From Topology Optimization Design to Additive Manufacturing: Today’s Success and Tomorrow’s Roadmap

Archives of Computational Methods in Engineering - Tập 27 Số 3 - Trang 805-830 - 2020
Liang Meng1, Weihong Zhang1, Dongliang Quan2, Guanghui Shi2, Lei Tang1, Yuliang Hou3, Piotr Breitkopf4, Jihong Zhu5, Tong Gao5
1State IJR Center of Aerospace Design and Additive Manufacturing, Northwestern Polytechnical University, Xi’an 710072, China
2Beijing Aerospace Technology Institute, Beijing 100074, China
3School of Mechanical Engineering, Zhengzhou University, Zhengzhou 450001, China
4Laboratoire Roberval, UMR 7337 UTC-CNRS, Sorbonne Universités, Université de Technologie de Compiègne, 60200, Compiègne, France
5Institute of Intelligence Material and Structure, Unmanned System Technologies, Northwestern Polytechnical University, Xi’an 710072, China

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Duysinx P, Bendsøe MP (1998) Topology optimization of continuum structures with local stress constraints. Int J Numer Methods Eng 43(8):1453

Allaire G, Jouve F, Maillot H (2004) Topology optimization for minimum stress design with the homogenization method. Struct Multidiscip Optim 28(2–3):87

Meng L, Zhang WH, Zhu JH, Xu Z, Cai SH (2016) Shape optimization of axisymmetric solids with the finite cell method using a fixed grid. Acta Mech Sin 32:510

Bendsoe MP, Sigmund O (2013) Topology optimization: theory, methods, and applications. Springer, Berlin

Zhang W, Sun S (2006) Scale-related topology optimization of cellular materials and structures. Int J Numer Methods Eng 68(9):993

Huang X, Xie M (2010) Evolutionary topology optimization of continuum structures: methods and applications. Wiley, New York

Xu Y, Zhu J, Wu Z, Cao Y, Zhao Y, Zhang W (2018) A review on the design of laminated composite structures: constant and variable stiffness design and topology optimization. Adv Compos Hybrid Mater 1–18

Rozvany GI (2009) A critical review of established methods of structural topology optimization. Struct Multidiscip Optim 37(3):217

Zhu JH, Zhang WH, Xia L (2016) Topology optimization in aircraft and aerospace structures design. Arch Comput Methods Eng 23(4):595

Liu J, Gaynor AT, Chen S, Kang Z, Suresh K, Takezawa A, Li L, Kato J, Tang J, Wang CC et al (2018) Current and future trends in topology optimization for additive manufacturing. Struct Multidiscip Optim 1–27

Gao T, Zhang W (2010) Topology optimization involving thermo-elastic stress loads. Struct Multidiscip Optim 42(5):725

Zhu J, Zhang W, Beckers P (2009) Integrated layout design of multi-component system. Int J Numer Methods Eng 78(6):631

Zhu J, Zhang W (2010) Integrated layout design of supports and structures. Comput Methods Appl Mech Eng 199(9–12):557

Zhou Y, Zhang W, Zhu J, Xu Z (2016) Feature-driven topology optimization method with signed distance function. Comput Methods Appl Mech Eng 310:1

Bruggi M, Duysinx P (2012) Topology optimization for minimum weight with compliance and stress constraints. Struct Multidiscip Optim 46(3):369

Zhang W, Zhou Y, Zhu J (2017) A comprehensive study of feature definitions with solids and voids for topology optimization. Comput Methods Appl Mech Eng 325:289

París J, Navarrina F, Colominas I, Casteleiro M (2009) Topology optimization of continuum structures with local and global stress constraints. Struct Multidiscip Optim 39(4):419

Cai S, Zhang W (2015) Stress constrained topology optimization with free-form design domains. Comput Methods Appl Mech Eng 289:267

Liu H, Zhang W, Gao T (2015) A comparative study of dynamic analysis methods for structural topology optimization under harmonic force excitations. Struct Multidiscip Optim 51(6):1321

Zhang W, Zhong W, Guo X (2014) An explicit length scale control approach in simp-based topology optimization. Comput Methods Appl Mech Eng 282:71

Allaire G, Jouve F, Michailidis G (2016) Thickness control in structural optimization via a level set method. Struct Multidiscip Optim 53(6):1349

Harzheim L, Graf G (2006) A review of optimization of cast parts using topology optimization. Struct Multidiscip Optim 31(5):388

