Advertisement

Design, optimization, and validation of mechanical properties of different cellular structures for biomedical application

  • Kalayu Mekonen Abate
  • Aamer Nazir
  • Yun-Peng Yeh
  • Jia-En Chen
  • Jeng-Ywan JengEmail author
ORIGINAL ARTICLE

Abstract

Cellular structures are promising applicants for additive manufacturing (AM), due to their best capabilities over solid ones such as high strength-to-weight ratio, having porosity, and light in weight. New vintile cellular structures and with the existing five different cellular structures namely cubic, tetrahedron, hexagon, octagon, and rhombic dodecahedron were designed and the effect of unit size, lattice topology, porosity, and optimization of cellular structures on the mechanical properties were discussed in this study. Eighty-four samples with different cell sizes, lattice topologies, and porosities were printed using VisiJet M3 Crystal material on Projet 3510 HDMax 3D printer. Then, electro-optical microscopic is used to determine the pore size. Based on predesigned cellular structures, finite element analysis (FEA) and experimental work were performed to estimate and evaluate the mechanical properties of cellular structures. Results shown that the cellular structure with vintile lattice topology performs less stress and less deformation than the other cellular structures. The experiment results were in good conformance with the result obtained from simulation. This study is not only limited to cellular structure design for biomedical applications but also compared the mechanical performance of uniform density and variable density cellular structures. Both non-optimized and optimized vintile cellular structures is finally tested with FEA and experiments have been carried out on samples fabricated by material jetting, and both results have shown that the optimized cellular structure had much less stress and lower deformation than the non-optimized cellular structure.

Keywords

Cellular structure Material jetting Additive manufacturing Biomedical implant Finite element analysis Mechanical property Design and optimization 

