Review Article

The Design Process of Additively Manufactured Mesoscale Lattice Structures: A Review

[+] Author and Article Information
Francesco Tamburrino

Department of Mechanical Engineering,
Politecnico di Milano,
Milan 20156, Italy
e-mail: francesco.tamburrino@polimi.it

Serena Graziosi

Department of Mechanical Engineering,
Politecnico di Milano,
Milan 20156, Italy
e-mail: serena.graziosi@polimi.it

Monica Bordegoni

Department of Mechanical Engineering,
Politecnico di Milano,
Milan 20156, Italy
e-mail: monica.bordegoni@polimi.it

1Corresponding author.

Contributed by the Computers and Information Division of ASME for publication in the JOURNAL OF COMPUTING AND INFORMATION SCIENCE IN ENGINEERING. Manuscript received January 2, 2018; final manuscript received April 26, 2018; published online July 3, 2018. Assoc. Editor: Charlie C. L. Wang.

J. Comput. Inf. Sci. Eng 18(4), 040801 (Jul 03, 2018) (16 pages) Paper No: JCISE-18-1004; doi: 10.1115/1.4040131 History: Received January 02, 2018; Revised April 26, 2018

This review focuses on the design process of additively manufactured mesoscale lattice structures (MSLSs). They are arrays of three-dimensional (3D) printed trussed unit cells, whose dimensions span from 0.1 to 10.0 mm. This study intends to detail the phases of the MSLSs design process (with a particular focus on MSLSs whose unit cells are made up of a network of struts and nodes), proposing an integrated and holistic view of it, which is currently lacking in the literature. It aims at guiding designers' decisions with respect to the settled functional requirements and the manufacturing constraints. It also aims to provide an overview for software developers and researchers concerning the design approaches and strategies currently available. A further objective of this review is to stimulate researchers in exploring new MSLSs functionalities, consciously considering the impact of each design phase on the whole process, and on the manufactured product.