Xia Q, Shi T, Wang MY, Liu S (2010) A level set based method for the optimization of cast part. Struct Multidiscip Optim 41(5):735

Xia Q, Shi T, Wang MY, Liu S (2011) Simultaneous optimization of cast part and parting direction using level set method. Struct Multidiscip Optim 44(6):751

Lu J, Chen Y (2012) Manufacturable mechanical part design with constrained topology optimization. Proc Inst Mech Eng Part B J Eng Manuf 226(10):1727

Gebisa A, Lemu H (2017) Design for manufacturing to design for additive manufacturing: analysis of implications for design optimality and product sustainability. Procedia Manuf 13:724

Xia L, Breitkopf P (2014) Concurrent topology optimization design of material and structure within fe2 nonlinear multiscale analysis framework. Comput Methods Appl Mech Eng 278:524

Xia L, Breitkopf P (2015) Multiscale structural topology optimization with an approximate constitutive model for local material microstructure. Comput Methods Appl Mech Eng 286:147

Xia L, Breitkopf P (2017) Recent advances on topology optimization of multiscale nonlinear structures. Arch Comput Methods Eng 24(2):227

Da D, Yvonnet J, Xia L, Le MV, Li G (2018) Topology optimization of periodic lattice structures taking into account strain gradient. Comput Struct 210:28–40

Wang Y, Xu H, Pasini D (2017) Multiscale isogeometric topology optimization for lattice materials. Comput Methods Appl Mech Eng 316:568

Liu S, Li Q, Chen W, Tong L, Cheng G (2015) An identification method for enclosed voids restriction in manufacturability design for additive manufacturing structures. Front Mech Eng 10(2):126

Zhou L, Zhang W (2018) Topology optimization method considering structural connectivity for additive manufacturing with void features. Struct Multidiscip Optim (under revision)

Gaynor AT, Guest JK (2016) Topology optimization considering overhang constraints: eliminating sacrificial support material in additive manufacturing through design. Struct Multidiscip Optim 54(5):1157

Mass Y, Amir O (2017) Topology optimization for additive manufacturing: accounting for overhang limitations using a virtual skeleton. Addit Manuf 18:58

Wu AS, Brown DW, Kumar M, Gallegos GF, King WE (2014) An experimental investigation into additive manufacturing-induced residual stresses in 316l stainless steel. Metall Mater Trans A 45(13):6260

Kohn RV, Strang G (1986) Optimal design and relaxation of variational problems, i. Commun Pure Appl Math 39(1):113

Bendsøe MP, Kikuchi N (1988) Generating optimal topologies in structural design using a homogenization method. Comput Methods Appl Mech Eng 71(2):197

Bendsøe MP (1989) Optimal shape design as a material distribution problem. Struct Optim 1(4):193

Andreassen E, Clausen A, Schevenels M, Lazarov BS, Sigmund O (2011) Efficient topology optimization in matlab using 88 lines of code. Struct Multidiscip Optim 43(1):1

Sigmund O (2001) A 99 line topology optimization code written in matlab. Struct Multidiscip Optim 21(2):120

Sigmund O, Maute K (2013) Topology optimization approaches. Struct Multidiscip Optim 48(6):1031

Sigmund O (2007) Morphology-based black and white filters for topology optimization. Struct Multidiscip Optim 33(4–5):401

Xie YM, Steven GP (1993) A simple evolutionary procedure for structural optimization. Comput Struct 49(5):885

Querin O, Young V, Steven G, Xie Y (2000) Computational efficiency and validation of bi-directional evolutionary structural optimisation. Comput Methods Appl Mech Eng 189(2):559

Huang X, Xie YM (2010) A further review of eso type methods for topology optimization. Struct Multidiscip Optim 41(5):671

Abdi M, Wildman R, Ashcroft I (2014) Evolutionary topology optimization using the extended finite element method and isolines. Eng Optim 46(5):628

Da D, Xia L, Li G, Huang X (2018) Evolutionary topology optimization of continuum structures with smooth boundary representation. Struct Multidiscip Optim 57(6):2143

Sigmund O, Petersson J (1998) Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Struct Optim 16(1):68

Zhou M, Shyy Y, Thomas H (2001) Checkerboard and minimum member size control in topology optimization. Struct Multidiscip Optim 21(2):152

Li Q, Steven G, Xie Y (2001) A simple checkerboard suppression algorithm for evolutionary structural optimization. Struct Multidiscip Optim 22(3):230

van Dijk NP, Maute K, Langelaar M, Van Keulen F (2013) Level-set methods for structural topology optimization: a review. Struct Multidiscip Optim 48(3):437

