On the application of additive manufacturing methods for auxetic structures: a review

doi:10.1007/s40436-021-00357-y

Abstract

Abstract: Auxetic structures are a special class of structural components that exhibit a negative Poisson's ratio (NPR) because of their constituent materials, internal microstructure, or structural geometry. To realize such structures, specialized manufacturing processes are required to achieve a dimensional accuracy, reduction of material wastage, and a quicker fabrication. Hence, additive manufacturing (AM) techniques play a pivotal role in this context. AM is a layer-wise manufacturing process and builds the structure as per the designed geometry with appreciable precision and accuracy. Hence, it is extremely beneficial to fabricate auxetic structures using AM, which is otherwise a tedious and expensive task. In this study, a detailed discussion of the various AM techniques used in the fabrication of auxetic structures is presented. The advancements and advantages put forward by the AM domain have offered a plethora of opportunities for the fabrication and development of unconventional structures. Therefore, the authors have attempted to provide a meaningful encapsulation and a detailed discussion of the most recent of such advancements pertaining to auxetic structures. The article opens with a brief history of the growth of auxetic materials and later auxetic structures. Subsequently, discussions centering on the different AM techniques employed for the realization of auxetic structures are conducted. The basic principle, advantages, and disadvantages of these processes are discussed to provide an in-depth understanding of the current level of research. Furthermore, the performance of some of the prominent auxetic structures realized through these methods is discussed to compare their benefits and shortcomings. In addition, the influences of geometric and process parameters on such structures are evaluated through a comprehensive review to assess their feasibility for the latermentioned applications. Finally, valuable insights into the applications, limitations, and prospects of AM for auxetic structures are provided to enable the readers to gauge the vitality of such manufacturing as a production method.

The full text can be downloaded at https://link.springer.com/article/10.1007%2Fs40436-021-00357-y

Key words: Auxetic, Additive manufacturing (AM), Negative Poisson's ratio (NPR), Mechanical performance, Unit-cell structure

Athul Joseph, Vinyas Mahesh, Dineshkumar Harursampath. On the application of additive manufacturing methods for auxetic structures: a review[J]. Advances in Manufacturing, 2021, 9(3): 342-368.

TrendMD

References

1. Lim TC (2015) Auxetic materials and structures. Springer, Singapore
2. Alderson A, Alderson KL (2007) Auxetic materials. J Aerosp Eng 221:565-575
3. Lakes R (1987) Foam structures with negative Poisson's ratio. Science 235:1038-1040
4. Yeganeh-Haeri A, Weidner DJ, Parise JB (1992) Elasticity of acristobalite:a silicon dioxide with a negative Poisson's ratio. Science 257(5070):650-652
5. Keskar NR, Chelikowsky JR (1992) Negative Poisson ratios in crystalline SiO₂ from first-principles calculations. Nature 358:222-224
6. Anurag C, Anvesh CK, Harsha AS (2015) Auxetic materials. Int J Trends Eng Technol 5:156-160
7. Wang Z, Zulifqar A, Hu H (2016) Auxetic composites in aerospace engineering. In:Sohel R and Raul F (eds) Advanced composite materials for aerospace engineering:processing, properties and applications, Woodhead Publishing, pp 213-240
8. Wang Z (2019) Recent advances in novel metallic honeycomb structure. Compos Part B Eng 166:731-741
9. Grima JN, Gatt R, Farrugia PS et al (2005) Auxetic cellular materials and structures. In:Proceedings of the ASME aerospace division 2005, Orlando, FL(US), pp 489-495
10. Novak N, Vesenjak M, Ren Z (2016) Auxetic cellular materialsa review. J Mech Eng 62:485-493
11. Gaspar N, Smith CW, Evans KE (2003) Effect of heterogeneity on the elastic properties of auxetic materials. J Appl Phys 94:6143-6149
12. Dirrenberger J, Forest S, Jeulin D (2012) Elastoplasticity of auxetic materials. Comput Mater Sci 64:57-61
13. Baughman RH (2003) Avoiding the shrink. Nature 425:667
14. Mazaev AV, Ajeneza O, Shitikova MV (2020) Auxetics materials:classification, mechanical properties and applications. IOP Conf Ser Mater Sci Eng 747:012008. https://doi.org/10.1088/1757-899X/747/1/012008
15. Xu Y, Zhang H, Schlangen E et al (2020) Cementitious cellular composites with auxetic behavior. Cem Concr Compos 111:103624. https://doi.org/10.1016/j.cemconcomp.2020.103624
16. Dirrenberger J, Forest S, Jeulin D et al (2011) Homogenization of periodic auxetic materials. Procedia Eng 10:1847-1852
17. Liu Y, Hu H (2010) A review on auxetic structures and polymeric materials. Sci Res Essays 5:1052-1063
18. Evans KE, Alderson KL (2000) Auxetic materials:the positive side of being negative. Eng Sci Educ J 9:148-154
19. Evans KE, Alderson A (2000) Auxetic materials:functional materials and structures from lateral thinking! Adv Mater 12:617-628