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Ashby, M. , 2006, “ The Properties of Foams and Lattices,” Philos. Trans. R. Soc. London A: Math., Phys. Eng. Sci., 364(1838), pp. 15–30. [CrossRef]
Hearn, G. , and Adams, E. , 2006, “ Shape Selection for Lattice Structures,” J. Struct. Eng., 132(11), pp. 1713–1720. [CrossRef]
Nguyen, J. , Park, S. , Rosen, D. W. , Folgar, L. , and Williams, J. , 2012, “ Conformal Lattice Structure Design and Fabrication,” Solid Freeform Fabrication Symposium (SFF), Austin, TX, Aug. 6–8, pp. 138–161. https://sffsymposium.engr.utexas.edu/Manuscripts/2012/2012-10-Nguyen.pdf
Tao, W. , and Leu, M. C. , 2016, “ Design of Lattice Structure for Additive Manufacturing,” International Symposium on Flexible Automation (ISFA), Cleveland, OH, Aug. 1–13, pp. 325–332.
Miyoshi, T. , Itoh, M. , Akiyama, S. , and Kitahara, A. , 2000, “ Alporas Aluminum Foam: Production Process, Properties, and Applications,” Adv. Eng. Mater., 2(4), pp. 179–183. [CrossRef]
Ashby, M. F. , Evans, T. , Fleck, N. A. , Hutchinson, J. , Wadley, H. , and Gibson, L. , 2000, Metal Foams: A Design Guide, Butterworth-Heinemann, Burlington, MA.
Aurenhammer, F. , 1991, “ Voronoi Diagrams—A Survey of a Fundamental Geometric Data Structure,” ACM Comput. Surv. (CSUR), 23(3), pp. 345–405. [CrossRef]
Nowak, A. , 2015, “ Application of Voronoi Diagrams in Contemporary Architecture and Town Planning,” Challenges Mod. Technol., 6(2), pp. 30–34. https://yadda.icm.edu.pl/baztech/element/bwmeta1.element.baztech-5259df1a-e1f7-442f-a68c-10c0c2b35c96/c/chmot62_06.pdf
Tonelli, D. , Pietroni, N. , Puppo, E. , Froli, M. , Cignoni, P. , Amendola, G. , and Scopigno, R. , 2016, “ Stability of Statics Aware Voronoi Grid-Shells,” Eng. Struct., 116, pp. 70–82. [CrossRef]
Michielsen, K. , and Stavenga, D. G. , 2008, “ Gyroid Cuticular Structures in Butterfly Wing Scales: Biological Photonic Crystals,” J. R. Soc. Interface, 5(18), pp. 85–94. [CrossRef] [PubMed]
Jung, Y. , and Torquato, S. , 2005, “ Fluid Permeabilities of Triply Periodic Minimal Surfaces,” Phys. Rev. E, 72(5), p. 056319. [CrossRef]
Hoare, S. H. N. , and Murphy, D. T. , 2012, “ Simulation of Acoustic Wave Propagation in 3-D Sonic Crystals Based on Triply Periodic Minimal Surfaces,” Baltic Nordic Acoustics Meeting (BNAM2012), Odense, Denmark, June 18–20, pp. 1–6.
Abueidda, D. W. , Bakir, M. , Al-Rub, R. K. A. , Bergström, J. S. , Sobh, N. A. , and Jasiuk, I. , 2017, “ Mechanical Properties of 3D Printed Polymeric Cellular Materials With Triply Periodic Minimal Surface Architectures,” Mater. Des., 122, pp. 255–267. [CrossRef]
Maskery, I. , Sturm, L. , Aremu, A. , Panesar, A. , Williams, C. , Tuck, C. , Wildman, R. , Ashcroft, I. , and Hague, R. , 2017, “ Insights Into the Mechanical Properties of Several Triply Periodic Minimal Surface Lattice Structures Made by Polymer Additive Manufacturing,” Polymer (in press).
Thompson, M. K. , Moroni, G. , Vaneker, T. , Fadel, G. , Campbell, R. I. , Gibson, I. , Bernard, A. , Schulz, J. , Graf, P. , Ahuja, B. , and Martina, F. , 2016, “ Design for Additive Manufacturing: Trends, Opportunities, Considerations, and Constraints,” CIRP Ann., 65(2), pp. 737–760. [CrossRef]
Ozbolat, I. T. , and Khoda, A. , 2014, “ Design of a New Parametric Path Plan for Additive Manufacturing of Hollow Porous Structures With Functionally Graded Materials,” ASME J. Comput. Inf. Sci. Eng., 14(4), p. 041005. [CrossRef]
Chu, C. , Graf, G. , and Rosen, D. W. , 2008, “ Design for Additive Manufacturing of Cellular Structures,” Comput.-Aided Des. Appl., 5(5), pp. 686–696. [CrossRef]
Deshpande, V. , Ashby, M. , and Fleck, N. , 2001, “ Foam Topology: Bending Versus Stretching Dominated Architectures,” Acta Mater., 49(6), pp. 1035–1040. [CrossRef]
