Skip to main content

Advertisement

Log in

A state-of-the-art review on types, design, optimization, and additive manufacturing of cellular structures

  • ORIGINAL ARTICLE
  • Published:
The International Journal of Advanced Manufacturing Technology Aims and scope Submit manuscript

Abstract

Cellular structures are made up of an interconnected network of plates, struts, or small unit cells and acquire many unique benefits such as, high strength-to-weight ratio, excellent energy absorption, and minimizing material requirements. When compared with the complicated conventional processes, additive manufacturing (AM) technology is capable of fabricating geometries in almost all types of shapes, even with the small cellular structures inside, by adding material layer-by-layer directly from the digital data file. All major industries have been exploiting the benefits of cellular structures due to their prevalence over a wide range of research fields. To date, there are a few state-of-the-art reviews compiled focusing on a specific area of lattice structures, but many aspects still need to be reviewed. Therefore, this paper aims to provide a comprehensive review of the various lattice morphologies, design, and the AM of the cellular structures. Furthermore, the superior properties of the additively fabricated structure, as well as the applications and challenges, are presented. The conducted review has identified the significant limitations and gaps in the existing literature and has highlighted the areas that need further research in the design, optimization, characteristics, and applications, and the AM of the cellular structures. This review would provide a more precise understanding and the state-of-the-art of AM with the cellular structures for engineers and researchers in both academia and industrial applications.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16

Similar content being viewed by others

References

  1. Wester T (2002) Nature teaching structures. Int J Sp Struct 17:135–147. https://doi.org/10.1260/026635102320321789

    Article  Google Scholar 

  2. Lian J, Gorski J, Ott S Bone structure and function. https://depts.washington.edu/bonebio/ASBMRed/structure.html. Accessed 23 Feb 2019

  3. Lagorce-Tachon A, Karbowiak T, Loupiac C et al (2015) The cork viewed from the inside. J Food Eng 149:214–221. https://doi.org/10.1016/J.JFOODENG.2014.10.023

    Article  Google Scholar 

  4. Gibson LJ, Ashby M (1997) Cellular Solids, structure and properties, 2nd edn. Cambridge University Press

  5. Stratasys Blog World’s first jet-powered, 3D printed UAV tops 150 MPH with lightweight Stratasys materials. http://blog.stratasys.com/2015/11/09/aurora-uav-3d-printing/. Accessed 20 Feb 2019

  6. Sundararajan VG (2010) Topology optimization for additive manufacturing of customized meso-structures using homogenization and parametric smoothing functions. The University of Texas at Austin

  7. Carbon The perfect fit: Carbon + Adidas collaborate to upend athletic footwear. https://www.carbon3d.com/stories/adidas/. Accessed 20 Feb 2019

  8. Hagel J, Brown JS (2015) The future of manufacturing-making things in a changing world. Deloitte Univ Press, Westlake, pp 4–18

    Google Scholar 

  9. Carbon The future of 3D manufacturing printers & Systems. https://www.carbon3d.com/. Accessed 20 Feb 2019

  10. Chen X, Zhao G, Wu Y et al (2017) Cellular carbon microstructures developed by using stereolithography. Carbon N Y 123:34–44. https://doi.org/10.1016/J.CARBON.2017.07.043

    Article  Google Scholar 

  11. Cheng L, Zhang P, Biyikli E et al (2017) Efficient design optimization of variable-density cellular structures for additive manufacturing: theory and experimental validation. Rapid Prototyp J 23:660–677. https://doi.org/10.1108/RPJ-04-2016-0069

    Article  Google Scholar 

  12. Rumpf RC, Pazos J, Garcia CR et al (2013) 3D printed lattices with spatially variant self-collimation. Prog Electromagn Res 139:1–15

    Article  Google Scholar 

  13. Iyibilgin O, Leu MC, Yigit C (2013) Experimental investigation of different cellular lattice structures manufactured by fused deposition modeling. In: Proceedings of the Solid Freeform Fabrication Symposium, Texas, pp 895–907

  14. Karamooz Ravari MR, Kadkhodaei M, Badrossamay M, Rezaei R (2014) Numerical investigation on mechanical properties of cellular lattice structures fabricated by fused deposition modeling. Int J Mech Sci 88:154–161. https://doi.org/10.1016/J.IJMECSCI.2014.08.009

    Article  Google Scholar 

  15. Snelling D, Li Q, Meisel N et al (2015) Lightweight metal cellular structures fabricated via 3d printing of sand cast molds. Adv Eng Mater 17:923–932. https://doi.org/10.1002/adem.201400524

    Article  Google Scholar 

  16. Tang Y, Zhou Y, Hoff T et al (2016) Elastic modulus of 316 stainless steel lattice structure fabricated via binder jetting process. Mater Sci Technol 32:648–656. https://doi.org/10.1179/1743284715Y.0000000084

    Article  Google Scholar 

  17. Druschitz A, Williams C, Snelling D, Seals M (2014) Additive manufacturing supports the production of complex castings. In: Shape Casting: 5th International Symposium 2014. Springer International Publishing, Cham, pp 51–57

    Google Scholar 

  18. Leary M, Mazur M, Elambasseril J et al (2016) Selective laser melting (SLM) of AlSi12Mg lattice structures. Mater Des 98:344–357. https://doi.org/10.1016/j.matdes.2016.02.127

    Article  Google Scholar 

  19. Hao L, Raymont D, Yan C et al (2011) Design and additive manufacturing of cellular lattice structures. In: Innovative Developments in Virtual and Physical Prototyping, pp 249–254

    Chapter  Google Scholar 

  20. Gu D (2015) Laser additive manufacturing (AM): classification, processing philosophy, and metallurgical mechanisms. In: Laser additive manufacturing of high-performance materials. Springer Berlin Heidelberg, Berlin, pp 15–71

    Google Scholar 

  21. Challis VJ, Xu X, Zhang LC et al (2014) High specific strength and stiffness structures produced using selective laser melting. Mater Des 63:783–788. https://doi.org/10.1016/j.matdes.2014.05.064

    Article  Google Scholar 

  22. Gibson I, Rosen DW (2010) Additive manufacturing technologies: rapid prototyping to direct digital manufacturing. In: Springer

