Koch Hierarchical Honeycomb: A Fractal-Based Design for Enhanced Mechanical Performance and Energy Absorption
Abstract
:1. Introduction
2. Design and Methods
2.1. Conceptual Fractal Design
2.2. Fabrication
2.3. Quasi-Static Compression Test
2.4. Finite Element Model
3. Results
3.1. Experimental Results
3.2. Comparison with Regular Honeycombs
4. Discussions
4.1. Effect of Hierarchical Order
4.2. Topology of Underlying Cell
5. Conclusions
- (a)
- The improvement in energy absorption performance of the structure by the Koch hierarchy is significant. With equal mass, the first-order Koch hierarchy honeycomb KH1 has 41.33% more platform force and 27.52% more TEA compared to the normal honeycomb KH0. Moreover, the CFE of KH1 is 2.5 times that of KH0. This is because by increasing the number of folded edges, the structure can undergo more folding after compression, thereby achieving better mechanical performance;
- (b)
- The increase in the hierarchical order can bring the enhancement of energy absorption, but this enhancement effect is limited. When the order number reaches 3, the shortest side edge length is extremely small. The structure shows large flexure during the crushing process and cannot form regular folds. For KH0–KH3, Pm, CFE, and SEA all have the same trend. It grows from order 0 to 2, reaches a maximum at KH2, and then starts to decrease from order 2 to order 3;
- (c)
- For the non-hexagonal base cell element, the Koch hierarchy still has a significant enhancement effect on specific energy absorption. Compared with KT0, SEA was improved by 28.4% for KT1 and 42.3% for KT2. Compared with KS0, KS1 improved by 33.9%, and KS2 improved by 41.6%.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
- Chai, J.; Zhou, Y.; Zhou, X.; Wang, S.; Zhang, Z.G.; Liu, Z. Analysis on shock effect of China’s high-speed railway on aviation transport. Transp. Res. Part A Policy Pract. 2018, 108, 35–44. [Google Scholar] [CrossRef]
- He, W.; Liu, J.; Wang, S.; Xie, D. Low-velocity impact response and post-impact flexural behaviour of composite sandwich structures with corrugated cores. Compos. Struct. 2018, 189, 37–53. [Google Scholar] [CrossRef]
- Rodríguez-Ramírez, J.D.; Castanié, B.; Bouvet, C. Damage Mechanics Modelling of the shear nonlinear behavior of Nomex honeycomb core. Application to sandwich beams. Mech. Adv. Mater. Struct. 2020, 27, 80–89. [Google Scholar] [CrossRef]
- Zhu, X.; Chen, A.; Huang, Z.; Chen, Z.; Lin, Y.; Li, Y. Quasi-static compression response of the origami thin-walled structure. Thin-Walled Struct. 2023, 183, 110376. [Google Scholar] [CrossRef]
- Baykasoğlu, C.; Baykasoğlu, A.; Cetin, E. Multi-objective crashworthiness optimization of square aluminum tubes with functionally graded BCC lattice structure filler. Int. J. Crashworthiness 2023, 1–15. [Google Scholar] [CrossRef]
- Bao, L.; Miura, Y.; Kemmochi, K. Improving bending characteristics of FRP sandwich structures with reinforcement webs. Adv. Compos. Mater. 2018, 27, 221–233. [Google Scholar] [CrossRef]
- Grünewald, J.; Parlevliet, P.P.; Matschinski, A.; Altstädt, V. Mechanical performance of CF/PEEK–PEI foam core sandwich structures. J. Sandw. Struct. Mater. 2019, 21, 2680–2699. [Google Scholar] [CrossRef]
- Li, S.; Guo, X.; Liao, J.; Li, Q.; Sun, G. Crushing analysis and design optimization for foam-filled aluminum/CFRP hybrid tube against transverse impact. Compos. Part B Eng. 2020, 196, 108029. [Google Scholar] [CrossRef]