Notes

References

  1. 1.
    Gibson LJ (2005) Biomechanics of cellular solids. J Biomech.  https://doi.org/10.1016/j.jbiomech.2004.09.027 CrossRefGoogle Scholar
  2. 2.
    Deshpande VS, Fleck NA, Ashby MF (2001) Effective properties of the octet-truss lattice material. J Mech Phys Solids 49:1747–1769.  https://doi.org/10.1016/S0022-5096(01)00010-2 CrossRefzbMATHGoogle Scholar
  3. 3.
    Ashby MF (2006) The properties of foams and lattices. Philos Trans R Soc A Math Phys Eng Sci 364:15–30.  https://doi.org/10.1098/rsta.2005.1678 MathSciNetCrossRefGoogle Scholar
  4. 4.
    Panda BN, Technology OF (2015) Design and Development of Cellular Structure for Additive Manufacturing 83Google Scholar
  5. 5.
    Pastrone JGF (2009) Mechanics of Microstructured Solids: Cellular Materials, Fibre Reinforced ... - Google Books, Vol 46. Springer Science & Business MediaGoogle Scholar
  6. 6.
    Liu C, Li F, Ma L-P et al (2010) Advanced materials for energy storage. Adv Mater 22:28–62.  https://doi.org/10.1002/adma.200903328 CrossRefGoogle Scholar
  7. 7.
    Evans AGG, He MYY, Deshpande VSS et al (2010) Concepts for enhanced energy absorption using hollow micro-lattices. Int J Impact Eng 37:947–959.  https://doi.org/10.1016/j.ijimpeng.2010.03.007 CrossRefGoogle Scholar
  8. 8.
    Hutmacher DW (2000) Scaffolds in tissue engineering bone and cartilage. Biomaterials 21:2529–2543.  https://doi.org/10.1016/S0142-9612(00)00121-6 CrossRefGoogle Scholar
  9. 9.
    Nguyen J, Park S-I, Rosen D (2013) Heuristic optimization method for cellular structure design of light weight components. Int J Precis Eng Manuf 14:1071–1078.  https://doi.org/10.1007/s12541-013-0144-5 CrossRefGoogle Scholar
  10. 10.
    Hedayati R, Sadighi M, Mohammadi-Aghdam M, Zadpoor AAA (2016) Mechanical properties of regular porous biomaterials made from truncated cube repeating unit cells: analytical solutions and computational models. Mater Sci Eng C 60:163–183.  https://doi.org/10.1016/j.msec.2015.11.001 CrossRefGoogle Scholar
  11. 11.
    Liu F, Zhang DZ, Zhang P, et al (2018) Mechanical properties of optimized diamond lattice structure for bone scaffolds fabricated via selective laser melting. Materials (Basel) 11.  https://doi.org/10.3390/ma11030374 CrossRefGoogle Scholar
  12. 12.
    Zheng X, Lee H, Weisgraber TH et al (2014) Ultralight, ultrastiff mechanical metamaterials. Science (80- ) 344:1373–1377.  https://doi.org/10.1126/science.1252291 CrossRefGoogle Scholar
  13. 13.
    Ali D, Sen S (2017) Finite element analysis of mechanical behavior, permeability and fluid induced wall shear stress of high porosity scaffolds with gyroid and lattice-based architectures. J Mech Behav Biomed Mater 75:262–270.  https://doi.org/10.1016/j.jmbbm.2017.07.035 CrossRefGoogle Scholar
  14. 14.
    Karageorgiou V, Kaplan D (2005) Porosity of 3D biomaterial scaffolds and osteogenesis. Biomaterials 26:5474–5491.  https://doi.org/10.1016/j.biomaterials.2005.02.002 CrossRefGoogle Scholar
  15. 15.
    Jetté B, Brailovski V, Dumas M, Simoneau C, Terriault P (2018) Femoral stem incorporating a diamond cubic lattice structure: design, manufacture and testing. J Mech Behav Biomed Mater 77:58–72.  https://doi.org/10.1016/j.jmbbm.2017.08.034 CrossRefGoogle Scholar
  16. 16.
    Yan C, Hao L, Hussein A et al (2015) Microstructure and mechanical properties of aluminium alloy cellular lattice structures manufactured by direct metal laser sintering. Mater Sci Eng A 628:238–246.  https://doi.org/10.1016/j.msea.2015.01.063 CrossRefGoogle Scholar
  17. 17.