    Google Scholar 

  23. Plotkowski A, Rios O, Sridharan N et al (2017) Evaluation of an Al-Ce alloy for laser additive manufacturing. Acta Mater 126:507–519. https://doi.org/10.1016/J.ACTAMAT.2016.12.065

    Article  Google Scholar 

  24. Williams SW, Martina F, Addison AC et al (2016) Wire + arc additive manufacturing. Mater Sci Technol 32:641–647. https://doi.org/10.1179/1743284715Y.0000000073

    Article  Google Scholar 

  25. Bandari YK, Lee YS, Nandwana P et al (2018) Effect of inter-layer cooling time on distortion and mechanical properties in metal additive manufacturing distortion and mechanical properties in metal additive manufacturing. In: Solid Freeform Fabrication 2018. Proceedings of the 29th Annual International Solid Freeform Fabrication Symposium – An Additive Manufacturing Conference

  26. Bandari Y, Williams S, Ding J, Martina F (2015) Additive manufacture of large structures: robotic or CNC systems? In: Proceedings of the 26th International Solid Freeform Fabrication Symposium, Austin, pp 12–14

  27. Thompson MK, Moroni G, Vaneker T et al (2016) Design for additive manufacturing: trends, opportunities, considerations, and constraints. CIRP Ann Manuf Technol 65:737–760. https://doi.org/10.1016/j.cirp.2016.05.004

    Article  Google Scholar 

  28. Gao W, Zhang Y, Ramanujan D et al (2015) The status, challenges, and future of additive manufacturing in engineering. Comput Des 69:65–89. https://doi.org/10.1016/j.cad.2015.04.001

    Article  Google Scholar 

  29. Huang Y, Leu MC, Mazumder J, Donmez A (2015) Additive manufacturing: current state, future potential, gaps and needs, and recommendations. J Manuf Sci Eng 137:014001. https://doi.org/10.1115/1.4028725

    Article  Google Scholar 

  30. Uriondo A, Esperon-Miguez M, Perinpanayagam S (2015) The present and future of additive manufacturing in the aerospace sector: a review of important aspects. Proc Inst Mech Eng Part G J Aerosp Eng 229:2132–2147. https://doi.org/10.1177/0954410014568797

    Article  Google Scholar 

  31. Jing SK, Song GH, Liu JH et al (2014) A review of product design for additive manufacturing. Appl Mech Mater 635–637:97–100. https://doi.org/10.4028/www.scientific.net/AMM.635-637.97

    Article  Google Scholar 

  32. Yap CY, Chua CK, Dong ZL et al (2015) Review of selective laser melting: materials and applications. Appl Phys Rev 2. https://doi.org/10.1063/1.4935926

    Article  Google Scholar 

  33. Vijayavenkataraman S, Lu WF, Fuh JYH (2016) 3D bioprinting of skin: a state-of-the-art review on modelling, materials, and processes. Biofabrication 8:032001. https://doi.org/10.1088/1758-5090/8/3/032001

    Article  Google Scholar 

  34. Wang J, Tang H (2016) Review on metals additively manufactured by SEBM. Mater Technol:1–4. https://doi.org/10.1179/1753555715Y.0000000081

  35. Savio G, Rosso S, Meneghello R, Concheri G (2018) Geometric modeling of cellular materials for additive manufacturing in biomedical field: a review. Appl Bionics Biomech 2018:1–14. https://doi.org/10.1155/2018/1654782

    Article  Google Scholar 

  36. Zok FW, Latture RM, Begley MR (2016) Periodic truss structures. J Mech Phys Solids 96:184–203. https://doi.org/10.1016/J.JMPS.2016.07.007

    Article  Google Scholar 

  37. Baldick R (2008) Applied optimization: formulation and algorithms for engineering systems. Cambridge University Press

  38. Jonbailey microscopy | bone. https://archimorph.com/2010/01/12/microscopy-bone/. Accessed 20 Feb 2019

  39. Great Plains Nature Center Insects | GPNC. https://gpnc.org/insects/. Accessed 2 Mar 2019

  40. 32 intriguing examples of fungi photography. https://www.thephotoargus.com/32-intriguing-examples-of-fungi-photography/. Accessed 30 Dec 2017

  41. Voronoi structures. https://www.pinterest.com/pin/341640321725152778/. Accessed 20 Feb 2019

  42. Wing of a dragonfly. https://www.pinterest.com/pin/457889487106234409/. Accessed 20 Feb 2019

  43. Jordan T, Oxman N Performance driven design & Prototyping. http://ming3d.com/DAAP/ARCH719sp11/?p=295. Accessed 20 Feb 2019

  44. Gibson LJ (2012) The hierarchical structure and mechanics of plant materials. J R Soc Interface 9:2749–2766. https://doi.org/10.1098/rsif.2012.0341

    Article  Google Scholar 

  45. Kamm RD (2002) Cellular fluid mechanics. Annu Rev Fluid Mech 34:211–232. https://doi.org/10.1146/annurev.fluid.34.082401.165302

    Article  MathSciNet  MATH  Google Scholar 

  46. Saranathan V, Osuji CO, Mochrie SGJ et al (2010) Structure, function, and self-assembly of single network gyroid (I4132) photonic crystals in butterfly wing scales. Proc Natl Acad Sci U S A 107:11676–11681. https://doi.org/10.1073/pnas.0909616107

    Article  Google Scholar 

  47. Launey ME, Buehler MJ, Ritchie RO (2010) On the mechanistic origins of toughness in bone. Annu Rev Mater Res 40:25–53. https://doi.org/10.1146/annurev-matsci-070909-104427

    Article  Google Scholar 

  48. Vincent JFV (1982) Structural biomaterials. Palgrave Macmillan Limited

  49. Wang A-J, McDowell DL (2005) Yield surfaces of various periodic metal honeycombs at intermediate relative density. Int J Plast 21:285–320. https://doi.org/10.1016/J.IJPLAS.2003.12.002

    Article  MATH  Google Scholar 

  50. 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

    Article  MATH  Google Scholar 

  51. Evans AG, Hutchinson JW, Fleck NA et al (2001) The topological design of multifunctional cellular metals. Prog Mater Sci 46:309–327. https://doi.org/10.1016/S0079-6425(00)00016-5

