Out-of-plane Impact Mechanical Behaviors of Honeycomb Filled with Cylindrical Tubes

SUN Yujin; SUN Deqiang; ZHAO Xiangmei

doi:10.19554/j.cnki.1001-3563.2026.05.032

PDF(3044 KB)

Packaging Engineering ›› 2026, Vol. 47 ›› Issue (5) : 317-324. DOI: 10.19554/j.cnki.1001-3563.2026.05.032

Defense Equipment

Out-of-plane Impact Mechanical Behaviors of Honeycomb Filled with Cylindrical Tubes

SUN Yujin¹, SUN Deqiang^2,*, ZHAO Xiangmei¹

Author information +

History +

Abstract

The work aims to systematically investigate the out-of-plane impact mechanical properties of hexagonal honeycombs filled with cylindrical tubes (HHFCTs) by combining the finite element method (FEM) with theoretical analysis, clarify its deformation modes, out-of-plane load-bearing capacity and energy absorption characteristics, derive the theoretical model of its quasi-static plateau stress, and provide a theoretical support and design basis for the engineering application of this composite honeycomb in packaging protection. A finite element model for the out-of-plane impact of HHFCTs was established based on the representative unit cell, and the reliability of the model was verified by the consistency between the load-displacement curve and the classical honeycomb mechanical response. On this basis, the theoretical model of its quasi-static plateau stress considering the cell coupling effect was derived by means of the simplified folding model theory and parametric simulation results. The results showed that the deformation mode of HHFCTs was dominated by the cylindrical honeycomb cells, presenting three typical modes including quasi-static, transitional and dynamic with the increase of impact velocity. Its out-of-plane load-bearing capacity and energy absorption performance were significantly superior to those of single honeycomb structures. When the strain was 0.8, the energy absorption per unit volume was more than 40% higher than the sum of that of the single hexagonal honeycomb and cylindrical honeycomb. The relative error between the calculation results of the established theoretical model and the numerical simulation results was less than 5%, showing high consistency and good prediction accuracy. It is concluded that the impact velocity is a key factor regulating the out-of-plane deformation mode of HHFCTs. The derived theoretical formula of quasi-static plateau stress can effectively predict its out-of-plane quasi-static mechanical properties. This composite honeycomb structure has the advantages of light weight, high load-bearing capacity and high energy absorption, and has good engineering application value in packaging and buffer protection.

Key words

hexagonal honeycomb filled with cylindrical tubes / finite element model / deformation mode / quasi-static plateau stress

Cite this article

EndNote

Ris (Procite)

Bibtex

Download Citations

SUN Yujin, SUN Deqiang, ZHAO Xiangmei. Out-of-plane Impact Mechanical Behaviors of Honeycomb Filled with Cylindrical Tubes[J]. Packaging Engineering. 2026, 47(5): 317-324 https://doi.org/10.19554/j.cnki.1001-3563.2026.05.032

