The lattice structure is a type of cellular material with trusslike frames which can be optimized for specific loading conditions. The fabrication of its intricate architecture is restricted by traditional manufacturing technologies. However, additive manufacturing (AM) enables the fabrication of complex structures by aggregation of materials in a layer-by-layer fashion, which has unlocked the potential of lattice structures. In the last decade, lattice structures have received considerable research attention focusing on the design, simulation, and fabrication for AM techniques. And different modeling approaches have been proposed to predict the mechanical performance of lattice structures. This review introduces the aspects of modeling of lattice structures and the correlation between them, summarizes the existing modeling approaches for simulation, and discusses the strength and weakness in different simulation methods. This review also summarizes the characteristics of AM in manufacturing cellular materials and discusses their influence on the modeling of lattice structures.
Issue Section:
Special Issue paper
Keywords:
Simulation-based design
References
1.
Merriam-Webster
, 2016
, “Lattice,” Merriam-Webster, Springfield, MA, accessed July 26, 2017, http://www.merriam-webster.com/dictionary/lattice2.
Schaedler
, T. A.
, and Carter
, W. B.
, 2016
, “Architected Cellular Materials
,” Annu. Rev. Mater. Res.
, 46
(1
), pp. 187
–210
.3.
Evans
, A. G.
, Hutchinson
, J.
, and Ashby
, M.
, 1998
, “Multifunctionality of Cellular Metal Systems
,” Prog. Mater. Sci.
, 43
(3
), pp. 171
–221
.4.
Gibson
, L. J.
, and Ashby
, M. F.
, 1997
, Cellular Solids: Structure and Properties
, 2nd ed., Cambridge University Press
, Cambridge, UK
.5.
Tang
, Y.
, 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
.6.
Wang
, H.
, Chen
, Y.
, and Rosen
, D. W.
, 2005
, “A Hybrid Geometric Modeling Method for Large Scale Conformal Cellular Structures
,” ASME
Paper No. DETC2005-85366.7.
Wang
, H.
, and Rosen
, D. W.
, 2002
, “Parametric Modeling Method for Truss Structures
,” ASME
Paper No. DETC2002/CIE-34495.8.
Wang
, H. V.
, 2005
, “A Unit Cell Approach for Lightweight Structure and Compliant Mechanism
,” Ph.D. dissertation
, Georgia Institute of Technology, Atlanta, GA.https://smartech.gatech.edu/handle/1853/75619.
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. 7–9, pp. 138–161.https://sffsymposium.engr.utexas.edu/Manuscripts/2012/2012-10-Nguyen.pdf10.
Queheillalt
, D. T.
, and Wadley
, H. N.
, 2005
, “Cellular Metal Lattices With Hollow Trusses
,” Acta Mater.
, 53
(2
), pp. 303
–313
.11.
Clough
, E. C.
, Ensberg
, J.
, Eckel
, Z. C.
, Ro
, C. J.
, and Schaedler
, T. A.
, 2016
, “Mechanical Performance of Hollow Tetrahedral Truss Cores
,” Int. J. Solids Struct.
, 91
, pp. 115
–126
.12.
Schaedler
, T. A.
, Ro
, C. J.
, Sorensen
, A. E.
, Eckel
, Z.
, Yang
, S. S.
, Carter
, W. B.
, and Jacobsen
, A. J.
, 2014
, “Designing Metallic Microlattices for Energy Absorber Applications
,” Adv. Eng. Mater.
, 16
(3
), pp. 276
–283
.13.
Lu
, T. J.
, Valdevit
, L.
, and Evans
, A. G.
, 2005
, “Active Cooling by Metallic Sandwich Structures With Periodic Cores
,” Prog. Mater. Sci.
, 50
(7
), pp. 789
–815
.14.
Wadley
, H. N.
, and Queheillalt
, D. T.
, 2007, “Thermal Applications of Cellular Lattice Structures
,” Mater. Sci. Forum
, 539–543
, pp. 242
–247
.http://www.virginia.edu/ms/research/wadley/Documents/Publications/Thermal_Applications_of_Cellular_Lattice_Structures.pdf15.
Valdevit
, L.
, Pantano
, A.
, Stone
, H. A.
, and Evans
, A. G.
, 2006
, “Optimal Active Cooling Performance of Metallic Sandwich Panels With Prismatic Cores
,” Int. J. Heat Mass Transfer
, 49
(21
), pp. 3819
–3830
.16.
Mota
, C.
, Puppi
, D.
, Chiellini
, F.
, and Chiellini
, E.
, 2015
, “Additive Manufacturing Techniques for the Production of Tissue Engineering Constructs
,” J. Tissue Eng. Regener. Med.