    Article  Google Scholar 

  52. Fleck NA (2004) An overview of the mechanical properties of foams and periodic lattice materials. In: Proceedings of the Symposium on Cellular Metals and Polymers, Furth, pp 3–7

  53. Wang J, Evans AG, Dharmasena K, Wadley HNG (2003) On the performance of truss panels with Kagomé cores. Int J Solids Struct 40:6981–6988. https://doi.org/10.1016/S0020-7683(03)00349-4

    Article  Google Scholar 

  54. Chu C, Graf G, Rosen DW (2008) Design for Additive manufacturing of cellular structures. Comput Aided Des Appl 5:686–696. https://doi.org/10.3722/cadaps.2008.686-696

    Article  Google Scholar 

  55. Winter RE, Cotton M, Harris EJ et al (2012) Plate-impact loading of cellular structures formed by selective laser melting. Trans Built Environ 126:1743–3509. https://doi.org/10.2495/SU120131

    Article  Google Scholar 

  56. Lehmhus D, Vesenjak M, Schampheleire S et al (2017) From stochastic foam to designed structure: balancing cost and performance of cellular metals. Materials (Basel) 10:922. https://doi.org/10.3390/ma10080922

    Article  Google Scholar 

  57. Contuzzi N, Campanelli S, Casavola C et al (2013) Manufacturing and characterization of 18Ni marage 300 lattice components by selective laser melting. Materials (Basel) 6:3451–3468. https://doi.org/10.3390/ma6083451

    Article  Google Scholar 

  58. Yang L, Harrysson O, West H, Cormier D (2015) Mechanical properties of 3D re-entrant honeycomb auxetic structures realized via additive manufacturing. Int J Solids Struct 69–70:475–490. https://doi.org/10.1016/J.IJSOLSTR.2015.05.005

    Article  Google Scholar 

  59. Yoo DJ (2011) Porous scaffold design using the distance field and triply periodic minimal surface models. Biomaterials 32:7741–7754. https://doi.org/10.1016/J.BIOMATERIALS.2011.07.019

    Article  Google Scholar 

  60. Gorguluarslan RM, Gandhi UN, Mandapati R, Choi S-K (2016) Design and fabrication of periodic lattice-based cellular structures. Comput Aided Des Appl 13:50–62. https://doi.org/10.1080/16864360.2015.1059194

    Article  Google Scholar 

  61. Yan C, Hao L, Hussein A et al (2014) Advanced lightweight 316L stainless steel cellular lattice structures fabricated via selective laser melting. Mater Des 55:533–541. https://doi.org/10.1016/j.matdes.2013.10.027

    Article  Google Scholar 

  62. Johnston SR, Rosen DW, Reed M, Wang HV (2006) Analysis of mesostructure unit cells comprised of octet-truss structures. In: Solid freeform fabrication symposium. Georgia Institute of Technology, Austin, pp 421–432

    Google Scholar 

  63. Chang PS, Rosen DW (2013) The size matching and scaling method: a synthesis method for the design of mesoscale cellular structures. Int J Comput Integr Manuf 26:907–927. https://doi.org/10.1080/0951192X.2011.650880

    Article  Google Scholar 

  64. Ataee A, Li Y, Fraser D et al (2018) Anisotropic Ti-6Al-4V gyroid scaffolds manufactured by electron beam melting (EBM) for bone implant applications. Mater Des 137:345–354. https://doi.org/10.1016/J.MATDES.2017.10.040

    Article  Google Scholar 

  65. Azman AH, Vignat F (2014) Evaluating current CAD tools performances in the context of design for additive manufacturing. In: Joint Conference on Mechanical, Design Engineering & Advanced Manufacturing, Toulouse, pp 1–7

  66. Bauer J, Hengsbach S, Tesari I et al (2014) High-strength cellular ceramic composites with 3D microarchitecture. Proc Natl Acad Sci U S A 111:2453–2458. https://doi.org/10.1073/pnas.1315147111

    Article  Google Scholar 

  67. Bernal Ostos J, Rinaldi RG, Hammetter CI et al (2012) Deformation stabilization of lattice structures via foam addition. Acta Mater 60:6476–6485. https://doi.org/10.1016/J.ACTAMAT.2012.07.053

    Article  Google Scholar 

  68. Brooks W, Sutcliffe C, Cantwell W et al (2005) Rapid design and manufacture of ultralight cellular materials. In: Proceedings of the Solid Freeform Fabrication Symposium, Texas, pp 231–241

  69. Santorinaios M, Brooks W, Sutcliffe CJ, Mines RAW (2006) Crush behaviour of open cellular latticestructures manufactured using selective laser melting. WIT Trans Built Environ 85. https://doi.org/10.2495/HPSM060471

  70. 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

    Article  Google Scholar 

  71. Cansizoglu O, Harrysson O, Cormier D et al (2008) Properties of Ti–6Al–4V non-stochastic lattice structures fabricated via electron beam melting. Mater Sci Eng A 492:468–474. https://doi.org/10.1016/J.MSEA.2008.04.002

    Article  Google Scholar 

  72. Cerardi A, Caneri M, Meneghello R et al (2013) Mechanical characterization of polyamide cellular structures fabricated using selective laser sintering technologies. Mater Des 46:910–915. https://doi.org/10.1016/j.matdes.2012.11.042

    Article  Google Scholar 

  73. Cheng XY, Li SJ, Murr LE et al (2012) Compression deformation behavior of Ti–6Al–4V alloy with cellular structures fabricated by electron beam melting. J Mech Behav Biomed Mater 16:153–162. https://doi.org/10.1016/J.JMBBM.2012.10.005

    Article  Google Scholar 

  74. Cheng L, Zhang P, Biyikli E et al (2015) Integration of topology optimization with efficient design of additive manufactured cellular structures. Solid Freeform Fabrication Symposium, Austin, pp 10–12

    Google Scholar 

  75. Dong L, Deshpande V, Wadley H (2015) Mechanical response of Ti–6Al–4V octet-truss lattice structures. Int J Solids Struct 60–61:107–124. https://doi.org/10.1016/J.IJSOLSTR.2015.02.020

    Article  Google Scholar 

  76. Xiao D, Yang Y, Su X et al (2012) Topology optimization of microstructure and selective laser melting fabrication for metallic biomaterial scaffolds. Trans Nonferrous Metals Soc China 22:2554–2561. https://doi.org/10.1016/S1003-6326(11)61500-8

