2. Energy absorption
characteristics of bio-inspired
hierarchical multi-cell square
tubes under axial crushing
Ngoc San Ha, Thong M. Pham, Hong
Hao, Guoxing Lu
International Journal of Mechanical Sciences
201 (2021) 106464
4. INTRODUCTION
Energy absorbers of lightweight and high
efficiency have been intensively studied
and applied for energy absorption
applications in various engineering fields
including aerospace, civil engineering,
transportation, and nuclear reactors
5. “thin-walled structures with a
simple cross-section such as
circular and square are
extensively utilized as energy
absorbers due to their low cost
and being easily manufactured”
7. A novel bio-inspired hierarchical
multi-cell square (BHMS) tube
mimicking the hierarchical fractal
design of biological structures such
as bone, bamboo, and wheat
Finite element analysis (FEA)
Intensive simulation study
A theoretical model to predict the MCF
8. Previous work
Koch fractal
side fractal structures
Wang J , Zhang Y , He N , Wang CH . Crashworthiness behaviour of Koch fractal structures. Mater Des
2018;144:229–44.
Zhang Y , He N , Song X , Chen T , Chen H . On impacting mechanical behaviours of side fractal
structures. Thin-Walled Struct 2020;146:106490.
EA = 0.24 – 1.608 kJ
EA = 1.56 – 3.51 kJ
9. METHODOLOGY
Total Energy Absorption
E𝑡𝑜𝑡𝑎𝑙 = E𝑀−𝑇 +E𝐵−𝑇
Membrane Energy
2-panel corner elements
3-panel corner elements
4-panel corner elements
Bending Energy
The Mean Crushing
Force
10. The evolution of the BHMS tubes
𝑙𝑛
′ =
𝑙0
′
2𝑛
𝑡0 =
𝑡𝑟
1 +
2
2
𝑡𝑛 =
𝑡𝑟
1 + (𝑛 + 1)
2
2
13. Simplified Super Folding Element
(SSFE) theory
The SSFE assumed that the wavelength
2H for each fold and wall thickness of
the tube are the same
Membrane Energy
where M0 = σ0 h2/4 is the fully plastic bending moment
per unit width, σ0 and h represents the flow stress and
wall thickness respectively
X. Zhang, H. Zhang, Theoretical and numerical investigation on the crush
resistance of rhombic and kagome honeycombs, Compos. Struct. 96
(2013) 143–152.
𝐸𝑚𝑒𝑚𝑏𝑟𝑎𝑛𝑒 = 𝜎0ℎ𝑑𝑠 = 4𝑀0∆𝑆/ℎ
14. 𝐸𝑚
2−𝑝𝑎𝑛𝑒𝑙
=
4𝑀0𝐻2
tan 𝛼
𝑡(tan 𝛼 + 0.05 tan 𝛼)/1.1
∆𝑆 = 𝐻2 tan
𝜃
2
Membrane Energy
2-panel corner membrane energy
The model of Zhang and Zhang is adopted to consider
the influence of central angle on crush resistance of
two-panel angle element
Xiong Zhang, HuiZhang, Experimental and numerical investigation on crush resistance of
polygonal columns and angle elements Thin-Walled Structures 57 (2012) 25–36
15. Membrane Energy
3-panel corner membrane energy
X. Zhang, H. Zhang, Numerical and theoretical studies on energy absorption of three-panel
angle elements, Int. J. Impact Eng. 46 (2012) 23–40
𝐸𝑚
3−𝑝𝑎𝑛𝑒𝑙
= 𝐸𝑚
𝑐𝑒𝑛𝑡𝑟𝑎𝑙 𝑝𝑎𝑛𝑒𝑙
+ 𝐸𝑚
2−𝑝𝑎𝑛𝑒𝑙
𝐸𝑚
3−𝑝𝑎𝑛𝑒𝑙
=
4𝑀0𝐻2
𝑡
tan 𝛼
(tan 𝛼 + 0.05 tan 𝛼)/1.1
+ 2 tan(𝛼 2)
16. Membrane Energy
4-panel corner membrane energy
Tran T, Hou S, Han X, Nguyen N, Chau M . Theoretical prediction and crashworthiness optimization
of multi-cell square tubes under oblique impact loading. Int J Mech Sci 2014;89:177–93.
𝐸𝑚
4−𝑝𝑎𝑛𝑒𝑙
=
8𝑀0𝐻2
𝑡
1 +
1
cos 𝛽
𝐸𝑚
𝐾−𝑠ℎ𝑎𝑝𝑒
=
19.314𝑀0𝐻2
𝑡
18. 𝛼 = 45°
𝐸𝑚
𝑐𝑜𝑟𝑛𝑒𝑟
=
7.504𝑀0𝐻2
𝑡
The Mean Crushing Force
The total energy of the BHMS is
Special case from 3-panel
𝛼 = 90°
Two right corners
Special case from 2-panel
𝛼 = 90°
𝑀𝐶𝐹. 2𝐻𝐾 = 2𝜋𝑀0𝐿𝑐 + 𝑁1𝐸𝑚
𝑐𝑜𝑟𝑛𝑒𝑟 + 𝑁2𝐸𝑚
𝑇−𝑠ℎ𝑎𝑝𝑒
+ 𝑁3𝐸𝑚
𝑘−𝑠ℎ𝑎𝑝𝑒
+ 𝑁4𝐸𝑚
𝑐𝑟𝑖𝑠𝑠−𝑐𝑟𝑜𝑠𝑠
𝐸𝑚
𝑇−𝑠ℎ𝑎𝑝𝑒
=
12.4𝑀0𝐻2
𝑡 𝐸𝑚,𝑠𝑦𝑚
𝑐𝑟𝑖𝑠𝑠−𝑐𝑟𝑜𝑠𝑠
=
16 𝑀0𝐻2
𝑡
19. The Mean Crushing Force
Where K is the coefficient
effective crushing distance, in this
paper, 𝐾 = 0.7 is obtained by
calculating the average value of
different folding waves of three
panels
31. 1
The SEA of the 3rd-order BHMS tube is 178.4% higher
than that of the 0th-order BHMS tube. Compared with the
square and multi-cell square tubes, the maximum
enhancement of the SEA of the BHMS tube reaches up to
173.7% and 128.1%, respectively.
The ULC of the 3rd order BHMS tube reduces up to 88.8%
and 85.7% compared to square and multi-cell tubes. It
indicates that the BHMS tube has great potential to
improve the energy absorption than the square tube and
conventional multi-cell square tube
CONCLUSIONS
2
32. Future work
1. Build a structure for the vehicle
bumper based on BHMScolumn (ATC)
2. Study the manufacturability of ATC
and study this effect on energy
absorption
3. Study to introduce new materials with
lightweight and easy to manufacture
33. CREDITS: This presentation template was
created by Slidesgo, including icons by
Flaticon, infographics & images by Freepik
and illustrations by Storyset
THANKS
Your comments are highly appreciated