Kranz, J. , Herzog, D. , and Emmelmann, C. , 2015, “ Design Guidelines for Laser Additive Manufacturing of Lightweight Structures in TiAl6V4,” J. Laser Appl., 27(S1), p. S14001. [CrossRef]
Tang, Y. , Dong, G. , Zhou, Q. , and Zhao, Y. F. , 2017, “ Lattice Structure Design and Optimization With Additive Manufacturing Constraints,” IEEE Trans. Autom. Sci. Eng., epub.
Maskery, I. , Hussey, A. , Panesar, A. , Aremu, A. , Tuck, C. , Ashcroft, I. , and Hague, R. , 2017, “ An Investigation Into Reinforced and Functionally Graded Lattice Structures,” J. Cellular Plast., 53(2), pp. 151–165. [CrossRef]
Aremu, A. , Brennan-Craddock, J. , Panesar, A. , Ashcroft, I. , Hague, R. J. , Wildman, R. D. , and Tuck, C. , 2017, “ A Voxel-Based Method of Constructing and Skinning Conformal and Functionally Graded Lattice Structures Suitable for Additive Manufacturing,” Addit. Manuf., 13, pp. 1–13. [CrossRef]
Brackett, D. , Ashcroft, I. , and Hague, R. , 2011, “ A Dithering Based Method to Generate Variable Volume Lattice Cells for Additive Manufacturing,” 22nd Annual International Solid Freeform Fabrication Symposium (SFF), Austin, TX, pp. 8–10. https://sffsymposium.engr.utexas.edu/Manuscripts/2011/2011-52-Brackett.pdf
Teufelhart, S. , and Reinhart, G. , 2012, “ Optimization of Strut Diameters in Lattice Structures,” 23th Annual Solid Freeform Fabrication Symposium (SFF), Austin, TX, Aug. 6–8, pp. 719–733. https://sffsymposium.engr.utexas.edu/Manuscripts/2012/2012-54-Teufelhart.pdf
Dong, G. , Tang, Y. , and Zhao, Y. F. , 2017, “ A Survey of Modeling of Lattice Structures Fabricated by Additive Manufacturing,” ASME J. Mech. Des., 139(10), p. 100906. [CrossRef]
Maskery, I. , Aboulkhair, N. T. , Aremu, A. , Tuck, C. , and Ashcroft, I. , 2017, “ Compressive Failure Modes and Energy Absorption in Additively Manufactured Double Gyroid Lattices,” Addit. Manuf., 16, pp. 24–29. [CrossRef]
Meeks, W. H. , and Rosenberg, H. , 1993, “ The Geometry of Periodic Minimal Surfaces,” Comment. Math. Helv., 68(1), pp. 538–578. [CrossRef]
Yan, C. , Hao, L. , Hussein, A. , and 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, pp. 61–73. [CrossRef] [PubMed]
Choy, S. Y. , Sun, C.-N. , Leong, K. F. , and Wei, J. , 2017, “ Compressive Properties of Ti-6Al-4V Lattice Structures Fabricated by Selective Laser Melting: Design, Orientation and Density,” Addit. Manuf., 16, pp. 213–224. [CrossRef]
Graf, G. C. , Chu, J. , Engelbrecht, S. , and Rosen, D. W. , 2009, “ Synthesis Methods for Lightweight Lattice Structures,” ASME Paper No. DETC2009-86993.
Pellegrino, S. , and Calladine, C. R. , 1986, “ Matrix Analysis of Statically and Kinematically Indeterminate Frameworks,” Int. J. Solids Struct., 22(4), pp. 409–428. [CrossRef]
Alkhader, M. , and Vural, M. , 2007, “ Effect of Microstructure in Cellular Solids: Bending Vs. stretch Dominated Topologies,” Third International Conference on Recent Advances in Space Technologies (RAST'07), Istanbul, Turkey, June 14–16, pp. 136–143.
Han, F. , Zhu, Z. , and Gao, J. , 1998, “ Compressive Deformation and Energy Absorbing Characteristic of Foamed Aluminum,” Metall. Mater. Trans. A, 29(10), pp. 2497–2502. [CrossRef]
Smith, M. , Guan, Z. , and Cantwell, W. , 2013, “ Finite Element Modelling of the Compressive Response of Lattice Structures Manufactured Using the Selective Laser Melting Technique,” Int. J. Mech. Sci., 67, pp. 28–41. [CrossRef]
Syam, W. P. , Jianwei, W. , Zhao, B. , Maskery, I. , Elmadih, W. , and Leach, R. , 2017, “ Design and Analysis of Strut-Based Lattice Structures for Vibration Isolation,” Precis. Eng. (in press).
Tanlak, N. , De Lange, D. F. , and Van Paepegem, W. , 2017, “ Numerical Prediction of the Printable Density Range of Lattice Structures for Additive Manufacturing,” Mater. Des., 133, pp. 549–558. [CrossRef]