, 9
(3
), pp. 174
–190
.17.
ASTM
, 2012
, “Standard Terminology for Additive Manufacturing Technologies
,” ASTM International, West Conshohocken, PA, Standard No. ASTM-F2792-12a
.https://www.astm.org/Standards/F2792.htm18.
Melchels
, F. P. W.
, Feijen
, J.
, and Grijpma
, D. W.
, 2010
, “A Review on Stereolithography and Its Applications in Biomedical Engineering
,” Biomaterials
, 31
(24
), pp. 6121
–6130
.19.
Rezaei
, R.
, Ravari
, M. K.
, Badrossamay
, M.
, and Kadkhodaei
, M.
, 2016
, “Mechanical Characterization and Finite Element Modeling of Polylactic Acid BCC-Z Cellular Lattice Structures Fabricated by Fused Deposition Modeling
,” Proc. Inst. Mech. Eng., Part C
, 231
(11
), pp. 1995
–2004
.20.
Naghieh
, S.
, Karamooz Ravari
, M. R.
, Badrossamay
, M.
, Foroozmehr
, E.
, and Kadkhodaei
, M.
, 2016
, “Numerical Investigation of the Mechanical Properties of the Additive Manufactured Bone Scaffolds Fabricated by FDM: The Effect of Layer Penetration and Post-Heating
,” J. Mech. Behav. Biomed. Mater.
, 59
, pp. 241
–250
.21.
Tang
, Y.
, Zhou
, Y.
, Hoff
, T.
, Garon
, M.
, and Zhao
, Y. F.
, 2016
, “Elastic Modulus of 316 Stainless Steel Lattice Structure Fabricated Via Binder Jetting Process
,” Mater. Sci. Technol.
, 32
(7
), pp. 648
–656
.22.
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
.23.
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
.24.
Murr
, L. E.
, Gaytan
, S. M.
, Medina
, F.
, Lopez
, M. I.
, Martinez
, E.
, and Wicker
, R. B.
, 2009
, “Additive Layered Manufacturing of Reticulated Ti-6Al-4V Biomedical Mesh Structures by Electron Beam Melting
,” 25th Southern Biomedical Engineering Conference
, Miami, FL, May 15–17, pp. 23
–28
.25.
Parthasarathy
, J.
, Starly
, B.
, Raman
, S.
, and Christensen
, A.
, 2010
, “Mechanical Evaluation of Porous Titanium (Ti6Al4V) Structures With Electron Beam Melting (EBM)
,” J. Mech. Behav. Biomed. Mater.
, 3
(3
), pp. 249
–259
.26.
Mun
, J.
, Yun
, B. G.
, Ju
, J.
, and Chang
, B. M.
, 2015
, “Indirect Additive Manufacturing Based Casting of a Periodic 3D Cellular Metal—Flow Simulation of Molten Aluminum Alloy
,” J. Manuf. Processes
, 17
, pp. 28
–40
.27.
Schaedler
, T. A.
, Jacobsen
, A. J.
, Torrents
, A.
, Sorensen
, A. E.
, Lian
, J.
, Greer
, J. R.
, Valdevit
, L.
, and Carter
, W. B.
, 2011
, “Ultralight Metallic Microlattices
,” Science
, 334
(6058
), pp. 962
–965
.28.
Cheung
, K. C.
, and Gershenfeld
, N.
, 2013
, “Reversibly Assembled Cellular Composite Materials
,” Science
, 341
(6151
), pp. 1219
–1221
.29.
Rosen
, D. W.
, 2007
, “Computer-Aided Design for Additive Manufacturing of Cellular Structures
,” Comput. Aided Des. Appl.
, 4
(5
), pp. 585
–594
.30.
Yang
, L.
, Harrysson
, O.
, Cormier
, D.
, West
, H.
, Gong
, H.
, and Stucker
, B.
, 2015
, “Additive Manufacturing of Metal Cellular Structures: Design and Fabrication
,” JOM
, 67
(3
), pp. 608
–615
.31.
Seepersad
, C. C.
, Shahan
, D.
, and Madhavan
, K.
, 2007
, “Multiscale Design for Solid Freeform Fabrication
,” Solid Freeform Fabrication Symposium
(SFF
), Austin, TX, Aug. 6–8, pp. 416–427.https://sffsymposium.engr.utexas.edu/Manuscripts/2007/2007-35-Seepersad.pdf32.
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.
, PP
(99
), pp. 1
–17
.33.
Gibson
, L.
, Ashby
, M.
, Schajer
, G.
, and Robertson
, C.
, 1982, “The Mechanics of Two-Dimensional Cellular Materials
,” Proc. R. Soc. London, Ser. A
, 382
(1782), pp. 25
–42
.34.
