Cellular structures are promising candidates for additive manufacturing (AM) due to their lower material and energy consumption. In this work, an efficient method is proposed for optimizing the topology of variable-density cellular structures to be fabricated by certain AM process. The method gains accuracy by relating the cellular structure's microstructure to continuous micromechanics models and achieves efficiency through conducting continuum topology optimization at macroscopic scale. The explicit cellular structure is then finally reconstructed by mapping the optimized continuous parameters (e.g., density) to cell structural parameters (e.g., strut diameter). The proposed method is validated by both finite element analysis and experimental tests on specimens manufactured by stereolithography.
Issue Section:
Research Papers
References
1.
Gibson
, L. J.
, Ashby
, M. F.
, and Harley
, B. A.
, 2010
, Cellular Materials in Nature and Medicine, Cambridge University, Cambridge, UK.2.
Gibson
, L. J.
, and Ashby
, M. F.
, 1999
, Cellular Solids: Structure and Properties, Cambridge University, Cambridge, UK.3.
Banhart
, J.
, 2001
, “Manufacture, Characterisation and Application of Cellular Metals and Metal Foams
,” Prog. Mater. Sci.
, 46
(6
), pp. 559
–632
.10.1016/S0079-6425(00)00002-54.
Lu
, T. J.
, Hess
, A.
, and Ashby
, M.
, 1999
, “Sound Absorption in Metallic Foams
,” J. Appl. Phys.
, 85
(11
), pp. 7528
–7539
.10.1063/1.3705505.
Harte
, A.-M.
, Fleck
, N. A.
, and Ashby
, M. F.
, 2000
, “Sandwich Panel Design Using Aluminum Alloy Foam
,” Adv. Eng. Mater.
, 2
(4
), pp. 219
–222
.10.1002/(SICI)1527-2648(200004)2:4<219::AID-ADEM219>3.0.CO;2-#6.
Hohe
, J.
, and Becker
, W.
, 2002
, “Effective Stress–Strain Relations for Two-Dimensional Cellular Sandwich Cores: Homogenization, Material Models, and Properties
,” ASME Appl. Mech. Rev.
, 55
(1
), pp. 61
–87
.10.1115/1.14253947.
Pritz
, T.
, 1994
, “Dynamic Young's Modulus and Loss Factor of Plastic Foams for Impact Sound Isolation
,” J. Sound Vib.
, 178
(3
), pp. 315
–322
.10.1006/jsvi.1994.14888.
Yilbas
, B. S.
, Akhtar
, S.
, and Keles
, O.
, 2013
, “Laser Cutting of Aluminum Foam: Experimental and Model Studies
,” ASME J. Manuf. Sci. Eng.
, 135
(5
), p. 051018
.10.1115/1.40250099.
Strano
, M.
, 2011
, “A New FEM Approach for Simulation of Metal Foam Filled Tubes
,” ASME J. Manuf. Sci. Eng.
, 133
(6
), p. 061003
.10.1115/1.400535410.
Nebosky
, P. S.
, and Schmid
, S. R.
, 2011
, “Formability of Porous Tantalum Sheet-Metal
,” ASME J. Manuf. Sci. Eng.
, 133
(6
), p. 061006
.10.1115/1.400535311.
Gibson
, L.
, 2000
, “Mechanical Behavior of Metallic Foams
,” Annu. Rev. Mater. Sci.
, 30
(1
), pp. 191
–227
.10.1146/annurev.matsci.30.1.19112.
Christensen
, R.
, 2000
, “Mechanics of Cellular and Other Low-Density Materials
,” Int. J. Solids Struct.
, 37
(1
), pp. 93
–104
.10.1016/S0020-7683(99)00080-313.
Lopatnikov
, S. L.
, Gama
, B. A.
, Jahirul Haque
, M.
, Krauthauser
, C.
, Gillespie
, J. W.
, Jr., Guden
, M.
, and Hall
, I. W.