Zhu J, Zhao Y, Zhang W, Gu X, Gao T, Kong J, Shi G, Xu Y, Quan D (2019) Bio-inspired feature-driven topology optimization for rudder structure design. Eng Sci. https://doi.org/10.30919/es8d716

Zhang W, Zhao L, Gao T, Cai S (2017) Topology optimization with closed b-splines and boolean operations. Comput Methods Appl Mech Eng 315:652

Guo X, Zhang W, Zhong W (2014) Doing topology optimization explicitly and geometrically—a new moving morphable components based framework. J Appl Mech 81(8):081009

Zhang W, Chen J, Zhu X, Zhou J, Xue D, Lei X, Guo X (2017) Explicit three dimensional topology optimization via moving morphable void (mmv) approach. Comput Methods Appl Mech Eng 322:590

Xie X, Wang S, Xu M, Wang Y (2018) A new isogeometric topology optimization using moving morphable components based on r-functions and collocation schemes. Comput Methods Appl Mech Eng 339:61

Sokołowski J, Żochowski A (2001) Encyclopedia of optimization, Springer, pp 2625–2626

Bourdin B, Chambolle A (2003) Design-dependent loads in topology optimization, ESAIM: control. Optim Calc Var 9:19

Gao T, Qiu L, Zhang W (2017) Topology optimization of continuum structures subjected to the variance constraint of reaction forces. Struct Multidiscip Optim 56(4):755

Zhang W, Yang J, Xu Y, Gao T (2014) Topology optimization of thermoelastic structures: mean compliance minimization or elastic strain energy minimization. Struct Multidiscip Optim 49(3):417

Stanford B, Beran P (2012) Optimal compliant flapping mechanism topologies with multiple load cases. J Mech Des 134(5):051007

Wang MY, Chen S, Wang X, Mei Y (2005) Design of multimaterial compliant mechanisms using level-set methods. J Mech Des 127(5):941

Zhu JH, Li Y, Zhang WH, Hou J (2016) Shape preserving design with structural topology optimization. Struct Multidiscip Optim 53(4):893

Wang ZP, Poh LH, Dirrenberger J, Zhu Y, Forest S (2017) Isogeometric shape optimization of smoothed petal auxetic structures via computational periodic homogenization. Comput Methods Appl Mech Eng 323:250

Wang ZP, Turteltaub S (2015) Isogeometric shape optimization for quasi-static processes. Int J Numer Methods Eng 104:347

Collet M, Bruggi M, Duysinx P (2017) Topology optimization for minimum weight with compliance and simplified nominal stress constraints for fatigue resistance. Struct Multidiscip Optim 55(3):839

Le C, Norato J, Bruns T, Ha C, Tortorelli D (2010) Stress-based topology optimization for continua. Struct Multidiscip Optim 41(4):605

Holmberg E, Torstenfelt B, Klarbring A (2013) Stress constrained topology optimization. Struct Multidiscip Optim 48(1):33

Díaaz AR, Kikuchi N (1992) Solutions to shape and topology eigenvalue optimization problems using a homogenization method. Int J Numer Methods Eng 35(7):1487

He W, Bindel D, Govindjee S (2009) Topology optimization in microelectromechanical resonator design, Department of Civil and Environmental Engineering, University of California

Ma ZD, Kikuchi N, Cheng HC (1995) Topological design for vibrating structures. Comput Methods Appl Mech Eng 121(1–4):259

Jog C (2002) Topology design of structures subjected to periodic loading. J Sound Vib 253(3):687

Zhang W, Liu H, Gao T (2015) Topology optimization of large-scale structures subjected to stationary random excitation: an efficient optimization procedure integrating pseudo excitation method and mode acceleration method. Comput Struct 158:61

Li Q, Steven GP, Xie Y (2001) Thermoelastic topology optimization for problems with varying temperature fields. J Therm Stress 24(4):347

Xia Q, Wang MY (2008) Topology optimization of thermoelastic structures using level set method. Comput Mech 42(6):837

Pedersen P, Pedersen NL (2010) Strength optimized designs of thermoelastic structures. Struct Multidiscip Optim 42(5):681

Michailidis G (2014) Manufacturing constraints and multi-phase shape and topology optimization via a level-set method. Ph.D. thesis, Ecole Polytechnique X