Gibson
, L. J.
, and Ashby
, M. F.
, 1982
, “The Mechanics of Three-Dimensional Cellular Materials
,” Proc. R. Soc. London, Ser. A
, 382
(1782), pp. 43
–59
.35.
Ashby
, M. F.
, and Medalist
, R. F. M.
, 1983
, “The Mechanical Properties of Cellular Solids
,” Metall. Trans. A
, 14
(9
), pp. 1755
–1769
.36.
Gibson
, L. J.
, 2005
, “Biomechanics of Cellular Solids
,” J. Biomech.
, 38
(3
), pp. 377
–399
.37.
Labeas
, G. N.
, and Sunaric
, M. M.
, 2010
, “Investigation on the Static Response and Failure Process of Metallic Open Lattice Cellular Structures
,” Strain
, 46
(2
), pp. 195
–204
.38.
Yang
, L.
, Cormier
, D.
, West
, H.
, Harrysson
, O.
, and Knowlson
, K.
, 2012
, “Non-Stochastic Ti-6Al-4V Foam Structures With Negative Poisson's Ratio
,” Mater. Sci. Eng. A
, 558
, pp. 579
–585
.39.
Alsalla
, H.
, Hao
, L.
, and Smith
, C.
, 2016
, “Fracture Toughness and Tensile Strength of 316L Stainless Steel Cellular Lattice Structures Manufactured Using the Selective Laser Melting Technique
,” Mater. Sci. Eng.: A
, 669
, pp. 1
–6
.40.
Winter
, R. E.
, Cotton
, M.
, Harris
, E. J.
, Maw
, J. R.
, Chapman
, D. J.
, Eakins
, D. E.
, and McShane
, G.
, 2014
, “Plate-Impact Loading of Cellular Structures Formed by Selective Laser Melting
,” Modell. Simul. Mater. Sci. Eng.
, 22
(2
), p. 025021.41.
Salehian
, A.
, and Inman
, D. J.
, 2008
, “Dynamic Analysis of a Lattice Structure by Homogenization: Experimental Validation
,” J. Sound Vib.
, 316
(1–5
), pp. 180
–197
.42.
Jamshidinia
, M.
, Wang
, L.
, Tong
, W.
, Ajlouni
, R.
, and Kovacevic
, R.
, 2015
, “Fatigue Properties of a Dental Implant Produced by Electron Beam Melting (EBM)
,” J. Mater. Process. Technol.
, 226
, pp. 255
–263
.43.
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
.44.
Williams
, J. M.
, Adewunmi
, A.
, Schek
, R. M.
, Flanagan
, C. L.
, Krebsbach
, P. H.
, Feinberg
, S. E.
, Hollister
, S. J.
, and Das
, S.
, 2005
, “Bone Tissue Engineering Using Polycaprolactone Scaffolds Fabricated Via Selective Laser Sintering
,” Biomaterials
, 26
(23
), pp. 4817
–4827
.45.
Johnston
, S. R.
, Reed
, M.
, Wang
, H. V.
, and Rosen
, D. W.
, 2006
, “Analysis of Mesostructure Unit Cells Comprised of Octet-Truss Structures
,” 17th Solid Freeform Fabrication Symposium
(SFF
), Austin, TX, Aug. 14–16, pp. 421
–432
.https://sffsymposium.engr.utexas.edu/Manuscripts/2006/2006-38-Johnston.pdf46.
Ravari
, M. R. K.
, Kadkhodaei
, M.
, Badrossamay
, M.
, and Rezaei
, R.
, 2014
, “Numerical Investigation on Mechanical Properties of Cellular Lattice Structures Fabricated by Fused Deposition Modeling
,” Int. J. Mech. Sci.
, 88
, pp. 154
–161
.47.
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
(1–2
), pp. 468
–474
.48.
de Formanoir
, C. C. C.
, 2016
, “Improving the Mechanical Efficiency of Electron Beam Melted Titanium Lattice Structures by Chemical Etching
,” Addit. Manuf.
, 11
, pp. 71
–76
.49.
Campoli
, G.
, Borleffs
, M. S.
, Amin Yavari
, S.
, Wauthle
, R.
, Weinans
, H.
, and Zadpoor
, A. A.
, 2013
, “Mechanical Properties of Open-Cell Metallic Biomaterials Manufactured Using Additive Manufacturing
,” Mater. Des.
, 49
, pp. 957
–965
.50.
Smith
, M.
, Guan
, Z.
, and Cantwell
, W. J.
, 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
.51.
Gümrük
, R.
, and Mines
, R. A. W.
, 2013
, “Compressive Behaviour of Stainless Steel Micro-Lattice Structures
,” Int. J. Mech. Sci.
