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Crushing Behaviors of Fractal Hexagonal Tubular Structures: Experiments and Plastic Analysis

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Abstract

Fractal tubular structures (FTSs) can greatly increase the anti-crushing and energy absorption capacity of the material. To reveal this mechanism, fractal hexagonal tubes (FHTs) with self-similar fractal structure were designed and prepared. Compression experiments were carried out to verify the crushing modes of structures with different scale factors. Compared with the single-cell structure, FHTs have much greater mean crushing force (MCF). According to the experiments and the numerical simulations, when the side length of the second-order hexagon is 0.3 times of the length of the first-order primary hexagon, the FTS has the greatest peak force (PF) and MCF as well as the most excellent energy-absorbing ability. Three folding styles were revealed by the experiments and the numerical simulation when changing the scale factor, including the overall folding mode, the local foaling mode and the hybrid folding mode. Theoretical plastic models were built, which consistently predicted the MCF.

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References

  1. Pugsley A. The large-scale crumpling of thin cylindrical columns. Q J Mech Appl Math. 1960;13(1):1–9.

    Article  MathSciNet  Google Scholar 

  2. Alexander JM. An approximate analysis of the collapse of thin cylindrical shells under axial loading. Q J Mech Appl Math. 1960;13(1):10–5.

    Article  MathSciNet  Google Scholar 

  3. Wierzbicki T, Abramowicz W. On the crushing mechanics of thin-walled structures. J Appl Mech. 1983;50:727–34.

    Article  Google Scholar 

  4. Hou SJ, Li Q, Long S. Design optimization of regular hexagonal thin-walled columns with crashworthiness criteria. Finite Elem Anal Des. 2007;43:555–65.

    Article  Google Scholar 

  5. Zhang X, Zhang H. Energy absorption of multi-cell stub columns under axial compression. Thin Wall Struct. 2013;68:156–63.

    Article  Google Scholar 

  6. Mahmoodi A, Shojaeefard MH, Saeidi Googarchin H. Theoretical development and numerical investigation on energy absorption behavior of tapered multi-cell tubes. Thin Wall Struct. 2016;102:98–110.

    Article  Google Scholar 

  7. Zahran MS, Xue P, Esa MS, Abdelwahab MM. A novel tailor-made technique for enhancing the crashworthiness by multi-stage tubular square tubes. Thin Wall Struct. 2018;122:64–82.

    Article  Google Scholar 

  8. Lakes RS. Materials with structural hierarchy. Nature. 1993;361:511–5.

    Article  Google Scholar 

  9. Fan HL, Jin FN, Fang DN. Mechanical properties of hierarchical cellular materials: part I. Anal Compos Sci Technol. 2008;68:3380–7.

    Article  Google Scholar 

  10. Fan HL, Zhao L, Chen HL, Kuang N, Yang CK, Huang SQ, Jiang YF. Ductile deformation mechanisms and designing instructions for integrated woven textile sandwich composites. Compos Sci Technol. 2012;72:1338–43.

    Article  Google Scholar 

  11. Fan HL, Sun FF, Yang L, Jin FN, Zhao DJ. Interlocked hierarchical lattice materials reinforced by woven textile sandwich composites. Compos Sci Technol. 2013;87:142–8.

    Article  Google Scholar 

  12. Sun FF, Lai CL, Fan HL, Fang DN. Crushing mechanism of hierarchical lattice structure. Mech Mater. 2016;97:164–83.

    Article  Google Scholar 

  13. Sun FF, Fan HL. In-plane compression behaviors of hierarchical triangular lattice structures. Mater Des. 2016;100:280–90.

    Article  Google Scholar 

  14. Hong W, Fan HL, Xia ZC, Jin FN, Zhou Q, Fang DN. Axial crushing behaviors of multi-cell tubes with triangular lattices. Int J Impact Eng. 2014;63:106–17.

    Article  Google Scholar 

  15. Luo YH, Fan HL. Investigation of lateral crushing behaviors of hierarchical quadrangular thin-walled tubular structures. Thin Wall Struct. 2018;125:100–6.

    Article  Google Scholar 

  16. Luo YH, Fan HL. Energy absorbing ability of rectangular self-similar multi-cell sandwich-walled tubular structures. Thin Wall Struct. 2018;124:88–97.

    Article  Google Scholar 

  17. Fang JG, Sun GY, Qiu N, Pang T, Li SF, Li Q. On hierarchical honeycombs under out-of-plane crushing. Int J Solids Struct. 2018;135:1–13.

    Article  Google Scholar 

  18. Chen YY, Li TT, Jia Z, Scarpa F, Yao CW, Wang LF. 3D printed hierarchical honeycombs with shape integrity under large compressive deformations. Mater Des. 2018;137:226–34.

    Article  Google Scholar 

  19. An LQ, Zhang XC, Wu HX, Jiang WQ. In-plane dynamic crushing and energy absorption capacity of self-similar hierarchical honeycombs. Adv Mech Eng. 2017;9(6):168781401770389.

    Article  Google Scholar 

  20. Chen Q, Shi Q, Signetti S, Sun FF, Li ZY, Zhu FP, He SY, Pugno NM. Plastic collapse of cylindrical shell-plate periodic honeycombs under uniaxial compression: experimental and numerical analyses. Int J Mech Sci. 2016;111–112:125–33.

    Article  Google Scholar 

  21. Li WW, Luo YH, Li M, Sun FF, Fan HL. A more weight-efficient hierarchical hexagonal multi-cell tubular absorber. Int J Mech Sci. 2018;140:241–9.

    Article  Google Scholar 

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Acknowledgements

Supports from the National Natural Science Foundation of China (11671230) and the State Key Laboratory of Mechanics and Control of Mechanical Structures (MCMS-0217G03) are gratefully acknowledged.

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Authors and Affiliations

  1. Research Center of Lightweight Structures and Intelligent Manufacturing, State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Weiwei Li & Hualin Fan

  2. State Key Laboratory for Disaster Prevention & Mitigation of Explosion & Impact, PLA Army Engineering University, Nanjing, 210007, China

    Bei Zhang

  3. Department of Civil Engineering, Nanyang Institute of Technology, Nanyang, 473004, China

    Weiwei Li

  4. Research Institute for National Defense Engineering of Academy of Military Science PLA, Luoyang, 471023, China

    Bei Zhang

Authors
  1. Weiwei Li
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  2. Bei Zhang
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  3. Hualin Fan
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Correspondence to Bei Zhang or Hualin Fan.

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Li, W., Zhang, B. & Fan, H. Crushing Behaviors of Fractal Hexagonal Tubular Structures: Experiments and Plastic Analysis. Acta Mech. Solida Sin. 32, 713–724 (2019). https://doi.org/10.1007/s10338-019-00097-4

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  • DOI: https://doi.org/10.1007/s10338-019-00097-4

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