-x, et al.. Influence of size of honeycomb structure on Poisson’s ratio and energy absorption. Materials for Mechanical Engineering, 2021, 45(3): 71-75[J]

[20] Choudhry N K, Panda B, Kumar S. In-plane energy absorption characteristics of a modified re-entrant auxetic structure fabricated via 3D printing. Composites Part B: Engineering, 2022, 228: 109437 J]

[21] Xiong J, Zhang M, Stocchi A, et al.. Mechanical behaviors of carbon fiber composite sandwich columns with three dimensional honeycomb cores under inplane compression. Composites Part B: Engineering, 2014, 60: 350-358 J]

[22] Gibson L J, Ashby M F, Schajer G S, et al.. The mechanics of two-dimensional cellular materials. Proceedings of the Royal Society of London A Mathematical and Physical Sciences, 1982, 382(1782): 25-42 J]

[23] Tankasala H, Deshpande V S, Fleck N A. The inplane elastic-plastic response of an incompressible, filled hexagonal honeycomb. Journal of the Mechanics and Physics of Solids, 2021, 155: 104536 J]

[24] Carlsson J, Li K, Deshpande V S, et al.. The in-plane, elastic-plastic response of a filled hexagonal honeycomb at finite strain. Journal of the Mechanics and Physics of Solids, 2022, 168: 105047 J]

[25] Qi C, Jiang F, Remennikov A, et al.. Quasi-static crushing behavior of novel re-entrant circular auxetic honeycombs. Composites Part B: Engineering, 2020, 197: 108117 J]

[26] Sun Y-t, Pugno N M. In plane stiffness of multifunctional hierarchical honeycombs with negative Poisson’s ratio sub-structures. Composite Structures, 2013, 106: 681-689 J]

[27] Liu Y-z, Zhao C-f, Xu C, et al.. Shape recovery effect and energy absorption of reusable honeycomb structures. Composite Structures, 2025, 352: 118708 J]

[28] Wang S, Liu H-t. Quasi-static compression response of a novel multi-step auxetic honeycomb with tunable transition strain. Aerospace Science and Technology, 2024, 155: 109730 J]

[29] Ou Y-x, Yan S-l, Wen P. In-plane impact dynamics analysis of re-entrant honeycomb with variable cross-section. Computer Modeling in Engineering & Sciences, 2021, 127(1): 209-222 J]

[30] Ha N S, Lu G-x. A review of recent research on bio-inspired structures and materials for energy absorption applications. Composites Part B: Engineering, 2020, 181: 107496 J]

[31] Fang J-g, Sun G-y, Qiu N, et al.. On hierarchical honeycombs under out-of-plane crushing. International Journal of Solids and Structures, 2018, 135: 1-13 J]

[32] Xie Y, Liu X-w, Wang Z-d, et al.. Performance enhancement of foam-filled parallel gradient and uniform honeycombs. Composite Structures, 2026, 379: 119937 J]

[33] Yan C-g, Guo J-x, Zhang P, et al.. Prevention of oil-immersed equipment rupture due to arcing faults based on metal foam. IEEE Transactions on Power Delivery, 2023, 38(4): 2965-2968 J]

[34] Zhang Z, Wang C, Wang Y, et al.. The topology and fault ride-through strategy of a novel fault current transfer consumption sub-module. High Voltage Engineering, 2023, 49(4): 1600-1610[J]

[35] Ding K, Jain M, Kalácska S, et al.. Enhanced energy absorption in 3D printed copper micro-honeycombs. Materials & Design, 2025, 260: 115090 J]

[36] Su Y-s, Chu H, Liu J, et al.. In-plane compressive performance of 3d-printed continuously carbon-fiber-reinforced hierarchical honeycombs composite. Composites Communications, 2026, 62: 102663 J]

[37] Li Z-d, Wang Z-g, Wang X-x, et al.. Bending behavior of sandwich beam with tailored hierarchical honeycomb cores. Thin-Walled Structures, 2020, 157: 107001 J]

[38] Wang Z-g, Deng J-j, He K-n, et al.. Out-of-plane crushing behavior of hybrid hierarchical square honeycombs. Thin-Walled Structures, 2022, 181: 110051 J]

[39] Cui Y J, Zhou Q, Xu Z H, et al.. Structure failure and strength evaluation of honeycomb-based sandwich composites under variable hydro-thermal-mechanical load. Composite Structures, 2025, 354: 118763 J]

[40] Su Y-p, Shi S, Wang C, et al.. Spider silk-inspired tough materials: Multi-pathway synthesis, advanced processing, and functional applications. Nano Today, 2024, 55: 102188 J]

[41] Chen S-m, Zhang Z-b, Gao H-l, et al.. Bottom-up film-to-bulk assembly toward bioinspired bulk structural nanocomposites. Advanced Materials, 2024, 36(23): e2313443 J]

[42] Xiao Y-y, Yin H-f, Fang H-b, et al.. Crashworthiness design of horsetail-bionic thin-walled structures under axial dynamic loading. International Journal of Mechanics and Materials in Design, 2016, 12(4): 563-576 J]

[43] Xiang J-w, Du J-x. Energy absorption characteristics of bio-inspired honeycomb structure under axial impact loading. Materials Science and Engineering: A, 2017, 696: 283-289 J]

[44] He Q, Feng J, Chen Y-j, et al.. Mechanical properties of spider-web hierarchical honeycombs subjected to out-of-plane impact loading. Journal of Sandwich Structures & Materials, 2020, 22(3): 771-796 J]

[45] Ha N S, Pham T M, Tran T T, et al.. Mechanical properties and energy absorption of bio-inspired hierarchical circular honeycomb. Composites Part B: Engineering, 2022, 236: 109818 J]

[46] Yu P-s, Liu Z-f, Li S-q. Design and impact resistance analysis of a new biomimetic honeycomb structure. Chinese Journal of High Pressure Physics, 2022, 36(1): 149-160[J]

[47] Pehlivan L, Baykasoğlu C. In-plane crushing behavior and energy absorption of CFRP honeycombs with different core topologies. Thin-Walled Structures, 2024, 205: 112566 J]

[48] Liu N, Mehreganian N, Sareh P. Never better than 5/6: The fundamental limit of energy absorption efficiency for negative-stiffness curved-beam honeycombs. Materials & Design, 2024, 243: 113024 J]

[49] LI Xiang, LI Ning-chuang, WU Hai-huan, et al. Crashworthiness of a novel bionic quasi-honeycomb structure based on variable cross-section design [J]. Acta Materiae Composiae Sinica, 2024: 283–289. DOI: https://doi.org/10.13801/j.cnki.fhclxb.20240813.001.(in Chinese)

[50] Liang H-y, Hao W-q, Xue G-l, et al.. Parametric design strategy of a novel self-similar hierarchical honeycomb for multi-stage energy absorption demand. International Journal of Mechanical Sciences, 2022, 217: 107029 J]

RIGHTS & PERMISSIONS

Central South University