Optimizing the Thickness of Functionally Graded Lattice Structures for High-Performance Energy Absorption: A Case Study Based on a Bicycle Helmet
Source abstract
Abstract
This study explores the complete production chain of designing, optimizing, and Additive Manufacturing (AM) of a helmet incorporating a functionally graded lattice structure (FGLS). The potential of FGLSs in impact energy absorption tasks is investigated, along with the demonstration of a novel lattice optimization approach. Fifteen conformal, strut-based lattices are implemented in a realistic mountain bike helmet geometry and simulated in a standardized impact scenario in accordance with EN 1078. One model is subjected to the optimization procedure, produced, and physically tested. The study addresses limitations in prior research, emphasizing manufacturability in an AM context, lattice type exploration, the comparability of different unit cell types, and numerical modeling choices. The findings provide insights into the performance of lattice structures during impact, emphasizing practical engineering aspects such as design choices, optimization approaches, and manufacturing constraints.
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Research context
OpenAlex topics: Cellular and Composite Structures · Transportation Safety and Impact Analysis · Acoustic Wave Phenomena Research
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Faculty of Science, Technology and Medicine, University of Luxembourg, L-1359 Luxembourg, Luxembourg
References (89)
Show source-provided references
1. Use of additive manufacturing for the fabrication of cellular and lattice materials: A review
2. A review on integration of lightweight gradient lattice structures in additive manufacturing parts10.1177/1687814020916951 ↗
3. Additively manufactured composite lattices: A state-of-the-art review on fabrications, architectures, constituent materials, mechanical properties, and future directions10.1016/j.tws.2023.111539 ↗
4. Foam topology: Bending versus stretching dominated architectures10.1016/S1359-6454(00)00379-7 ↗
5. The Design Process of Additively Manufactured Mesoscale Lattice Structures: A Review10.1115/1.4040131 ↗
6. The properties of foams and lattices10.1098/rsta.2005.1678 ↗
7. Gibson, L.J., and Ashby, M.F. (1997). Cellular Solids: Structure & Properties, Cambridge University Press.10.1017/CBO9781139878326 ↗
8. SLM lattice structures: Properties, performance, applications and challenges10.1016/j.matdes.2019.108137 ↗
9. Song, B., Zhang, L., and Shi, Y. (2023). Metamaterial Design and Additive Manufacturing, Elsevier.
10. Yan, C., Hao, L., Yang, L., Hussein, A.Y., Young, P.G., Li, Z., and Li, Y. (2021). Triply Periodic Minimal Surface Lattices Additively Manufactured by Selective Laser Melting, Elsevier.
11. Additively-manufactured metallic micro-lattice materials for high specific energy absorption under static and dynamic loading10.1016/j.actamat.2016.05.054 ↗
12. Static mechanical behaviours of stainless steel micro-lattice structures under different loading conditions10.1016/j.msea.2013.07.070 ↗
13. Strength analysis and modeling of cellular lattice structures manufactured using selective laser melting for tooling applications10.1016/j.matdes.2016.05.020 ↗
14. Numerical modelling of the mechanical response of lattice structures produced through AM10.1016/j.prostr.2021.10.079 ↗
15. Auxetic Materials for Sports Applications10.1016/j.proeng.2014.06.079 ↗
16. Design of energy-dissipating structure with functionally graded auxetic cellular material10.1080/13588265.2017.1328764 ↗
17. Xue, Y., Gao, P., Zhou, L., and Han, F. (2020). An Enhanced Three-Dimensional Auxetic Lattice. Materials, 13.10.3390/ma13041008 ↗
18. Re-entrant auxetic lattices with enhanced stiffness: A numerical study10.1016/j.ijmecsci.2020.105619 ↗
