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SCIENCE CHINA Technological Sciences, Volume 63 , Issue 1 : 140-154(2020) https://doi.org/10.1007/s11431-018-9467-6

Crashworthiness analysis of a cylindrical auxetic structure under axial impact loading

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  • ReceivedAug 12, 2018
  • AcceptedFeb 22, 2019
  • PublishedNov 25, 2019

Abstract

Structures with negative Poisson’s ratio (NPR) have been widely used in engineering application due to its unusual properties. In this paper, crashworthiness of a novel cylindrical auxetic structure under axial impact loading is investigated by the numerical methods. The software LS-DYNA is adopted to analyze the effects of the geometry parameters on the force, energy absorption (EA) and specific energy absorption (SEA). It is found that an overlarge number of layers and cells will make NPR structure extend outward from the mid; NPR structures with small number of layers and cells will make some layers of structures rotate in final crushing state. If the thickness of the long-inclined bean (L-beam) is larger than that of short-inclined beam (S-beam), there will be a smoother transition from the lower to a higher value in crushing force. Conversely, the force will maintain a relatively steady value, which determined by the sum of the thickness of L- and S-beams. In addition, there is also a critical inner circle radius which distinguishes different deformation modes. Once the critical inner circle radius is smaller than the critical value, NPR structures tend to deform unsteadily.


Funded by

China Scholarship Council(Grant,No.,201606840046)

which sponsored one of the authors as a visiting scholar for two years at the University of Michigan

Ann Arbor

Michigan

USA. This work was also supported by National Natural Science Foundation of China(Grant,No.,51675281)

and the National Key Research and Development Program of China(Grant,No.,2017YFC0803904)


Acknowledgment

This work was supported by China Scholarship Council (Grant No. 201606840046), which sponsored one of the authors as a visiting scholar for two years at the University of Michigan, Ann Arbor, Michigan, USA. This work was also supported by the National Natural Science Foundation of China (Grant No. 51675281), and the National Key Research and Development Program of China (Grant No. 2017YFC0803904).


Supplement

Supporting Information

The supporting information is available online at tech.scichina.com and link.springer.com. The supporting materials are published as submitted, without typesetting or editing. The responsibility for scientific accuracy and content remains entirely with the authors.


References

[1] Chen D Y, Wang L M, Wang C Z, et al. Finite element based improvement of a light truck design to optimize crashworthiness. Int J Automot Technol, 2015, 16: 39-49 CrossRef Google Scholar

[2] Alipour R, Farokhi Nejad A, Izman S. The reliability of finite element analysis results of the low impact test in predicting the energy absorption performance of thin-walled structures. J Mech Sci Technol, 2015, 29: 2035-2045 CrossRef Google Scholar

[3] Vinayagar K, Senthil Kumar A. Crashworthiness analysis of double section bi-tubular thin-walled structures. Thin-Walled Struct, 2017, 112: 184-193 CrossRef Google Scholar

[4] Liu W, Lin Z, He J, et al. Crushing behavior and multi-objective optimization on the crashworthiness of sandwich structure with star-shaped tube in the center. Thin-Walled Struct, 2016, 108: 205-214 CrossRef Google Scholar

[5] Qiu N, Gao Y, Fang J, et al. Crashworthiness analysis and design of multi-cell hexagonal columns under multiple loading cases. Finite Elem Anal Des, 2015, 104: 89-101 CrossRef Google Scholar

[6] Song X, Sun G, Li G, et al. Crashworthiness optimization of foam-filled tapered thin-walled structure using multiple surrogate models. Struct Multidisc Optim, 2013, 47: 221-231 CrossRef Google Scholar

[7] Gao Q, Wang L, Wang Y, et al. Crushing analysis and multiobjective crashworthiness optimization of foam-filled ellipse tubes under oblique impact loading. Thin-Walled Struct, 2016, 100: 105-112 CrossRef Google Scholar

