[1] [1] Pan C, Han Y F and Lu J P 2020 Design and optimization of lattice structures: a review Appl. Sci. 10 6374

[2] [2] Zhang C, Zhu J K, Zheng H, Li H, Liu S and Cheng G J 2020 A review on microstructures and properties of high entropy alloys manufactured by selective laser melting Int. J. Extreme Manuf. 2 032003

[3] [3] Queheillalt D T and Wadley H N G 2005 Cellular metal lattices with hollow trusses Acta Mater. 53 303-13

[4] [4] 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 49-61

[5] [5] Cheng X M, Wei K, He R J, Pei Y M and Fang D N 2016 The equivalent thermal conductivity of lattice core sandwich structure: a predictive model Appl. Therm. Eng. 93 236-43

[6] [6] Hu Y Y, Miles B T, Ho Y L D, Taverne M P C, Chen L F, Gersen H, Rarity J G and Faul C F J 2017 Toward direct laser writing of actively tuneable 3D photonic crystals Adv. Opt. Mater. 5 1600458

[7] [7] Arabnejad S, Johnston R B, 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. 30 345-56

[8] [8] Gupta A and Talha M 2015 Recent development in modeling and analysis of functionally graded materials and structures Prog. Aerosp. Sci. 79 1-14

[9] [9] Kang J F, Dong E C, Li D C, Dong S P, Zhang C and Wang L 2020 Anisotropy characteristics of microstructures for bone substitutes and porous implants with application of additive manufacturing in orthopaedic Mater. Des. 191 108608

[10] [10] Yin S, Chen H Y, Wu Y B, Li Y B and Xu J 2018 Introducing composite lattice core sandwich structure as an alternative proposal for engine hood Compos. Struct. 201 131-40

[11] [11] Tamburrino F, Graziosi S and Bordegoni M 2018 The design process of additively manufactured mesoscale lattice structures: a review J. Comput. Inf. Sci. Eng. 18 040801

[12] [12] Zhang L, Feih S, Daynes S, Chang S, Wang M Y, Wei J and Lu W F 2018 Energy absorption characteristics of metallic triply periodic minimal surface sheet structures under compressive loading Addit. Manuf. 23 505-15

[13] [13] Soro N, Saintier N, Merzeau J, Veidt M and Dargusch M S 2021 Quasi-static and fatigue properties of graded Ti-6A-4V lattices produced updates by laser powder bed fusion (LPBF) Addit. Manuf. 37 101653

[14] [14] Gümrük R, Mines R A W and Karadeniz S 2013 Static mechanical behaviours of stainless steel micro-lattice structures under different loading conditions Mater. Sci. Eng. A 586 392-406

[15] [15] Ushijima K, Cantwell W J, Mines R A W, Tsopanos S and Smith M 2011 An investigation into the compressive properties of stainless steel micro-lattice structures J. Sandw. Struct. Mater. 13 303-29

[16] [16] Traxel K D, Groden C, Valladares J and Bandyopadhyay A 2021 Mechanical properties of additively manufactured variable lattice structures of Ti6Al4V Mater. Sci. Eng. A 809 140925

[17] [17] Tancogne-Dejean T and Mohr D 2018 Stiffness and specific energy absorption of additively-manufactured metallic BCC metamaterials composed of tapered beams Int. J. Mech. Sci. 141 101-16

[18] [18] Wang S, Wang J, Xu Y J, Zhang W H and Zhu J H 2020 Compressive behavior and energy absorption of polymeric lattice structures made by additive manufacturing Front. Mech. Eng. 15 319-27

[19] [19] Du Y X, Gu D D, Xi L X, Dai D H, Gao T, Zhu J H and Ma C L 2020 Laser additive manufacturing of bio-inspired lattice structure: forming quality, microstructure and energy absorption behavior Mater. Sci. Eng. A 773 138857

[20] [20] Lin K J, Gu D D, Hu K M, Yang J K, Wang H R, Yuan L H, Shi X Y and Meng L 2021 Laser powder bed fusion of bio-inspired honeycomb structures: effect of twist angle on compressive behaviors Thin-Walled Struct. 159 107252

[21] [21] Meng L, Shi J X, Yang C, Gao T, Hou Y L, Song L L, Gu D D, Zhu J H, Breitkopf P and Zhang W H 2020 An emerging class of hyperbolic lattice exhibiting tunable elastic properties and impact absorption through chiral twisting Extreme Mech. Lett. 40 100869