, 68
, pp. 125
–139
.52.
Malek
, N. M. S. A.
, Mohamed
, S. R.
, Ghani
, S. A. C.
, and Harun
, W. S. W.
, 2015
, “Critical Evaluation on Structural Stiffness of Porous Cellular Structure of Cobalt Chromium Alloy
,” IOP Conf. Ser.: Mater. Sci. Eng.
, 100
, p. 012019
.53.
Yan
, C.
, Hao
, L.
, Hussein
, A.
, Bubb
, S. L.
, Young
, P.
, and Raymont
, D.
, 2014
, “Evaluation of Light-Weight AlSi10Mg Periodic Cellular Lattice Structures Fabricated Via Direct Metal Laser Sintering
,” J. Mater. Process. Technol.
, 214
(4
), pp. 856
–864
.54.
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
.55.
Arabnejad
, S.
, Burnett Johnston
, R.
, Pura
, J. A.
, Singh
, B.
, Tanzer
, M.
, and Pasini
, D.
, 2016
, “High-Strength Porous Biomaterials for Bone Replacement: A Strategy to Assess the Interplay Between Cell Morphology, Mechanical Properties, Bone Ingrowth and Manufacturing Constraints
,” Acta Biomater.
, 30
, pp. 345
–356
.56.
Yan
, C.
, Hao
, L.
, Hussein
, A.
, Young
, P.
, Huang
, J.
, and Zhu
, W.
, 2015
, “Microstructure and Mechanical Properties of Aluminium Alloy Cellular Lattice Structures Manufactured by Direct Metal Laser Sintering
,” Mater. Sci. Eng. A
, 628
, pp. 238
–246
.57.
Suard
, M.
, Lhuissier
, P.
, Dendievel
, R.
, Blandin
, J. J.
, Vignat
, F.
, and Villeneuve
, F.
, 2014
, “Towards Stiffness Prediction of Cellular Structures Made by Electron Beam Melting (EBM)
,” Powder Metall.
, 57
(3
), pp. 190
–195
.58.
Qiu
, C.
, Yue
, S.
, Adkins
, N. J. E.
, 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
.59.
Hernández-Nava
, E.
, Smith
, C. J.
, Derguti
, F.
, Tammas-Williams
, S.
, Leonard
, F.
, Withers
, P. J.
, Todd
, I.
, and Goodall
, R.
, 2016
, “The Effect of Defects on the Mechanical Response of Ti-6Al-4V Cubic Lattice Structures Fabricated by Electron Beam Melting
,” Acta Mater.
, 108
, pp. 279
–292
.60.
Hassani
, B.
, and Hinton
, E.
, 1998
, “A Review of Homogenization and Topology Optimization: I—Homogenization Theory for Media With Periodic Structure
,” Comput. Struct.
, 69
(6
), pp. 707
–717
.61.
Bensoussan
, A.
, Lions
, J.-L.
, and Papanicolaou
, G.
, 1978
, Asymptotic Analysis for Periodic Structures
, American Mathematical Society
, Providence, RI
.62.
Cioranescu
, D.
, and Paulin
, J. S. J.
, 1979
, “Homogenization in Open Sets With Holes
,” J. Math. Anal. Appl.
, 71
(2
), pp. 590
–607
.63.
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
.64.
Ptochos
, E.
, and Labeas
, G.
, 2012
, “Elastic Modulus and Poisson's Ratio Determination of Micro-Lattice Cellular Structures by Analytical, Numerical and Homogenisation Methods
,” J. Sandwich Struct. Mater.
, 14
(5
), pp. 597
–626
.65.
Bendsøe
, M. P.
, and Kikuchi
, N.
, 1988
, “Generating Optimal Topologies in Structural Design Using a Homogenization Method
,” Comput. Methods Appl. Mech. Eng.
, 71
(2
), pp. 197
–224
.66.
Rabczuk
, T.
, Kim
, J.
, Samaniego
, E.
, and Belytschko
, T.
, 2004
, “Homogenization of Sandwich Structures
,” Int. J. Numer. Methods Eng.
, 61
(7
), pp. 1009
–1027
.67.
Florence
, C.
, and Sab
, K.
, 2005
, “Overall Ultimate Yield Surface of Periodic Tetrakaidecahedral Lattice With Non-Symmetric Material Distribution
,” J. Mater. Sci.
, 40
(22
), pp. 5883
–5892
.68.
Florence
, C.
, and Sab
, K.
, 2006
, “A Rigorous Homogenization Method for the Determination of the Overall Ultimate Strength of Periodic Discrete Media and an Application to General Hexagonal Lattices of Beams
,” Eur. J. Mech., A
, 25
(1
), pp. 72
–97
.69.