20. Wieding J, Fritsche A, Heinl P et al (2013) Biomechanical behavior of bone scaffolds made of additive manufactured tricalciumphosphate and titanium alloy under different loading conditions. J Appl Biomater Funct Mater 11:159-166
21. Hou X, Hu H, Silberschmidt V (2012) A novel concept to develop composite structures with isotropic negative Poisson's ratio:effects of random inclusions. Compos Sci Technol 72:1848-1854
22. Carneiro VH, Meireles J, Puga H (2013) Auxetic materials-a review. Mater Sci Pol 31:561-571
23. Papadopoulou A, Laucks J, Tibbits S (2017) Auxetic materials in design and architecture. Nat Rev Mater 2:1-3
24. Mistry D, Connell SD, Mickthwaite SL et al (2018) Coincident molecular auxeticity and negative order parameter in a liquid crystal elastomer. Nat Commun 9:1-9
25. Saxena KK, Das R, Calius EP (2016) Three decades of auxetics research-materials with negative Poisson's ratio:a review. Adv Eng Mater 18:1847-1870
26. Ren X, Shen J, Ghaedizadeh A et al (2015) Experiments and parametric studies on 3D metallic auxetic metamaterials with tuneable mechanical properties. Smart Mater Struct 24:095016. https://doi.org/10.1088/0964-1726/24/9/095016
27. Valente J, Plum E, Youngs IJ et al (2016) Nano- and microauxetic plasmonic materials. Adv Mater 28:5176-5180
28. Grima JN (2000) New auxetic mater. https://doi.org/10.1155/2014/753496
29. Yang W, Li ZM, Shi W et al (2004) Review on auxetic materials. J Mater Sci 39:3269-3279
30. Grima JN, Gatt R, Alderson A et al (2005) On the origin of auxetic behaviour in the silicate a-cristobalite. J Mater Chem 15:4003-4005
31. Prawoto Y (2012) Seeing auxetic materials from the mechanics point of view:a structural review on the negative Poisson's ratio. Comput Mater Sci 58:140-153
32. Ulissi ZW, Govind Rajan A, Strano MS (2016) Persistently auxetic materials:engineering the Poisson ratio of 2D selfavoiding membranes under conditions of non-zero anisotropic strain. ACS Nano 10:7542-7549
33. Scarpa F, Ciffo LG, Yates JR (2004) Dynamic properties of high structural integrity auxetic open cell foam. Smart Mater Struct 13:49-56
34. Sloan MR, Wright JR, Evans KE (2011) The helical auxetic yarn-a novel structure for composites and textiles; geometry, manufacture and mechanical properties. Mech Mater 43:476-486
35. Critchley R, Corni I, Wharton JA et al (2013) A review of the manufacture, mechanical properties and potential applications of auxetic foams. Phys Status Solidi Basic Res 250:1963-1982
36. Li Y, Zeng C (2016) Room-temperature, near-instantaneous fabrication of auxetic materials with constant Poisson's ratio over large deformation. Adv Mater 28:2822-2826
37. Rossiter J, Takashima K, Scarpa F et al (2014) Shape memory polymer hexachiral auxetic structures with tunable stiffness. Smart Mater Struct 23:045007. https://doi.org/10.1088/0964-1726/23/4/045007
38. Alderson KL, Evans KE (1992) The fabrication of microporous polyethylene having a negative Poisson's ratio. Polymer 33:4435-4438
39. Mohsenizadeh S, Alipour R, Nejad AF et al (2015) Experimental investigation on energy absorption of auxetic foam-filled thin-walled square tubes under quasi-static loading. Procedia Manuf 2:331-336
40. Pichandi S, Rana S, Oliveira DV et al (2014) Development of novel auxetic structures based on braided composites. Mater Des 61:286-295
41. Yang L (2015) Experimental-assisted design development for an octahedral cellular structure using additive manufacturing. Rapid Prototyp J 21:168-176
42. Aslam MU, Darwish SM (2015) Development and analysis of different density auxetic cellular structures. Int J Recent Innov Trends Comput Commun 3:27-32
43. Biasetto L, Boschetti G, Minto R (2017) Robotic additive printing of cylindrical auxetic structures. Adv Ital Mech Sci 18:394-403
44. Wei K, Xiao X, Chen J et al (2021) Additively manufactured bimaterial metamaterial to program a wide range of thermal expansion. Mater Des 198:109343. https://doi.org/10.1016/j.matdes.2020.109343
45. Peng Y, Wei K, Mei M et al (2020) Simultaneously program thermal expansion and Poisson's ratio in three dimensional mechanical metamaterial. Compos Struct 262:113365. https://doi.org/10.1016/j.compstruct.2020.113365
46. Wei K, Peng Y, Qu Z et al (2018) A cellular metastructure incorporating coupled negative thermal expansion and negative Poisson's ratio. Int J Solids Struct 150:255-267
47. Wei K, Xu W, Ling B et al (2021) Multi-functional cylindrical metastructures to simultaneously program both thermal expansion and Poisson's ratio. Extrem Mech Lett 43:101177. https://doi.org/10.1016/j.eml.2021.101177
48. Ding Y, Kovacevic R (2016) Feasibility study on 3-D printing of metallic structural materials with robotized laser-based metal additive manufacturing. JOM 68:1774-1779
49. D'Alessandro L, Zega V, Ardito R et al (2018) 3D auxetic single material periodic structure with ultra-wide tunable bandgap. Sci Rep 8:1-9
50. De Lima CR, Paulino GH (2019) Auxetic structure design using compliant mechanisms:a topology optimization approach with polygonal finite elements. Adv Eng Softw 129:69-80