Aremu, A. , Maskery, I. , Tuck, C. , Ashcroft, I. , Wildman, R. , and Hague, R. , 2016, “ Effects of Net and Solid Skins on Self-Supporting Lattice Structures,” Challenges in Mechanics of Time Dependent Materials, Vol. 2, Springer, Cham, Switzerland, pp. 83–89. [CrossRef]
Hussein, A. , Hao, L. , Yan, C. , Everson, R. , and Young, P. , 2013, “ Advanced Lattice Support Structures for Metal Additive Manufacturing,” J. Mater. Process. Technol., 213(7), pp. 1019–1026. [CrossRef]
Qiu, C. , Yue, S. , Adkins, N. J. , Ward, M. , Hassanin, H. , Lee, P. D. , Withers, P. J. , and Attallah, M. M. , 2015, “ Influence of Processing Conditions on Strut Structure and Compressive Properties of Cellular Lattice Structures Fabricated by Selective Laser Melting,” Mater. Sci. Eng.: A, 628, pp. 188–197. [CrossRef]
Gibson, I. , Rosen, D. , and Stucker, B. , 2011, Additive Manufacturing Technologies, 3D Printing, Rapid Prototyping, and Direct Digital Manufacturing, 2nd ed., Springer, Berlin.
Yang, L. , Harrysson, O. , West, H. , and Cormier, D. , 2015, “ Mechanical Properties of 3D Re-Entrant Honeycomb Auxetic Structures Realized Via Additive Manufacturing,” Int. J. Solids Struct., 69–70, pp. 475–490. [CrossRef]
Everhart, W. , Sawyer, E. , Neidt, T. , Dinardo, J. , and Brown, B. , 2016, “ The Effect of Surface Finish on Tensile Behavior of Additively Manufactured Tensile Bars,” J. Mater. Sci., 51(8), pp. 3836–3845. [CrossRef]
Pyka, G. , Kerckhofs, G. , Papantoniou, I. , Speirs, M. , Schrooten, J. , and Wevers, M. , 2013, “ Surface Roughness and Morphology Customization of Additive Manufactured Open Porous Ti6Al4V Structures,” Materials, 6(10), pp. 4737–4757. [CrossRef] [PubMed]
de Formanoir, C. , Suard, M. , Dendievel, R. , Martin, G. , and Godet, S. , 2016, “ Improving the Mechanical Efficiency of Electron Beam Melted Titanium Lattice Structures by Chemical Etching,” Addit. Manuf., 11, pp. 71–76. [CrossRef]
Ziemian, C. , Sharma, M. , and Ziemian, S. , 2012, “ Anisotropic Mechanical Properties of ABS Parts Fabricated by Fused Deposition Modelling,” Mechanical Engineering, InTechOpen, Rijeka, Croatia. [CrossRef]
Hutchinson, R. , and Fleck, N. , 2006, “ The Structural Performance of the Periodic Truss,” J. Mech. Phys. Solids, 54(4), pp. 756–782. [CrossRef]
Vongbunyong, S. , and Kara, S. , 2017, “ Rapid Generation of Uniform Cellular Structure by Using Prefabricated Unit Cells,” Int. J. Comput. Integr. Manuf., 30(8), pp. 792–804. [CrossRef]
Engelbrecht, S. , Folgar, L. , Rosen, D. W. , Schulberger, G. , and Williams, J. , 2009, “ Cellular Structures for Optimal Performance,” 20th Annual International Solid Freeform Fabrication Symposium (SFF), Austin, TX, Aug. 3–5, pp. 831–842. https://sffsymposium.engr.utexas.edu/Manuscripts/2009/2009-73-Rosen.pdf
Tang, Y. , and Zhao, Y. , 2015, “ Lattice-Skin Structures Design With Orientation Optimization,” Solid Freeform Fabrication Symposium (SFF), Austin, TX, Aug. 13–15, pp. 1378–1393. https://sffsymposium.engr.utexas.edu/sites/default/files/2015/2015-111-Tang.pdf
Reinhart, G. , and Teufelhart, S. , 2013, “ Optimization of Mechanical Loaded Lattice Structures by Orientating Their Struts Along the Flux of Force,” Procedia CIRP, 12, pp. 175–180. [CrossRef]
Wu, J. , Wang, C. C. , Zhang, X. , and Westermann, R. , 2016, “ Self-Supporting Rhombic Infill Structures for Additive Manufacturing,” Comput.-Aided Des., 80, pp. 32–42. [CrossRef]
Kolken, H. M. , Janbaz, S. , Leeflang, S. M. , Lietaert, K. , Weinans, H. H. , and Zadpoor, A. A. , 2018, “ Rationally Designed Meta-Implants: A Combination of Auxetic and Conventional Meta-Biomaterials,” Mater. Horiz., 5(1), pp. 28–35. [CrossRef]
Tang, Y. , Tang, Y. , Zhao, Y. F. , and Zhao, Y. F. , 2016, “ A Survey of the Design Methods for Additive Manufacturing to Improve Functional Performance,” Rapid Prototyping J., 22(3), pp. 569–590. [CrossRef]