19. Design and mechanical characteristics of auxetic metamaterial with tunable stiffness10.1016/j.ijmecsci.2022.107286 ↗
20. Damage-tolerant architected materials inspired by crystal microstructure10.1038/s41586-018-0850-3 ↗
21. Al-Ketan, O., Lee, D.-W., Rowshan, R., and Abu Al-Rub, R.K. (2020). Functionally graded and multi-morphology sheet TPMS lattices: Design, manufacturing, and mechanical properties. J. Mech. Behav. Biomed. Mater., 102.10.1016/j.jmbbm.2019.103520 ↗
22. Effective design and simulation of surface-based lattice structures featuring volume fraction and cell type grading10.1016/j.matdes.2018.05.058 ↗
23. Mechanical properties and energy absorption capabilities of functionally graded lattice structures: Experiments and simulations10.1016/j.ijmecsci.2020.105735 ↗
24. Graded lattice structures: Simultaneous enhancement in stiffness and energy absorption10.1016/j.matdes.2020.109129 ↗
25. An investigation into reinforced and functionally graded lattice structures10.1177/0021955X16639035 ↗
26. Compressive properties of functionally graded lattice structures manufactured by selective laser melting10.1016/j.matdes.2017.06.006 ↗
27. Dynamic crushing and energy absorption of regular, irregular and functionally graded cellular structures10.1016/j.ijsolstr.2010.10.018 ↗
28. Tao, W., Sutton, A., Kolan, K., and Leu, M.C. (2018, January 15–19). Design of Lattice Structures with Graded Density Fabricated by Additive Manufacturing. Proceedings of the International Symposium on Flexible Automation 2018 International Symposium on Flexible Automation, Kanazawa, Japan.10.29007/w9vt ↗
29. Compressive properties of bidirectionally graded lattice structures10.1016/j.matdes.2022.110683 ↗
30. Compressive Properties of 316L Stainless Steel Topology-Optimized Lattice Structures Fabricated by Selective Laser Melting10.1002/adem.202000957 ↗
31. Evaluation of topology-optimized lattice structures manufactured via selective laser melting10.1016/j.matdes.2018.01.023 ↗
32. Topology optimization-guided lattice composites and their mechanical characterizations10.1016/j.compositesb.2018.12.027 ↗
33. Topological design optimization of lattice structures to maximize shear stiffness10.1016/j.advengsoft.2017.04.011 ↗
34. A Novel Design Method for Nonuniform Lattice Structures Based on Topology Optimization10.1115/1.4040546 ↗
35. Optimisation of functionally graded lattice structures using isostatic lines10.1016/j.matdes.2017.04.082 ↗
36. Design and Optimization of Conforming Lattice Structures10.1109/TVCG.2019.2938946 ↗
37. Wang, X., Zhu, L., Sun, L., and Li, N. (2020, January 29–31). A study of functionally graded lattice structural design and optimisation. Proceedings of the 2020 6th International Conference on Mechanical Engineering and Automation Science (ICMEAS), Moscow, Russia.10.1109/ICMEAS51739.2020.00017 ↗
38. Method to optimize an additively-manufactured functionally-graded lattice structure for effective liquid cooling
39. Multifunctional heat exchangers derived from three-dimensional micro-lattice structures10.1016/j.ijheatmasstransfer.2012.01.011 ↗
40. Coupling lattice structure topology optimization with design-dependent feature evolution for additive manufactured heat conduction design10.1016/j.cma.2017.12.024 ↗
41. 3D printed sound absorbers using functionally-graded sonic crystals10.1121/1.5035582 ↗
42. Recent bicycle helmet designs and directions for future research: A comprehensive review from material and structural mechanics aspects10.1016/j.ijimpeng.2022.104317 ↗
43. (2023, November 27). Bontrager. Available online: https://www.trekbikes.com/international/en_IN_TL/bontrager?clear=true.
44. (2021, November 19). WaveCel Helmets|Trek Bikes. Available online: https://www.trekbikes.com/us/en_US/wavecel/.
45. (2023, November 24). Koroyd. Available online: https://koroyd.com/.
46. (2023, November 27). Hexr. Available online: https://hexr.com.