    Article  Google Scholar 

  77. Doty RE, Kolodziejska JA, Jacobsen AJ (2012) Hierarchical polymer microlattice structures. Adv Eng Mater 14:503–507. https://doi.org/10.1002/adem.201200007

    Article  Google Scholar 

  78. Evans AG, He MY, Deshpande VS 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

    Article  Google Scholar 

  79. Feng R, Liu F, Xu W et al (2016) Topology optimization method of lattice structures based on a genetic algorithm. Int J Steel Struct 16:743–753. https://doi.org/10.1007/s13296-015-0208-8

    Article  Google Scholar 

  80. Gandy PJF, Cvijović D, Mackay AL, Klinowski J (1999) Exact computation of the triply periodic D (‘diamond’) minimal surface. Chem Phys Lett 314:543–551. https://doi.org/10.1016/S0009-2614(99)01000-3

    Article  Google Scholar 

  81. Gandy PJF, Klinowski J (2000) Exact computation of the triply periodic Schwarz P minimal surface. Chem Phys Lett 322:579–586. https://doi.org/10.1016/S0009-2614(00)00453-X

    Article  Google Scholar 

  82. Gandy PJ, Klinowski J (2000) Exact computation of the triply periodic G (‘Gyroid’) minimal surface. Chem Phys Lett 321:363–371. https://doi.org/10.1016/S0009-2614(00)00373-0

    Article  Google Scholar 

  83. Gandy PJF, Bardhan S, Mackay AL, Klinowski J (2001) Nodal surface approximations to the P,G,D and I-WP triply periodic minimal surfaces. Chem Phys Lett 336:187–195. https://doi.org/10.1016/S0009-2614(00)01418-4

    Article  Google Scholar 

  84. Gandhi UN, Gorguluarslan RM, Song Y, Mandapati R (2015) Designing lattice structures for 3D printing. SPE Automotive Composites Conference & Exhibition, pp 1–14

  85. Gautam R, Idapalapati S, Feih S (2018) Printing and characterisation of Kagome lattice structures by fused deposition modelling. Mater Des 137:266–275. https://doi.org/10.1016/J.MATDES.2017.10.022

    Article  Google Scholar 

  86. Gorny B, Niendorf T, Lackmann J et al (2011) In situ characterization of the deformation and failure behavior of non-stochastic porous structures processed by selective laser melting. Mater Sci Eng A 528:7962–7967. https://doi.org/10.1016/J.MSEA.2011.07.026

    Article  Google Scholar 

  87. Guessasma S, Tao L, Belhabib S et al (2018) Analysis of microstructure and mechanical performance of polymeric cellular structures designed using stereolithography. Eur Polym J 98:72–82. https://doi.org/10.1016/J.EURPOLYMJ.2017.10.034

    Article  Google Scholar 

  88. Gümrük R, Mines RAW (2013) Compressive behaviour of stainless steel micro-lattice structures. Int J Mech Sci 68:125–139. https://doi.org/10.1016/J.IJMECSCI.2013.01.006

    Article  Google Scholar 

  89. Gümrük R, Mines RAW, Karadeniz S (2013) Static mechanical behaviours of stainless steel micro-lattice structures under different loading conditions. Mater Sci Eng A 586:392–406. https://doi.org/10.1016/J.MSEA.2013.07.070

    Article  Google Scholar 

  90. Hammetter CI, Rinaldi RG, Zok FW (2013) Pyramidal lattice structures for high strength and energy absorption. J Appl Mech 80:041015. https://doi.org/10.1115/1.4007865

    Article  Google Scholar 

  91. Hedayati R, Sadighi M, Mohammadi Aghdam M et al (2016) Mechanical properties of additively manufactured thick honeycombs. Materials (Basel) 9:613. https://doi.org/10.3390/ma9080613

    Article  Google Scholar 

  92. Heinl P, Körner C, Singer RF (2008) Selective electron beam melting of cellular titanium: mechanical properties. Adv Eng Mater 10:882–888. https://doi.org/10.1002/adem.200800137

    Article  Google Scholar 

  93. Helou M, Vongbunyong S, Kara S (2016) Finite element analysis and validation of cellular structures. Procedia CIRP 50:94–99. https://doi.org/10.1016/J.PROCIR.2016.05.018

    Article  Google Scholar 

  94. 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

    Article  Google Scholar 

  95. Hussein A, Hao L, Yan C et al (2013) Advanced lattice support structures for metal additive manufacturing. J Mater Process Technol 213:1019–1026. https://doi.org/10.1016/J.JMATPROTEC.2013.01.020

    Article  Google Scholar 

  96. Hyun S, Karlsson AM, Torquato S, Evans AG (2003) Simulated properties of Kagomé and tetragonal truss core panels. Int J Solids Struct 40:6989–6998. https://doi.org/10.1016/S0020-7683(03)00350-0

    Article  MATH  Google Scholar 

  97. Jacobsen AJ, Barvosa-Carter W, Nutt S (2007) Micro-scale truss structures formed from self-propagating photopolymer waveguides. Adv Mater 19:3892–3896. https://doi.org/10.1002/adma.200700797

    Article  Google Scholar 

  98. Jacobsen AJ, Barvosa-Carter W, Nutt S (2007) Compression behavior of micro-scale truss structures formed from self-propagating polymer waveguides. Acta Mater 55:6724–6733. https://doi.org/10.1016/J.ACTAMAT.2007.08.036

    Article  Google Scholar 

  99. Jacobsen AJ, Barvosa-Carter W, Nutt S (2008) Micro-scale truss structures with three-fold and six-fold symmetry formed from self-propagating polymer waveguides. Acta Mater 56:2540–2548. https://doi.org/10.1016/J.ACTAMAT.2008.01.051

    Article  Google Scholar 

  100. Lee J-W, Choi H-J, Jung T-K et al (2016) Mechanical properties of a tetrahedrally cored titanium lattice structure fabricated by pressure-assisted investment casting. J Nanosci Nanotechnol 16:11214–11218. https://doi.org/10.1166/jnn.2016.13480

    Article  Google Scholar 

  101. Li SJ, Murr LE, Cheng XY et al (2012) Compression fatigue behavior of Ti–6Al–4V mesh arrays fabricated by electron beam melting. Acta Mater 60:793–802. https://doi.org/10.1016/J.ACTAMAT.2011.10.051