Zhou M, Fleury R, Shyy YK, Thomas H, Brennan J (2002) 9th AIAA/ISSMO symposium on multidisciplinary analysis and optimization, p 5614

Krog L, Tucker A, Rollema G (2002) Proceedings of 3rd Altair UK HyperWorks users Conference

Krog L, Tucker A, Kemp M, Boyd R (2004) 10th AIAA/ISSMO multidisciplinary analysis and optimization conference, p 4481

Kono D, Nishio S, Yamaji I, Matsubara A (2015) A method for stiffness tuning of machine tool supports considering contact stiffness. Int J Mach Tools Manuf 90:50

Liu H, Jiakun W, Yongqing W (2015) Impact of anchor bolts creep relaxation on geometric accuracy decline of large computer numerical control machine tools. J Xi’an Jiaotong Univ 49(9):14

Mahdavi A, Balaji R, Frecker M, Mockensturm E (2006) Topology optimization of 2d continua for minimum compliance using parallel computing. Struct Multidiscip Optim 32(2):121

Brandt M, Sun SJ, Leary M, Feih S, Elambasseril J, Liu QC (2013) Advanced materials research, vol 633, Trans Tech Publ, pp 135–147

Beaman JJ, Deckard CR (1990) Selective laser sintering with assisted powder handling. US Patent 4,938,816

Herzog D, Seyda V, Wycisk E, Emmelmann C (2016) Additive manufacturing of metals. Acta Mater 117:371

State-of-the-art for additive manufacturing of metals (2017). URLhttp://www.metalliskamaterial.se/globalassets/3-forskning/rapporter/2016-03898---state-of-the-art-for-additive-manufacturing-of-metals-2_1.pdf

Shellabear M, Nyrhilä O (2004) Dmls-development history and state of the art. Laser Assisted Netshape engineering 4, proceedings of the 4th LANE, pp 21–24

Calignano F, Manfredi D, Ambrosio E, Iuliano L, Fino P (2013) Influence of process parameters on surface roughness of aluminum parts produced by dmls. Int J Adv Manuf Technol 67(9–12):2743

Frazier WE (2014) Metal additive manufacturing: a review. J Mater Eng Perform 23(6):1917

Brandl E, Palm F, Michailov V, Viehweger B, Leyens C (2011) Mechanical properties of additive manufactured titanium (ti–6al–4v) blocks deposited by a solid-state laser and wire. Mater Des 32(10):4665

Crivello JV, Reichmanis E (2013) Photopolymer materials and processes for advanced technologies. Chem Mater 26(1):533

Guo N, Leu MC (2013) Additive manufacturing: technology, applications and research needs. Front Mech Eng 8(3):215

Wilkes J, Hagedorn YC, Meiners W, Wissenbach K (2013) Additive manufacturing of zro2–al2o3 ceramic components by selective laser melting. Rapid Prototyp J 19(1):51

Deckers J, Vleugels J, Kruth JP (2014) Additive manufacturing of ceramics: a review. J Ceram Sci Technol 5(4):245

Agrawal BK (1988) Introduction to engineering materials. Tata McGraw-Hill Education, New York

Badrossamay M, Childs T (2007) Further studies in selective laser melting of stainless and tool steel powders. Int J Mach Tools Manuf 47(5):779

Abd-Elghany K, Bourell D (2012) Property evaluation of 304l stainless steel fabricated by selective laser melting. Rapid Prototyp J 18(5):420

Kempen K, Yasa E, Thijs L, Kruth JP, Van Humbeeck J (2011) Microstructure and mechanical properties of selective laser melted 18ni-300 steel. Phys Procedia 12:255

Cormier D, Harrysson O, West H (2004) Characterization of h13 steel produced via electron beam melting. Rapid Prototyp J 10(1):35

Snoxall N (2018) Titanium challenge-design proposal. https://altairuniversity.com/wp-content/uploads/2013/09/Design-Proposal-Altair.pdf. Accessed 1 Aug 2018

Tan X, Kok Y, Tan YJ, Descoins M, Mangelinck D, Tor SB, Leong KF, Chua CK (2015) Graded microstructure and mechanical properties of additive manufactured ti–6al–4v via electron beam melting. Acta Mater 97:1

Baufeld B, Brandl E, Van der Biest O (2011) Wire based additive layer manufacturing: comparison of microstructure and mechanical properties of ti–6al–4v components fabricated by laser-beam deposition and shaped metal deposition. J Mater Process Technol 211(6):1146