, 2003
, “Dynamics of Metal Foam Deformation During Taylor Cylinder–Hopkinson Bar Impact Experiment
,” Compos. Struct.
, 61
(1
), pp. 61
–71
.10.1016/S0263-8223(03)00039-414.
Elnasri
, I.
, Pattofatto
, S.
, Zhao
, H.
, Tsitsiris
, H.
, Hild
, F.
, and Girard
, Y.
, 2007
, “Shock Enhancement of Cellular Structures Under Impact Loading: Part I Experiments
,” J. Mech. Phys. Solids
, 55
(12
), pp. 2652
–2671
.10.1016/j.jmps.2007.04.00515.
Golovin
, I.
, and Sinning
, H.-R.
, 2003
, “Damping in Some Cellular Metallic Materials
,” J. Alloys Compd.
, 355
(1
), pp. 2
–9
.10.1016/S0925-8388(03)00241-X16.
Banhart
, J.
, Baumeister
, J.
, and Weber
, M.
, 1996
, “Damping Properties of Aluminium Foams
,” Mater. Sci. Eng. A
, 205
(1
), pp. 221
–228
.10.1016/0921-5093(95)09973-517.
Andrews
, E.
, and Gibson
, L.
, 2001
, “The Influence of Cracks, Notches and Holes on the Tensile Strength of Cellular Solids
,” Acta Mater.
, 49
(15
), pp. 2975
–2979
.10.1016/S1359-6454(01)00203-818.
Fleck
, N.
, Deshpande
, V.
, and Ashby
, M.
, 2010
, “Micro-Architectured Materials: Past, Present and Future
,” Proc. R. Soc. A
, 466
(2121
), pp. 2495
–2516
.10.1098/rspa.2010.021519.
Ashby
, M. F.
, and Medalist
, R. M.
, 1983
, “The Mechanical Properties of Cellular Solids
,” Metall. Trans. A
, 14
(9
), pp. 1755
–1769
.10.1007/BF0264554620.
Evans
, A.
, Hutchinson
, J.
, Fleck
, N.
, Ashby
, M.
, and Wadley
, H.
, 2001
, “The Topological Design of Multifunctional Cellular Metals
,” Prog. Mater. Sci.
, 46
(3
), pp. 309
–327
.10.1016/S0079-6425(00)00016-521.
Wadley
, H. N.
, 2006
, “Multifunctional Periodic Cellular Metals
,” Philos. Trans. R. Soc. A
, 364
(1838
), pp. 31
–68
.10.1098/rsta.2005.169722.
Evans
, A. G.
, Hutchinson
, J.
, and Ashby
, M.
, 1998
, “Multifunctionality of Cellular Metal Systems
,” Prog. Mater. Sci.
, 43
(3
), pp. 171
–221
.10.1016/S0079-6425(98)00004-823.
To
, A.
, Tao
, J.
, Kirca
, M.
, and Schalk
, L.
, 2011
, “Ligament and Joint Sizes Govern Softening in Nanoporous Aluminum
,” Appl. Phys. Lett.
, 98
(5
), p. 051903
.10.1063/1.354985824.
Giri
, A.
, Tao
, J.
, Wang
, L.
, Kirca
, M.
, and To
, A. C.
, 2013
, “Compressive Behavior and Deformation Mechanism of Nanoporous Open-Cell Foam With Ultrathin Ligaments
,” J. Nanomech. Micromech.
, 4
(2
), p. A4013012.10.1061/(ASCE)NM.2153-5477.000007925.
Chmielus
, M.
, Zhang
, X.
, Witherspoon
, C.
, Dunand
, D.
, and Müllner
, P.
, 2009
, “Giant Magnetic-Field-Induced Strains in Polycrystalline Ni–Mn–Ga Foams
,” Nat. Mater.
, 8
(11
), pp. 863
–866
.10.1038/nmat252726.
Boonyongmaneerat
, Y.