51. Grimmelsmann N, Meissner H, Ehrmann A (2016) 3D printed auxetic forms on knitted fabrics for adjustable permeability and mechanical properties. IOP Conf Ser Mater Sci Eng 137:012011. https://doi.org/10.1088/1757-899X/137/1/012011
52. Yang L, Harrysson O, Cormier D et al (2015) Additive manufacturing of metal cellular structures:design and fabrication. JOM 67:608-615
53. McCaw JCS, Cuan-Urquizo E (2018) Curved-layered additive manufacturing of non-planar, parametric lattice structures. Mater Des 160:949-963
54. Meena K, Singamneni S (2019) A new auxetic structure with significantly reduced stress concentration effects. Mater Des 173:107779. https://doi.org/10.1016/j.matdes.2019.107779
55. Warner JJ, Gillies AR, Hwang HH et al (2017) 3D-printed biomaterials with regional auxetic properties. J Mech Behav Biomed Mater 76:145-152
56. Yao Y, Wang L, Li J et al (2020) A novel auxetic structure based bone screw design:tensile mechanical characterization and pullout fixation strength evaluation. Mater Des 188:108424. https://doi.org/10.1016/j.matdes.2019.108424
57. Gleadall A, Visscher D, Yang J et al (2018) Review of additive manufactured tissue engineering scaffolds:relationship between geometry and performance. Burn Trauma 6:1-16
58. Wong J, Gong AT, Defnet PA et al (2019) 3D Printing ionogel auxetic frameworks for stretchable sensors. Adv Mater Technol 4:1-6
59. Xue Y, Wang X, Wang W et al (2018) Compressive property of Al-based auxetic lattice structures fabricated by 3-D printing combined with investment casting. Mater Sci Eng A 722:255-262
60. Gao Y, Zhou Z, Hu H (2021) New concept of carbon fiber reinforced composite 3D auxetic lattice structures based on stretching-dominated cells. Mech Adv Mater Struct 152:103661. https://doi.org/10.1016/j.mechmat.2020.103661
61. Pandini S, Inverardi N, Scalet G et al (2020) Shape memory response and hierarchical motion capabilities of 4D printed auxetic structures. Mech Res Commun 103:103463. https://doi.org/10.1016/j.mechrescom.2019.103463
62. Lei M, Hong W, Zhao Z et al (2019) 3D printing of auxetic metamaterials with digitally reprogrammable shape. ACS Appl Mater Interfaces 11:22768-22776
63. Wagner M, Chen T, Shea K (2017) Large shape transforming 4D auxetic structures. 3D Print Addit Manuf 4:133-141
64. Yousuf MH, Abuzaid W, Alkhader M (2020) 4D printed auxetic structures with tunable mechanical properties. Addit Manuf 35:101364. https://doi.org/10.1016/j.addma.2020.101364
65. Wu JT, Zhao Z, Kuang X et al (2018) Reversible shape change structures by grayscale pattern 4D printing. Multifunct Mater 1:015002. https://doi.org/10.1088/2399-7532/aac322
66. Wong KV, Hernandez A (2012) A review of additive manufacturing. Int Sch Res Notices 2012:208760. https://doi.org/10.5402/2012/208760
67. Brischetto S, Ferro CG, Torre R et al (2018) 3D FDM production and mechanical behavior of polymeric sandwich specimens embedding classical and honeycomb cores. Curved Layer Struct 5:80-94
68. Carton MA, Ganter M (2019) Fast and simple printing of graded auxetic structures. In:Proceedings of the 30th annual international solid freeform fabrication symposium-an additive manufacturing conference, 12-14 August 2019, Austin, Texas, US, pp 2270-2279
69. Ingrole A, Hao A, Liang R (2017) Design and modeling of auxetic and hybrid honeycomb structures for in-plane property enhancement. Mater Des 117:72-83
70. Khondoker MAH, Sameoto D (2019) Direct coupling of fixed screw extruders using flexible heated hoses for FDM printing of extremely soft thermoplastic elastomers. Prog Addit Manuf 4:197-209
71. Li T, Chen Y, Hu X et al (2018) Exploiting negative Poisson's ratio to design 3D-printed composites with enhanced mechanical properties. Mater Des 142:247-258
72. Lira C, Scarpa F, Rajasekaran R (2011) A gradient cellular core for aeroengine fan blades based on auxetic configurations. J Intell Mater Syst Struct 22:907-917
73. Smardzewski J, Wojciechowski KW, Poźniak A (2018) Auxetic lattice truss cores fabricated of laywood. BioResources 13:8823-8838
74. Wang XT, Chen YL, Ma L (2018) The manufacture and characterization of composite three-dimensional re-entrant auxetic cellular structures made from carbon fiber reinforced polymer. J Compos Mater 52:3265-3273
75. Wang T, Wang L, Ma Z et al (2018) Elastic analysis of auxetic cellular structure consisting of re-entrant hexagonal cells using a strain-based expansion homogenization method. Mater Des 160:284-293
76. Vyavahare S, Kumar S (2020) Re-entrant auxetic structures fabricated by fused deposition modeling:an experimental study of influence of process parameters under compressive loading. Polym Eng Sci 60:3183-3196
77. Yang C, Vora HD, Chang YB (2016) Evaluation of auxetic polymeric structures for use in protective pads. ASME Int Mech Eng Congr Expo Proc 9:1-7
78. Dziewit P, Platek P, Janiszewski J et al (2017) Mechanical response of additive manufactured regular cellular structures in quasi-static loading conditions-Part I experimental investigations. In:Proceedings of the 7th international conference on mechanics and materials in design. pp 1061-1074.