Vilaro T, Colin C, Bartout JD (2011) As-fabricated and heat-treated microstructures of the ti–6al–4v alloy processed by selective laser melting. Metall Mater Trans A 42(10):3190

Brice C, Shenoy R, Kral M, Buchannan K (2015) Precipitation behavior of aluminum alloy 2139 fabricated using additive manufacturing. Mater Sci Eng A 648:9

Yang KK, Zhu JH, Wang C, Jia DS, Song LL, Zhang WH (2018) Experimental validation of 3d printed material behaviors and their influence on the structural topology design. Comput Mech 61(5):581–598

Yuan S, Shen F, Chua CK, Zhou K (2018) Polymeric composites for powder-based additive manufacturing: Materials and applications. Prog Polym Sci

Yuan S, Zheng Y, Chua CK, Yan Q, Zhou K (2018) Electrical and thermal conductivities of mwcnt/polymer composites fabricated by selective laser sintering. Compos Part A Appl Sci Manuf 105:203

Stratasys (2014) Direct digital manufacturing at bmw (January 15, 2014). URLhttp://3dprinting.trimech.com/case-study-fdm-bmw

Jauhar S, Asthankar K, Kuthe A (2012) Cost benefit analysis of rapid manufacturing in automotive industries. Adv Mech Eng Appl (AMEA) 2(3):181

Center FM (2014) Ford 3d-printed auto parts save millions, boost quality. URLhttps://www.plasticstoday.com/content/ford-3d-printed-auto-parts-save-millions-boost-quality/97214356120060

Fleming J (2018) Additive manufacturing in the automotive industry: insights from ford and bmw (September 15, 2018). URLhttps://generisgp.com/2018/01/02/additive-manufacturing-automotive-ford-bmw/

Press DU (2018) 3d opportunity in the automotive undustry—additive manufacturing hits the road (September 15, 2018). URLhttps://www2.deloitte.com/content/dam/insights/us/articles/additive-manufacturing-3d-opportunity-in-automotive/DUP_707-3D-Opportunity-Auto-Industry_MASTER.pdf

D. printing industry (2018) Volkswagen to mass customise 100,000 3d printed units per year using the newly launched hp metal jet 3d printer (September 14, 2018). URLhttps://spare-parts-3d.com/2018/09/14/vw-customise-100000-3d-printed-hp-metal-jet/

ENGINEER (2018) Bmw group to invest over 10 m €in new additive manufacturing campus (April 18, 2018). URLhttps://www.theengineer.co.uk/bmw-group-additive-manufacturing-campus/

Tomlin M, Meyer J (2011) Proceeding of the 7th altair CAE technology conference, pp 1–9

Machunze W, Lehmann T, Hein O (2013) 2013 European altair technology conference, pp 1–25

Snoxall N (2013) Topology optimization for additive manufacture: Titanium challenge—design proposal. URLhttps://altairuniversity.com/wp-content/uploads/2013/09/Design-Proposal-Altair.pdf

Sher D (2013) 5-m long titanium airplane part 3d printed in one piece (January 18, 2013). URLhttps://www.3ders.org/articles/20130118-3-meter-long-titanium-airplane-part-3d-printed-in-one-piece.html

Sher D (2018) Ge aviation already 3d printed 30,000 fuel nozzles for its leap engine (October 5, 2018). URLhttps://www.3dprintingmedia.network/ge-aviation-already-3d-printed-30000-fuel-nozzles-for-its-leap-engine/

Tripathy S (2016) Topology optimization for additive manufacturing applications. http://blogs.3ds.com/simulia/topology-optimization-for-additive-manufacturing-applications/. Accessed 23 Aug 2016

EOS (2018) Aerospace: Ruag-additive manufacturing of satellite components (September 15, 2018). URLhttps://www.eos.info/case_studies/additive-manufacturing-of-antenna-bracket-for-satellite

EOS (2018) Eos and airbus group innovations team on aerospace sustainability study for industrial 3d printing. https://www.eos.info/eos-airbusgroupinnovationteam-aerospace-sustainability-study. Accessed 31 June 2018

Kranz J, Herzog D, Emmelmann C (2015) Design guidelines for laser additive manufacturing of lightweight structures in ti–al6–v4. J Laser Appl 27(S1):S14001

Zelinski P (2016) 7 Helpful numbers quantify design rules for additive manufacturing. URLhttps://www.additivemanufacturing.media/blog/post/7-helpful-numbers-quantify-design-rules-for-am

Hu K, Jin S, Wang CC (2015) Support slimming for single material based additive manufacturing. Comput Aided Des 65:1