    Kang H, Lin CY, Hollister SJ (2010) Topology optimization of three dimensional tissue engineering scaffold architectures for prescribed bulk modulus and diffusivity. Struct Multidiscip Optim 42:633–644.  https://doi.org/10.1007/s00158-010-0508-8 CrossRefGoogle Scholar
  18. 18.
    Higuchi A, Ling QD, Hsu ST, Umezawa A (2012) Biomimetic cell culture proteins as extracellular matrices for stem cell differentiation. Chem Rev 112:4507–4540.  https://doi.org/10.1021/cr3000169 CrossRefGoogle Scholar
  19. 19.
    Hollister S (2006) Porous scaffold design for tissue engineering. Nat Mater 5:590.  https://doi.org/10.1038/nmat1683 CrossRefGoogle Scholar
  20. 20.
    Murr LE, Gaytan SM, Medina F et al (2010) Next-generation biomedical implants using additive manufacturing of complex, cellular and functional mesh arrays. Philos Trans A Math Phys Eng Sci 368:1999–2032.  https://doi.org/10.1098/rsta.2010.0010 CrossRefGoogle Scholar
  21. 21.
    Wauthle R, Van Der Stok J, Yavari SA et al (2015) Additively manufactured porous tantalum implants. Acta Biomater 14:217–225.  https://doi.org/10.1016/j.actbio.2014.12.003 CrossRefGoogle Scholar
  22. 22.
    Hong D, Chou DT, Velikokhatnyi OI et al (2016) Binder-jetting 3D printing and alloy development of new biodegradable Fe-Mn-Ca/Mg alloys. Acta Biomater.  https://doi.org/10.1016/j.actbio.2016.08.032 CrossRefGoogle Scholar
  23. 23.
    Yan C, Hao L, Hussein A, Young P (2015) Ti-6Al-4V triply periodic minimal surface structures for bone implants fabricated via selective laser melting. J Mech Behav Biomed Mater 51:61–73.  https://doi.org/10.1016/j.jmbbm.2015.06.024 CrossRefGoogle Scholar
  24. 24.
    Kadkhodapour J, Montazerian H, Darabi ACC et al (2015) Failure mechanisms of additively manufactured porous biomaterials: effects of porosity and type of unit cell. J Mech Behav Biomed Mater 50:180–191CrossRefGoogle Scholar
  25. 25.
    Mullen L, Stamp RC, Brooks WK et al (2009) Selective laser melting: a regular unit cell approach for the manufacture of porous, titanium, bone in-growth constructs, suitable for orthopedic applications. J Biomed Mater Res Part B Appl Biomater 89B:325–334.  https://doi.org/10.1002/jbm.b.31219 CrossRefGoogle Scholar
  26. 26.
    Han C, Yan C, Wen S et al (2017) Effects of the unit cell topology on the compression properties of porous Co-Cr scaffolds fabricated via selective laser melting. Rapid Prototyp J 23:16–27.  https://doi.org/10.1108/RPJ-08-2015-0114 CrossRefGoogle Scholar
  27. 27.
    Li X, Wang C, Zhang W, Li Y (2010) Fabrication and compressive properties of Ti6Al4V implant with honeycomb-like structure for biomedical applications. Rapid Prototyp J 16:44–49.  https://doi.org/10.1108/13552541011011703 CrossRefGoogle Scholar
  28. 28.
    Hu LL, Yu TX (2013) Mechanical behavior of hexagonal honeycombs under low-velocity impact – theory and simulations. Int J Solids Struct 50:3152–3165.  https://doi.org/10.1016/J.IJSOLSTR.2013.05.017 CrossRefGoogle Scholar
  29. 29.
    Sullivan RM, Ghosn LJ, Lerch BA (2008) A general tetrakaidecahedron model for open-celled foams. Int J Solids Struct 45:1754–1765.  https://doi.org/10.1016/J.IJSOLSTR.2007.10.028 CrossRefzbMATHGoogle Scholar
  30. 30.
    Babaee S, Jahromi BH, Ajdari A et al (2012) Mechanical properties of open-cell rhombic dodecahedron cellular structures. Acta Mater 60:2873–2885.  https://doi.org/10.1016/J.ACTAMAT.2012.01.052 CrossRefGoogle Scholar
  31. 31.
    Wieding J, Wolf A, Bader R (2014) Numerical optimization of open-porous bone scaffold structures to match the elastic properties of human cortical bone. J Mech Behav Biomed Mater 37:56–68.  https://doi.org/10.1016/j.jmbbm.2014.05.002 CrossRefGoogle Scholar
  32. 32.