Arabnejad
, S.
, and Pasini
, D.
, 2013
, “Mechanical Properties of Lattice Materials Via Asymptotic Homogenization and Comparison With Alternative Homogenization Methods
,” Int. J. Mech. Sci.
, 77
, pp. 249
–262
.70.
Tollenaere
, H.
, and Caillerie
, D.
, 1998
, “Continuous Modeling of Lattice Structures by Homogenization
,” Adv. Eng. Software
, 29
(7
), pp. 699
–705
.71.
Caillerie
, D.
, Mourad
, A.
, and Raoult
, A.
, 2006
, “Discrete Homogenization in Graphene Sheet Modeling
,” J. Elasticity
, 84
(1
), pp. 33
–68
.72.
Dos Reis
, F.
, and Ganghoffer
, J.
, 2010
, “Discrete Homogenization of Architectured Materials: Implementation of the Method in a Simulation Tool for the Systematic Prediction of Their Effective Elastic Properties
,” Tech. Mech.
, 30
(1–3
), pp. 85
–109
.http://www.ovgu.de/ifme/zeitschrift_tm/2010_Heft1_3/07_DosReis.pdf73.
Dos Reis
, F.
, and Ganghoffer
, J. F.
, 2012
, “Equivalent Mechanical Properties of Auxetic Lattices From Discrete Homogenization
,” Comput. Mater. Sci.
, 51
(1
), pp. 314
–321
.74.
Dell'Isola
, F.
, Giorgio
, I.
, Pawlikowski
, M.
, and Rizzi
, N. L.
, 2016
, “Large Deformations of Planar Extensible Beams and Pantographic Lattices: Heuristic Homogenization, Experimental and Numerical Examples of Equilibrium
,” Proc. R. Soc. A
, 472
(2185
), p. 20150790.75.
Park
, S.
, and Rosen
, D. W.
, 2016
, “Homogenization of Mechanical Properties for Additively Manufactured Periodic Lattice Structures Considering Joint Stiffening Effects
,” ASME
Paper No. DETC2016-59730.76.
Assidi
, M.
, Dos Reis
, F.
, and Ganghoffer
, J. F.
, 2011
, “Equivalent Mechanical Properties of Biological Membranes From Lattice Homogenization
,” J. Mech. Behav. Biomed. Mater.
, 4
(8
), pp. 1833
–1845
.77.
Goda
, I.
, Assidi
, M.
, Belouettar
, S.
, and Ganghoffer
, J. F.
, 2012
, “A Micropolar Anisotropic Constitutive Model of Cancellous Bone From Discrete Homogenization
,” J. Mech. Behav. Biomed. Mater.
, 16
(1
), pp. 87
–108
.78.
Goda
, I.
, Assidi
, M.
, and Ganghoffer
, J. F.
, 2014
, “A 3D Elastic Micropolar Model of Vertebral Trabecular Bone From Lattice Homogenization of the Bone Microstructure
,” Biomech. Model. Mechanobiol.
, 13
(1
), pp. 53
–83
.79.
Goda
, I.
, Dos Reis
, F.
, and Ganghoffer
, J. F.
, 2016
, “Limit Analysis of Lattices Based on the Asymptotic Homogenization Method and Prediction of Size Effects in Bone Plastic Collapse
,” Advanced Structured Materials
, Springer, Cham, Switzerland, pp. 179
–211
.80.
Hutchinson
, R.
, and Fleck
, N.
, 2006
, “The Structural Performance of the Periodic Truss
,” J. Mech. Phys. Solids
, 54
(4
), pp. 756
–782
.81.
Vigliotti
, A.
, and Pasini
, D.
, 2012
, “Linear Multiscale Analysis and Finite Element Validation of Stretching and Bending Dominated Lattice Materials
,” Mech. Mater.
, 46
, pp. 57
–68
.82.
Vigliotti
, A.
, and Pasini
, D.
, 2012
, “Stiffness and Strength of Tridimensional Periodic Lattices
,” Comput. Methods Appl. Mech. Eng.
, 229–232
, pp. 27
–43
.83.
Vigliotti
, A.
, Deshpande
, V. S.
, and Pasini
, D.
, 2014
, “Non Linear Constitutive Models for Lattice Materials
,” J. Mech. Phys. Solids
, 64
, pp. 44
–60
.84.
Park
, S. I.
, Rosen
, D. W.
, Choi
, S. K.
, and Duty
, C. E.
, 2014
, “Effective Mechanical Properties of Lattice Material Fabricated by Material Extrusion Additive Manufacturing
,” Addit. Manuf.
, 1–4
, pp. 12
–23
.85.
Andreassen
, E.
, and Andreasen
, C. S.