    Article  Google Scholar 

  102. Li SJ, Xu QS, Wang Z et al (2014) Influence of cell shape on mechanical properties of Ti–6Al–4V meshes fabricated by electron beam melting method. Acta Biomater 10:4537–4547. https://doi.org/10.1016/J.ACTBIO.2014.06.010

    Article  Google Scholar 

  103. McKown S, Shen Y, Brookes WK et al (2008) The quasi-static and blast loading response of lattice structures. Int J Impact Eng 35:795–810. https://doi.org/10.1016/J.IJIMPENG.2007.10.005

    Article  Google Scholar 

  104. Messner MC (2016) Optimal lattice-structured materials. J Mech Phys Solids 96:162–183. https://doi.org/10.1016/J.JMPS.2016.07.010

    Article  MathSciNet  Google Scholar 

  105. Mines R, McKown S, Cantwell W, Brooks W (2007) On the progressive collapse of micro lattice structures. In: Experimental Analysis of Nano and Engineering Materials and Structures. Springer, pp 743–744

  106. 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 R Soc A Math Phys Eng Sci 368:1999–2032. https://doi.org/10.1098/rsta.2010.0010

    Article  Google Scholar 

  107. Murr LE, Amato KN, Li SJ et al (2011) Microstructure and mechanical properties of open-cellular biomaterials prototypes for total knee replacement implants fabricated by electron beam melting. J Mech Behav Biomed Mater 4:1396–1411. https://doi.org/10.1016/J.JMBBM.2011.05.010

    Article  Google Scholar 

  108. Nguyen J, Park S, 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

    Article  Google Scholar 

  109. Ozdemir Z, Hernandez-Nava E, Tyas A et al (2016) Energy absorption in lattice structures in dynamics: experiments. Int J Impact Eng 89:49–61. https://doi.org/10.1016/J.IJIMPENG.2015.10.007

    Article  Google Scholar 

  110. Pettermann HE, Hüsing J (2012) Modeling and simulation of relaxation in viscoelastic open cell materials and structures. Int J Solids Struct 49:2848–2853. https://doi.org/10.1016/J.IJSOLSTR.2012.04.027

    Article  Google Scholar 

  111. Queheillalt D, Deshpande V, Wadley H (2007) Truss waviness effects in cellular lattice structures. J Mech Mater Struct 2:1657–1675. https://doi.org/10.2140/jomms.2007.2.1657

    Article  Google Scholar 

  112. Ramirez DA, Murr LE, Li SJ et al (2011) Open-cellular copper structures fabricated by additive manufacturing using electron beam melting. Mater Sci Eng A 528:5379–5386. https://doi.org/10.1016/J.MSEA.2011.03.053

    Article  Google Scholar 

  113. Raney JR, Lewis JA (2015) Printing mesoscale architectures. MRS Bull 40:943–950. https://doi.org/10.1557/mrs.2015.235

    Article  Google Scholar 

  114. Rathbun HJ, Wei Z, He MY et al (2004) Measurement and simulation of the performance of a lightweight metallic sandwich structure with a tetrahedral truss core. J Appl Mech 71:368. https://doi.org/10.1115/1.1757487

    Article  MATH  Google Scholar 

  115. Rehme O, Emmelmann C (2006) Rapid manufacturing of lattice structures with selective laser melting. In: Bachmann FG, Hoving W, Lu Y, Washio K (eds) Laser based micropackaging. International Society for Optics and Photonics, p 61070K

  116. Schaedler TA, Jacobsen AJ, Torrents A et al (2011) Ultralight metallic microlattices. Science 334:962–965. https://doi.org/10.1126/science.1211649

    Article  Google Scholar 

  117. Schoen AH (1970) Infinite periodic minimal surfaces without self-intersections. NASA Technical Report# D5541

  118. Seo H, Heo SG, Lee H, Yoon H (2017) Preparation of PEG materials for constructing complex structures by stereolithographic 3D printing. RSC Adv 7:28684–28688. https://doi.org/10.1039/C7RA04492E

    Article  Google Scholar 

  119. Smith M, Cantwell W, Guan Z et al (2011) The quasi-static and blast response of steel lattice structures. J Sandw Struct Mater 13:479–501. https://doi.org/10.1177/1099636210388983

    Article  Google Scholar 

  120. Smith M, Guan Z, Cantwell WJ (2013) Finite element modelling of the compressive response of lattice structures manufactured using the selective laser melting technique. Int J Mech Sci 67:28–41. https://doi.org/10.1016/j.ijmecsci.2012.12.004

    Article  Google Scholar 

  121. Snelling DA, Williams CB, Suchicital CTA, Druschitz AP (2017) Binder jetting advanced ceramics for metal-ceramic composite structures. Int J Adv Manuf Technol 92:531–545. https://doi.org/10.1007/s00170-017-0139-y

    Article  Google Scholar 

  122. Strano G, Hao L, Everson RM, Evans KE (2013) A new approach to the design and optimisation of support structures in additive manufacturing. Int J Adv Manuf Technol 66. https://doi.org/10.1007/s00170-012-4403-x

    Article  Google Scholar 

  123. 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

    Article  Google Scholar 

  124. Surmeneva MA, Surmenev RA, Chudinova EA et al (2017) Fabrication of multiple-layered gradient cellular metal scaffold via electron beam melting for segmental bone reconstruction. Mater Des 133:195–204. https://doi.org/10.1016/J.MATDES.2017.07.059

    Article  Google Scholar 

  125. Tancogne-Dejean T, Spierings AB, Mohr D (2016) Additively manufactured metallic micro-lattice materials for high specific energy absorption under static and dynamic loading. Acta Mater 116:14–28. https://doi.org/10.1016/J.ACTAMAT.2016.05.054

    Article  Google Scholar 

  126. Teufelhart S, Solid GR (2012) Optimization of strut diameters in lattice structures. In: 23th Annual Solid Freeform Fabrication Symposium (SFF). sffsymposium.engr.utexas.edu, pp 6–8

  127. Teufelhart S (2014) Investigation of the capability of flux of force oriented lattice structures for lightweight design. Adv Mater Res 907:75–87. https://doi.org/10.4028/www.scientific.net/AMR.907.75