    Campoli G, Borleffs MS, Amin Yavari S et al (2013) Mechanical properties of open-cell metallic biomaterials manufactured using additive manufacturing. Mater Des 49:957–965.  https://doi.org/10.1016/j.matdes.2013.01.071 CrossRefGoogle Scholar
  33. 33.
    Wallach JC, Gibson LJ (2001) Mechanical behavior of a three-dimensional truss material. Int J Solids Struct 38:7181–7196.  https://doi.org/10.1016/S0020-7683(00)00400-5 CrossRefzbMATHGoogle Scholar
  34. 34.
    Zhang P, Toman J, Yu Y et al (2014) Efficient design-optimization of variable-density hexagonal cellular structure by additive manufacturing: theory and validation. J Manuf Sci Eng 137:021004.  https://doi.org/10.1115/1.4028724 CrossRefGoogle Scholar
  35. 35.
    McGregor DJ, Tawfick S, King WP (2019) Mechanical properties of hexagonal lattice structures fabricated using continuous liquid interface production additive manufacturing. Addit Manuf 25:10–18.  https://doi.org/10.1016/J.ADDMA.2018.11.002 CrossRefGoogle Scholar
  36. 36.
    Ahmadi SMM, Campoli G, Amin Yavari S, Sajadi B, Wauthle R, Schrooten J, Weinans H, Zadpoor AA (2014) Mechanical behavior of regular open-cell porous biomaterials made of diamond lattice unit cells. J Mech Behav Biomed Mater 34:106–115.  https://doi.org/10.1016/j.jmbbm.2014.02.003 CrossRefGoogle Scholar
  37. 37.
    Fan HL, Fang DN, Jing FN (2008) Yield surfaces and micro-failure mechanism of block lattice truss materials. Mater Des 29:2038–2042.  https://doi.org/10.1016/J.MATDES.2008.04.013 CrossRefGoogle Scholar
  38. 38.
    Sun J, Yang Y, Wang D (2013) Mechanical properties of a Ti6Al4V porous structure produced by selective laser melting. Mater Des 49:545–552.  https://doi.org/10.1016/j.matdes.2013.01.038 CrossRefGoogle Scholar
  39. 39.
    Jung JW, Park JH, Hong JM, Kang HW, Cho DW (2014) Octahedron pore architecture to enhance flexibility of nasal implant-shaped scaffold for rhinoplasty. Int J Precis Eng Manuf 15:2611–2616.  https://doi.org/10.1007/s12541-014-0634-0 CrossRefGoogle Scholar
  40. 40.
    Zadpoor AA, Hedayati R (2016) Analytical relationships for prediction of the mechanical properties of additively manufactured porous biomaterials. J Biomed Mater Res - Part A 104:3164–3174.  https://doi.org/10.1002/jbm.a.35855 CrossRefGoogle Scholar
  41. 41.
    Xiao L, Song W, Wang C et al (2015) Mechanical behavior of open-cell rhombic dodecahedron Ti–6Al–4V lattice structure. Mater Sci Eng A 640:375–384.  https://doi.org/10.1016/J.MSEA.2015.06.018 CrossRefGoogle Scholar
  42. 42.
    Shulmeister V, Van der Burg MWD, Van der Giessen E, Marissen R (1998) A numerical study of large deformations of low-density elastomeric open-cell foams. Mech Mater 30:125–140.  https://doi.org/10.1016/S0167-6636(98)00033-7 CrossRefGoogle Scholar
  43. 43.
    Amirkhani S, Bagheri R, Zehtab Yazdi A (2012) Effect of pore geometry and loading direction on deformation mechanism of rapid prototyped scaffolds. Acta Mater 60:2778–2789.  https://doi.org/10.1016/J.ACTAMAT.2012.01.044 CrossRefGoogle Scholar
  44. 44.
    3D Systems (2017) MultiJet Plastic Printers VisiJet ® M3 Advanced PlasticsGoogle Scholar
  45. 45.
    Alaboodi AS, Sivasankaran S (2018) Experimental design and investigation on the mechanical behavior of novel 3D printed biocompatibility polycarbonate scaffolds for medical applications. J Manuf Process 35:479–491.  https://doi.org/10.1016/j.jmapro.2018.08.035 CrossRefGoogle Scholar
  46. 46.
    Khoshkhoo A, Carrano AL, Blersch DM (2018) Effect of build orientation and part thickness on dimensional distortion in material jetting processes. Rapid Prototyp J 24:1563–1571.  https://doi.org/10.1108/RPJ-10-2017-0210 CrossRefGoogle Scholar
  47. 47.