Choy, S. Y. , Sun, C.-N. , Leong, K. F. , and Wei, J. , 2017, “ Compressive Properties of Functionally Graded Lattice Structures Manufactured by Selective Laser Melting,” Mater. Des., 131, pp. 112–120. [CrossRef]
Reinhart, G. , and Teufelhart, S. , 2011, “ Load-Adapted Design of Generative Manufactured Lattice Structures,” Phys. Procedia, 12(Pt. A), pp. 385–392. [CrossRef]
Brackett, D. , Ashcroft, I. , Wildman, R. , and Hague, R. J. , 2014, “ An Error Diffusion Based Method to Generate Functionally Graded Cellular Structures,” Comput. Struct., 138, pp. 102–111. [CrossRef]
Luxner, M. H. , Stampfl, J. , and Pettermann, H. E. , 2005, “ Finite Element Modeling Concepts and Linear Analyses of 3D Regular Open Cell Structures,” J. Mater. Sci., 40(22), pp. 5859–5866. [CrossRef]
Salonitis, K. , Chantzis, D. , and Kappatos, V. , 2017, “ A Hybrid Finite Element Analysis and Evolutionary Computation Method for the Design of Lightweight Lattice Components With Optimized Strut Diameter,” Int. J. Adv. Manuf. Technol., 90(9–12), pp. 2689–2701. [CrossRef]
Labeas, G. , and Sunaric, M. , 2010, “ Investigation on the Static Response and Failure Process of Metallic Open Lattice Cellular Structures,” Strain, 46(2), pp. 195–204. [CrossRef]
Bici, M. , Campana, F. , and De Michelis, M. , 2017, “ Mesoscale Geometric Modeling of Cellular Materials for Finite Element Analysis,” Comput.-Aided Des. Appl., 14(6), pp. 760–769. [CrossRef]
Boniotti, L. , Beretta, S. , Foletti, S. , and Patriarca, L. , 2017, “ Strain Concentrations in BCC Micro Lattices Obtained by Am,” Procedia Struct. Integr., 7, pp. 166–173. [CrossRef]
Ushijima, K. , Cantwell, W. , Mines, R. , Tsopanos, S. , and Smith, M. , 2011, “ An Investigation Into the Compressive Properties of Stainless Steel Micro-Lattice Structures,” J. Sandwich Struct. Mater., 13(3), pp. 303–329. [CrossRef]
Wong, K. V. , and Hernandez, A. , 2012, “ A Review of Additive Manufacturing,” ISRN Mech. Eng., 2012, p. 208760.
Frazier, W. E. , 2014, “ Metal Additive Manufacturing: A Review,” J. Mater. Eng. Perform., 23(6), pp. 1917–1928. [CrossRef]
Yan, C. , Hao, L. , Hussein, A. , and Raymont, D. , 2012, “ Evaluations of Cellular Lattice Structures Manufactured Using Selective Laser Melting,” Int. J. Mach. Tools Manuf., 62, pp. 32–38. [CrossRef]
Brackett, D. , Ashcroft, I. , and Hague, R. , 2011, “ Topology Optimization for Additive Manufacturing,” Solid Freeform Fabrication Symposium (SFF), Austin, TX, pp. 348–362. https://sffsymposium.engr.utexas.edu/Manuscripts/2011/2011-27-Brackett.pdf
Wang, Y. , Zhang, L. , Daynes, S. , Zhang, H. , Feih, S. , and Wang, M. Y. , 2018, “ Design of Graded Lattice Structure With Optimized Mesostructures for Additive Manufacturing,” Mater. Des., 142, pp. 114–123. [CrossRef]
Wang, Y. , Chen, F. , and Wang, M. Y. , 2017, “ Concurrent Design With Connectable Graded Microstructures,” Comput. Methods Appl. Mech. Eng., 317, pp. 84–101. [CrossRef]
Alexandersen, J. , and Lazarov, B. S. , 2015, “ Topology Optimisation of Manufacturable Microstructural Details Without Length Scale Separation Using a Spectral Coarse Basis Preconditioner,” Comput. Methods Appl. Mech. Eng., 290, pp. 156–182. [CrossRef]
Wu, J. , Aage, N. , Westermann, R. , and Sigmund, O. , 2018, “ Infill Optimization for Additive Manufacturing—Approaching Bone-Like Porous Structures,” IEEE Trans. Visualization Comput. Graphics, 24(2), pp. 1127–1140. [CrossRef]
Beyer, C. , 2014, “ Strategic Implications of Current Trends in Additive Manufacturing,” ASME J. Manuf. Sci. Eng., 136(6), p. 064701. [CrossRef]
Panesar, A. , Abdi, M. , Hickman, D. , and Ashcroft, I. , 2018, “ Strategies for Functionally Graded Lattice Structures Derived Using Topology Optimisation for Additive Manufacturing,” Addit. Manuf., 19, pp. 81–94. [CrossRef]
