Nanoporous materials functionalized liquid (NMFL)-filled structures demonstrate significant potential in the field of energy absorption and cushioning. To thoroughly investigate the behavior of NMFL-filled tubes under axial loading, this study establishes an analytical model based on the ring-shaped crushing hypothesis, deriving analytical expressions for peak stress and mean crushing stress, with the accuracy of the theoretical model validated through finite element analysis. The results show that the crushing process of NMFL-filled tubes exhibits three distinct stages: elastic, yield, and strengthening. For a representative configuration, the FE-predicted peak stress and mean crushing stress in the yield stage are 20.94 MPa and 16.00 MPa, respectively, while the corresponding theoretical predictions are 23.68 MPa and 16.99 MPa. Parametric analysis reveals that the infiltration pressure of the NMFL and the wall thickness of the tube are key parameters controlling the crushing morphology, and global buckling instability occurs when the infiltration pressure exceeds 14 MPa. This study fills the gap in the theoretical modeling of axial crushing for NMFL-filled structures and provides a scientific basis for developing new high-performance cushioning and energy-absorbing materials.
SunGXuFLiG, et al.Crashing analysis and multiobjective optimization for thin-walled structures with functionally graded thickness. Int J Impact Eng2014; 64: 62–74. https://doi.org/10.1016/j.ijimpeng.2013.10.004
AlexanderJ. An approximate analysis of the collapse of thin cylindrical shells under axial loading. Q J Mech Appl Math1960; 13: 10–15. https://doi.org/10.1093/qjmam/13.1.10
7.
GrzebietaR. An alternative method for determining the behaviour of round stocky tubes subjected to an axial crush load. Thin-Walled Struct1990; 9: 61–89. https://doi.org/10.1016/0263-8231(90)90039-2
AndrewsKRFEnglandGLGhaniE. Classification of the axial collapse of cylindrical tubes under quasi-static loading. Int J Mech Sci1983; 25: 687–696. https://doi.org/10.1016/0020-7403(83)90076-0
EyvazianAHabibi MKHamoudaAM, et al.Axial crushing behavior and energy absorption efficiency of corrugated tubes. Mater Des2014; 54: 1028–1038. https://doi.org/10.1016/j.matdes.2013.09.031
14.
QiCYangS. Crashworthiness and lightweight optimisation of thin-walled conical tubes subjected to an oblique impact. Mater Des2014; 19: 334–351. https://doi.org/10.1080/13588265.2014.893788
15.
ElgalaiAMMahdiEHamoudaAMS, et al.Crushing response of composite corrugated tubes to quasi-static axial loading. Compos Struct2004; 66: 665–671. https://doi.org/10.1016/j.compstruct.2004.06.002
16.
WadleyH. Fabrication and structural performance of periodic cellular metal sandwich structures. Compos Sci Technol2003; 63: 2331–2343. https://doi.org/10.1016/s0266-3538(03)00266-5
17.
PirmohammadSEsmaeili-MarzdashtiS. Multi-objective optimization of multi-cell conical structures under dynamic loads. J Cent South Univ2019; 26: 2464–2481. https://doi.org/10.1007/s11771-019-4187-3
18.
MahdiEMokhtarASAsariNA, et al.Nonlinear finite element analysis of axially crushed cotton fibre composite corrugated tubes. Compos Struct2006; 75: 39–48. https://doi.org/10.1016/j.compstruct.2006.04.057
MamalisAGJohnsonW. The quasi-static crumpling of thin-walled circular cylinders and frusta under axial compression. Int J Mech Sci1983; 25: 713–732. https://doi.org/10.1016/0020-7403(83)90078-4
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
23.
HanssenAGHopperstadOSLangsethM, et al.Validation of constitutive models applicable to aluminium foams. Int J Mech Sci2002; 44: 359–406. https://doi.org/10.1016/s0020-7403(01)00091-1
24.
DuarteIKrstulović-OparaLVesenjakM. Characterisation of aluminium alloy tubes filled with aluminium alloy integral-skin foam under axial compressive loads. Compos Struct2015; 121: 154–162. https://doi.org/10.1016/j.compstruct.2014.11.003
25.
DuarteIVesenjakMKrstulović-OparaL, et al.Compressive performance evaluation of APM (advanced pore morphology) foam filled tubes. Compos Struct2015; 134: 409–420. https://doi.org/10.1016/j.compstruct.2015.08.097
26.