, 2014
, “How to Determine Composite Material Properties Using Numerical Homogenization
,” Comput. Mater. Sci.
, 83
, pp. 488
–495
.86.
Dirrenberger
, J.
, Forest
, S.
, Jeulin
, D.
, and Colin
, C.
, 2011
, “Homogenization of Periodic Auxetic Materials
,” Procedia Eng.
, 10
, pp. 1847
–1852
.87.
van Dijk
, N. P.
, 2016
, “Formulation and Implementation of Stress-Driven and/or Strain-Driven Computational Homogenization for Finite Strain
,” Int. J. Numer. Methods Eng.
, 107
(12
), pp. 1009
–1028
.88.
Schwerdtfeger
, J.
, Schury
, F.
, Stingl
, M.
, Wein
, F.
, Singer
, R. F.
, and Körner
, C.
, 2012
, “Mechanical Characterisation of a Periodic Auxetic Structure Produced by SEBM
,” Phys. Status Solidi B
, 249
(7
), pp. 1347
–1352
.89.
Zhu
, H. X.
, Hobdell
, J. R.
, and Windle
, A. H.
, 2000
, “Effects of Cell Irregularity on the Elastic Properties of Open-Cell Foams
,” Acta Mater.
, 48
(20
), pp. 4893
–4900
.90.
Zhu
, H. X.
, Hobdell
, J. R.
, and Windle
, A. H.
, 2001
, “Effects of Cell Irregularity on the Elastic Properties of 2D Voronoi Honeycombs
,” J. Mech. Phys. Solids
, 49
(4
), pp. 857
–870
.91.
Zhou
, J.
, Shrotriya
, P.
, and Soboyejo
, W. O.
, 2004
, “On the Deformation of Aluminum Lattice Block Structures: From Struts to Structures
,” Mech. Mater.
, 36
(8
), pp. 723
–737
.92.
Gan
, Y. X.
, Chen
, C.
, and Shen
, Y. P.
, 2005
, “Three-Dimensional Modeling of the Mechanical Property of Linearly Elastic Open Cell Foams
,” Int. J. Solids Struct.
, 42
(26
), pp. 6628
–6642
.93.
Cuan-Urquizo
, E.
, Yang
, S.
, and Bhaskar
, A.
, 2015
, “Mechanical Characterisation of Additively Manufactured Material Having Lattice Microstructure
,” IOP Conf. Ser.: Mater. Sci. Eng.
, 74
, p. 012004
.94.
Alkhader
, M.
, and Vural
, M.
, 2007
, “Effect of Microstructure in Cellular Solids: Bending vs. Stretch Dominated Topologies
,” The Third International Conference on Recent Advances in Space Technologies
(RAST
), Istanbul, Turkey, June 14–16, pp. 136
–143
.95.
Alkhader
, M.
, and Vural
, M.
, 2008
, “Mechanical Response of Cellular Solids: Role of Cellular Topology and Microstructural Irregularity
,” Int. J. Eng. Sci.
, 46
(10
), pp. 1035
–1051
.96.
Ahmadi
, S. M.
, Campoli
, G.
, Amin Yavari
, S.
, Sajadi
, B.
, Wauthle
, R.
, Schrooten
, J.
, Weinans
, H.
, and Zadpoor
, A. A.
, 2014
, “Mechanical Behavior of Regular Open-Cell Porous Biomaterials Made of Diamond Lattice Unit Cells
,” J. Mech. Behav. Biomed. Mater.
, 34
, pp. 106
–115
.97.
Aremu
, A. O.
, Maskery
, I. A.
, Tuck
, C. J.
, Ashcroft
, I. A.
, Wildman
, R. D.
, and Hague
, R. J. M.
, 2016
, Effects of Net and Solid Skins on Self-Supporting Lattice Structures
, Springer
, Cham, Switzerland
, pp. 83
–89
.98.
Chantarapanich
, N.
, Puttawibul
, P.
, Sucharitpwatskul
, S.
, Jeamwatthanachai
, P.
, Inglam
, S.
, and Sitthiseripratip
, K.
, 2012
, “Scaffold Library for Tissue Engineering: A Geometric Evaluation
,” Comput. Math. Methods Med.
, 2012
, p. 407805
.99.
Zargarian
, A.
, Esfahanian
, M.
, Kadkhodapour
, J.
, and Ziaei-Rad
, S.
, 2014
, “Effect of Solid Distribution on Elastic Properties of Open-Cell Cellular Solids Using Numerical and Experimental Methods
,” J. Mech. Behav. Biomed. Mater.
, 37
, pp. 264
–273
.100.
Ullah
, I.
, Elambasseril
, J.
, Brandt
, M.
, and Feih
, S.