Hao, L. , Raymond, D. , Yan, C. , Hussein, A. , and Young, P. , 2011, “ Design and Additive Manufacturing of Cellular Lattice Structures,” International Conference on Advanced Research in Virtual and Rapid Prototyping (VRAP), Leiria, Portugal, Sept. 28–Oct. 1, pp. 249–254.
Kantareddy, S. , Roh, B. , Simpson, T. , Joshi, S. , Dickman, C. , and Lehtihet, E. , 2016, “ Saving Weight With Metallic Lattice Structures: Design Challenges With a Real-World Example,” Solid Freeform Fabrication Symposium (SFF), Austin, TX, Aug. 8–10, pp. 8–10. https://sffsymposium.engr.utexas.edu/sites/default/files/2016/171-Kantareddy.pdf
Hadi, A. , Vignat, F. , and Villeneuve, F. , 2015, “ Design Configurations and Creation of Lattice Structures for Metallic Additive Manufacturing,” 14ème Colloque National AIP PRIMECA, La Plagne, France, pp. 1–8.
Segerman, H. , 2012, “ 3D Printing for Mathematical Visualisation,” Math. Intell., 34(4), pp. 56–62. [CrossRef]
Savio, G. , Rosso, S. , Meneghello, R. , and Concheri, G. , 2018, “ Geometric Modeling of Cellular Materials for Additive Manufacturing in Biomedical Field: A Review,” Appl. Bionics Biomech., 2018, p. 1654782.
Savio, G. , Meneghello, R. , and Concheri, G. , 2018, “ Geometric Modeling of Lattice Structures for Additive Manufacturing,” Rapid Prototyping J., 24(2), pp. 351–360. [CrossRef]
ASTM, 2016, “ Standard Guidelines for Design for Additive Manufacturing,” ASTM International, West Conshohocken, PA, Standard No. ASTM52910-17.
Parthasarathy, J. , Starly, B. , and Raman, S. , 2011, “ A Design for the Additive Manufacture of Functionally Graded Porous Structures With Tailored Mechanical Properties for Biomedical Applications,” J. Manuf. Processes, 13(2), pp. 160–170. [CrossRef]
Aversa, R. , Petrescu, F. I. T. , Petrescu, R. V. V. , and Apicella, A. , 2016, “ Biomimetic Finite Element Analysis Bone Modeling for Customized Hybrid Biological Prostheses Development,” Am. J. Appl. Sci., 13(11), pp. 1060–1067. [CrossRef]
Murr, L. , Gaytan, S. , Medina, F. , Lopez, H. , Martinez, E. , Machado, B. , Hernandez, D. , Martinez, L. , Lopez, M. I. , Wicker, R. B. , and Bracke, J. , 2010, “ Next-Generation Biomedical Implants Using Additive Manufacturing of Complex, Cellular and Functional Mesh Arrays,” Philos. Trans. R. Soc. London A: Math., Phys. Eng. Sci., 368(1917), pp. 1999–2032. [CrossRef]
Petrovic, V. , Vicente Haro Gonzalez, J. , Jorda Ferrando, O. , Delgado Gordillo, J. , Ramon Blasco Puchades, J. , and Portoles Grinan, L. , 2011, “ Additive Layered Manufacturing: Sectors of Industrial Application Shown Through Case Studies,” Int. J. Prod. Res., 49(4), pp. 1061–1079. [CrossRef]
Limmahakhun, S. , Oloyede, A. , Sitthiseripratip, K. , Xiao, Y. , and Yan, C. , 2017, “ 3D-Printed Cellular Structures for Bone Biomimetic Implants,” Addit. Manuf., 15, pp. 93–101. [CrossRef]
de Wild, M. , Zimmermann, S. , Rüegg, J. , Schumacher, R. , Fleischmann, T. , Ghayor, C. , and Weber, F. E. , 2016, “ Influence of Microarchitecture on Osteoconduction and Mechanics of Porous Titanium Scaffolds Generated by Selective Laser Melting,” 3D Printing Addit. Manuf., 3(3), pp. 142–151. [CrossRef]
Gao, W. , Zhang, Y. , Ramanujan, D. , Ramani, K. , Chen, Y. , Williams, C. B. , Wang, C. C. , Shin, Y. C. , Zhang, S. , and Zavattieri, P. D. , 2015, “ The Status, Challenges, and Future of Additive Manufacturing in Engineering,” Comput.-Aided Des., 69, pp. 65–89. [CrossRef]
Wadley, H. N. , 2006, “ Multifunctional Periodic Cellular Metals,” Philos. Trans. R. Soc. London A: Math., Phys. Eng. Sci., 364(1838), pp. 31–68. [CrossRef]
Brooks, H. , and Brigden, K. , 2016, “ Design of Conformal Cooling Layers With Self-Supporting Lattices for Additively Manufactured Tooling,” Addit. Manuf., 11, pp. 16–22. [CrossRef]