    Kechagias J, Stavropoulos P, Koutsomichalis A, et al Dimensional Accuracy Optimization of Prototypes produced by PolyJet Direct 3D Printing Technology. 61–65Google Scholar
  48. 48.
    Kechagias J (2007) Investigation of LOM process quality using design of experiments approach. Rapid Prototyp J 13:316–323.  https://doi.org/10.1108/13552540710824823 CrossRefGoogle Scholar
  49. 49.
    Sigmund O, Maute K (2013) Topology optimization approaches: a comparative review. Struct Multidiscip Optim 48:1031–1055.  https://doi.org/10.1007/s00158-013-0978-6 MathSciNetCrossRefGoogle Scholar
  50. 50.
    Wang Y, Zhang L, Daynes S et al (2018) Design of graded lattice structure with optimized mesostructures for additive manufacturing. Mater Des 142:114–123.  https://doi.org/10.1016/j.matdes.2018.01.011 CrossRefGoogle Scholar
  51. 51.
    Huang X, Xie YM (2008) Optimal design of periodic structures using evolutionary topology optimization. Struct Multidiscip Optim 36:597–606.  https://doi.org/10.1007/s00158-007-0196-1 CrossRefGoogle Scholar
  52. 52.
    Huang X, Xie YM (2010) A further review of ESO type methods for topology optimization. Struct Multidiscip Optim 41:671–683.  https://doi.org/10.1007/s00158-010-0487-9 CrossRefGoogle Scholar
  53. 53.
    Torquato S, Hyun S, Donev A (2003) Optimal design of manufacturable three-dimensional composites with multifunctional characteristics. J Appl Phys 94:5748–5755.  https://doi.org/10.1063/1.1611631 CrossRefGoogle Scholar
  54. 54.
    Bendsoe MP, Kikuchi N (1988) Generating optimal topologies in structural design using a homogenization method. Comput Methods Appl Mech Eng 71:197–224MathSciNetCrossRefGoogle Scholar
  55. 55.
    Xie YM, Steven GP (1996) Evolutionary structural optimization for dynamic problems. Comput Struct 58:1067–1073.  https://doi.org/10.1016/0045-7949(95)00235-9 CrossRefzbMATHGoogle Scholar
  56. 56.
    Bendsøe MP, Sigmund O (1999) Material interpolation schemes in topology optimization. Arch Appl Mech 69:635–654.  https://doi.org/10.1007/s004190050248 CrossRefzbMATHGoogle Scholar
  57. 57.
    Dai X, Tang P, Cheng X, Wu M (2013) A variational binary level set method for structural topology optimization. Commun Comput Phys 13:1292–1308.  https://doi.org/10.4208/cicp.160911.110512a MathSciNetCrossRefzbMATHGoogle Scholar
  58. 58.
    Ning J, Liang SY (2018) Model-driven determination of Johnson-cook material constants using temperature and force measurements. Int J Adv Manuf Technol 97:1053–1060CrossRefGoogle Scholar
  59. 59.
    Ning J, Liang SY (2019) Inverse identification of Johnson-Cook material constants based on modified chip formation model and iterative gradient search using temperature and force measurements. Int J Adv Manuf Technol 102:2865–2876.  https://doi.org/10.1007/s00170-019-03286-0 CrossRefGoogle Scholar
  60. 60.
    Ning J, Nguyen V, Huang Y et al (2018) Inverse determination of Johnson–Cook model constants of ultra-fine-grained titanium based on chip formation model and iterative gradient search. Int J Adv Manuf Technol 99:1131–1140.  https://doi.org/10.1007/s00170-018-2508-6 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  • Kalayu Mekonen Abate
    • 1
    • 2
  • Aamer Nazir
    • 1
    • 2
  • Yun-Peng Yeh
    • 1
    • 2
  • Jia-En Chen
    • 3
  • Jeng-Ywan Jeng
    • 1
    • 2
    Email author
  1. 1.High Speed 3D Printing Research CenterNational Taiwan University of Science and TechnologyTaipeiRepublic of China
  2. 2.Department of Mechanical EngineeringNational Taiwan University of Science and TechnologyTaipeiRepublic of China
  3. 3.Department of Biomedical EngineeringNational Defense Medical CenterTaipeiTaiwan

Personalised recommendations