    Article  Google Scholar 

  128. Wang HV, Chen Y, Rosen DW (2005) A hybrid geometric modeling method for large scale conformal cellular structures. ASME Comput Inf Eng Conf 2005:421–427. https://doi.org/10.1115/DETC2005-85366

    Article  Google Scholar 

  129. Watts DM, Hague RJM (2006) Exploiting the design freedom of RM. In: Proceedings of the 17th Solid Freeform Fabrication Symposium (SFF), Texas, pp 656–667

  130. Wendy Gu X, Greer JR (2015) Ultra-strong architected Cu meso-lattices. Extreme Mech Lett 2:7–14. https://doi.org/10.1016/J.EML.2015.01.006

    Article  Google Scholar 

  131. Wicks N, Hutchinson JW (2001) Optimal truss plates. Int J Solids Struct 38:5165–5183. https://doi.org/10.1016/S0020-7683(00)00315-2

    Article  MATH  Google Scholar 

  132. Williams CB, Cochran JK, Rosen DW (2011) Additive manufacturing of metallic cellular materials via three-dimensional printing. Int J Adv Manuf Technol 53:231–239. https://doi.org/10.1007/s00170-010-2812-2

    Article  Google Scholar 

  133. Winter RE, Cotton M, Harris EJ et al (2014) Plate-impact loading of cellular structures formed by selective laser melting. Model Simul Mater Sci Eng 22:025021. https://doi.org/10.1088/0965-0393/22/2/025021

    Article  Google Scholar 

  134. Yang L, Harrysson O, Cormier D et al (2015) Additive manufacturing of metal cellular structures: design and fabrication. JOM 67:608–615. https://doi.org/10.1007/s11837-015-1322-y

    Article  Google Scholar 

  135. Yang L (2015) Experimental-assisted design development for an octahedral cellular structure using additive manufacturing. Rapid Prototyp J 21:168–176. https://doi.org/10.1108/RPJ-12-2014-0178

    Article  Google Scholar 

  136. Yan C, Hao L, Hussein A, Raymont D (2012) Evaluations of cellular lattice structures manufactured using selective laser melting. Int J Mach Tools Manuf 62:32–38. https://doi.org/10.1016/j.ijmachtools.2012.06.002

    Article  Google Scholar 

  137. Zheng X, Lee H, Weisgraber TH et al (2014) Ultralight, ultrastiff mechanical metamaterials. Science 344:1373–1377. https://doi.org/10.1126/science.1252291

    Article  Google Scholar 

  138. Zhang P, Toman J, Yu Y et al (2015) 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

    Article  Google Scholar 

  139. Rosen DW (2007) Computer-aided design for additive manufacturing of cellular structures. Comput Aided Des Appl 4:585–594. https://doi.org/10.1080/16864360.2007.10738493

    Article  Google Scholar 

  140. Schwarz HA (1890) Gesammelte mathematische Abhandlungen, Volume 1. J. In: Springer

    Google Scholar 

  141. Wang Y (2007) Periodic surface modeling for computer aided nano design. Comput Des 39:179–189. https://doi.org/10.1016/J.CAD.2006.09.005

    Article  Google Scholar 

  142. Lakes R (1993) Materials with structural hierarchy. Nature 361:511–515. https://doi.org/10.1038/361511a0

    Article  Google Scholar 

  143. Ashby MF, Evans A, Fleck NA et al (2000) Metal foams: a design guide. Butterworth-Heinemann Elsevier

  144. Kang K-J (2009) A wire-woven cellular metal of ultrahigh strength. Acta Mater 57:1865–1874. https://doi.org/10.1016/J.ACTAMAT.2008.12.027

    Article  Google Scholar 

  145. Leach AG (1993) The thermal conductivity of foams. I. Models for heat conduction. J Phys D Appl Phys 26:733–739. https://doi.org/10.1088/0022-3727/26/5/003

    Article  Google Scholar 

  146. ROHACELL High-performance structural foam cores. https://www.rohacell.com/product/rohacell/en/about/. Accessed 2 Mar 2019

  147. Shinko Wire Company, Ltd. http://www.shinko-wire.co.jp/english/. Accessed 20 Feb 2019

  148. Banhart J (2001) Manufacture, characterisation and application of cellular metals and metal foams. Prog Mater Sci 46:559–632. https://doi.org/10.1016/S0079-6425(00)00002-5

    Article  Google Scholar 

  149. Frulloni E, Kenny JM, Conti P, Torre L (2007) Experimental study and finite element analysis of the elastic instability of composite lattice structures for aeronautic applications. Compos Struct 78:519–528. https://doi.org/10.1016/J.COMPSTRUCT.2005.11.013

    Article  Google Scholar 

  150. Maheshwaraa U, Bourell D, Conner Seepersad C (2007) Design and freeform fabrication of deployable structures with lattice skins. Rapid Prototyp J 13:213–225. https://doi.org/10.1108/13552540710776160

    Article  Google Scholar 

  151. Maheshwaraa Namasivayam U, Conner Seepersad C (2011) Topology design and freeform fabrication of deployable structures with lattice skins. Rapid Prototyp J 17:5–16. https://doi.org/10.1108/13552541111098581

    Article  Google Scholar 

  152. Paz R, Monzón MD, González B et al (2016) Lightweight parametric optimisation method for cellular structures in additive manufactured parts. Int J Simul Multidiscip Des Optim 7:A6. https://doi.org/10.1051/smdo/2016009

    Article  Google Scholar 

  153. Dakshnamoorthy V (2016) Automated lattice optimization of hinge fitting with displacement constraint (doctoral dissertation). University of Texas Arlington

  154. Knight A (2015) Cancer patient receives 3D printed ribs in world-first surgery - CSIROscope. https://blog.csiro.au/cancer-patient-receives-3d-printed-ribs-in-world-first-surgery/. Accessed 20 Feb 2019

  155. Sutradhar A, Park J, Carrau D, Miller MJ (2014) Experimental validation of 3D printed patient-specific implants using digital image correlation and finite element analysis. Comput Biol Med 52:8–17. https://doi.org/10.1016/J.COMPBIOMED.2014.06.002