Ozdemir, Z. , Hernandez-Nava, E. , Tyas, A. , Warren, J. A. , Fay, S. D. , Goodall, R. , Todd, I. , and Askes, H. , 2016, “ Energy Absorption in Lattice Structures in Dynamics: Experiments,” Int. J. Impact Eng., 89, pp. 49–61. [CrossRef]
Hasib, H. , Rennie, A. , Burns, N. , and Geekie, L. , 2015, “ Non-Stochastic Lattice Structures for Novel Filter Applications Fabricated Via Additive Manufacturing,” Filtration, 15(3), pp. 174–180. https://www.researchgate.net/publication/278962837_Non-stochastic_lattice_structures_for_novel_filter_applications_fabricated_via_additive_manufacturing
Sugimura, Y. , 2004, “ Mechanical Response of Single-Layer Tetrahedral Trusses Under Shear Loading,” Mech. Mater., 36(8), pp. 715–721. [CrossRef]
Moongkhamklang, P. , Deshpande, V. , and Wadley, H. , 2010, “ The Compressive and Shear Response of Titanium Matrix Composite Lattice Structures,” Acta Mater., 58(8), pp. 2822–2835. [CrossRef]
Ptochos, E. , and Labeas, G. , 2012, “ Shear Modulus Determination of Cuboid Metallic Open-Lattice Cellular Structures by Analytical, Numerical and Homogenisation Methods,” Strain, 48(5), pp. 415–429. [CrossRef]
Kooistra, G. W. , Queheillalt, D. T. , and Wadley, H. N. , 2008, “ Shear Behavior of Aluminum Lattice Truss Sandwich Panel Structures,” Mater. Sci. Eng.: A, 472(1–2), pp. 242–250. [CrossRef]
Queheillalt, D. T. , and Wadley, H. N. , 2009, “ Titanium Alloy Lattice Truss Structures,” Mater. Des., 30(6), pp. 1966–1975. [CrossRef]
Dong, L. , and Wadley, H. , 2016, “ Shear Response of Carbon Fiber Composite Octet-Truss Lattice Structures,” Compos. Part A: Appl. Sci. Manuf., 81, pp. 182–192. [CrossRef]
Ion, A. , Frohnhofen, J. , Wall, L. , Kovacs, R. , Alistar, M. , Lindsay, J. , Lopes, P. , Chen, H.-T. , and Baudisch, P. , 2016, “ Metamaterial Mechanisms,” 29th Annual Symposium on User Interface Software and Technology, Tokyo, Japan, Oct. 16–19, pp. 529–539.
Bertoldi, K. , Vitelli, V. , Christensen, J. , and van Hecke, M. , 2017, “ Flexible Mechanical Metamaterials,” Nat. Rev. Mater., 2(11), p. 17066. [CrossRef]
Yuan, S. , Shen, F. , Bai, J. , Chua, C. K. , Wei, J. , and Zhou, K. , 2017, “ 3D Soft Auxetic Lattice Structures Fabricated by Selective Laser Sintering: TPU Powder Evaluation and Process Optimization,” Mater. Des., 120, pp. 317–327. [CrossRef]
Li, T. , Hu, X. , Chen, Y. , and Wang, L. , 2017, “ Harnessing Out-of-Plane Deformation to Design 3D Architected Lattice Metamaterials With Tunable Poisson's Ratio,” Sci. Rep., 7(1), p. 8949. [CrossRef] [PubMed]
Choi, J. , Kwon, O.-C. , Jo, W. , Lee, H. J. , and Moon, M.-W. , 2015, “ 4D Printing Technology: A Review,” 3D Printing Addit. Manuf., 2(4), pp. 159–167. [CrossRef]
Bogue, R. , 2012, “ Smart Materials: A Review of Recent Developments,” Assem. Autom., 32(1), pp. 3–7. [CrossRef]
Gao, B. , Yang, Q. , Zhao, X. , Jin, G. , Ma, Y. , and Xu, F. , 2016, “ 4D Bioprinting for Biomedical Applications,” Trends Biotechnol., 34(9), pp. 746–756. [CrossRef] [PubMed]
Gladman, A. S. , Matsumoto, E. A. , Nuzzo, R. G. , Mahadevan, L. , and Lewis, J. A. , 2016, “ Biomimetic 4D Printing,” Nat. Mater., 15(4), pp. 413–418. [CrossRef] [PubMed]
Meisel, N. A. , Elliott, A. M. , and Williams, C. B. , 2015, “ A Procedure for Creating Actuated Joints Via Embedding Shape Memory Alloys in Polyjet 3D Printing,” J. Intell. Mater. Syst. Struct., 26(12), pp. 1498–1512. [CrossRef]
Wagner, M. , Chen, T. , and Shea, K. , 2017, “ Large Shape Transforming 4D Auxetic Structures,” 3D Printing Addit. Manuf., 4(3), pp. 133–142. [CrossRef]
Truby, R. L. , and Lewis, J. A. , 2016, “ Printing Soft Matter in Three Dimensions,” Nature, 540(7633), pp. 371–378. [CrossRef] [PubMed]
Jiang, Y. , and Wang, Q. , 2016, “ Highly-Stretchable 3D-Architected Mechanical Metamaterials,” Sci. Rep., 6(1), p. 34147. [CrossRef] [PubMed]