, 2014
, “Performance of Bio-Inspired Kagome Truss Core Structures Under Compression and Shear Loading
,” Compos. Struct.
, 118
(1
), pp. 294
–302
.101.
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
.102.
Huo
, J.
, Dérand
, P.
, Rännar
, L. E.
, Hirsch
, J. M.
, and Gamstedt
, E. K.
, 2015
, “Failure Location Prediction by Finite Element Analysis for an Additive Manufactured Mandible Implant
,” Med. Eng. Phys.
, 37
(9
), pp. 862
–869
.103.
Wettergreen
, M. A.
, Bucklen
, B. S.
, Starly
, B.
, Yuksel
, E.
, Sun
, W.
, and Liebschner
, M. A. K.
, 2005
, “Creation of a Unit Block Library of Architectures for Use in Assembled Scaffold Engineering
,” Comput. Aided Des.
, 37
(11
), pp. 1141
–1149
.104.
Cahill
, S.
, Lohfeld
, S.
, and McHugh
, P.
, 2009
, “Finite Element Predictions Compared to Experimental Results for the Effective Modulus of Bone Tissue Engineering Scaffolds Fabricated by Selective Laser Sintering
,” J. Mater. Sci.: Mater. Med.
, 20
(6
), pp. 1255
–1262
.105.
Hedayati
, R.
, Sadighi
, M.
, Mohammadi-Aghdam
, M.
, and Zadpoor
, A. A.
, 2016
, “Mechanical Properties of Regular Porous Biomaterials Made From Truncated Cube Repeating Unit Cells: Analytical Solutions and Computational Models
,” Mater. Sci. Eng. C
, 60
, pp. 163
–183
.106.
Hedayati
, R.
, Sadighi
, M.
, Mohammadi-Aghdam
, M.
, and Zadpoor
, A. A.
, 2016
, “Mechanics of Additively Manufactured Porous Biomaterials Based on the Rhombicuboctahedron Unit Cell
,” J. Mech. Behav. Biomed. Mater.
, 53
, pp. 272
–294
.107.
Coelho
, P. G.
, Hollister
, S. J.
, Flanagan
, C. L.
, and Fernandes
, P. R.
, 2015
, “Bioresorbable Scaffolds for Bone Tissue Engineering: Optimal Design, Fabrication, Mechanical Testing and Scale-Size Effects Analysis
,” Med. Eng. Phys.
, 37
(3
), pp. 287
–296
.108.
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
.109.
Zargarian
, A.
, Esfahanian
, M.
, Kadkhodapour
, J.
, and Ziaei-Rad
, S.
, 2016
, “Numerical Simulation of the Fatigue Behavior of Additive Manufactured Titanium Porous Lattice Structures
,” Mater. Sci. Eng. C
, 60
, pp. 339
–347
.110.
Sercombe
, T. B.
, Xu
, X.
, Challis
, V. J.
, Green
, R.
, Yue
, S.
, Zhang
, Z.
, and Lee
, P. D.
, 2015
, “Failure Modes in High Strength and Stiffness to Weight Scaffolds Produced by Selective Laser Melting
,” Mater. Des.
, 67
, pp. 501
–508
.111.
Park
, S. I.
, and Rosen
, D. W.
, 2016
, “Quantifying Effects of Material Extrusion Additive Manufacturing Process on Mechanical Properties of Lattice Structures Using As-Fabricated Voxel Modeling
,” Addit. Manuf.
, 12
(Pt. B), pp. 265
–273
.112.
Sachdeva
, A.
, Singh
, S.
, and Sharma
, V. S.
, 2013
, “Investigating Surface Roughness of Parts Produced by SLS Process
,” Int. J. Adv. Manuf. Technol.
, 64
(9–12
), pp. 1505
–1516
.113.
Pupo
, Y.
, Monroy
, K. P.
, and Ciurana
, J.
, 2015
, “Influence of Process Parameters on Surface Quality of CoCrMo Produced by Selective Laser Melting
,” Int. J. Adv. Manuf. Technol.
, 80
(5–8
), pp. 985
–995
.114.
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
.115.
Shanjani
, Y.
, Hu
, Y.
, Pilliar
, R. M.
, and Toyserkani
, E.
, 2011
, “Mechanical Characteristics of Solid-Freeform-Fabricated Porous Calcium Polyphosphate Structures With Oriented Stacked Layers
,” Acta Biomater.
, 7
(4
), pp. 1788
–1796
.116.
Ladani
, L.
, Razmi
, J.
, and Choudhury
, S. F.
, 2014
, “Mechanical Anisotropy and Strain Rate Dependency Behavior of Ti6Al4V Produced Using E-Beam Additive Fabrication
,” ASME J. Eng. Mater. Technol.