79. Ling B, Wei K, Wang Z et al (2020) Experimentally program large magnitude of Poisson's ratio in additively manufactured mechanical metamaterials. Int J Mech Sci 173:105466. https://doi.org/10.1016/j.ijmecsci.2020.105466
80. Ling B, Wei K, Qu Z et al (2021) Design and analysis for large magnitudes of programmable Poisson's ratio in a series of lightweight cylindrical metastructures. Int J Mech Sci 195:106220. https://doi.org/10.1016/j.ijmecsci.2020.106220
81. Bodaghi M, Serjouei A, Zolfagharian A et al (2020) Reversible energy absorbing meta-sandwiches by FDM 4D printing. Int J Mech Sci 173:105451. https://doi.org/10.1016/j.ijmecsci.2020.105451
82. Bodaghi M, Noroozi R, Zolfagharian A et al (2019) 4D printing self-morphing structures. Materials 12:1353. https://doi.org/10.3390/ma12081353
83. Lvov VA, Senatov FS, Stepashkin AA et al (2020) Low-cycle fatigue behavior of 3D-printed metallic auxetic structure. Mater Today Proc 33:1979-1983
84. Alomarah A, Zhang J, Ruan D et al (2017) Mechanical properties of the 2D re-entrant honeycomb made via direct metal printing. IOP Conf Ser Mater Sci Eng 229:012038. https://doi.org/10.1088/1757-899X/229/1/012038
85. Dong Z, Li Y, Zhao T et al (2019) Experimental and numerical studies on the compressive mechanical properties of the metallic auxetic reentrant honeycomb. Mater Des 182:108036. https://doi.org/10.1016/j.matdes.2019.108036
86. Khan SZ, Masood SH, Cottam R (2015) Mechanical properties in tensile loading of H13 re-entrant honeycomb auxetic structure manufactured by direct metal deposition. In:Proceedings of the 2nd international conference on mechatronics and mechanical engineering. Singapore, pp 23-25
87. Platek P, Sienkiewicz J, Janiszewski J et al (2020) Investigations on mechanical properties of lattice structures with different values of relative density made from 316L by selective laser melting (SLM). Materials 13:2204. https://doi.org/10.3390/ma13092204
88. Arjunan A, Singh M, Baroutaji A et al (2020) Additively manufactured AlSi10Mg inherently stable thin and thick-walled lattice with negative Poisson's ratio. Compos Struct 247:112469. https://doi.org/10.1016/j.compstruct.2020.112469
89. Lei H, Li C, Meng J et al (2019) Evaluation of compressive properties of SLM-fabricated multi-layer lattice structures by experimental test and l-CT-based finite element analysis. Mater Des 169:107685. https://doi.org/10.1016/j.matdes.2019.107685
90. Xiong J, Gu D, Chen H et al (2017) Structural optimization of re-entrant negative Poisson's ratio structure fabricated by selective laser melting. Mater Des 120:307-316
91. Li S, Hassanin H, Attallah MM et al (2016) The development of TiNi-based negative Poisson's ratio structure using selective laser melting. Acta Mater 105:75-83
92. Kolken HMA, Janbaz S, Leeflang SMA et al (2018) Rationally designed meta-implants:a combination of auxetic and conventional meta-biomaterials. Mater Horizons 5:28-35
93. Maconachie T, Leary M, Lozanovski B et al (2019) SLM lattice structures:properties, performance, applications and challenges. Mater Des 183:108137. https://doi.org/10.1016/j.matdes.2019.108137
94. Al-Saedi DSJ, Masood SH, Faizan-Ur-Rab M et al (2018) Mechanical properties and energy absorption capability of functionally graded F2BCC lattice fabricated by SLM. Mater Des 144:32-44
95. Geng L, Wu W, Sun L et al (2019) Damage characterizations and simulation of selective laser melting fabricated 3D re-entrant lattices based on in-situ CT testing and geometric reconstruction. Int J Mech Sci 157/158:231-242
96. Sienkiewicz J, Płatek P, Jiang F et al (2020) Investigations on the mechanical response of gradient lattice structures manufactured via SLM. Metals 10:213. https://doi.org/10.3390/met10020213
97. Fíla T, Zlámal P, Jiroušek O et al (2017) Impact testing of polymer-filled auxetics using split Hopkinson pressure bar. Adv Eng Mater 19:1-13
98. Ma Y, Scarpa F, Zhang D et al (2013) A nonlinear auxetic structural vibration damper with metal rubber particles. Smart Mater Struct 22:084012. https://doi.org/10.1088/0964-1726/22/8/084012
99. Smardzewski J, Kłos R, Fabisiak B (2013) Design of small auxetic springs for furniture. Mater Des 51:723-728
100. Theodoras T, Angelos C (2013) Choreographic architecture:inscribing instructions in an auxetic based material system. Simul Ser 45:102-109
101. Yang J, Sun Y, Lueth TC (2019) Construction of a production line for auxetic structures using novel modeling method. In:IEEE international conference on robotics and biomimetics, 6-8 December 2019, Dali, China, pp 1627-1632
102. Yuan S, Chua CK, Zhou K (2019) 3D-printed mechanical metamaterials with high energy absorption. Adv Mater Technol 4:1-9
103. Yuan S, Shen F, Bai J et al (2017) 3D soft auxetic lattice structures fabricated by selective laser sintering:TPU powder evaluation and process optimization. Mater Des 120:317-327
104. Tee KF, Spadoni A, Scarpa F et al (2010) Wave propagation in auxetic tetrachiral honeycombs. J Vib Acoust Trans 132:0310071. https://doi.org/10.1115/1.4000785
105. Wu W, Geng L, Niu Y et al (2018) Compression twist deformation of novel tetrachiral architected cylindrical tube inspired by towel gourd tendrils. Extrem Mech Lett 20:104-111
106. Yuan S (2017) Development and optimization of selective laser sintered-polymeric composites and structures for functional applications. Dissertation. Nanyang Technological University, Singapore