- Li, Z.; Wang, X.; Li, X.; Wang, Z.; Zhai, W. New Class of Multifunctional Bioinspired Microlattice with Excellent Sound Absorption, Damage Tolerance, and High Specific Strength. ACS Appl. Mater. Interfaces 2023, 15, 9940–9952. [Google Scholar] [CrossRef]
- Bhawe, A.K.; Shah, K.M.; Somani, S.; Shenoy, S.; Zuber, M.; Chethan, K.N. Static structural analysis of the effect of change in femoral head sizes used in Total Hip Arthroplasty using finite element method. Cogent Eng. 2022, 9, 2027080. [Google Scholar] [CrossRef]
- Wang, Y.J.; Zhang, Z.J.; Xue, X.M.; Zhang, L. Free vibration analysis of composite sandwich panels with hierarchical honeycomb sandwich core. Thin-Walled Struct. 2019, 145, 106425. [Google Scholar] [CrossRef]
- Li, S.; Li, X.; Wang, Z.; Wu, G.; Lu, G.; Zhao, L. Sandwich panels with layered graded aluminum honeycomb cores under blast loading. Compos. Struct. 2017, 173, 242–254. [Google Scholar] [CrossRef]
- Chang, C.; Wu, W.; Zhang, H.; Chen, J.; Xu, Y.; Lin, J.; Ding, L. Mechanical characteristics of superimposed 316L lattice structures under static and dynamic loading. Adv. Eng. Mater. 2021, 23, 2001536. [Google Scholar] [CrossRef]
- Zhang, X.; Zhang, J.; Chen, Z.; Li, Y. Investigations on deflection effect of a Z-shaped grillage subjected to an obliquely penetrating ogive-nose projectile. Thin-Walled Struct. 2023, 183, 110339. [Google Scholar] [CrossRef]
- Kotzem, D.; Gerdes, L.; Walther, F. Microstructure and strain rate-dependent deformation behavior of PBF-EB Ti6Al4V lattice structures. Mater. Test. 2021, 63, 529–536. [Google Scholar] [CrossRef]
- Xiao, L.; Song, W. Additively-manufactured functionally graded Ti-6Al-4V lattice structures with high strength under static and dynamic loading: Experiments. Int. J. Impact Eng. 2018, 111, 255–272. [Google Scholar] [CrossRef]
- Li, Z.; Li, X.; Wang, Z.; Zhai, W. Multifunctional sound-absorbing and mechanical metamaterials via a decoupled mechanism design approach. Mater. Horiz. 2023, 10, 75–87. [Google Scholar] [CrossRef] [PubMed]
- Wu, Y.; Sun, L.; Yang, P.; Fang, J.; Li, W. Energy absorption of additively manufactured functionally bi-graded thickness honeycombs subjected to axial loads. Thin-Walled Struct. 2021, 164, 107810. [Google Scholar] [CrossRef]
- Li, Z.; Yang, Q.; Fang, R.; Chen, W.; Hao, H. Crushing performances of Kirigami modified honeycomb structure in three axial directions. Thin-Walled Struct. 2021, 160, 107365. [Google Scholar] [CrossRef]
- Pal, N.; Dutta, G.; Kharashi, K.; Murray, E.P. Investigation of an Impedimetric LaSrMnO3-Au/Y2O3-ZrO2-Al2O3 Composite NOx Sensor. Materials 2022, 15, 1165. [Google Scholar] [CrossRef]
- Sala, R.; Regondi, S.; Graziosi, S.; Pugliese, R. Insights into the printing parameters and characterization of thermoplastic polyurethane soft triply periodic minimal surface and honeycomb lattices for broadening material extrusion applicability. Addit. Manuf. 2022, 58, 102976. [Google Scholar] [CrossRef]
- Chen, X.; Chen, L.; Lu, Y. Imperfection sensitivity of nonlinear primary resonance behavior in bi-directional functionally graded porous material beam. Compos. Struct. 2021, 271, 114142. [Google Scholar] [CrossRef]
- Zhang, C.L.; Ba, S.B.; Zhao, Z.F.; Li, L.; Tang, H.S.; Wang, X.L. Energy absorption characteristics of novel bio-inspired hierarchical anti-tetrachiral structures. Compos. Struct. 2023, 116860, 0263–8223. [Google Scholar]
- Liu, R.; Yao, G.; Gao, K.; Xu, Z.; Yang, Y.; Guo, X.; Yu, Z.; Zhang, Z.; Han, C. Study on mechanical properties of lattice structures strengthened by synergistic hierarchical arrangement. Compos. Struct. 2023, 304, 116304. [Google Scholar] [CrossRef]
