Effective elastic modulus and energy absorption performance evaluations of a novel re-entrant chiral hybrid honeycomb

doi:10.1007/s10483-025-3246-9

Abstract

Abstract:

Re-entrant honeycombs are widely used in safeguard structures due to their geometric simplicity and excellent energy absorption capacities. However, traditional re-entrant honeycombs exhibit insufficient stiffness and stability owing to the lack of internal support. This paper proposes a new hybrid honeycomb by integrating a chiral component inside the re-entrant honeycomb. Since Young's modulus is a key parameter to evaluate the energy absorption performance and stiffness, an analytical model is given to predict the effective Young's modulus of the proposed hybrid honeycomb. It is found that the optimal design scheme is to directly insert a circular ring inside the re-entrant honeycomb. The normalized specific energy absorption (SEA) of the hybrid honeycomb is 95% larger than that of the traditional re-entrant honeycomb. The normalized SEA first increases to a peak value and then decreases with the cell wall thickness. The optimal thickness of the cell wall for the maximum SEA is derived in terms of the geometric configuration of the unit cell. The normalized SEA first decreases to a valley value and then increases with the re-entrant angle. A longer horizontal cell wall results in a smaller normalized SEA. This paper provides a new design method for safeguard structures with high stiffness and energy absorption performance.

Key words: re-entrant honeycomb, chiral metamaterial, effective Young's modulus, energy absorption performance

2010 MSC Number:

O341

Youjiang CUI, Zhihui XU, Que ZHOU, Baolin WANG, Kaifa WANG, Biao WANG. Effective elastic modulus and energy absorption performance evaluations of a novel re-entrant chiral hybrid honeycomb. Applied Mathematics and Mechanics (English Edition), 2025, 46(5): 781-794.

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Figures/Tables 9

Fig. 1

Fig. 2

Fig. 3

Table 1

Young's modulus and Poisson's ratio of 3D-printed PLA-K5 and nylon-7000"

Base material	Young's modulus	Poisson's ratio	Tensile strength	Yield strength
PLA-K5	$E d = 2 990.8$ MPa	$ν d = 0.367$	$σ b = 36.73$ MPa	$σ p0 .2 = 33.94$ MPa
Nylon-7000	$E d = 579.5$ MPa	$ν d = 0.413$	$σ b = 23.42$ MPa	$σ p0 .2 = 16.18$ MPa

Table 1

Table 2

Effective Young's modulus of honeycomb structure"

Base material	Compressive experiment $E ea$ /MPa	Theoretical prediction $E ep$ /MPa	Relative error $e$ /%
PLA-K5	86.4	82.8	4.2
Nylon-7000	15.7	16.1	2.5

Table 2

Fig. 4

Fig. 5

Fig. 6

Table 3

Comparison of the SEA between the re-entrant chiral hybrid honeycomb and other recently reported 2D auxetic honeycombs[3,38-41]"

Strain	SEA/ $(J ⋅ g − 1)$	Ref.	Strain	SEA/ $(J ⋅ g − 1)$	Ref.
0.55	3.02	–	0.60	0.88	[39]
0.50	1.59	[38]	0.60	2.98	[40]
0.48	2.00	[3]	0.60	2.28	[41]