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Fig. 1

The concept of lattice applied to different dimensional scales: structures defining the atoms arrangement in the microscale; structures of cellular materials in the mesoscale; specific architectural structures in the macroscale

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Fig. 2

Cellular structures can be divided into stochastic and nonstochastic ones. Both the arrangement as well as the geometry of the unit cells of 2D and 3D nonstochastic structures can be designed. This paper is focused on the design process of 3D strut-and-node based lattice structures. This type of cellular structure is highlighted in the image. This figure is inspired by Tao and Leu [4], while the TPMS structure has been modeled using the software, developed at the University of Nottingham, mentioned in Ref. [14].

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Fig. 3

The MSLSs design workflow. Starting from the available design space and the functional targets to be reached, the design process is then structured into five main phases. During these phases manufacturing constraints will also be taken into account to guarantee the printability of the structure.

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Fig. 4

Two examples of unit cells: a TPMS (cell modeled using the software, developed at the University of Nottingham, mentioned in Ref. [14]) and a 3D strut-and-node based cell

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Fig. 5

The qualitative stress/strain curves of stretch-dominated and bending-dominated unit cells. The stress/strain curve of stretch-dominated unit cells is characterized by high stiffness and high initial strength, followed by postyield softening. The stress/strain curve of bending-dominated unit cells is characterized by a lower stiffness, a lower initial strength and a large deformation at relatively low and constant stress (plateau stress). The last part of both curves shows the densification phase, that is the moment when the struts merge. The image is inspired by the work [1].

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Fig. 6

Maxwell's Criterion (see Eq. (2)). The unit cell on the left has M < 0: it is bending-dominated (nodes are all locked). The unit cell in the center has M = 0: it is stretch-dominated. Adding a further strut to this cell will make M > 0. In this case, if nodes are unlocked there is a state of self-stress: the struts carry stress also if no external loads are applied. If nodes are locked, the cell is still stretch-dominated and can be manufactured using AM technologies. Figure inspired by Ashby [1].

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Fig. 7

Unit cell optimization according to six loading conditions (xx, yy, zz, yz, xy, xz). Considering, as design requirements, the stiffness and the strength as well as the loading conditions, the unit cell is optimized through a proper strut positioning for each loading condition. The combined results lead to the final cell developed and optimized in all directions. Figure inspired by Nguyen et al. [3].

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Fig. 8

The aspect ratio of a BCC unit cell. When W and, thus, the aspect ratio (W/H) decreases, the unit cell shows higher stiffness and yield stress. In particular, the amplitude of the angles between the struts changes. The amplitude of the angles at the bottom, and at the top of the unit cell, decreases while, for the angles at the sides (α) of the unit cell, the amplitude increases. This figure is used to summarize some considerations provided in Ref. [34].

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Fig. 9

The total area moment of inertia values (I) of the cells about centroid coordinate axes. The figure shows how three different geometric configurations of unit cells, having the same W, H, and D values (respectively 10 mm, 10 mm, and 1 mm), but a different struts number and arrangement, have different I values.

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Fig. 10

The figure shows the deviation between the thickness of the virtual model of the struts and the additively manufactured ones (dashed lines) as discussed in Ref. [20]: both for horizontal and sloped struts such deviation is related to the change of the D value. For horizontal struts, this value can vary between tmax and tmin. For sloped struts the cross section is no more a circle but it can vary between ta and tb. This figure has been inspired by the work [20].

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Fig. 11

The uniform population is based on a periodic unit cell distribution. The figure shows how all unit cells have the same shape and dimensions. Dashed lines are used to highlight that the unit cells integrity, at the boundary, is accidental.

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Fig. 12

The conformal population is based on a distribution of the unit cells that is conformal to the boundaries of the design space. The figure shows that the unit cells do not have the same shape and dimensions. The dashed lines and the box highlight that they are fully conformal to the boundaries and their integrity is preserved.

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Fig. 13

The figure shows the application of a heterogeneous gradient through the use of a gray scale image that is overlaid to a uniform lattice structure. The darker areas have a higher relative density (through the struts thickening), while the clearer ones have a lower relative density. Both the uniform and graded structures were modeled using the software, developed at the University of Nottingham, mentioned in Ref. [14].

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Fig. 14

The figure shows the model that has been used in Ref. [34] for performing a FEA on BCC and BCC-Z unit cells. The solid model is based on the use of struts wholly straight and with a constant diameter. A compression test is simulated applying the same loading conditions on the planar face at the top of each unit cell and using a rigid plate to crush the same unit cells progressively.

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Fig. 15

The figure shows how shear bands (dashed lines) can occur when an array of unit cells less regular, like BCC-Z with the characteristic vertical strut in the middle, is loaded (see also Fig. 14). In these cases, a simulation performed on a single unit cell can be not sufficient to get information on the deformability of a lattice structure. This image has been inspired by the work [34].



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