- Zhou, J.; Dong, C.; Chen, B.; Qin, R.; Li, D. Out-of-plane crushing performances of cell-based hierarchical honeycombs based on the evaluation criteria for ideal energy absorption. Thin-Walled Struct. 2023, 182, 110246. [Google Scholar] [CrossRef]
- Keshwala, U.; Rawat, S.; Ray, K. Honeycomb shaped fractal antenna with defected ground structure for UWB applications. In Proceedings of the 2019 6th International Conference on Signal Processing and Integrated Networks (SPIN), Noida, India, 7–8 March 2019; pp. 341–345. [Google Scholar]
- Liu, H.; Zhang, E.T.; Ng, B.F. In-plane dynamic crushing of a novel honeycomb with functionally graded fractal self-similarity. Compos. Struct. 2021, 270, 114106. [Google Scholar] [CrossRef]
- Wang, J.; Zhang, Y.; He, N.; Wang, C.H. Crashworthiness behavior of Koch fractal structures. Mater. Des. 2018, 144, 229–244. [Google Scholar] [CrossRef]
- Zhang, Y.; Wang, J.; Wang, C.; Zeng, Y.; Chen, T. Crashworthiness of bionic fractal hierarchical structures. Mater. Des. 2018, 158, 147–159. [Google Scholar] [CrossRef]
- Li, Z.; Shen, L.; Wei, K.; Wang, Z. Compressive behaviors of fractal-like honeycombs with different array configurations under low velocity impact loading. Thin-Walled Struct. 2021, 163, 107759. [Google Scholar] [CrossRef]
- Cetin, E.; Baykasoğlu, C. Crashworthiness of graded lattice structure filled thin-walled tubes under multiple impact loadings. Thin-Walled Struct. 2020, 154, 106849. [Google Scholar] [CrossRef]
- Li, Z.; Zhai, W.; Li, X.; Yu, X.; Guo, Z.; Wang, Z. Additively manufactured dual-functional metamaterials with customisable mechanical and sound-absorbing properties. Virtual Phys. Prototyp. 2022, 17, 864–880. [Google Scholar] [CrossRef]
- Tao, Y.; Li, W.; Cheng, T.; Wang, Z.; Chen, L.; Pei, Y.; Fang, D. Out-of-plane dynamic crushing behavior of joint-based hierarchical honeycombs. J. Sandw. Struct. Mater. 2021, 23, 2832–2855. [Google Scholar] [CrossRef]
- Li, Z.; Wang, Z.; Guo, Z.; Wang, X.; Liang, X. Ultra-broadband sound absorption of a hierarchical acoustic metamaterial at high temperatures. Appl. Phys. Lett. 2021, 118, 161903. [Google Scholar] [CrossRef]
- Cetin, E.; Baykasoğlu, C. Energy absorption of thin-walled tubes enhanced by lattice structures. Int. J. Mech. Sci. 2019, 157, 471–484. [Google Scholar] [CrossRef]
- An, L.Q.; Zhang, X.C.; Wu, H.X.; Jiang, W.Q. In-plane dynamic crushing and energy absorption capacity of self-similar hierarchical honeycombs. Adv. Mech. Eng. 2017, 9, 1687814017703896. [Google Scholar] [CrossRef]
- He, Q.; Feng, J.; Zhou, H. A numerical study on the in-plane dynamic crushing of self-similar hierarchical honeycombs. Mech. Mater. 2019, 138, 103151. [Google Scholar] [CrossRef]
- Cetin, E.; Baykasoğlu, A.; Erdin, M.E.; Baykasoğlu, C. Experimental investigation of the axial crushing behavior of aluminum/CFRP hybrid tubes with circular-hole triggering mechanism. Thin-Walled Struct. 2023, 182, 110321. [Google Scholar] [CrossRef]
- Li, Z.; Li, X.; Chua, J.W.; Lim, C.H.; Yu, X.; Wang, Z.; Zhai, W. Architected lightweight, sound-absorbing, and mechanically efficient microlattice metamaterials by digital light processing 3D printing. Virtual Phys. Prototyp. 2023, 18, e2166851. [Google Scholar] [CrossRef]
- Zhang, D.; Fei, Q.; Jiang, D.; Li, Y. Numerical and analytical investigation on crushing of fractal-like honeycombs with self-similar hierarchy. Compos. Struct. 2018, 192, 289–299. [Google Scholar] [CrossRef]