Table 3

References 41

[1]	QI, C., JIANG, F., and YANG, S.Advanced honeycomb designs for improving mechanical properties: a review. Composites Part B: Engineering, 227, 109393 (2021)
[2]	TIAN, R. L., GUAN, H. T., LU, X. H., ZHANG, X. L., HAO, H. N., FENG, W. J., and ZHANG, G. L.Dynamic crushing behavior and energy absorption of hybrid auxetic metamaterial inspired by Islamic motif art. Applied Mathematics and Mechanics (English Edition), 44(3), 345–362 (2023) https://doi.org/10.1007/s10483-023-2962-9
[3]	CHEN, Z. Y., LI, J. H., WU, B. S., CHEN, X., and XIE, Y. M.Enhanced mechanical properties of re-entrant auxetic honeycomb with self-similar inclusion. Composite Structures, 331, 117921 (2024)
[4]	ZHANG, J. and LU, G.Energy absorption of re-entrant honeycombs in tension and compression. Engineering Structures, 288, 116237 (2023)
[5]	JIANG, H. Y., REN, Y. R., JIN, Q. D., ZHU, G. H., HU, Y. S., and CHENG, F.Crashworthiness of novel concentric auxetic reentrant honeycomb with negative Poisson's ratio biologically inspired by coconut palm. Thin-Walled Structures, 154, 106911 (2020)
[6]	ALOMARAH, A., YUAN, Y., and RUAN, D.A bio-inspired auxetic metamaterial with two plateau regimes: compressive properties and energy absorption. Thin-Walled Structures, 192, 111175 (2023)
[7]	MA, J. M., ZHANG, H. R., LEE, T. U., LU, H. J., XIE, Y. M., and HA, N. S.Auxetic behavior and energy absorption characteristics of a lattice structure inspired by deep-sea sponge. Composite Structures, 354, 118835 (2025)
[8]	WANG, W. J., ZHANG, W. M., GUO, M. F., YANG, H., and MA, L.Impact resistance of assembled plate-lattice auxetic structures. Composite Structures, 338, 118132 (2024)
[9]	ZHANG, Q. and SUN, Y. X.Statics, vibration, and buckling of sandwich plates with metamaterial cores characterized by negative thermal expansion and negative Poisson's ratio. Applied Mathematics and Mechanics (English Edition), 44(9), 1457–1486 (2023) https://doi.org/10.1007/s10483-023-3024-6
[10]	YIN, H. F., ZHANG, W. Z., ZHU, L. C., MENG, F. B., LIU, J., and WEN, G. L.Review on lattice structures for energy absorption properties. Composite Structures, 304, 116397 (2023)
[11]	MOMOH, E. O., JAYASINGHE, A., HAJSADEGHI, M., VINAI, R., EVANS, K. E., KRIPAKARAN, P., and ORR, J.A state-of-the-art review on the application of auxetic materials in cementitious composites. Thin-Walled Structures, 196, 111447 (2024)
[12]	MONTGOMERY-LILJEROTH, E., SCHIEVANO, S., and BURRIESCI, G.Elastic properties of 2D auxetic honeycomb structures — a review. Applied Materials Today, 30, 101722 (2023)
[13]	CUI, Y. J., LIU, C., CHEN, J. P., WANG, B., and WANG, B. L.Thermo-electric-mechanical coupling bending property and strength analysis of thermoelectric devices with the negative Poisson's ratio ratio architecture (in Chinese). Applied Mathematics and Mechanics, 45(10), 1243–1255 (2024)
[14]	KHALILI, S. M. R. and ALAVI, S. M. A.Computation of the homogenized linear elastic response of 2D microcellular re-entrant auxetic honeycombs based on modified strain gradient theory. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 45, 19 (2023)
[15]	JAHANGIRI, S., GHORBANPOUR ARANI, A., and KHODDAMI MARAGHI, Z.Dynamics of a rotating ring-stiffened sandwich conical shell with an auxetic honeycomb core. Applied Mathematics and Mechanics (English Edition), 45(6), 963–982 (2024) https://doi.org/10.1007/s10483-024-3124-7
[16]	PHUNG-VAN, P., NGUYEN-XUAN, H., HUNG, P. T., ABDEL-WAHAB, M., and THAI, C. H.Nonlocal strain gradient analysis of honeycomb sandwich nanoscale plates. Thin-Walled Structures, 198, 111746 (2024)
[17]	YANG, L., HARRYSSON, O., WEST, H., and CORMIER, D.Mechanical properties of 3D re-entrant honeycomb auxetic structures realized via additive manufacturing. International Journal of Solids and Structures, 69-70, 475–490 (2015)
[18]	ZHANG, X. Y., REN, X., ZHANG, Y., and XIE, Y. M.A novel auxetic metamaterial with enhanced mechanical properties and tunable auxeticity. Thin-Walled Structure, 174, 109162 (2022)
[19]	ZHAN, C., LI, M. Z., MCCOY, R., ZHAO, L. S., and LU, W. Y.3D-printed hierarchical re-entrant honeycomb with improved structural stability under quasi-static compressive loading. ASME 2021 International Mechanical Engineering Congress and Exposition, 3, V003T03A053 (2021)
[20]	TENG, X. C., REN, X., ZHANG, Y., JIANG, W., PAN, Y., ZHANG, X. G., ZHANG, X. Y, and XIE, Y. M.A simple 3D re-entrant auxetic metamaterial with enhanced energy absorption. International Journal of Mechanical Sciences, 229, 107524 (2022)