107. Eldesouky I, Harrysson O, West H (2017) Electron beam melted scaffolds for orthopedic applications. Addit Manuf 17:169-175
108. Gong X, Anderson T, Chou K (2014) Review on powder-based electron beam additive manufacturing technology. Manuf Rev 1:2-13
109. Horn TJ, Harrysson OLA, Marcellin-Little DJ et al (2014) Flexural properties of Ti6Al4V rhombic dodecahedron open cellular structures fabricated with electron beam melting. Addit Manuf 1:2-11
110. Yang L, Harrysson OLA, West H et al (2011) Design and characterization of orthotropic re-entrant auxetic structures made via EBM using Ti6Al4V and pure copper. In:22nd annual international solid freeform fabrication symposium, 8-10 August 2011, University of Texas, Austin, TX, USA, pp 464-474
111. Yang L, Cormier D, West H et al (2012) Non-stochastic Ti-6Al-4V foam structures with negative Poisson's ratio. Mater Sci Eng A 558:579-585
112. Suard M, Lhuissier P, Dendievel R et al (2014) Towards stiffness prediction of cellular structures made by electron beam melting (EBM). Powder Metall 57:190-195
113. Yang L, Harrysson O, West H et al (2013) Modeling of uniaxial compression in a 3D periodic re-entrant lattice structure. J Mater Sci 48:1413-1422
114. Mitschke H, Schwerdtfeger J, Schury F et al (2011) Finding auxetic frameworks in periodic tessellations. Adv Mater 23:2669-2674
115. Novak N, Krstulović-Opara L, Ren Z et al (2020) Compression and shear behaviour of graded chiral auxetic structures. Mech Mater 148:103524. https://doi.org/10.1016/j.mechmat.2020.103524
116. Novak N, Vesenjak M, Ren Z (2017) Computational simulation and optimization of functionally graded auxetic structures made from inverted tetrapods. Phys Status Solidi Basic Res 254:1-7
117. Novak N, Krstulović-Opara L, Ren Z et al (2020) Mechanical properties of hybrid metamaterial with auxetic chiral cellular structure and silicon filler. Compos Struct 234:111718. https://doi.org/10.1016/j.compstruct.2019.111718
118. Schwerdtfeger J, Heinl P, Singer RF et al (2010) Auxetic cellular structures through selective electron-beam melting. Phys Status Solidi Basic Res 247:269-272
119. Schwerdtfeger J, Schury F, Stingl M et al (2012) Mechanical characterisation of a periodic auxetic structure produced by SEBM. Phys Status Solidi Basic Res 249:1347-1352
120. Schwerdtfeger J, Wein F, Leugering G et al (2011) Design of auxetic structures via mathematical optimization. Adv Mater 23:2650-2654
121. Alomarah A, Ruan D, Masood S et al (2018) An investigation of in-plane tensile properties of re-entrant chiral auxetic structure. Int J Adv Manuf Technol 96:2013-2029
122. Yu X, Zhou J, Liang H et al (2018) Mechanical metamaterials associated with stiffness, rigidity and compressibility:a brief review. Prog Mater Sci 94:114-173
123. Wang F (2018) Systematic design of 3D auxetic lattice materials with programmable Poisson's ratio for finite strains. J Mech Phys Solids 114:303-318
124. Berwind MF, Kamas A, Eberl C (2018) A hierarchical programmable mechanical metamaterial unit cell showing metastable shape memory. Adv Eng Mater 20:1-6
125. Gao Q, Liao WH, Wang L (2020) An analytical model of cylindrical double-arrowed honeycomb with negative Poisson's ratio. Int J Mech Sci 173:105400. https://doi.org/10.1016/j.ijmecsci.2019.105400
126. Gao S, Liu W, Zhang L (2020) A new polymer-based mechanical metamaterial with tailorable large negative Poisson's ratios. Polymers 12:1-15
127. Lantada AD, De Blas RA, Schwentenwein M et al (2016) Lithography-based ceramic manufacture (LCM) of auxetic structures:present capabilities and challenges. Smart Mater Struct 25:054015. https://doi.org/10.1088/0964-1726/25/5/054015
128. Lu Y, Chang CJ, Lin PT et al (2006) Negative-Poisson's-ratio (NPR) microstructural material by soft-joint mechanism. NSTI Nanotech 3:397-400
129. Munib Z, Ali MN, Ansari U et al (2015) Auxetic polymeric bone stent for tubular fractures:design, fabrication and structural analysis. Polym-Plast Technol Eng 54:1667-1678
130. Ruan XL, Li JJ, Song XK et al (2018) Mechanical design of antichiral-reentrant hybrid intravascular stent. Int J Appl Mech 10:1850105. https://doi.org/10.1142/S1758825118501053
131. Proffit M, Kennedy J (2020) Dynamic response of auxetic structures. Vibroeng Proc 31:1-6
132. Shaat M, Wagih A (2020) Hinged-3D metamaterials with giant and strain-independent Poisson's ratios. Sci Rep Nat Res 10:1-10
133. Gupta V, Adhikari S, Bhattacharya B (2020) Locally resonant mechanical dome metastructures for bandgap estimation. Proc Active Passive Smart Struct Integr Syst XIV:1137626. https://doi.org/10.1117/12.2558931
134. Wang S, Wang J, Xu Y et al (2020) Compressive behavior and energy absorption of polymeric lattice structures made by additive manufacturing. Front Mech Eng 15:319-327
135. Yu L, Tan H, Zhou Z (2020) Mechanical properties of 3D auxetic closed-cell cellular structures. Int J Mech Sci 177:105596. https://doi.org/10.1016/j.ijmecsci.2020.105596
136. Hengsbach S, Lantada AD (2014) Direct laser writing of auxetic structures:present capabilities and challenges. Smart Mater Struct 23:085033. https://doi.org/10.1088/0964-1726/23/8/085033
137. Lee KS, Kim RH, Prabhakaran P et al (2007) Two-photon stereolithography. J Nonlinear Opt Phys Mater 16:59-73
138. Guney MG, Fedder GK (2016) Estimation of line dimensions in 3D direct laser writing lithography. J Micromech Microeng 26:105011. https://doi.org/10.1088/0960-1317/26/10/105011