, Chmielus
, M.
, Dunand
, D. C.
, and Müllner
, P.
, 2007
, “Increasing Magnetoplasticity in Polycrystalline Ni–Mn–Ga by Reducing Internal Constraints Through Porosity
,” Phys. Rev. Lett.
, 99
(24
), p. 247201
.10.1103/PhysRevLett.99.24720127.
Wadley
, H. N.
, 2002
, “Cellular Metals Manufacturing
,” Adv. Eng. Mater.
, 4
(10
), pp. 726
–733
.10.1002/1527-2648(20021014)4:10<726::AID-ADEM726>3.0.CO;2-Y28.
Sundarram
, S. S.
, Jiang
, W.
, and Li
, W.
, 2014
, “Fabrication of Small Pore-Size Nickel Foams Using Electroless Plating of Solid-State Foamed Immiscible Polymer Blends
,” ASME J. Manuf. Sci. Eng.
, 136
(2
), p. 021002
.10.1115/1.402541829.
Barletta
, M.
, Gisario
, A.
, Guarino
, S.
, and Rubino
, G.
, 2009
, “Production of Open Cell Aluminum Foams by Using the Dissolution and Sintering Process (DSP)
,” ASME J. Manuf. Sci. Eng.
, 131
(4
), p. 041009
.10.1115/1.315904430.
Burblies
, A.
, and Busse
, M.
, 2006, “Computer Based Porosity Design by Multi Phase Topology Optimization
,” AIP Conference Proceedings
, 973
(15–18), pp. 285–290.31.
Harrysson
, O. L.
, Cansizoglu
, O.
, Marcellin-Little
, D. J.
, Cormier
, D. R.
, and West
, II, H. A.
, 2008
, “Direct Metal Fabrication of Titanium Implants With Tailored Materials and Mechanical Properties Using Electron Beam Melting Technology
,” Mater. Sci. Eng. C
, 28
(3
), pp. 366
–373
.10.1016/j.msec.2007.04.02232.
Murr
, L.
, Gaytan
, S.
, Medina
, F.
, Lopez
, H.
, Martinez
, E.
, Machado
, B.
, Hernandez
, D.
, Martinez
, L.
, Lopez
, M.
, and Wicker
, R.
, 2010
, “Next-Generation Biomedical Implants Using Additive Manufacturing of Complex, Cellular and Functional Mesh Arrays
,” Philos. Trans. R. Soc. A
, 368
(1917
), pp. 1999
–2032
.10.1098/rsta.2010.001033.
Nguyen
, J.
, Park
, S.-i.
, and Rosen
, D.
, 2013
, “Heuristic Optimization Method for Cellular Structure Design of Light Weight Components
,” Int. J. Precis. Eng. Manuf.
, 14
(6
), pp. 1071
–1078
.10.1007/s12541-013-0144-534.
Gibson
, I.
, Rosen
, D. W.
, and Stucker
, B.
, 2010
, Additive Manufacturing Technologies
, Springer
, New York
.10.1007/978-1-4419-1120-935.
Kruth
, J.-P.
, Leu
, M.
, and Nakagawa
, T.
, 1998
, “Progress in Additive Manufacturing and Rapid Prototyping
,” CIRP Ann. Manuf. Technol.
, 47
(2
), pp. 525
–540
.10.1016/S0007-8506(07)63240-536.
Wohlers
, T.
, 2011
, Wohlers Report 2011: Additive Manufacturing and 3D Printing, State of the lndustry
, Wohlers Associates
, Ft. Collins, CO
.37.
Scott
, J.
, Gupta
, N.
, Weber
, C. L.
, Newsome
, S.
, Wohlers
, T.
, and Caffrey
, T.
, 2012
, Additive Manufacturing: Status and Opportunities
, Science and Technology Policy Institute
, Washington, DC
, pp. 1
–29
.38.
Conley
, J.
, and Marcus
, H.
