In response to the growing regulatory emphasis on evaluating non-axial impact conditions in crash safety assessments, this study investigates the crashworthiness of thin-walled tubular energy absorbers under offset impact using Finite Element simulations, performed with LS-DYNA. Four typologies were analysed: Simple Tubes (ST), Tapered Tubes (TT), Multi-Cell Tubes (MCT) and Bi-Tubular Tubes (BTT). Larger cross-sectional dimensions (above 225 mm) significantly improved energy absorption and promoted progressive folding, while wall thickness had minimal effect on stability. While BTT and MCT achieved the highest absolute energy absorption, they also exhibited the greatest performance decline under offset conditions. Conversely, ST and TT showed the lowest change in performance. Cross-sectional shape critically influenced deformation: narrow corner angles (e.g., triangles, squares) enhanced folding and stability, while wider shapes (e.g., octagons) increased buckling risk. These findings inform optimal design strategies for energy absorbers under realistic off-axis impact conditions.
ZhaoZXuP. Analysis and optimization of an expansion energy-absorbing anti-crawler for rail vehicles. Sustainability2023. DOI: 10.3390/su15076288. Epub ahead of print 1 April 2023.
7.
ReddyTYReidSR. Axial splitting of circular metal tubes, 1986.
8.
HuangXLuGYuTX. Collapse of square metal tubes in splitting and curling mode. Proc Inst Mech Eng C J Mech Eng Sci2006; 220: 1–13. https://doi.org/10.1243/095440606x78254
9.
AbramowiczW. Thin-walled structures as impact energy absorbers. In: Thin-Walled Structures, 2003, pp. 91–107.
10.
BaroutajiASajjiaMOlabiAG. On the crashworthiness performance of thin-walled energy absorbers: recent advances and future developments. Thin-Walled Struct2017; 118: 137–163. https://doi.org/10.1016/j.tws.2017.05.018
11.
AbramowiczWJonesN. Dynamic axial crushing of square tubes, 1984.
12.
FanZLuGYuTX, et al.Axial crushing of triangular tubes. Int J Appl Mech; 5. DOI: 10.1142/S1758825113500087. Epub ahead of print March 2013.
13.
XuPXuKYaoS, et al.Parameter study and multi-objective optimisation of an axisymmetric rectangular tube with diaphragms for subways. Thin-Walled Struct2019; 136: 186–199. https://doi.org/10.1016/j.tws.2018.12.025
14.
Alavi NiaAParsapourM. Comparative analysis of energy absorption capacity of simple and multi-cell thin-walled tubes with triangular, square, hexagonal and octagonal sections. Thin-Walled Struct2014; 74: 155–165. https://doi.org/10.1016/j.tws.2013.10.005
15.
XingSJiangZZhaoJ, et al.Failure mechanism and crashworthiness optimization of variable stiffness nested origami crash box. Eng Fail Anal; 167. DOI: 10.1016/j.engfailanal.2024.108953. Epub ahead of print 1 January 2025.
16.
YaoSZhuHLiuM, et al.Energy absorption of origami tubes with polygonal cross-sections. Thin-Walled Struct; 157. DOI: 10.1016/j.tws.2020.107013. Epub ahead of print 1 December 2020.
17.
LiuKJingLWangK, et al.Design optimization of the bamboo-inspired foam-filled tube for high-speed train collision energy absorption. Int J Mech Sci; 271. DOI: 10.1016/j.ijmecsci.2024.109128. Epub ahead of print 1 June 2024.
18.
ChenWWierzbickiT. Relative merits of single-cell, multi-cell and foam-filled thin-walled structures in energy absorption. Epub ahead of print2001; 39: 287–306. https://doi.org/10.1016/S0263-8231(01)00006-4
19.
ZhengGPangTSunG, et al.Theoretical, numerical, and experimental study on laterally variable thickness (LVT) multi-cell tubes for crashworthiness. Int J Mech Sci2016; 118: 283–297. https://doi.org/10.1016/j.ijmecsci.2016.09.015
20.