139. Jayne RK, Stark TJ, Reeves JB et al (2018) Dynamic actuation of soft 3D micromechanical structures using micro-electromechanical systems (MEMS). Adv Mater Technol 3:1-6
140. Jonušauskas L, Varapnickas S, Rimšelis G et al (2017) Plasmonically enhanced 3D laser lithography for high-throughput nanoprecision fabrication. Proc Laser-Based Micro-Nanoprocess XI:10092. https://doi.org/10.1117/12.2249595
141. Lin Z, Novelino LS, Wei H et al (2020) Folding at the microscale:enabling multifunctional 3D origami-architected metamaterials. Small 16:1-9
142. Hou S, Li T, Jia Z et al (2018) Mechanical properties of sandwich composites with 3D-printed auxetic and non-auxetic lattice cores under low velocity impact. Mater Des 160:1305-1321
143. Khare E, Temple S, Tomov I et al (2018) Low fatigue dynamic auxetic lattices with 3D printable, multistable, and tuneable unit cells. Front Mater 5:1-11
144. Xue Y, Han F (2019) Compressive mechanical property of a new three-dimensional aluminum based double-V lattice structure. Mater Lett 254:99-102
145. Yang H, Wang B, Ma L (2019) Mechanical properties of 3D double-U auxetic structures. Int J Solids Struct 180/181:13-29
146. Auricchio F, Bacigalupo A, Gambarotta L et al (2019) A novel layered topology of auxetic materials based on the tetrachiral honeycomb microstructure. Mater Des 179:107883. https://doi.org/10.1016/j.matdes.2019.107883
147. Carneiro VH, Puga H (2018) Axisymmetric auxetics. Compos Struct 204:438-444
148. Chen Z, Wang Z, Zhou S et al (2018) Novel negative poisson's ratio lattice structures with enhanced stiffness and energy absorption capacity. Materials 11:1095. https://doi.org/10.3390/ma11071095
149. Fu MH, Bin ZB, Li WH (2017) A novel chiral three-dimensional material with negative Poisson's ratio and the equivalent elastic parameters. Compos Struct 176:442-448
150. Hou Y, Neville R, Scarpa F et al (2014) Graded conventionalauxetic Kirigami sandwich structures:flatwise compression and edgewise loading. Compos Part B Eng 59:33-42
151. Jiang Y, Li Y (2017) 3D printed chiral cellular solids with amplified auxetic effects due to elevated internal rotation. Adv Eng Mater 19:1-8
152. Li X, Wang Q, Yang Z et al (2019) Novel auxetic structures with enhanced mechanical properties. Extrem Mech Lett 27:59-65
153. Lu ZX, Li X, Yang ZY et al (2016) Novel structure with negative Poisson's ratio and enhanced Young's modulus. Compos Struct 138:243-252
154. Lu Z, Wang Q, Li X, Yang Z (2017) Elastic properties of two novel auxetic 3D cellular structures. Int J Solids Struct 124:46-56
155. Meena K, Calius EP, Singamneni S (2019) An enhanced squaregrid structure for additive manufacturing and improved auxetic responses. Int J Mech Mater Des 15:413-426
156. Michalski J, Strek T (2019) Fatigue life of auxetic re-entrant honeycomb structure. In Gapiński B, Szostak M, Ivanov V (eds) Advances in Manufacturing II. Lecture Notes in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-16943-5_5
157. Naboni R, Sartori S, Mirante L (2018) Adaptive-curvature structures with auxetic materials. Adv Mater Res 1149:53-63
158. Wang H, Zhang Y, Lin W et al (2020) A novel two-dimensional mechanical metamaterial with negative Poisson's ratio. Comput Mater Sci 171:109232. https://doi.org/10.1016/j.commatsci.2019.109232
159. Koudelka P, Jiroušek O, Fíla T et al (2016) Compressive properties of auxetic structures produced with direct 3D printing. Mater Tehnol 50:311-317
160. Lee W, Jeong Y, Yoo J et al (2019) Effect of auxetic structures on crash behavior of cylindrical tube. Compos Struct 208:836-846
161. Novak N, Borovinšek M, Vesenjak M et al (2019) Crushing behavior of graded auxetic structures built from inverted tetrapods under impact. Phys Status Solidi Basic Res 256:1-7
162. Novak N, Vesenjak M, Tanaka S et al (2020) Compressive behaviour of chiral auxetic cellular structures at different strain rates. Int J Impact Eng 141:103566. https://doi.org/10.1016/j.ijimpeng.2020.103566
163. Yang L, Harrysson O, West H et al (2012) Compressive properties of Ti-6Al-4V auxetic mesh structures made by electron beam melting. Acta Mater 60:3370-3379
164. Wang Q, Yang Z, Lu Z et al (2020) Mechanical responses of 3D cross-chiral auxetic materials under uniaxial compression. Mater Des 186:108226. https://doi.org/10.1016/j.matdes.2019.108226
165. Novak N, Hokamoto K, Vesenjak M et al (2018) Mechanical behaviour of auxetic cellular structures built from inverted tetrapods at high strain rates. Int J Impact Eng 122:83-90
166. Zhao Z, Yuan C, Lei M et al (2019) Three-dimensionally printed mechanical metamaterials with thermally tunable auxetic behavior. Phys Rev Appl 11:044074. https://doi.org/10.1103/PhysRevApplied.11.044074
167. Lozanovski B, Leary M, Tran P et al (2019) Computational modeling of strut defects in SLM manufactured lattice structures. Mater Des 171:107671. https://doi.org/10.1016/j.matdes.2019.107671
168. Hassanin H, Abena A, Elsayed MA et al (2020) 4D printing of NiTi auxetic structure with improved ballistic performance. Micromachines 11:1-19
169. Imbalzano G, Linforth S, Ngo TD et al (2018) Blast resistance of auxetic and honeycomb sandwich panels:comparisons and parametric designs. Compos Struct 183:242-261
170. Imbalzano G, Tran P, Ngo TD et al (2016) A numerical study of auxetic composite panels under blast loadings. Compos Struct 135:339-352
171. Liu J, Chen W, Hao H et al (2021) In-plane crushing behaviors of hexagonal honeycombs with different Poisson's ratio induced by topological diversity. Thin-Walled Struct 159:107223. https://doi.org/10.1016/j.tws.2020.107223