[8] Ghamarian A, Zarei H R, Abadi M T. Experimental and numerical crashworthiness investigation of empty and foam-filled end-capped conical tubes. Thin-Walled Struct, 2011, 49: 1312-1319 CrossRef Google Scholar

[9] Zarei H R, Ghamarian A. Experimental and numerical crashworthiness investigation of empty and foam-filled thin-walled tubes with shallow spherical caps. Exp Mech, 2014, 54: 115-126 CrossRef Google Scholar

[10] Kim H C, Shin D K, Lee J J, et al. Crashworthiness of aluminum/CFRP square hollow section beam under axial impact loading for crash box application. Composite Struct, 2014, 112: 1-10 CrossRef Google Scholar

[11] Xie S, Yang W, Wang N, et al. Crashworthiness analysis of multi-cell square tubes under axial loads. Int J Mech Sci, 2017, 121: 106-118 CrossRef Google Scholar

[12] Costas M, Morin D, Langseth M, et al. Static crushing of aluminium tubes filled with PET foam and a GFRP skeleton. Numerical modelling and multiobjective optimization. Int J Mech Sci, 2017, 131-132: 205-217 CrossRef Google Scholar

[13] Mohsenizadeh S, Alipour R, Nejad A F, et al. Experimental investigation on energy absorption of auxetic foam-filled thin-walled square tubes under quasi-static loading. Procedia Manufacturing, 2015, 2: 331-336 CrossRef Google Scholar

[14] Mohsenizadeh S, Alipour R, Ahmad Z, et al. Influence of auxetic foam in quasi-static axial crushing. Int J Mater Res, 2016, 107: 916-924 CrossRef Google Scholar

[15] Najarian F, Alipour R, Shokri Rad M, et al. Multi-objective optimization of converting process of auxetic foam using three different statistical methods. Measurement, 2018, 119: 108-116 CrossRef Google Scholar

[16] Tran T N, Hou S, Han X, et al. Theoretical prediction and crashworthiness optimization of multi-cell square tubes under oblique impact loading. Int J Mech Sci, 2014, 89: 177-193 CrossRef Google Scholar

[17] Gao Q, Wang L, Wang Y, et al. Optimization of foam-filled double ellipse tubes under multiple loading cases. Adv Eng Software, 2016, 99: 27-35 CrossRef Google Scholar

[18] Tran T N, Hou S, Han X, et al. Theoretical prediction and crashworthiness optimization of multi-cell triangular tubes. Thin-Walled Struct, 2014, 82: 183-195 CrossRef Google Scholar

[19] Hou S, Dong D, Ren L, et al. Multivariable crashworthiness optimization of vehicle body by unreplicated saturated factorial design. Struct Multidisc Optim, 2012, 46: 891-905 CrossRef Google Scholar

[20] Hou S, Liu T, Dong D, et al. Factor screening and multivariable crashworthiness optimization for vehicle side impact by factorial design. Struct Multidisc Optim, 2014, 49: 147-167 CrossRef Google Scholar

[21] Grujicic M, Galgalikar R, Snipes J S, et al. Multi-physics modeling of the fabrication and dynamic performance of all-metal auxetic-hexagonal sandwich-structures. Mater Des, 2013, 51: 113-130 CrossRef Google Scholar

[22] Lira C, Innocenti P, Scarpa F. Transverse elastic shear of auxetic multi re-entrant honeycombs. Composite Struct, 2009, 90: 314-322 CrossRef Google Scholar

[23] Yang L, Harrysson O, West H, et al. Mechanical properties of 3D re-entrant honeycomb auxetic structures realized via additive manufacturing. Int J Solids Struct, 2015, 69-70: 475–90. Google Scholar

[24] Zhang Z, Liu S, Tang Z. Crashworthiness investigation of kagome honeycomb sandwich cylindrical column under axial crushing loads. Thin-Walled Struct, 2010, 48: 9-18 CrossRef Google Scholar

[25] Mohsenizadeh S, Alipour R, Shokri Rad M, et al. Crashworthiness assessment of auxetic foam-filled tube under quasi-static axial loading. Mater Des, 2015, 88: 258-268 CrossRef Google Scholar