DuarteIVesenjakMKrstulović-OparaL, et al.Manufacturing and bending behaviour of in situ foam-filled aluminium alloy tubes. Mater Des2015; 66: 532–544. https://doi.org/10.1016/j.matdes.2014.04.082
27.
DuarteIVesenjakMKrstulović-OparaL, et al.Static and dynamic axial crush performance of in-situ foam-filled tubes. Compos Struct2015; 124: 128–139. https://doi.org/10.1016/j.compstruct.2015.01.014
ThorntonPH. Energy absorption by foam filled structures. SAE Technical Paper. 1980; 800081. https://doi.org/10.4271/800081
30.
ToksoyAKGüdenM. The strengthening effect of polystyrene foam filling in aluminum thin-walled cylindrical tubes. Thin-Walled Struct2005; 43: 333–350. https://doi.org/10.1016/j.tws.2004.07.007
31.
HusseinRDRuanDLuG, et al.Crushing response of square aluminium tubes filled with polyurethane foam and aluminium honeycomb. Thin-Walled Struct2017; 110: 140–154. https://doi.org/10.1016/j.tws.2016.10.023
XiaoYWuQZangM, et al.Analysis of factors influencing the energy absorption characteristics of gradient foam-filled thin-walled circular tubes with variable thickness and origami patterns. Mech Adv Mater Struct2025; 33: 1–20. https://doi.org/10.1080/15376494.2025.2456107
34.
LuoGLiuJLiL, et al.Crashworthiness analysis and multi-objective optimization design for foam-filled spiral tube. Int J Mech Sci2024; 282: 109588. https://doi.org/10.1016/j.ijmecsci.2024.109588
35.
ZhouBZhangHHanS, et al.Crashworthiness analysis and optimization of a novel thin-walled multi-cell structure inspired by bamboo. Structures2024; 59: 105827. https://doi.org/10.1016/j.istruc.2023.105827
36.
YingLWangSGaoT, et al.Crashworthiness analysis and imization of multi-functional gradient foam-aluminum filled hierarchical thin-walled structures. Thin-Walled Struct2023; 189: 110906. https://doi.org/10.1016/j.tws.2023.110906
37.
YaoRPangTZhangB, et al.On the crashworthiness of thin-walled multi-cell structures and materials: state of the art and prospects. Thin-Walled Struct2023; 189: 110734. https://doi.org/10.1016/j.tws.2023.110734
KrukMJaroniecM. Gas adsorption characterization of ordered organic−inorganic nanocomposite materials. Chem Mater2001; 13: 3169–3183. https://doi.org/10.1021/cm0101069
43.
PolarzSAntoniettiM. Porous materials via nanocasting procedures: innovative materials and learning about soft-matter organization. Chem Commun. 2002; 22: 2593–2604. https://doi.org/10.1039/b205708p
44.
SunYRoggeSMJLamaireA, et al.High-rate nanofluidic energy absorption in porous zeolitic frameworks. Nat Mater2021; 20: 1015–1023. https://doi.org/10.1038/s41563-021-00977-6
45.
FrauxGCoudertF-XBoutinA, et al.Forced intrusion of water and aqueous solutions in microporous materials: from fundamental thermodynamics to energy storage devices. Chem Soc Rev2017; 46: 7421–7437. https://doi.org/10.1039/c7cs00478h
46.
FangDLiuCChenY, et al.Elucidating and manipulating pressure-induced water intrusion–extrusion in tunable hydrophobic Co/Zn bimetallic ZIFs: roles of pore size and hydrogen bond. Nano Res2024; 17: 344–353. https://doi.org/10.1007/s12274-023-5967-5
47.
AmayuelasESharmaSKMorJ, et al.Effect of linker hybridization on the wetting of hydrophobic metal-organic frameworks. Microporous Mesoporous Mater2025; 383: 113423. https://doi.org/10.1016/j.micromeso.2024.113423
ChenXSuraniFBKongX, et al.Energy absorption performance of steel tubes enhanced by a nanoporous material functionalized liquid. Appl Phys Lett2006; 89: 241918. https://doi.org/10.1063/1.2405852
ZhaoJCulliganPJGermaineJT, et al.Experimental study on energy dissipation of electrolytes in nanopores. Langmuir2009; 25: 12687–12696. https://doi.org/10.1021/la901696t
52.
GibsonLJAshbyMF. Cellular solids: structure and properties. Cambridge University Press, 1997.
53.
SunYLiYZhaoC, et al.Crushing of circular steel tubes filled with nanoporous-materials-functionalized liquid. Int J Damage Mech2018; 27: 439–450. https://doi.org/10.1177/1056789516683539