172. Shen J, Zhou S, Huang X et al (2015) Inertia effect on bucklinginduced auxetic metamaterials. Int J Prot Struct 6:311-322
173. Imbalzano G, Tran P, Lee PVS et al (2016) Influences of material and geometry in the performance of auxetic composite structure under blast Loading. Appl Mech Mater 846:476-481
174. Guo Y, Zhang J, Chen L et al (2020) Deformation behaviors and energy absorption of auxetic lattice cylindrical structures under axial crushing load. Aerosp Sci Technol 98:105662. https://doi.org/10.1016/j.ast.2019.105662
175. Najafi M, Ahmadi H, Liaghat GH (2020) Experimental and numerical investigation of energy absorption in auxetic structures under quasi-static loading. Modares Mech Eng 20:415-424
176. Shepherd T, Winwood K, Venkatraman P et al (2020) Validation of a finite element modeling process for auxetic structures under impact. Phys Status Solidi Basic Res 257:1900197. https://doi.org/10.1002/pssb.201900197
177. Lim TC, Alderson A, Alderson KL (2014) Experimental studies on the impact properties of auxetic materials. Phys Status Solidi Basic Res 251:307-313
178. Sarbinowski F, Labudzki R, Patalas A (2018) A numerical and experimental study of the energy absorption capacity of auxetic structures. In:Proceedings of the 6th international conference integrity-reliability-failure, 22-26 July 2018, Lisbon, Portugal, pp 399-402
179. Shokri RM, Hatami H, Alipouri R et al (2019) Determination of energy absorption in different cellular auxetic structures. Mech Ind 20:15-20
180. Beharic A, Rodriguez Egui R, Yang L (2018) Drop-weight impact characteristics of additively manufactured sandwich structures with different cellular designs. Mater Des 145:122-134
181. Ulbin M, Borovinšek M, Vesenjak M et al (2020) Computational fatigue analysis of auxetic cellular structures made of SLM AlSi10mg alloy. Metals 10(7):945. https://doi.org/10.3390/met10070945
182. Filho SLMR, Silva TAA, Brandão LC et al (2014) Failure analysis and Taguchi design of auxetic recycled rubber structures. Phys Status Solidi Basic Res 251:338-348
183. Filho SLMR, Silva TAA, Vieira LMG et al (2014) Geometric effects of sustainable auxetic structures integrating the particle swarm optimization and finite element method. Mater Res 17:747-757
184. Lvov VA, Senatov FS, Korsunsky AM et al (2020) Design and mechanical properties of 3D-printed auxetic honeycomb structure. Mater Today Commun 24:101173. https://doi.org/10.1016/j.mtcomm.2020.101173
185. Zhang J, Lu G, Wang Z et al (2018) Large deformation of an auxetic structure in tension:experiments and finite element analysis. Compos Struct 184:92-101
186. Geng LC, Ruan XL, Wu WW et al (2019) Mechanical properties of selective laser sintering (SLS) additive manufactured chiral auxetic cylindrical stent. Exp Mech 59:913-925
187. Gu L, Xu Q, Du Z (2020) Analysis of tensile behaviour of hyperelastic auxetic cellular materials with re-entrant hexagonal cells. J Text Inst 112:173-186
188. Dogan E, Bhusal A, Cecen B et al (2020) 3D printing metamaterials towards tissue engineering. Appl Mater Today 20:100752. https://doi.org/10.1016/j.apmt.2020.100752
189. Mardling P, Alderson A, Jordan-Mahy N et al (2020) The use of auxetic materials in tissue engineering. Biomater Sci 8:2074-2083
190. Abdelaal O, Darwish S (2012) Analysis, fabrication and a biomedical application of auxetic cellular structures. Int J Eng Innov Technol 2:218-223
191. Ali MN, Busfield JJC, Rehman IU (2014) Auxetic oesophageal stents:structure and mechanical properties. J Mater Sci Mater Med 25:527-553
192. Mir M, Ali MN, Sami J et al (2014) Review of mechanics and applications of auxetic structures. Adv Mater Sci Eng 2014:753496. https://doi.org/10.1155/2014/753496
193. Darwish SMH, Aslam MU (2014) Auxetic cellular structures for custom made orthopedic implants using additive manufacturing. Int J Eng Adv Technol 4:10-15
194. Mir M, Ali MN, Sami J et al (2014) Review of mechanics and applications of auxetic structures. Adv Mater Sci Eng 2014:1-17
195. Flamourakis G, Spanos I, Vangelatos Z et al (2020) Laser-made 3D auxetic metamaterial scaffolds for tissue engineering applications. Macromol Mater Eng 305:1-9
196. Lantada AD, Muslija A, Garcia-Ruiz JP (2015) Auxetic tissue engineering scaffolds with nanometric features and resonances in the megahertz range. Smart Mater Struct 24:055013. https://doi.org/10.1088/0964-1726/24/5/055013
197. Raminhos JS, Borges JP, Velhinho A (2019) Development of polymeric anepectic meshes:auxetic metamaterials with negative thermal expansion. Smart Mater Struct 28:045010. https://doi.org/10.1088/1361-665X/ab034b
198. Scarpa F (2008) Auxetic materials for bioprostheses. IEEE Signal Process Mag 25:10180273. https://doi.org/10.1109/MSP.2008.926663
199. Mohanraj H, Filho RSLM, Panzera TH et al (2016) Hybrid auxetic foam and perforated plate composites for human body support. Phys Status Solidi Basic Res 253:1378-1386. https://doi.org/10.1002/pssb.20160010
200. Arjunan A, Zahid S, Baroutaji A et al (2021) 3D printed auxetic nasopharyngeal swabs for COVID-19 sample collection. J Mech Behav Biomed Mater 114:104175. https://doi.org/10.1016/j.jmbbm.2020.104175
201. Duncan O, Shepherd T, Moroney C et al (2018) Review of auxetic materials for sports applications:expanding options in comfort and protection. Appl Sci 8(6):941. https://doi.org/10.3390/app8060941