[22] [22] Tao W J and Leu M C 2016 Design of lattice structure for additive manufacturing Proc. 2016 Int. Symp. on Flexible Automation (Cleveland, OH: IEEE) pp 325-32

[23] [23] Wang Y 2007 Periodic surface modeling for computer aided nano design Comput. Aided Des. 39 179-89

[24] [24] Duan S Y, Xi L, Wen W B and Fang D N 2020 Mechanical performance of topology-optimized 3D lattice materials manufactured via selective laser sintering Compos. Struct. 238 111985

[25] [25] Gupta V and Tandon P 2015 Heterogeneous object modeling with material convolution surfaces Comput. Aided Des. 62 236-47

[26] [26] Pasko A, Fryazinov O, Vilbrandt T, Fayolle P A and Adzhiev V 2011 Procedural function-based modelling of volumetric microstructures Graph. Models 73 165-81

[27] [27] Nazir A, Abate K M, Kumar A and Jeng J Y 2019 A state-of-the-art review on types, design, optimization, and additive manufacturing of cellular structures Int. J. Adv. Manuf. Technol. 104 3489-510

[28] [28] Zhu J H, Zhou H, Wang C, Zhou L, Yuan S Q and Zhang W H 2021 A review of topology optimization for additive manufacturing: status and challenges Chin. J. Aeronaut. 34 91-110

[29] [29] Song J, Wang Y J, Zhou W Z, Fan R, Yu B, Lu Y and Li L X 2019 Topology optimization-guided lattice composites and their mechanical characterizations Composites B 160 402-11

[30] [30] Osanov M and Guest J K 2016 Topology optimization for architected materials design Ann. Rev. Mater. Res. 46 211-33

[31] [31] Teimouri M and Asgari M 2021 Mechanical performance of additively manufactured uniform and graded porous structures based on topology-optimized unit cells Proc. Inst. Mech. Eng. C 235 1593-618

[32] [32] Xiao Z F, Yang Y Q, Xiao R, Bai Y C, Song C H and Wang D 2018 Evaluation of topology-optimized lattice structures manufactured via selective laser melting Mater. Des. 143 27-37

[33] [33] Zhang L, Song B, Fu J J, Wei S S, Yang L, Yan C Z, Li H, Gao L and Shi Y S 2020 Topology-optimized lattice structures with simultaneously high stiffness and light weight fabricated by selective laser melting: design, manufacturing and characterization J. Manuf. Process. 56 1166-77

[34] [34] Seharing A, Azman A H and Abdullah S 2020 A review on integration of lightweight gradient lattice structures in additive manufacturing parts Adv. Mech. Eng. 12 1-21

[35] [35] Mahmoud D and Elbestawi M A 2017 Lattice structures and functionally graded materials applications in additive manufacturing of orthopedic implants: a review J. Manuf. Mater. Process. 1 13

[36] [36] 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. Cell. Plast. 53 151-65

[37] [37] Choy S Y, Sun C N, Sin W J, Leong K F, Su P C, Wei J and Wang P 2021 Superior energy absorption of continuously graded microlattices by electron beam additive manufacturing Virtual Phys. Prototyp. 16 14-28

[38] [38] Xiao L J, Song W D and Xu X 2020 Experimental study on the collapse behavior of graded Ti-6Al-4V micro-lattice structures printed by selective laser melting under high speed impact Thin-Walled Struct. 155 106970

[39] [39] Maskery I, Aboulkhair N T, Aremu A O, Tuck C J, Ashcroft I A, Wildman R D and Hague R J M 2016 A mechanical property evaluation of graded density Al-Si10-Mg lattice structures manufactured by selective laser melting Mater. Sci. Eng. A 670 264-74

[40] [40] Arifvianto B and Zhou J 2014 Fabrication of metallic biomedical scaffolds with the space holder method: a review Materials 7 3588-622

[41] [41] Gu D D, Guo M, Zhang H M, Sun Y X, Wang R and Zhang L 2020 Effects of laser scanning strategies on selective laser melting of pure tungsten Int. J. Extrem. Manuf. 2 025001

[42] [42] Wei C, Zhang Z Z, Cheng D X, Sun Z, Zhu M H and Li L 2021 An overview of laser-based multiple metallic material additive manufacturing: from macro- to micro-scales Int. J. Extrem. Manuf. 3 012003

[43] [43] Gu D D, Shi X Y, Poprawe R, Bourell D L, Setchi R and Zhu J H 2021 Material-structure-performance integrated laser-metal additive manufacturing Science 372 eabg1487