    Article  Google Scholar 

  156. Sutradhar A, Paulino GH, Miller MJ, Nguyen TH (2010) Topological optimization for designing patient-specific large craniofacial segmental bone replacements. In: Proceedings of the National Academy of Sciences of the United States of America, National Academy of Sciences, pp 13222–13227

  157. Tarik Arafat M, Gibson I, Li X (2014) State of the art and future direction of additive manufactured scaffolds-based bone tissue engineering. Rapid Prototyp J 20:13–26. https://doi.org/10.1108/RPJ-03-2012-0023

    Article  Google Scholar 

  158. Armillotta A, Pelzer R (2008) Modeling of porous structures for rapid prototyping of tissue engineering scaffolds. Int J Adv Manuf Technol 39:501–511. https://doi.org/10.1007/s00170-007-1247-x

    Article  Google Scholar 

  159. Ohldin P (2010) Series production of CE-certified orthopedic implants with integrated porous structures for improved bone ingrowth. In: Proceedings of the 21st International DAAAM Symposium. DAAAM International, pp 1585–1587

  160. Dias MR, Guedes JM, Flanagan CL et al (2014) Optimization of scaffold design for bone tissue engineering: a computational and experimental study. Med Eng Phys 36:448–457. https://doi.org/10.1016/J.MEDENGPHY.2014.02.010

    Article  Google Scholar 

  161. Giannitelli SM, Accoto D, Trombetta M, Rainer A (2014) Current trends in the design of scaffolds for computer-aided tissue engineering. Acta Biomater 10:580–594. https://doi.org/10.1016/J.ACTBIO.2013.10.024

    Article  Google Scholar 

  162. Hutmacher DW (2000) Scaffolds in tissue engineering bone and cartilage. Biomater Silver Jubil Compend:175–189. https://doi.org/10.1016/B978-008045154-1.50021-6

    Chapter  Google Scholar 

  163. Wheeler K, Karagianes M, Sump K (1983) Titanium alloys in surgical implants. ASTM International

  164. Dabrowski B, Swieszkowski W, Godlinski D, Kurzydlowski KJ (2010) Highly porous titanium scaffolds for orthopaedic applications. J Biomed Mater Res B Appl Biomater 95B:53–61. https://doi.org/10.1002/jbm.b.31682

    Article  Google Scholar 

  165. Cooper LF (2000) A role for surface topography in creating and maintaining bone at titanium endosseous implants. J Prosthet Dent 84:522–534. https://doi.org/10.1067/MPR.2000.111966

    Article  Google Scholar 

  166. Hansson S, Norton M (1999) The relation between surface roughness and interfacial shear strength for bone-anchored implants. A mathematical model. J Biomech 32:829–836. https://doi.org/10.1016/S0021-9290(99)00058-5

    Article  Google Scholar 

  167. Colombo P, Degischer HP (2012) Highly porous metals and ceramics. Adv Eng Mater 14:1051. https://doi.org/10.1002/adem.201200347

    Article  Google Scholar 

  168. Yang L, Harrysson O, West H, Cormier D (2012) Compressive properties of Ti–6Al–4V auxetic mesh structures made by electron beam melting. Acta Mater 60:3370–3379. https://doi.org/10.1016/J.ACTAMAT.2012.03.015

    Article  Google Scholar 

  169. Vayre B, Vignat F, Villeneuve F (2013) Identification on some design key parameters for additive manufacturing: application on electron beam melting. Procedia CIRP 7:264–269. https://doi.org/10.1016/J.PROCIR.2013.05.045

    Article  Google Scholar 

  170. Adam GAO, Zimmer D (2014) Design for additive manufacturing—element transitions and aggregated structures. CIRP J Manuf Sci Technol 7:20–28. https://doi.org/10.1016/J.CIRPJ.2013.10.001

    Article  Google Scholar 

  171. Thompson MK, Moroni G, Vaneker T et al (2016) Design for additive manufacturing: trends, opportunities, considerations, and constraints. C I R P Annals, 24. CIRP Ann Technol 65:737–760. https://doi.org/10.1016/j.cirp.2016.05.004

    Article  Google Scholar 

  172. Doubrovski E, Verlinden J, Horvath I (2012) First steps towards collaboratively edited design for additive manufacturing knowledge. In: Solid Freeform Fabrication Symposium. University of Texas at Austin, Texas, pp 891–901

    Google Scholar 

  173. Hascoet J, Ponche R, Kerbrat O (2011) From functional specifications to optimized CAD model: proposition of a new DFAM methodology. In: Proceedings of the ASME Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASME, pp 767–472

    Google Scholar 

  174. Ponche R, Kerbrat O, Mognol P, Hascoet J-Y (2014) A novel methodology of design for additive manufacturing applied to additive laser manufacturing process. Robot Comput Integr Manuf 30:389–398. https://doi.org/10.1016/J.RCIM.2013.12.001

    Article  Google Scholar 

  175. Seepersad CC (2014) Challenges and opportunities in design for additive manufacturing. 3D Print Addit Manuf 1:10–13. https://doi.org/10.1089/3dp.2013.0006

    Article  Google Scholar 

  176. Vayre B, Vignat F, Villeneuve F (2012) Designing for additive manufacturing. Procedia CIRP 3:632–637. https://doi.org/10.1016/J.PROCIR.2012.07.108

    Article  Google Scholar 

  177. Gausemeier J, Echterhoff N, Kokoschka M, Wall M (2011) Thinking ahead the future of additive manufacturing–analysis of promising industries, Pederborn

  178. Rosen DW (2007) Design for additive manufacturing: a method to explore unexplored regions of the design space. In: Eighteenth Annual Solid Freeform Fabrication Symposium. University of Texas at Austin, Austin, pp 402–415

    Google Scholar 

  179. Gibson I, Rosen DW, Stucker B (2010) Additive manufacturing technologies. Springer, Boston, MA

    Book  Google Scholar 

  180. ANSYS (2017) Additive manufacturing simulation | ANSYS. https://www.ansys.com/products/structures/additive-manufacturing. Accessed 18 Jun 2019