, 1997
, “Rapid Prototyping and Solid Free Form Fabrication
,” ASME J. Manuf. Sci. Eng.
, 119
(4B
), pp. 811
–816
.10.1115/1.283682839.
Beyer
, C.
, “Additive Manufacturing—Implications of a Breakthrough Technology
,” ASME J. Manuf. Sci. Eng.
(to be published).10.1115/1.402859940.
Haapala
, K. R.
, Zhao
, F.
, Camelio
, J.
, Sutherland
, J. W.
, Skerlos
, S. J.
, Dornfeld
, D. A.
, Jawahir
, I.
, Clarens
, A. F.
, and Rickli
, J. L.
, 2013
, “A Review of Engineering Research in Sustainable Manufacturing
,” ASME J. Manuf. Sci. Eng.
, 135
(4
), p. 041013
.10.1115/1.402404041.
Gu
, D.
, Meiners
, W.
, Wissenbach
, K.
, and Poprawe
, R.
, 2012
, “Laser Additive Manufacturing of Metallic Components: Materials, Processes and Mechanisms
,” Int. Mater. Rev.
, 57
(3
), pp. 133
–164
.10.1179/1743280411Y.000000001442.
Murr
, L. E.
, Gaytan
, S. M.
, Ramirez
, D. A.
, Martinez
, E.
, Hernandez
, J.
, Amato
, K. N.
, Shindo
, P. W.
, Medina
, F. R.
, and Wicker
, R. B.
, 2012
, “Metal Fabrication by Additive Manufacturing Using Laser and Electron Beam Melting Technologies
,” J. Mater. Sci. Technol.
, 28
(1
), pp. 1
–14
.10.1016/S1005-0302(12)60016-443.
Bártolo
, P. J.
, 2011
, Stereolithography: Materials, Processes and Applications
, Springer
, New York
.44.
Edwards
, P.
, O'Conner
, A.
, and Ramulu
, M.
, 2013
, “Electron Beam Additive Manufacturing of Titanium Components: Properties and Performance
,” ASME J. Manuf. Sci. Eng.
, 135
(6
), p. 061016
.10.1115/1.402577345.
Schultz
, B.
, and Rohatgi
, P.
, 2014
, “Laser Engineered Net Shaping Process for 316L/15% Nickel Coated Titanium Carbide Metal Matrix Composite
,” ASME J. Manuf. Sci. Eng.
, 136
(5
), p. 051007
.10.1115/1.402775846.
Kruth
, J. P.
, Leu
, M.
, and Nakagawa
, T.
, 1998
, “Progress in Additive Manufacturing and Rapid Prototyping
,” CIRP Ann. Manuf. Technol.
, 47
(2
), pp. 525
–540
.10.1016/S0007-8506(07)63240-547.
Luo
, J.
, Pan
, H.
, and Kinzel
, E.
, “Additive Manufacturing of Glass
,” ASME J. Manuf. Sci. Eng.
(to be published).10.1115/1.402853148.
Dimas
, L. S.
, Bratzel
, G. H.
, Eylon
, I.
, and Buehler
, M. J.
, 2013
, “Tough Composites Inspired by Mineralized Natural Materials: Computation, 3D Printing, and Testing
,” Adv. Funct. Mater.
, 23
(36
), pp. 4629
–4638
.10.1002/adfm.20130021549.
Li
, Y.
, Kaynia
, N.
, Rudykh
, S.
, and Boyce
, M. C.
, 2013
, “Wrinkling of Interfacial Layers in Stratified Composites
,” Adv. Eng. Mater.
, 15
(10
), pp. 921
–926
.10.1002/adem.20130014750.
Gaytan
, S.
, Murr
, L.
, Martinez
, E.
, Martinez
, J.
, Machado
, B.
, Ramirez
, D.
, Medina
, F.
, Collins
, S.
, and Wicker
, R.