[26] Yang S, Qi C, Wang D, et al. A comparative study of ballistic resistance of sandwich panels with aluminum foam and auxetic honeycomb cores. Adv Mech Eng, 2013, 5: 589216 CrossRef Google Scholar

[27] Schleyer G, Brebbia C A. Structures Under Shock and Impact XII. Southampton: WIT Press, 2013. Google Scholar

[28] Zhang X C, An L Q, Ding H M, et al. The influence of cell micro-structure on the in-plane dynamic crushing of honeycombs with negative Poisson’s ratio. Jnl of Sandwich Struct Mater, 2015, 17: 26–55. Google Scholar

[29] Grima J N, Gatt R, Alderson A, et al. On the potential of connected stars as auxetic systems. Mol Simul, 2005, 31: 925-935 CrossRef Google Scholar

[30] Prall D, Lakes R S. Properties of a chiral honeycomb with a Poisson’s ratio of—1. Int J Mech Sci, 1997, 39: 305-314 CrossRef Google Scholar

[31] Alderson A, Alderson K L, Attard D, et al. Elastic constants of 3-, 4- and 6-connected chiral and anti-chiral honeycombs subject to uniaxial in-plane loading. Compos Sci Tech, 2010, 70: 1042-1048 CrossRef Google Scholar

[32] Grima J N, Evans K E. Auxetic behavior from rotating squares. J Mater Sci Lett, 2000, 19: 1563-1565 CrossRef Google Scholar

[33] Rad M S, Mohsenizadeh S, Ahmad Z. Finite element approach and mathematical formulation of viscoelastic auxetic honeycomb structures for impact mitigation. J Eng Sci Tech, 2017, 12: 471–490. Google Scholar

[34] Wu J, Chen X, Wang L. Design and dynamics of a novel solar tracker with parallel mechanism. IEEE/ASME Trans Mechatron, 2016, 21: 88–97. Google Scholar

[35] Wu J, Wang J, Wang L, et al. Dynamics and control of a planar 3-DOF parallel manipulator with actuation redundancy. Mechanism Machine Theor, 2009, 44: 835-849 CrossRef Google Scholar

[36] Wu J, Yu G, Gao Y, et al. Mechatronics modeling and vibration analysis of a 2-DOF parallel manipulator in a 5-DOF hybrid machine tool. Mechanism Machine Theor, 2018, 121: 430-445 CrossRef Google Scholar

[37] Wu J, Gao Y, Zhang B, et al. Workspace and dynamic performance evaluation of the parallel manipulators in a spray-painting equipment. Robotics Comput-Integrated Manufacturing, 2017, 44: 199-207 CrossRef Google Scholar

[38] Larsen U D, Sigmund O, Bouwstra S. Design and fabrication of compliant micromechanisms and structures with negative Poisson’s ratio. J Microelectromech Syst, 1997, 6: 99–106. Google Scholar

[39] Lim T C. A 3D auxetic material based on intersecting double arrowheads. Phys Status Solidi B, 2016, 253: 1252-1260 CrossRef ADS Google Scholar

[40] Ma Z D, Bian H, Sun C, et al. Functionally-graded NPR (negative Poisson’s ratio) material for a blast-protective deflector. In: Proceedings of the 2010 Ndia Ground Vehicle Systems Engineering And Technology Symposium Modeling & Simulation, Testing And Validation (Mstv) Mini-Symposium. Dearborn, 2010. Google Scholar

[41] Zhou G, Ma Z D, Gu J, et al. Design optimization of a NPR structure based on HAM optimization method. Struct Multidisc Optim, 2016, 53: 635-643 CrossRef Google Scholar

[42] Zhou G, Ma Z D, Li G, et al. Design optimization of a novel NPR crash box based on multi-objective genetic algorithm. Struct Multidisc Optim, 2016, 54: 673-684 CrossRef Google Scholar