References

[1] 李成兵, 肖可, 李锐, 等. 新型蜂窝结构的耐撞性能研究[J]. 固体力学学报, 2025, 46(5): 693-706.
LI C B, XIAO K, LI R, et al.Research on the Crashworthiness of New Honeycomb Structures[J]. Chinese Journal of Solid Mechanics, 2025, 46(5): 693-706.
[2] GIBSON L J, ASHBY M F.Cellular solids[M]. Cambridge: Cambridge University Press, 1997: 1-150.
[3] NIU X Q, XU F X, ZOU Z, et al.In-Plane Dynamic Crashing Behavior and Energy Absorption of Novel Bionic Honeycomb Structures[J]. Composite Structures, 2022, 299: 116064.
[4] 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[J]. International Journal of Mechanical Sciences, 2020, 173: 105402.
[5] WANG Z G, DENG J J, HE K N, et al.Out-of-Plane Crushing Behavior of Hybrid Hierarchical Square Honeycombs[J]. Thin-Walled Structures, 2022, 181: 110051.
[6] ZHOU J X, DONG C, CHEN B Z, et al.Out-of-Plane Crushing Performances of Cell-Based Hierarchical Honeycombs Based on the Evaluation Criteria for Ideal Energy Absorption[J]. Thin-Walled Structures, 2023, 182: 110246.
[7] JIANG F, YANG S, DING C, et al.Quasi-Static Crushing Behavior of Novel Circular Double Arrowed Auxetic Honeycombs: Experimental Test and Numerical Simulation[J]. Thin-Walled Structures, 2022, 177: 109434.
[8] QI C, JIANG F, REMENNIKOV A, et al.Quasi-Static Crushing Behavior of Novel Re-Entrant Circular Auxetic Honeycombs[J]. Composites Part B: Engineering, 2020, 197: 108117.
[9] 张闯东, 赵荃晔, 周影影. 吸波蜂窝复合材料结构设计及性能研究[J]. 材料导报, 2026, 40(15): 25080024.
ZHANG C D, ZHAO Q Y, ZHOU Y Y.Research on the Structural Design and Performance of Absorbing Honeycomb Composite Materials[J]. Materials Reports.2026, 40(15): 25080024.
[10] XU X, ZHANG Y, WANG X, et al.Searching Superior Crashworthiness Performance by Constructing Variable Thickness Honeycombs with Biomimetic Cells[J]. International Journal of Mechanical Sciences, 2022, 235: 107718.
[11] WANG Z G.Recent Advances in Novel Metallic Honeycomb Structure[J]. Composites Part B: Engineering, 2019, 166: 731-741.
[12] SANTOSA S, WIERZBICKI T.Crash Behavior of Box Columns Filled with Aluminum Honeycomb or Foam[J]. Computers & Structures, 1998, 68(4): 343-367.
[13] AKTAY L, ÇAKıROĞLU C, GÜDEN M. Quasi-Static Axial Crushing Behavior of Honeycomb-Filled Thin-Walled Aluminum Tubes[J]. The Open Materials Science Journal, 2011, 5(1): 184-193.
[14] ZAREI H R, KRÖGER M. Crashworthiness Optimization of Empty and Filled Aluminum Crash Boxes[J]. International Journal of Crashworthiness, 2007, 12(3): 255-264.
[15] 郝乾崇, 孙德强, 马兴元, 等. 基于纸张本构模型的蜂窝纸板共面压缩仿真研究[J]. 包装工程, 2025, 46(3): 150-157.
HAO Q C, SUN D Q, MA X Y, et al.In-Plane Compression Simulation of Honeycomb Paperboard Based on the Constitutive Model of Paper[J]. Packaging Engineering, 2025, 46(3): 150-157.
[16] WANG Z G, LIU J F.Numerical and Theoretical Analysis of Honeycomb Structure Filled with Circular Aluminum Tubes Subjected to Axial Compression[J]. Composites Part B: Engineering, 2019, 165: 626-635.
[17] ZHANG X, ZHANG H.Numerical and Theoretical Studies on Energy Absorption of Three-Panel Angle Elements[J]. International Journal of Impact Engineering, 2012, 46: 23-40.
[18] SUN D Q, LI G Z, SUN Y J.The In-Plane Crashworthiness of Multi-Layer Regularly Arranged Circular Honeycombs[J]. Science Progress, 2020, 103(1): 1-28.
[19] LI X C, LU F Y, ZHANG Y W, et al.Experimental Study on Out-of-Plane Mechanical and Energy Absorption Properties of Combined Hexagonal Aluminum Honeycombs under Dynamic Impact[J]. Materials & Design, 2020, 194: 108900.
[20] 张新春, 刘颖. 密度梯度蜂窝材料动力学性能研究[J]. 工程力学, 2012, 29(8): 372-377.
ZHANG X C, LIU Y.Research on the Dynamic Crushing of Honeycombs with Density Gradient[J]. Engineering Mechanics, 2012, 29(8): 372-377.
[21] 孙德强, 李钟波, 李国志, 等. 基于特征单元的三角形蜂窝异面压缩的有限元分析[J]. 包装工程, 2019, 40(19): 80-85.
SUN D Q, LI Z B, LI G Z, et al.Finite Element Analysis on Out-of-Plane Compression of Triangular Honeycomb Based on Representative Cells[J]. Packaging Engineering, 2019, 40(19): 80-85.
[22] CHEN W G, WIERZBICKI T.Relative Merits of Single-Cell, Multi-Cell and Foam-Filled Thin-Walled Structures in Energy Absorption[J]. Thin-Walled Structures, 2001, 39(4): 287-306.
[23] WIERZBICKI T, BHAT S U, ABRAMOWICZ W, et al.Alexander Revisited—A Two Folding Elements Model of Progressive Crushing of Tubes[J]. International Journal of Solids and Structures, 1992, 29(24): 3269-3288.
[24] 尹汉锋, 文桂林. 基于简化基本折叠单元法的蜂窝耐撞性优化设计[J]. 机械工程学报, 2011, 47(16): 93-100.
YIN H F, WEN G L.Crashworthiness Optimization Design of Honeycombs Based on the Simplified Basic Folding Element Method[J]. Journal of Mechanical Engineering, 2011, 47(16): 93-100.