- Zerbst, U.; Bruno, G.; Buffiere, J.Y.; Wegener, T.; Niendorf, T.; Wu, T.; Zhang, X.; Kashaev, N.; Meneghetti, G.; Hrabe, N.; et al. Damage tolerant design of additively manufactured metallic components subjected to cyclic loading: State of the art and challenges. Prog. Mater. Sci. 2021, 121, 100786. [Google Scholar] [CrossRef] [PubMed]
- Laquai, R.; Müller, B.R.; Kasperovich, G.; Requena, G.; Haubrich, J.; Bruno, G. Classification of defect types in SLM Ti-6Al-V4 by X-ray refraction topography. Mater. Perform. Charact. (MPC) 2020, 9, 82–93. [Google Scholar] [CrossRef]
- Tunay, M.; Baykasoğlu, C.; Akyildiz, O.; To, A.C. A fully coupled thermal–microstructural–mechanical finite element process model for directed energy deposition additive manufacturing of Ti–6Al–4V. Sci. Technol. Weld. Join. 2023, 28, 118–127. [Google Scholar] [CrossRef]
- KN, C.; Bhat, N.S.; Zuber, M.; Shenoy, B.S. Evolution of different designs and wear studies in total hip prosthesis using finite element analysis: A review. Cogent Eng. 2022, 9, 2027081. [Google Scholar]
- Sienkiewicz, J.; Płatek, P.; Jiang, F.; Sun, X.; Rusinek, A. Investigations on the mechanical response of gradient lattice structures manufactured via SLM. Metals 2020, 10, 213. [Google Scholar] [CrossRef]
- Zhong, T.; He, K.; Li, H.; Yang, L. Mechanical properties of lightweight 316L stainless steel lattice structures fabricated by selective laser melting. Mater. Des. 2019, 181, 108076. [Google Scholar] [CrossRef]
- Li, X.; Lu, F.; Lin, Y.; Zhang, Y.; Chen, R. Influence of cell size effect on the vertical cutting of hexagonal thin-walled honeycombs by parallel blades. Thin-Walled Struct. 2020, 157, 107137. [Google Scholar] [CrossRef]
- Wang, Z.; Liu, J. Numerical and theoretical analysis of honeycomb structure filled with circular aluminum tubes subjected to axial compression. Compos. Part B Eng. 2019, 165, 626–635. [Google Scholar] [CrossRef]
ρ (kg·m−3) | Young’s Modulus (GPa) | Poisson’s Ratio | Yield Stress (MPa) | |
---|---|---|---|---|
316 L | 7980 | 200 | 0.33 | 308 |
ρ (kg·m−3) | Young’s Modulus (GPa) | Poisson’s Ratio | Yield Stress (MPa) | |
---|---|---|---|---|
5052-H18 | 2680 | 69.3 | 0.33 | 215 |
Peak Force (kN) | (kN) | TEA (J) | CFE | SEA (J/g) | |
---|---|---|---|---|---|
KH0 | 23.84 | 2.94 | 102.48 | 0.12 | 9.58 |
KH1 | 21.52 | 4.15 | 136.84 | 0.19 | 12.8 |
KH2 | 22.01 | 5.65 | 193.05 | 0.26 | 18.06 |
KH3 | 21.69 | 4.22 | 148.66 | 0.19 | 13.91 |
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |
© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Zhu, Y.; Deng, J.; Xiong, W.; You, T.; Zhou, W. Koch Hierarchical Honeycomb: A Fractal-Based Design for Enhanced Mechanical Performance and Energy Absorption. Materials 2023, 16, 3670. https://doi.org/10.3390/ma16103670
Zhu Y, Deng J, Xiong W, You T, Zhou W. Koch Hierarchical Honeycomb: A Fractal-Based Design for Enhanced Mechanical Performance and Energy Absorption. Materials. 2023; 16(10):3670. https://doi.org/10.3390/ma16103670
Chicago/Turabian StyleZhu, Yuwen, Junjie Deng, Wei Xiong, Tianyu You, and Wei Zhou. 2023. "Koch Hierarchical Honeycomb: A Fractal-Based Design for Enhanced Mechanical Performance and Energy Absorption" Materials 16, no. 10: 3670. https://doi.org/10.3390/ma16103670
APA StyleZhu, Y., Deng, J., Xiong, W., You, T., & Zhou, W. (2023). Koch Hierarchical Honeycomb: A Fractal-Based Design for Enhanced Mechanical Performance and Energy Absorption. Materials, 16(10), 3670. https://doi.org/10.3390/ma16103670