Morgan H, Cherry J, Jonnalagadda S, Ewing D, Sienz J (2016) Part orientation optimisation for the additive layer manufacture of metal components. Int J Adv Manuf Technol 86(5–8):1679

Pandey PM, Thrimurthulu K, Reddy NV (2004) Optimal part deposition orientation in fdm by using a multicriteria genetic algorithm. Int J Prod Res 42(19):4069

Phatak AM, Pande S (2012) Optimum part orientation in rapid prototyping using genetic algorithm. J Manuf Syst 31(4):395

Huang X, Ye C, Wu S, Guo K, Mo J (2009) Sloping wall structure support generation for fused deposition modeling. Int J Adv Manuf Technol 42(11–12):1074

Vanek J, Galicia JAG, Benes B (2014) Computer graphics forum, vol 33, Wiley Online Library, pp 117–125

Mezzadri F, Bouriakov V, Qian X (2018) Topology optimization of self-supporting support structures for additive manufacturing. Addit Manuf 21:666

Dumas J, Hergel J, Lefebvre S (2014) Bridging the gap: automated steady scaffoldings for 3d printing. ACM Trans Gr (TOG) 33(4):98

Barnett E, Gosselin C (2015) Weak support material techniques for alternative additive manufacturing materials. Addit Manuf 8:95

Brackett D, Ashcroft I, Hague R (2011) Proceedings of the solid freeform fabrication symposium, Austin, TX, vol 1, pp 348–362

Zhang W, Zhou L (2018) Topology optimization of self-supporting structures with polygon features for additive manufacturing. Comput Methods Appl Mech Eng 334:56

Meyer B, Minn E (2016) Accuracy in additive manufacturing. Mach Des 84:56

Murr LE, Gaytan S, Ceylan A, Martinez E, Martinez J, Hernandez D, Machado B, Ramirez D, Medina F, Collins S et al (2010) Characterization of titanium aluminide alloy components fabricated by additive manufacturing using electron beam melting. Acta Mater 58(5):1887

Press DU (2018) Ultrasonic additive manufacturing (September 15, 2018). URLhttps://fabrisonic.com/ultrasonic-additive-manufacturing-overview/

Murr LE, Gaytan SM, Ramirez DA, Martinez E, Hernandez J, Amato KN, Shindo PW, Medina FR, Wicker RB (2012) Metal fabrication by additive manufacturing using laser and electron beam melting technologies. J Mater Sci Technol 28(1):1

Mower TM, Long MJ (2016) Mechanical behavior of additive manufactured, powder-bed laser-fused materials. Mater Sci Eng A 651:198

Tripathy S, Chin C, London T, Ankalkhope U, Oancea V (2017) Process modeling and validation of powder bed metal additive manufacturing. In: NAFEMS world congress, Stockholm, Sweden

Wu X, Liang J, Mei J, Mitchell C, Goodwin P, Voice W (2004) Microstructures of laser-deposited ti–6al–4v. Mater Des 25(2):137

Mok SH, Bi G, Folkes J, Pashby I (2008) Deposition of ti–6al–4v using a high power diode laser and wire, part i: investigation on the process characteristics. Surf Coat Technol 202(16):3933

Zhu Y, Tian X, Li J, Wang H (2015) The anisotropy of laser melting deposition additive manufacturing ti–6.5 al–3.5 mo–1.5 zr–0.3 si titanium alloy. Mater Des 67:538

Brandl E, Baufeld B, Leyens C, Gault R (2010) Additive manufactured ti–6al–4v using welding wire: comparison of laser and arc beam deposition and evaluation with respect to aerospace material specifications. Phys Procedia 5(Pt 2):595

Baufeld B (2012) Effect of deposition parameters on mechanical properties of shaped metal deposition parts. Proc Inst Mech Eng Part B J Eng Manuf 226(1):126

Kruth JP, Mercelis P, Van Vaerenbergh J, Froyen L, Rombouts M (2005) Binding mechanisms in selective laser sintering and selective laser melting. Rapid Prototyp J 11(1):26

Thijs L, Verhaeghe F, Craeghs T, Van Humbeeck J, Kruth JP (2010) A study of the microstructural evolution during selective laser melting of ti–6al–4v. Acta Mater 58(9):3303

Papadakis L, Loizou A, Risse J, Bremen S, Schrage J (2014) A computational reduction model for appraising structural effects in selective laser melting manufacturing: a methodical model reduction proposed for time-efficient finite element analysis of larger components in selective laser melting. Virtual Phys Prototyp 9(1):17