ZhangXWenZZhangH. Axial crushing and optimal design of square tubes with graded thickness. Thin-Walled Struct2014; 84: 263–274. https://doi.org/10.1016/j.tws.2014.07.004
21.
European Committee for Standardization. Railway applications - crashworthiness requirements for rail vehicle. Standard No. EN15227:2024. English version. Eur Comm2024.
22.
XuTHuJDongJ, et al.Optimization of carbody structure in the Hong Kong LRV project through health monitoring. High-speed Railway2025. DOI: 10.1016/j.hspr.2025.11.003. Epub ahead of print.
23.
XuKXuPYangC, et al.Crashworthiness optimisation for the rectangular tubes with axisymmetric and uniform thicknesses under offset loading. Struct Multidiscip Optim2020; 62: 957–977. https://doi.org/10.1007/s00158-020-02535-1
24.
YaoSXiaoXXuP, et al.The impact performance of honeycomb-filled structures under eccentric loading for subway vehicles. Thin-Walled Struct2018; 123: 360–370. https://doi.org/10.1016/j.tws.2017.10.031
25.
GrassoM. About the preliminary design of a self-aligning energy absorber system for railway vehicles. Int J Crashworthiness2013; 18: 544–557. https://doi.org/10.1080/13588265.2013.815022
PatelSVusaVRGuedes SoaresC. Crashworthiness analysis of polymer composites under axial and oblique impact loading. Int J Mech Sci2019; 156: 221–234. https://doi.org/10.1016/j.ijmecsci.2019.03.038
28.
QiCYangSDongF. Crushing analysis and multiobjective crashworthiness optimization of tapered square tubes under oblique impact loading. Thin-Walled Struct2012; 59: 103–119. https://doi.org/10.1016/j.tws.2012.05.008
ZhangJXieJZhangT, et al.A prediction method for oblique load stability of multi-cell tubes based on SVM. Eng Struct; 283. DOI: 10.1016/j.engstruct.2023.115885. Epub ahead of print 15 May 2023.
31.
WangPYuanYGuoJ, et al.Bio-inspired vertex-offset lattices with high stress and stable deformation under axial and oblique impacts. Int J Impact Eng; 207. DOI: 10.1016/j.ijimpeng.2025.105484. Epub ahead of print 1 January 2026.
32.
LiSZhangJHouL, et al.Finite element modeling and crushing energy absorption analysis of AA6063/CFRP hybrid thin-walled tube subjected to quasi-static load. Compos Struct2026; 381: 120058. https://doi.org/10.1016/j.compstruct.2026.120058
33.
QureshiOMBertocchiEQaiserZ, et al.Frequency embedded box beam crash absorbers under oblique impacts. Thin-Walled Struct2014; 75: 1–7. https://doi.org/10.1016/j.tws.2013.09.020
34.
YaoRPangTZhangB, et al.On the crashworthiness of thin-walled multi-cell structures and materials: state of the art and prospects. Thin-Walled Struct2023. DOI: 10.1016/j.tws.2023.110734. Epub ahead of print 1 August 2023.
35.
RahmanAPraveen BabuD. Simulation of car frontal fascia during crash using LS-DYNA. Epub ahead of print2019. DOI: 10.17577/IJERTV8IS070261.
36.
AbramowiczWWierzbickiT. Axial crushing of multicorner sheet metal columns. Epub ahead of print1998. DOI: 10.1115/1.3176030.
37.
MorenoCReidSWilliamsT. Experimental and numerical assessment of oblique loading quasi-static testing of railway anticlimbers. Proc Inst Mech Eng F J Rail Rapid Transit2021; 235: 143–154. https://doi.org/10.1177/0954409720908992
38.
GuanWYuYGaoG. Crashworthiness performance and multiobjective optimization of a combined splitting circular tube energy absorber under eccentric impact for subway vehicles. Int J Impact Eng2021. DOI: 10.1016/j.ijimpeng.2021.104006, Epub ahead of print 1 December 2021.