[43] Zhang W, Ma Z, Hu P. Mechanical properties of a cellular vehicle body structure with negative Poisson’s ratio and enhanced strength. J Reinforced Plastics Compos, 2014, 33: 342-349 CrossRef Google Scholar

[44] Qiao J, Chen C Q. Analyses on the in-plane impact resistance of auxetic double arrowhead honeycombs. J Appl Mech, 2015, 82: 051007 CrossRef ADS Google Scholar

[45] Qiao J X, Chen C Q. Impact resistance of uniform and functionally graded auxetic double arrowhead honeycombs. Int J Impact Eng, 2015, 83: 47-58 CrossRef Google Scholar

[46] Wang Y, Wang L, Ma Z, et al. A negative Poisson’s ratio suspension jounce bumper. Mater Des, 2016, 103: 90-99 CrossRef Google Scholar

[47] Wang Y, Zhao W, Zhou G, et al. Optimization of an auxetic jounce bumper based on Gaussian process metamodel and series hybrid GA-SQP algorithm. Struct Multidisc Optim, 2018, 57: 2515-2525 CrossRef Google Scholar

  • Figure 1

    (Color online) Schematic map of the NPR structure. (a) Unit cell; (b) macro structure.

  • Figure 2

    (Color online) Schematic map of the relative density of the structure.

  • Figure 3

    Mesh convergence test results.

  • Figure 4

    (Color online) Quasi-static compression test. (a) Experimental prototype; (b) numerical model.

  • Figure 5

    (Color online) The comparison of force-displacement of the experimental and numerical models.

  • Figure 6

    (Color online) Deformation configuration of the different models at different displacement. (a) Model A; (b) model B.

  • Figure 7

    (Color online) Effects of the number of layers NL on force-displacement curve by adjusting effective height he. (a) Displacement 0–200 mm; (b) displacement 0–6 mm.

  • Figure 8

    (Color online) Schematic diagram of the deformation mode for the double-V unit cell.

  • Figure 9

    (Color online) Comparison of the deformation mode of NPR structure with different NL. (a) NL=12; (b) NL=13.

  • Figure 10

    (Color online) Effects of layer number NL on EA by adjusting effective height.

  • Figure 11

    (Color online) Comparison of the deformation mode of NPR structure with different NL. (a) NL=12; (b) NL=11.

  • Figure 12

    (Color online) Effects of layer number NL on SEA by adjusting effective height.

  • Figure 13

    (Color online) Effects of the number of layers NL on Force-Displacement curve by adjusting L-beam height hl. (a) Displacement 0–200 mm; (b) displacement 0–6 mm.

  • Figure 14

    (Color online) Effects of layer number NL on EA by adjusting L-beam height hl.

  • Figure 15

    (Color online) Effects of layer number NL on EA by adjusting L-beam height hl.

  • Figure 16

    (Color online) Effects of the cell number NC on Force-Displacement curve by adjusting L-beam height hl. (a) Displacement 0–200 mm; (b) displacement 0–6 mm.

  • Figure 17

    (Color online) Comparison of the deformation modes of NPR structure with different NC. (a) NC=6; (b) NC=15; (c) NC=21.

  • Figure 18

    (Color online) Effects of cell number NC on EA.

  • Figure 19

    (Color online) Effects of cell number NC on SEA.

  • Figure 20

    (Color online) Effects of the thickness of L-beam TL on force-displacement curve by adjusting effective height he. (a) Displacement 0–200 mm; (b) displacement 0–6 mm.

  • Figure 21

    (Color online) Effects of the thickness of L-beam TL on SEA by adjusting effective height he.

  • Figure 22

    (Color online) Effects of the thickness of S-beam TS on force-displacement curve by adjusting effective height he. (a) Displacement 0–200 mm; (b) displacement 0–6 mm.

  • Figure 23

    (Color online) Effects of the thickness of S-beam TS on SEA by adjusting effective height he.

  • Figure 24

    (Color online) Effects of the inner circle radius ri on force-displacement curve. (a) Displacement 0–200 mm; (b) displacement 0–6 mm.