Smith J, Xiong W, Yan W, Lin S, Cheng P, Kafka OL, Wagner GJ, Cao J, Liu WK (2016) Linking process, structure, property, and performance for metal-based additive manufacturing: computational approaches with experimental support. Comput Mech 57(4):583

Contuzzi N, Campanelli S, Ludovico A (2011) 3 d finite element analysis in the selective laser melting process. Int J Simul Model 10(3):113

Abe F, Osakada K, Shiomi M, Uematsu K, Matsumoto M (2001) The manufacturing of hard tools from metallic powders by selective laser melting. J Mater Process Technol 111(1–3):210

Alyoshin N, Murashov V, Grigoryev M, Yevgenov A, Karachevtsev F, Shchipakov N, Vasilenko S (2017) Defects of heat-resistant alloys synthesized by the method of selective laser melting. Inorg Mater Appl Res 8(1):27

Hussein A, Hao L, Yan C, Everson R (2013) Finite element simulation of the temperature and stress fields in single layers built without-support in selective laser melting. Mater Des 52:638

De A, DebRoy T (2006) Improving reliability of heat and fluid flow calculation during conduction mode laser spot welding by multivariable optimisation. Sci Technol Weld Join 11(2):143

Patterson AE, Messimer SL, Farrington PA (2017) Overhanging features and the slm/dmls residual stresses problem: review and future research need. Technologies 5(2):15

Kruth JP, Deckers J, Yasa E, Wauthlé R (2012) Assessing and comparing influencing factors of residual stresses in selective laser melting using a novel analysis method. Proc Inst Mech Eng Part B J Eng Manuf 226(6):980

Carter LN, Martin C, Withers PJ, Attallah MM (2014) The influence of the laser scan strategy on grain structure and cracking behaviour in slm powder-bed fabricated nickel superalloy. J Alloys Compd 615:338

Guan K, Wang Z, Gao M, Li X, Zeng X (2013) Effects of processing parameters on tensile properties of selective laser melted 304 stainless steel. Mater Des 50:581

Shiomi M, Osakada K, Nakamura K, Yamashita T, Abe F (2004) Residual stress within metallic model made by selective laser melting process. CIRP Ann Manuf Technol 53(1):195

Popovich V, Borisov E, Popovich A, Sufiiarov VS, Masaylo D, Alzina L (2017) Functionally graded inconel 718 processed by additive manufacturing: crystallographic texture, anisotropy of microstructure and mechanical properties. Mater Des 114:441

Carroll BE, Palmer TA, Beese AM (2015) Anisotropic tensile behavior of ti–6al–4v components fabricated with directed energy deposition additive manufacturing. Acta Mater 87:309

Murr L (2015) Metallurgy of additive manufacturing: examples from electron beam melting. Addit Manuf 5:40

Froes F, Friedrich H, Kiese J, Bergoint D (2004) Titanium in the family automobile: the cost challenge. JOM 56(2):40

Withers P, Bhadeshia H (2001) Residual stress. Part 1—measurement techniques. Mater Sci Technol 17(4):355

Meng L, Breitkopf P, Raghavan B, Mauvoisin G, Bartier O, Hernot X (2015) Identification of material properties using indentation test and shape manifold learning approach. Comput Methods Appl Mech Eng 297:239

Mott BW (1956) Micro-indentation hardness testing. Butterworths Scientific Publications, London

Tabor D (1951) The hardness of metals, vol 10. Clarendon Press, Oxford

Smith RL, Sandly GE (1922) An accurate method of determining the hardness of metals, with particular reference to those of a high degree of hardness. Proc Inst Mech Eng 102(1):623

Meng L, Breitkopf P, Le Quilliec G (2017) An insight into the identifiability of material properties by instrumented indentation test using manifold approach based on ph curve and imprint shape. Int J Solids Struct 106:13

Meng L, Breitkopf P, Raghavan B, Mauvoisin G, Bartier O, Hernot X (2018) On the study of mystical materials identified by indentation on power law and voce hardening solids. Int J Mater Form 1–16

Mukhopadhyay A (1999) Comparative study of indentation fatigue in structural ceramics. J Mater Sci Lett 18(4):333

Kamali-Bernard S, Keinde D, Bernard F (2014) Effect of aggregate type on the concrete matrix/aggregates interface and its influence on the overall mechanical behavior. A numerical study. Key Eng Mater 617:14