NagelGMThambiratnamDP. Dynamic simulation and energy absorption of tapered thin-walled tubes under oblique impact loading. Int J Impact Eng2006; 32: 1595–1620. https://doi.org/10.1016/j.ijimpeng.2005.01.002
41.
GuoWYangCXuP, et al.Crashworthiness optimization for cutting energy-absorbing structures based on the multiobjective G-CBW method. Alex Eng J2023; 72: 363–383. https://doi.org/10.1016/j.aej.2023.04.004
42.
WierzbickiTAbramowiczW. On the crushing mechanics of thin-walled structures. Epub ahead of print 1983. DOI: 10.1115/1.3167137.
43.
DongSJingTZhangJ. A few-shot learning-based crashworthiness analysis and optimization for multi-cell structure of high-speed train. Machines2022; 10: 696. https://doi.org/10.3390/machines10080696
44.
WuEJiangW-S. Axial crush of metallic honeycombs, 1997.
45.
MalekshahiAShiraziKHShishesazM, et al.A novel theoretical approach for estimation of axial crushing behavior of polygonal hollow sections. Int J Appl Mech; 12. DOI: 10.1142/S1758825120500088. Epub ahead of print 1 January 2020.
XuPShangYJiangS, et al.Theoretical development and multi-objective optimisation of a double-tapered rectangular tube with diaphragms. Int J Crashworthiness2022; 27: 206–220. https://doi.org/10.1080/13588265.2020.1785109
48.
Jafarzadeh-AghdamNSchröderKU. Mechanism of reproducible axial impact of square crash boxes. Thin-Walled Struct; 176. DOI: 10.1016/j.tws.2022.109062. Epub ahead of print 1 July 2022.
49.
XuBWangLLiuQ, et al.Effect of boundary conditions and angles on the compressive performance of the corner element. Buildings; 15. DOI: 10.3390/buildings15010121. Epub ahead of print 1 January 2025.
50.
YinHWenGBaiZ, et al.Theoretical prediction and crashworthiness optimization of multi-cell polygonal tubes. J Sandw Struct Mater2020; 22: 190–219. https://doi.org/10.1177/1099636217737330
51.
AbramowiczWJonesN. Transition from initial global bending to progressive buckling of tubes loaded statically and dynamically, 1997.
HanssenAGArteliusALangsethM. Validation of the simplified super folding element theory applied for axial crushing of complex aluminium extrusions. Int J Crashworthiness2007; 12: 591–596. https://doi.org/10.1080/13588260701497813
54.
TabacuSDucuC. An analytical solution for the estimate of the mean crushing force of structures with polygonal and star-shaped cross-sections subjected to axial load. Int J Mech Sci2019. DOI: 10.1016/j.ijmecsci.2019.105010, Epub ahead of print 1 October 2019.
AbramowiczW. The effective crushing distance in axially compressed thin-walled metal columns. 1983. Epub ahead of print 1983. DOI: 10.1016/0734-743X(83)90025-8.
57.
DengXLiuWLinZ. Experimental and theoretical study on crashworthiness of star-shaped tubes under axial compression. Thin-Walled Struct2018; 130: 321–331. https://doi.org/10.1016/j.tws.2018.06.002
HaNSPhamTMChenW, et al.Energy absorption characteristics of bio-inspired hierarchical multi-cell bi-tubular tubes. Int J Mech Sci2023. DOI: 10.1016/j.ijmecsci.2023.108260, Epub ahead of print 1 August 2023.
Please find the following supplemental material available below.
For Open Access articles published under a Creative Commons License, all supplemental material carries the same license as the article it is associated with.
For non-Open Access articles published, all supplemental material carries a non-exclusive license, and permission requests for re-use of supplemental material or any part of supplemental material shall be sent directly to the copyright owner as specified in the copyright notice associated with the article.