  • Figure 25

    (Color online) Effects of the inner circle radius ri on SEA.

  • Table 1   Parameters of the base model

    Number of layers NL

    Effective height he (mm)

    L-beam height hl (mm)

    Number of cells NC

    Thickness ofL-beam TL (mm)

    Thickness ofS-beam TS (mm)

    Outer circle radius ro (mm)

    Inner circleradius ri (mm)

    Total heighthtotal (mm)

    Base model

    11

    19.9

    40

    15

    1

    1

    80

    50

    250

    Model B

    16

    55

    11.4

    4

    2

    1.6

    80

    50

    250

  • Table 2   Parameters of NPR structures with varying layer number NL by adjusting effective height

    Number of layers NL

    Effective height he (mm)

    L-beam heighthl (mm)

    Number ofcells NC

    Thickness ofL-beam TL (mm)

    Thickness ofS-beam TS (mm)

    Outer circleradius ro (mm)

    Inner circleradius ri (mm)

    Total heighthtotal(mm)

    8

    28.857

    40

    15

    1

    1

    40

    25

    250

    9

    25.125

    40

    15

    1

    1

    40

    25

    250

    10

    22.222

    40

    15

    1

    1

    40

    25

    250

    11

    19.900

    40

    15

    1

    1

    40

    25

    250

    12

    18.000

    40

    15

    1

    1

    40

    25

    250

    13

    16.417

    40

    15

    1

    1

    40

    25

    250

  • Table 3   Parameters of NPR structures with varying layer number NL by adjusting L-beam height

    Number of layers NL

    Effective height he (mm)

    L-beam height hl (mm)

    Number ofcells NC

    Thickness ofL-beam TL (mm)

    Thickness ofS-beam TS (mm)

    Outer circleradius ro (mm)

    Inner circleradius ri (mm)

    Total heighthtotal (mm)

    8

    18

    116

    15

    1

    1

    40

    25

    250

    9

    18

    97

    15

    1

    1

    40

    25

    250

    10

    18

    78

    15

    1

    1

    40

    25

    250

    11

    18

    59

    15

    1

    1

    40

    25

    250

    12

    18

    40

    15

    1

    1

    40

    25

    250

    13

    18

    21

    15

    1

    1

    40

    25

    250

  • Table 4   Parameters of NPR structures with varying thickness of L-beam by adjusting effective height

    Number of layers NL

    Effective height he (mm)

    L-beam heighthl (mm)

    Number ofcells NC

    Thickness ofL-beam TL (mm)

    Thickness ofS-beam TS (mm)

    Outer circleradius ro (mm)

    Inner circleradius ri (mm)

    Total heighthtotal (mm)

    11

    20.175

    40

    15

    0.5

    1

    40

    25

    250

    11

    20.038

    40

    15

    0.75

    1

    40

    25

    250

    11

    19.969

    40

    15

    0.875

    1

    40

    25

    250

    11

    19.900

    40

    15

    1

    1

    40

    25

    250

    11

    19.831

    40

    15

    1.125

    1

    40

    25

    250

    11

    19.763

    40

    15

    1.25

    1

    40

    25

    250

    11

    19.625

    40

    15

    1.5

    1

    40

    25

    250

  • Table 5   Parameters of NPR structures with varying thickness of S-beam by adjusting effective height

    Number of layers NL

    Effective height he (mm)

    L-beam height hl (mm)

    Number ofcells NC

    Thickness ofL-beam TL (mm)

    Thickness ofS-beam TS (mm)

    Outer circleradius ro (mm)

    Inner circleradius ri (mm)

    Total heighthtotal (mm)

    11

    20.175

    40

    15

    1

    0.5

    40

    25

    250

    11

    20.038

    40

    15

    1

    0.75

    40

    25

    250

    11

    19.900

    40

    15

    1

    1

    40

    25

    250

    11

    19.763

    40

    15

    1

    1.25

    40

    25

    250

    11

    19.625

    40

    15

    1

    1.5

    40

    25

    250

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