Lu Y, Shinozaki D (2005) Effects of substrate constraint on micro-indentation testing of polymer coatings. Mater Sci Eng A 396(1–2):77

Sabnis PA, Forest S, Arakere NK, Yastrebov VA (2013) Crystal plasticity analysis of cylindrical indentation on a ni-base single crystal superalloy. Int J Plast 51:200

Moy CK, Bocciarelli M, Ringer SP, Ranzi G (2011) Identification of the material properties of al 2024 alloy by means of inverse analysis and indentation tests. Mater Sci Eng A 529:119

Moussa C, Bartier O, Mauvoisin G, Hernot X, Collin JM, Delattre G (2014) Experimental and numerical investigation on carbonitrided steel characterization with spherical indentation. Surf Coat Technol 258:782

Zeng Y, Yu X, Wang H (2018) A new pod-based approximate Bayesian computation method to identify parameters for formed ahss. Int J Solids Struct 160:120–133

Chen X, Yan J, Karlsson AM (2006) On the determination of residual stress and mechanical properties by indentation. Mater Sci Eng A 416(1):139

Rickhey F, Lee JH, Lee H (2015) A contact size-independent approach to the estimation of biaxial residual stresses by knoop indentation. Mater Des 84:300

Shen L, He Y, Liu D, Gong Q, Zhang B, Lei J (2015) A novel method for determining surface residual stress components and their directions in spherical indentation. J Mater Res 30(08):1078

Wang X, Xu S, Zhou S, Xu W, Leary M, Choong P, Qian M, Brandt M, Xie YM (2016) Topological design and additive manufacturing of porous metals for bone scaffolds and orthopaedic implants: a review. Biomaterials 83:127

Collet M, Noël L, Bruggi M, Duysinx P (2018) Topology optimization for microstructural design under stress constraints. Struct Multidiscip Optim 58(6):2677–2695

Deshpande VS, Fleck NA, Ashby MF (2001) Effective properties of the octet-truss lattice material. J Mech Phys Solids 49(8):1747

Wallach J, Gibson L (2001) Mechanical behavior of a three-dimensional truss material. Int J Solids Struct 38(40–41):7181

Wang AJ, McDowell D (2003) Optimization of a metal honeycomb sandwich beam-bar subjected to torsion and bending. Int J Solids Struct 40(9):2085

Wang H, Chen Y, Rosen DW (2005) ASME 2005 international design engineering technical conferences and computers and information in engineering conference, American Society of Mechanical Engineers, pp 421–427

Yuan S, Chua CK, Zhou K (2018) 3d-printed mechanical metamaterials with high energy absorption. Adv Mater Technol 1800419

Doubrovski Z, Verlinden JC, Geraedts JM (2011) ASME 2011 international design engineering technical conferences and computers and information in engineering conference, American Society of Mechanical Engineers, pp 635–646

Eiamsa-ard K, Ruan J, Ren L, Liou FW (2005) ASME 2005 international design engineering technical conferences and computers and information in engineering conference, American Society of Mechanical Engineers, pp 1309–1319

Kanakanala D, Routhu S, Ruan J, Liu XF, Liou F (2010) ASME 2010 international design engineering technical conferences and computers and information in engineering conference, American Society of Mechanical Engineers, pp 425–432

Routhu S, Kanakanala D, Ruan J, Liu XF, Liou F (2010) ASME 2010 international design engineering technical conferences and computers and information in engineering conference, American Society of Mechanical Engineers, pp 415–423

Hou Y, Sapanathan T, Dumon A, Culière P, Rachik M (2018) A novel development of bi-level reduced surrogate model to predict ductile fracture behaviors. Eng Fract Mech 188:232

Hou Y, Tie Y, Li C, Sapanathan T, Rachik M (2019) Low-velocity impact behaviors of repaired cfrp laminates: effect of impact location and external patch configurations. Compos Part B Eng 163:669

Idriss M, Bartier O, Mauvoisin G, Hernot X (2019) Determining the stress level of monotonic plastically pre-hardened metal sheets using the spherical instrumented indentation technique. J Mech Sci Technol 33(1):183

Chen X, Ogasawara N, Zhao M, Chiba N (2007) On the uniqueness of measuring elastoplastic properties from indentation: the indistinguishable mystical materials. J Mech Phys Solids 55(8):1618

Meng L, Raghavan B, Bartier O et al (2017) An objective meta-modeling approach for indentation-based material characterization. Mech Mater 107:31–44