  181. Dassault Systèmes (2018) CATIA 3DExperience. https://www.3ds.com/products-services/catia/. Accessed 18 Jun 2019

  182. PTC (2011) 3D CAD Software | Creo. https://www.ptc.com/en/products/cad/creo. Accessed 18 Jun 2019

  183. Dassault Systems (2018) Solidworks. https://www.solidworks.com/. Accessed 18 Jun 2019

  184. Materialise (2017) Materialise Mimics. https://www.materialise.com/en/medical/software/mimics. Accessed 18 Jun 2019

  185. Wang H, Rosen DW (2002) Parametric modeling method for truss structures. In: 22nd Computers and Information in Engineering Conference. ASME, Quebec, pp 759–767

    Google Scholar 

  186. Rosen D, Wang H (2001) Computer-aided design methods for additive fabrication of truss structures (Master’s thesis). Georgia Institute of Technology

  187. Chu J, Engelbrecht S, Graf G, Rosen DW (2010) A comparison of synthesis methods for cellular structures with application to additive manufacturing. Rapid Prototyp J 16:275–283. https://doi.org/10.1108/13552541011049298

    Article  Google Scholar 

  188. Chen VCP, Tsui K-L, Barton RR, Meckesheimer M (2006) A review on design, modeling and applications of computer experiments. IIE Trans 38:273–291. https://doi.org/10.1080/07408170500232495

    Article  Google Scholar 

  189. Dressler MM (2009) Art of surface interpolation (Doctoral Dissertation). KUNSTAT

  190. Sakata S, Ashida F, Zako M (2004) An efficient algorithm for Kriging approximation and optimization with large-scale sampling data. Comput Methods Appl Mech Eng 193:385–404. https://doi.org/10.1016/J.CMA.2003.10.006

    Article  MATH  Google Scholar 

  191. K3DSurf:3d surface generator. http://k3dsurf.sourceforge.net/. Accessed 21 Feb 2019

  192. Within Medical | Medical 3D printing software & Implant design | Autodesk. https://www.autodesk.com/products/within-medical/overview. Accessed 21 Feb 2019

  193. Hyperwork. https://web.altair.com/altair-acquires-simsolid. Accessed 21 Feb 2019

  194. Autodesk Additive Manufacturing and Design Software | Netfabb. https://www.autodesk.com/products/netfabb/overview. Accessed 21 Feb 2019

  195. Synopsys 3D Image Processing. https://www.synopsys.com/simpleware.html. Accessed 21 Feb 2019

  196. Materialise Materialise | 3D Printing Innovators. https://www.materialise.com/. Accessed 21 Feb 2019

  197. PARAMOUNTIND. https://www.paramountind.com/. Accessed 21 Feb 2019

  198. Paramatters. https://paramatters.com/. Accessed 21 Feb 2019

  199. Tao W, Leu MC (2016) Design of lattice structure for additive manufacturing. In: International Symposium on Flexible Automation (ISFA). IEEE, pp 325–332

  200. Chen Y, Epstein D (2006) A mesh-based geometric modeling method for general structures. In: 26th Computers and Information in Engineering Conference. ASME, pp 269–281

  201. Rozvany GIN, Querin OM, Gaspar Z, Pomezanski V (2003) Weight-increasing effect of topology simplification. Struct Multidiscip Optim 25:459–465. https://doi.org/10.1007/s00158-003-0334-3

    Article  Google Scholar 

  202. Bendsoe M, Sigmund O (2013) Topology optimization: theory, methods, and applications. Springer Sci Bus Media

    MATH  Google Scholar 

  203. Bendsøe MP, Kikuchi N (1988) Generating optimal topologies in structural design using a homogenization method. Comput Methods Appl Mech Eng 71:197–224. https://doi.org/10.1016/0045-7825(88)90086-2

    Article  MathSciNet  MATH  Google Scholar 

  204. Starly B (2006) Biomimetic design and fabrication of tissue engineered scaffolds using computer aided tissue engineering (Doctoral Dissertation). Drexel University

  205. Gabbrielli R (2009) Foam geometry and structural design of porous material (Doctoral Dissertation). University of Bath

  206. Gabbrielli R, Turner IG, Bowen CR (2007) Development of modelling methods for materials to be used as bone substitutes. Key Eng Mater 361:903–906. https://doi.org/10.4028/www.scientific.net/KEM.361-363.903

    Article  Google Scholar 

  207. Pasko A, Vilbrandt T, Fryazinov O, Adzhiev V (2010) Procedural function-based spatial microstructures. In: 2010 Shape Modeling International Conference. IEEE, pp 47–56

  208. Pasko A, Fryazinov O, Vilbrandt T et al (2011) Procedural function-based modelling of volumetric microstructures. Graph Model 73:165–181. https://doi.org/10.1016/J.GMOD.2011.03.001

    Article  Google Scholar 

  209. Sypeck DJ, Wadley HNG (2002) Cellular metal truss core sandwich structures. Adv Eng Mater 4:759–764. https://doi.org/10.1002/1527-2648(20021014)4:10<759::AID-ADEM759>3.0.CO;2-A

    Article  Google Scholar 

  210. Kooistra GW, Wadley HNG (2007) Lattice truss structures from expanded metal sheet. Mater Des 28:507–514. https://doi.org/10.1016/J.MATDES.2005.08.013

    Article  Google Scholar 

  211. Deshpande V, Fleck N (2001) Collapse of truss core sandwich beams in 3-point bending. Int J Solids Struct 38:6275–6305. https://doi.org/10.1016/S0020-7683(01)00103-2

    Article  MATH  Google Scholar 

  212. Chiras S, Mumm DR, Evans AG et al (2002) The structural performance of near-optimized truss core panels. Int J Solids Struct 39:4093–4115. https://doi.org/10.1016/S0020-7683(02)00241-X

    Article  Google Scholar 

  213. Santorinaios M, Brooks W, Sutcliffe CJ, Mines RAW (2006) Crush behaviour of open cellular lattice structures manufactured using selective laser melting. In: WIT Transactions on the Built Environment. pp 481–490

Download references

Funding

This work was financially supported by the High Speed 3D Printing Research Center from the Featured Areas Research Center Program within the framework of the Higher Education Sprout Project by the Minister of Education (MOE) Taiwan.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jeng-Ywan Jeng.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nazir, A., Abate, K.M., Kumar, A. et al. A state-of-the-art review on types, design, optimization, and additive manufacturing of cellular structures. Int J Adv Manuf Technol 104, 3489–3510 (2019). https://doi.org/10.1007/s00170-019-04085-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-019-04085-3

Keywords

Navigation