, 136
(3
), p. 031006
.117.
Sridharan
, N.
, Gussev
, M.
, Seibert
, R.
, Parish
, C.
, Norfolk
, M.
, Terrani
, K.
, and Babu
, S. S.
, 2016
, “Rationalization of Anisotropic Mechanical Properties of Al-6061 Fabricated Using Ultrasonic Additive Manufacturing
,” Acta Mater.
, 117
, pp. 228
–237
.118.
Ahn
, S. H.
, Montero
, M.
, Odell
, D.
, Roundy
, S.
, and Wright
, P. K.
, 2002
, “Anisotropic Material Properties of Fused Deposition Modeling ABS
,” Rapid Prototyping J.
, 8
(4
), pp. 248
–257
.119.
Hambali
, R. H.
, Smith
, P.
, and Rennie
, A. E. W.
, 2012
, “Determination of the Effect of Part Orientation to the Strength Value on Additive Manufacturing FDM for End-Use Parts by Physical Testing and Validation Via Three-Dimensional Finite Element Analysis
,” Int. J. Mater. Eng. Innovation
, 3
(3–4
), pp. 269
–281
.120.
Ogden
, S.
, and Kessler
, S.
, 2014, “Anisotropic Finite Element Modeling of the Fused Deposition Modeling Process
,” TMS Annual Meeting
, San Diego, CA, Feb. 16–20, pp. 235
–246
.http://www.programmaster.org/PM/PM.nsf/ApprovedAbstracts/F56F01304DC5E2D685257BA40083769C?OpenDocument121.
Carroll
, B. E.
, Palmer
, T. A.
, and Beese
, A. M.
, 2015
, “Anisotropic Tensile Behavior of Ti-6Al-4V Components Fabricated With Directed Energy Deposition Additive Manufacturing
,” Acta Mater.
, 87
, pp. 309
–320
.122.
Åkerfeldt
, P.
, Antti
, M. L.
, and Pederson
, R.
, 2016
, “Influence of Microstructure on Mechanical Properties of Laser Metal Wire-Deposited Ti-6Al-4V
,” Mater. Sci. Eng. A
, 674
, pp. 428
–437
.123.
Zhang
, Q.
, Chen
, J.
, Zhao
, Z.
, Tan
, H.
, Lin
, X.
, and Huang
, W.
, 2016
, “Microstructure and Anisotropic Tensile Behavior of Laser Additive Manufactured TC21 Titanium Alloy
,” Mater. Sci. Eng. A
, 673
, pp. 204
–212
.124.
Wauthle
, R.
, Vrancken
, B.
, Beynaerts
, B.
, Jorissen
, K.
, Schrooten
, J.
, Kruth
, J. P.
, and Van Humbeeck
, J.
, 2015
, “Effects of Build Orientation and Heat Treatment on the Microstructure and Mechanical Properties of Selective Laser Melted Ti6Al4V Lattice Structures
,” Addit. Manuf.
, 5
, pp. 77
–84
.125.
Reinhart
, G.
, Teufelhart
, S.
, and Riss
, F.
, 2012
, “Investigation of the Geometry-Dependent Anisotropic Material Behavior of Filigree Struts in ALM-Produced Lattice Structures
,” Phys. Procedia
, 39
, pp. 471
–479
.126.
List
, F. A.
, Dehoff
, R. R.
, Lowe
, L. E.
, and Sames
, W. J.
, 2014
, “Properties of Inconel 625 Mesh Structures Grown by Electron Beam Additive Manufacturing
,” Mater. Sci. Eng. A
, 615
, pp. 191
–197
.127.
Galeta
, T.
, Raos
, P.
, and Somolanji
, M.
, 2012
, “Impact of Structure and Building Orientation on Strength of 3D Printed Models
,” KGK
, 65
(10
), pp. 36
–42
.https://www.tib.eu/de/suchen/id/BLSE%3ARN320332459/Impact-of-Structure-and-Building-Orientation-on/128.
Castilho
, M.
, Dias
, M.
, Gbureck
, U.
, Groll
, J.
, Fernandes
, P.
, Pires
, I.
, Gouveia
, B.
, Rodrigues
, J.
, and Vorndran
, E.
, 2013
, “Fabrication of Computationally Designed Scaffolds by Low Temperature 3D Printing
,” Biofabrication
, 5
(3
), p. 035012
.129.
Zhang
, P.
, and To
, A. C.
, 2016
, “Transversely Isotropic Hyperelastic-Viscoplastic Model for Glassy Polymers With Application to Additive Manufactured Photopolymers
,” Int. J. Plast.
, 80
, pp. 56
–74
.Copyright © 2017 by ASME
You do not currently have access to this content.