[21]	HU, Q. F., ZHANG, X. Y., ZHANG, J. J., LU, G. X., and TSE, K. M.A review on energy absorption performance of auxetic composites with fillings. Thin-Walled Structures, 205, 112348 (2024)
[22]	MA, N., HAN, Q., HAN, S. H., and LI, C. L.Hierarchical re-entrant honeycomb metamaterial for energy absorption and vibration insulation. International Journal of Mechanical Sciences, 250, 108307 (2023)
[23]	DENG, X. and QIN, S.In-plane energy absorption characteristics and mechanical properties of novel re-entrant honeycombs. Composite Structures, 313, 116951 (2023)
[24]	MA, N., HAN, S., XU, W. H., HAN, Q., and LI, C. L.Compressive response and optimization design of a novel hierarchical re-entrant origami honeycomb metastructure. Engineering Structures, 306, 117819 (2024)
[25]	ZHU, Y., LUO, Y., GAO, D. F., YU, C., REN, X., and ZHANG, C. Z.In-plane elastic properties of a novel re-entrant auxetic honeycomb with zigzag inclined ligaments. Engineering Structures, 268, 114788 (2022)
[26]	LI, W., ZHONG, Y., ZHU, Y. L., CAO, H. W., and LIU, R.Enhancing the structural stiffness and energy absorption of re-entrant auxetic honeycombs using folded stiffeners. Thin-Walled Structures, 205, 11250 (2024)
[27]	SHUAIBU, A. S., DENG, J. J., XU, C. C., ADE-OKE, V. P., ALIYU, A., and MOMOH, D.Advancing auxetic materials: emerging development and innovative applications. Reviews on Advanced Materials Science, 63(1), 20240021 (2024)
[28]	WU, W. W., HU, W. X., QIAN, G. A., LIAO, H. T., XU, X. Y., and BERTO, F.Mechanical design and multifunctional applications of chiral mechanical metamaterials: a review. Materials & Design, 180, 107950 (2019)
[29]	LI, T. T. and LI, Y. N.Mechanical behaviors of three-dimensional chiral mechanical metamaterials. Composites Part B: Engineering, 270, 111141 (2024)
[30]	WANG, J. J., CHEN, Z. C., JIAO, P. C., and ALAVI, A. H.Coupling chiral cuboids with wholly auxetic response. Research, 7, 0463 (2024)
[31]	CHEN, C. Q., HE, Y. L., XU, R., GAO, C., LI, X., and LU, M. H.Dynamic behaviors of sandwich panels with 3D-printed gradient auxetic cores subjected to blast load. International Journal of Impact Engineering, 188, 104943 (2024)
[32]	MIZZI, L., GRASSELLI, L., and SPAGGIARI, A.Clockwise vs anti-clockwise chiral metamaterials: influence of base tessellation symmetry and rotational direction of chiralisation on mechanical properties. Thin-Walled Structures, 205, 112381 (2024)
[33]	ALOMARAH, A., AL-IBRAHEEMI, Z. A., and RUAN, D.3D printed auxetic stents with re-entrant and chiral topologies. Smart Materials and Structures, 32, 115028 (2023)
[34]	YIN, L., ZHANG, M. C., ZHU, Y. Z., LI, B. H., and WEN, Y. X.Quasi-static cyclic tension-compression behavior of circular anti-chiral auxetic metamaterials. Construction and Building Materials, 450, 138519 (2024)
[35]	MALEK, S. and GIBSON, L.Effective elastic properties of periodic hexagonal honeycombs. Mechanics of Materials, 91, 226–240 (2015)
[36]	SMARDZEWSKI, J. and TOKARCZYK, M.Lightweight honeycomb furniture panels with discreetly located strengthening blocks. Composite Structures, 331, 117927 (2024)
[37]	QIU, N., YU, Z. Q., WANG, D. P., XIAO, M. W., ZHANG, Y. M., KIM, N. H., and FANG, J. G.Bayesian optimization of origami multi-cell tubes for energy absorption considering mixed categorical-continuous variables. Thin-Walled Structures, 199, 111799 (2024)
[38]	BASTOLA, N., MA, J. F., and JAHAN, M. P.Enhancing mechanical and energy absorption properties of additively manufactured polyamide lattice structures through hybrid-structuring and strut reinforcement: a numerical and experimental study. International Journal of Advanced Manufacturing Technology, 136, 2397–2426 (2025)
[39]	XU, H., LIU, H. T., and LI, G. F.In-plane characteristics of a multi-arc re-entrant auxetic honeycomb with enhanced negative Poisson's ratio effect and energy absorption. European Journal of Mechanics-A/Solids, 109, 105473 (2025)
[40]	DENG, Y. F., JIN, Y. X., LI, H. L., and WANG, X.A new hybrid auxetic structure capable of uniform deformation exhibits excellent energy absorption. Smart Materials and Structures, 33, 085031 (2024)
[41]	HOU, X. H., WANG, B., and DENG, Z. C.Tailored energy absorption for a novel auxetic honeycomb structure under large deformation. Science China Physics, Mechanics & Astronomy, 67, 254611 (2024)