47. Evaluation of a novel bicycle helmet concept in oblique impact testing10.1016/j.aap.2018.12.017 ↗
48. Feasibility of optimising bicycle helmet design safety through the use of additive manufactured TPE cellular structures10.1007/s00170-015-6972-y ↗
49. Khosroshahi, S.F., Duckworth, H., Galvanetto, U., and Ghajari, M. (2019). The effects of topology and relative density of lattice liners on traumatic brain injury mitigation. J. Biomech., 97.10.1016/j.jbiomech.2019.109376 ↗
50. Crashworthiness Study of an Innovative Helmet Liner Composed of an Auxetic Lattice Structure and PU Foam
51. Impact behavior of energy absorbing helmet liners with PA12 lattice structures: A computational study10.1016/j.ijmecsci.2022.107673 ↗
52. Decker, T., and Kedziora, S. (2023). Local Thickness Optimization of Functionally Graded Lattice Structures in Compression. Appl. Sci., 13.10.3390/app132312969 ↗
53. (2023, December 10). nTop. Available online: https://www.ntop.com.
54. Decker, T., Kedziora, S., and Wolf, C. (2020, January 25–25). Practical Implementation of Functionally Graded Lattice Structures in a Bicycle Crank Arm. Proceedings of the 885th International Conference on Science, Technology, Engineering and Management (ICSTEM), Vienna, Austria.
55. Kedziora, S., Decker, T., and Museyibov, E. (2023). Application of Functionally Graded Shell Lattice as Infill in Additive Manufacturing. Materials, 16.10.20944/preprints202304.0976.v1 ↗
56. Helmets for Pedal Cyclists and for Users of Skateboards and Roller Skates (Standard No. EN 1078:2012). Available online: https://standards.cencenelec.eu/dyn/www/f?p=205:110:0::::FSP_ORG_ID,FSP_LANG_ID:6139,25&cs=111AFC3A202BD0C5CF21D58F9A377B263.
57. U.S. Department of Transportation—National Highway Traffic Safety Administration (2024, January 16). Occupant Protection in Interior Impact—Upper Interior Impact Protection, Available online: https://www.nhtsa.gov/sites/nhtsa.gov/files/documents/tp-201u-02_tag.pdf.
58. Estimation of the Probability of Head Injury at a Given Abbreviated Injury Scale Level by Means of a Fuction of Head Injury Criterion10.2478/czoto-2020-0012 ↗
59. (2023, November 24). SQLab GmbH. Available online: https://www.sq-lab.com/en/.
60. Stroud, I. (2006). Boundary Representation Modelling Techniques, Springer Science and Business Media LLC.
61. Allen, G. (2020, April 20). nTopology Modeling Technology. nTopology, 26 November 2019. Available online: https://www.ntop.com/resources/guides/whitepaper-implicit-modeling-technology/.
62. (2023, November 24). Altair HyperMesh. Available online: https://altair.com/hypermesh/.
63. (2023, November 24). Altair RADIOSS. Available online: https://altair.com/radioss.
64. (2023, November 24). Altair HyperStudy. Available online: https://altair.com/hyperstudy/.
65. (2023, November 24). MATLAB. Available online: https://www.mathworks.com/products/matlab.html.
66. Headforms for Use in the Testing of Protective Helmets (Standard No. EN 960:2006). Available online: https://standards.cencenelec.eu/dyn/www/f?p=205:110:0::::FSP_PROJECT:6481&cs=1D4762919EDD7581CBAB25E02CD719CA9.
67. Centiles for adult head circumference10.1136/adc.67.10.1286 ↗
68. (2023, October 31). HP Multi Jet Fusion 3D Printing Technology. Available online: https://www.hp.com/us-en/printers/3d-printers/learning-center/3d-printing-process.html#section=hp-multi-jet-fusion.