[44] [44] Zhao D L, Liang H, Han C J, Li J J, Liu J, Zhou K, Yang C and Wei Q S 2021 3D printing of a titanium-tantalum gyroid scaffold with superb elastic admissible strain, bioactivity and in-situ bone regeneration capability Addit. Manuf. 47 102223

[45] [45] Han C J, Li Y, Wang Q, Wen S F, Wei Q S, Yan C Z, Hao L, Liu J and Shi Y S 2018 Continuous functionally graded porous titanium scaffolds manufactured by selective laser melting for bone implants J. Mech. Behav. Biomed. Mater. 80 119-27

[46] [46] Han C J, Fang Q H, Shi Y S, Tor S B, Chua C K and Zhou K 2020 Recent advances on high-entropy alloys for 3D printing Adv. Mater. 32 1903855

[47] [47] Zhang B P, Han X S, Chen C P, Zhang W Q, Liao H L and Chen B J 2021 Effect of the strut size and tilt angle on the geometric characteristics of selective laser melting AlSi10Mg Rapid Prototyp. J. 27 879-89

[48] [48] Wang X B et al 2020 Effect of process parameters on the phase transformation behavior and tensile properties of NiTi shape memory alloys fabricated by selective laser melting Addit. Manuf. 36 101545

[49] [49] Elahinia M, Moghaddam N S, Andani M T, Amerinatanzi A, Bimber B A and Hamilton R F 2016 Fabrication of NiTi through additive manufacturing: a review Prog. Mater. Sci. 83 630-63

[50] [50] Yang C X, Xu P, Xie S C and Yao S G 2020 Mechanical performances of four lattice materials guided by topology optimisation Scr. Mater. 178 339-45

[51] [51] Ma C L, Gu D D, Gao J, Chen W, Song Y J and Setchi R 2021 Mechanical behavior of NiTi-based circular tube chiral structure manufactured by selective laser melting Sustainable Design and Manufacturing ed S G Scholz, R J Howlett and R Setchi (Singapore: Springer) pp 227-37

[52] [52] Yu C, Kang G Z, Kan Q H and Xu X 2017 Physical mechanism based crystal plasticity model of NiTi shape memory alloys addressing the thermo-mechanical cyclic degeneration of shape memory effect Mech. Mater. 112 1-17

[53] [53] Stebner A P, Brown D W and Brinson L C 2013 Measurement of elastic constants of monoclinic nickel-titanium and validation of first principles calculations Appl. Phys. Lett. 102 211908

[54] [54] Rajagopalan S and Little A L 2005 Elastic modulus of shape-memory NiTi from in situ neutron diffraction during macroscopic loading, instrumented indentation, and extensometry Appl. Phys. Lett. 86 081901

[55] [55] Al-Saedi D S J, Masood S H, Faizan-Ur-Rab M, Alomarah A and Ponnusamy P 2018 Mechanical properties and energy absorption capability of functionally graded F2BCC lattice fabricated by SLM Mater. Des. 144 32-44

[56] [56] Bucsek A N, Paranjape H M and Stebner A P 2016 Myths and truths of nitinol mechanics: elasticity and tension-compression asymmetry Shape Mem. Superelasticity 2 264-71

[57] [57] Stebner A, Gao X J, Brown D W and Brinson L C 2011 Neutron diffraction studies and multivariant simulations of shape memory alloys: empirical texture development-mechanical response relations of martensitic nickel-titanium Acta Mater. 59 2841-9

[58] [58] Oliveira J P, Cavaleiro A J, Schell N, Stark A, Miranda R M, Ocana J L and Braz Fernandes F M 2018 Effects of laser processing on the transformation characteristics of NiTi: a contribute to additive manufacturing Scr. Mater. 152 122-6

[59] [59] Andani M T, Saedi S, Turabi A S, Karamooz M R, Haberland C, Karaca H E and Elahinia M 2017 Mechanical and shape memory properties of porous Ni50.1Ti49.9 alloys manufactured by selective laser melting J. Mech. Behav. Biomed. Mater. 68 224-31

[60] [60] Wang X B, Kustov S and Van Humbeeck J 2018 A short review on the microstructure, transformation behavior and functional properties of NiTi shape memory alloys fabricated by selective laser melting Materials 11 1683

[61] [61] Frenzel J, George E P, Dlouhy A, Somsen C, Wagner M F X and Eggeler G 2010 Influence of Ni on martensitic phase transformations in NiTi shape memory alloys Acta Mater. 58 3444-58