, 2010
, “Comparison of Microstructures and Mechanical Properties for Solid and Mesh Cobalt-Base Alloy Prototypes Fabricated by Electron Beam Melting
,” Metall. Mater. Trans. A
, 41
(12
), pp. 3216
–3227
.10.1007/s11661-010-0388-y51.
Cansizoglu
, O.
, Harrysson
, O.
, Cormier
, D.
, West
, H.
, and Mahale
, T.
, 2008
, “Properties of Ti–6Al–4V Non-Stochastic Lattice Structures Fabricated Via Electron Beam Melting
,” Mater. Sci. Eng. A
, 492
(1
), pp. 468
–474
.10.1016/j.msea.2008.04.00252.
Heinl
, P.
, Müller
, L.
, Körner
, C.
, Singer
, R. F.
, and Müller
, F. A.
, 2008
, “Cellular Ti–6Al–4V Structures With Interconnected Macro Porosity for Bone Implants Fabricated by Selective Electron Beam Melting
,” Acta Biomater.
, 4
(5
), pp. 1536
–1544
.10.1016/j.actbio.2008.03.01353.
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
.10.1016/j.jmapro.2011.01.00454.
Brooks
, W.
, Sutcliffe
, C.
, Cantwell
, W.
, Fox
, P.
, Todd
, J.
, and Mines
, R.
, 2005, “Rapid Design and Manufacture of Ultralight Cellular Materials
,” Proceedings of the Solid Freeform Fabrication Symposium
, Austin, TX
, pp. 231–241.55.
Winter
, R.
, Cotton
, M.
, Harris
, E.
, Chapman
, D.
, Eakins
, D.
, and McShane
, G.
, 2013
, “Plate-Impact Loading of Cellular Structures Formed by Selective Laser Melting
,” Structures Under Shock and Impact XII
, Vol. 126
, WIT Press
, Southampton, UK, pp. 145
–156
.10.2495/SU12013156.
Cerardi
, A.
, Caneri
, M.
, Meneghello
, R.
, Concheri
, G.
, and Ricotta
, M.
, 2013
, “Mechanical Characterization of Polyamide Cellular Structures Fabricated Using Selective Laser Sintering Technologies
,” Mater. Des.
, 46
, pp. 910
–915
.10.1016/j.matdes.2012.11.04257.
Hazlehurst
, K.
, Wang
, C. J.
, and Stanford
, M.
, 2013
, “Evaluation of the Stiffness Characteristics of Square Pore CoCrMo Cellular Structures Manufactured Using Laser Melting Technology for Potential Orthopaedic Applications
,” Mater. Des.
, 51
, pp. 949
–955
.10.1016/j.matdes.2013.05.009 58.
Yan
, C.
, Hao
, L.
, Hussein
, A.
, Young
, P.
, and Raymont
, D.
, 2014
, “Advanced Lightweight 316L Stainless Steel Cellular Lattice Structures Fabricated via Selective Laser Melting
,” Mater. Des.
, 55
, pp. 533
–541
.10.1016/j.matdes.2013.10.02759.
Tsopanos
, S.
, Mines
, R.
, McKown
, S.
, Shen
, Y.
, Cantwell
, W.
, Brooks
, W.
, and Sutcliffe
, C.
, 2010
, “The Influence of Processing Parameters on the Mechanical Properties of Selectively Laser Melted Stainless Steel Microlattice Structures
,” ASME J. Manuf. Sci. Eng.
, 132
(4
), p. 041011
.10.1115/1.400174360.
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
.10.3722/cadaps.2008.686-69661.
Rosen
, D. W.
, 2007
, “Computer-Aided Design for Additive Manufacturing of Cellular Structures
,” Comput. Aided Des. Appl.
, 4
(5
), pp. 585
–594
.10.1080/16864360.2007.1073849362.
Williams
, C. B.
, Cochran
, J. K.
, and Rosen
, D. W.
, 2011
, “Additive Manufacturing of Metallic Cellular Materials via Three-Dimensional Printing
,” Int. J. Adv. Manuf. Technol.