69. Compressive response of polymeric foams under quasi-static, medium and high strain rate conditions10.1016/j.polymertesting.2006.05.005 ↗
70. Tensile behavior of polycarbonate over a wide range of strain rates10.1016/j.msea.2010.03.088 ↗
71. (2024, January 16). Mg AZ91. Available online: https://www.matweb.com/search/datasheet.aspx?MatGUID=07baafbb9c364fb18fd413bceced867f.
72. Comparison of Strength Properties of Common Powder Bed Fusion and Stereolithography Materials10.4028/p-Sgu1sR ↗
73. Friction Coefficients and Surface Properties for Laser Sintered Parts
74. Friction and wear properties of oriented Polaymide 12 objects manufactured by SLS Technology
75. Experimental and numerical analysis of friction and wear behavior of polycarbonate10.1016/S0043-1648(01)00788-8 ↗
76. (2023, December 01). Altair RADIOSS LAW70 Tabulated Viscoelastic Foam Material Law. Available online: https://2021.help.altair.com/2021/hwsolvers/rad/topics/solvers/rad/mat_law70_foam_tab_starter_r.htm.
77. (2023, December 01). Altair RADIOSS LAW36 Elastic Plastic Piecewise Linear Material. Available online: https://2021.help.altair.com/2021/hwsolvers/rad/topics/solvers/rad/explicit_structural_fea_elasto_plastic_c.htm#elastic_plastic_piecewise_linear_material_r.
78. (2023, December 01). Altair RADIOSS LAW2 Johnson-Cook Elastic-Plastic Material Model. Available online: https://2021.help.altair.com/2021/hwsolvers/rad/topics/solvers/rad/mat_law2_plas_johns_starter_r.htm.
79. (2023, December 01). Altair RADIOSS TYPE7 General Contact Interface. Available online: https://2021.help.altair.com/2021/hwsolvers/rad/topics/solvers/rad/default_inter_type7_starter_r.htm?zoom_highlight=type7.
80. (2023, December 01). Altair RADIOSS TYPE11 Edge-to-Edge Contact Interface. Available online: https://2021.help.altair.com/2021/hwsolvers/rad/topics/solvers/rad/default_inter_type11_starter_r.htm?zoom_highlight=type11.
81. (2012). Plastics-Determination of Tensile Properties-Part 2: Test Conditions for Moulding and Extrusion Plastics (Standard No. ISO 527-2:2012). Available online: https://www.iso.org/standard/56046.html.
82. (2023, November 24). Modifiable Extensible Lattice Sequence (MELS). Available online: https://2021.help.altair.com/2021.2/hwdesktop/hst/topics/design_exploration/method_modified_extensible_lattice_sequence_doe_r.htm.
83. (2023, November 24). Global Response Search Method (GRSM). Available online: https://2021.help.altair.com/2021.2/hwdesktop/hst/topics/design_exploration/method_global_response_surface_method_r.htm.
84. (2023, November 27). TCL/TK Homepage. Available online: https://www.tcl.tk.
85. Pummelos as Concept Generators for Biomimetically Inspired Low Weight Structures with Excellent Damping Properties10.1002/adem.201080065 ↗
86. HP Development Company (2021, October 05). HP 3D High Reusability PA 12. pp. 5–6. Available online: http://www8.hp.com/h20195/v2/getpdf.aspx/4AA7-0716ENE.pdf.
87. Gong, H. (2013). Generation and Detection of Defects in Metallic Parts Fabricated by Selective Laser Melting and Electron Beam Melting and Their Effects on Mechanical Properties. [Ph.D. Thesis, University of Louisville].
88. Vera-Rodríguez, G., Moreno-Corrales, L., Marín-González, I., Barba, D., Montáns, F.J., and Sanz-Gómez, M. (2024). Incorporation of Defects in Finite Elements to Model Effective Mechanical Properties of Metamaterial Cells Printed by Selective Laser Melting. Sustainability, 16.10.3390/su16031167 ↗
89. Intelligent orientation of parts based on defect prediction in Multi Jet Fusion process10.1007/s40964-021-00199-x ↗