, 53
(1–4
), pp. 231
–239
.10.1007/s00170-010-2812-263.
Gaurav
, G.
, and Carolyn
, S.
, 2008
, “Topology Design of Compliant Cellular Structures With Contact-Enabled, Graded Stiffness
,” AIAA
Paper No. 2008-2262. 10.2514/6.2008-226264.
Rodrigues
, H.
, 2007
, “Topology Optimization of Structures: Applications in the Simulation and Design of Cellular Materials
,” Computational Methods in Engineering & Science
, Springer
, Berlin, Germany
, pp. 101
–112
.10.1007/978-3-540-48260-4_1065.
Sigmund
, O.
, 2000
, “Topology Optimization: A Tool for the Tailoring of Structures and Materials
,” Philos. Trans. R. Soc. Lond. Ser. A
, 358
(1765
), pp. 211
–227
.10.1098/rsta.2000.052866.
Brackett
, D.
, Ashcroft
, I.
, and Hague
, R.
, 2011, “Topology Optimization for Additive Manufacturing
,” Proceedings of the Solid Freeform Fabrication Symposium
, Austin, TX, pp. 348–362.68.
Seepersad
, C. C.
, Allen
, J. K.
, McDowell
, D. L.
, and Mistree
, F.
, 2008
, “Multifunctional Topology Design of Cellular Material Structures
,” ASME J. Mech. Des.
, 130
(3
), p. 031404
.10.1115/1.282987669.
Li
, S.
, and Wang
, G.
, 2008
, Introduction to Micromechanics and Nanomechanics
, World Scientific
, Singapore
.70.
Simone
, A.
, and Gibson
, L.
, 1998
, “Effects of Solid Distribution on the Stiffness and Strength of Metallic Foams
,” Acta Mater.
, 46
(6
), pp. 2139
–2150
.10.1016/S1359-6454(97)00421-771.
Hearmon
, R.
, 1961
, An Introduction to Applied Anisotropic Elasticity
, Oxford University
, London, UK
.72.
Nye
, J. F.
, 1985
, Physical Properties of Crystals: Their Representation by Tensors and Matrices
, Oxford University
, Oxford, UK
.73.
Bendsoe
, M. P.
, 2003
, Topology Optimization: Theory, Methods and Applications, Springer, Berlin, Germany.74.
Huang
, X.
, and Xie
, M.
, 2010
, Evolutionary Topology Optimization of Continuum Structures: Methods and Applications
, Wiley
, Chichester, UK
.75.
Eschenauer
, H. A.
, and Olhoff
, N.
, 2001
, “Topology Optimization of Continuum Structures: A Review
,” ASME Appl. Mech. Rev.
, 54
(4
), pp. 331
–390
.10.1115/1.138807576.
Bendsøe
, M. P.
, and Sigmund
, O.
, 1999
, “Material Interpolation Schemes in Topology Optimization
,” Arch. Appl. Mech.
, 69
(9–10
), pp. 635
–654
.10.1007/s00419005024877.
Hughes
, T. J. R.
, 2000
, The Finite Element Method: Linear Static and Dynamic Finite Element Analysis
, Dover
, New York
.78.
Andreassen
, E.
, Clausen
, A.
, Schevenels
, M.
, Lazarov
, B. S.
, and Sigmund
, O.
, 2011
, “Efficient Topology Optimization in MATLAB Using 88 Lines of Code
,” Struct. Multidiscip. Optim.
, 43
(1
), pp. 1
–16
.10.1007/s00158-010-0594-779.
Zhou
, M.
, Shyy
, Y.
, and Thomas
, H.
, 2001
, “Checkerboard and Minimum Member Size Control in Topology Optimization
,” Struct. Multidiscip. Optim.
, 21
(2
), pp. 152
–158
.10.1007/s001580050179Copyright © 2015 by ASME
You do not currently have access to this content.