202. Duncan O (2019) Auxetic foams for sports applications. Sheffield Hallam University.
203. Sanami M, Ravirala N, Alderson K et al (2014) Auxetic materials for sports applications. Procedia Eng 72:453-458
204. Hadjigeorgiou EP, Stavroulakis GE (2004) The use of auxetic materials in smart structures. Comput Methods Sci Technol 10:147-160
205. Han SC, Kang DS, Kang K (2019) Two nature-mimicking auxetic materials with potential for high energy absorption. Mater Today 26:30-39
206. Cheng Q, Liu Y, Lyu J et al (2020) 3D printing-directed auxetic Kevlar aerogel architectures with multiple functionalization options. J Mater Chem A 8:14243-14253
207. Shanian A, Jette FX, Salehii M et al (2019) Application of multifunctional mechanical metamaterials. Adv Eng Mater 21:1-6
208. Underhill RS (2014) Defence applications of auxetic materials. DSIAC J 1:7-13
209. Ngo T, Mohotti D, Remenikov A (2015) Use of polyurea-auxetic composite system for protecting structures from close-in detonations. In:Proceedings of the international conference of protective structures, pp 3-6
210. Mohotti D, Ali M, Ngo T et al (2014) Strain rate dependent constitutive model for predicting the material behaviour of polyurea under high strain rate tensile loading. Mater Des 53:830-837
211. Mohotti D, Ngo T, Mendis P et al (2013) Polyurea coated composite aluminium plates subjected to high velocity projectile impact. Mater Des 52:1-16
212. Mohotti D, Ngo T, Raman SN et al (2014) Plastic deformation of polyurea coated composite aluminium plates subjected to low velocity impact. Mater Des 56:696-713
213. Rana S, Magalhães R, Fangueiro R (2017) Advanced auxetic fibrous structures and composites for industrial applications. In:Proceedings of the 7th international conference on mechanics and materials in design, 11-15 June 2017, Portugal
214. Seepersad CC, Dempsey BM, Allen JK et al (2004) Design of multifunctional honeycomb materials. AIAA J 42:1025-1033
215. Lim TC (2015) Thermal stresses in auxetic plates and shells. Mech Adv Mater Struct 22:205-212
216. Sun Y, Pugno NM (2013) In plane stiffness of multifunctional hierarchical honeycombs with negative Poisson's ratio substructures. Compos Struct 106:681-689
217. Yang L, Harrysson O, Cormier D et al (2013) Design of auxetic sandwich panels for structural applications. In:Proceedings of the 24th international SFF symposium, University of Texas at Austin (freeform), pp 929-938
218. Novak N, Dobnik Dubrovski P, Borovinšek M et al (2020) Deformation behaviour of advanced textile composites with auxetic structure. Compos Struct 252:1-9
219. Naboni R, Mirante L (2015) Metamaterial computation and fabrication of auxetic patterns for architecture 2:129-136
220. Elipe MDÁ, Díaz JA (2018) Development of reentrant hexatruss structures to apply to architecture. Rev La Constr 17:209-214
221. Kasal A, Kuskun T, Smardzewski J (2020) Experimental and numerical study on withdrawal strength of different types of auxetic dowels for furniture joints. Materials 13(19):4252. https://doi.org/10.3390/ma13194252
222. Iyer S, Alkhader M, Venkatesh TA (2015) Electromechanical behavior of auxetic piezoelectric cellular solids. Scr Mater 99:65-68
223. Jiang Y, Li Y (2018) 3D printed auxetic mechanical metamaterial with chiral cells and re-entrant cores. Sci Rep 8:1-11
224. Le DH, Xu Y, Tentzeris MM et al (2020) Transformation from 2D meta-pixel to 3D meta-pixel using auxetic kirigami for programmable multifunctional electromagnetic response. Extrem Mech Lett 36:100670. https://doi.org/10.1016/j.eml.2020.100670
225. Wang Y, Yu Y, Li Z et al (2019) A novel electro-active bushing based on dielectric elastomer and circular double-V auxetic structure. AIP Adv 9:125109. https://doi.org/10.1063/1.5100017
226. Shakor P, Nejadi S, Paul G et al (2018) Review of emerging additive manufacturing technologies in 3D printing of cementitious materials in the construction industry. Front Built Environ 4:85. https://doi.org/10.3389/fbuil.2018.00085
227. Gibbons G (2010) 3D printing of cement composites. Adv Appl Ceram 109:287-290
228. De JJPJ, De Erik B (2013) Innovation lessons from 3-D printing. IEEE Eng Manage Rev 42:86-94
229. Chen L, He Y, Yang Y et al (2017) The research status and development trend of additive manufacturing technology. Int J Adv Manuf Technol 89:3651-3660
230. Sreenivasan R, Bourell DL (2009) Sustainability study in selective laser sintering-an energy perspective. In:Proceedings of the 20th annual solid freeform fabrication symposium, University of Texas at Austin (freeform), pp 257-265
231. Parupelli SK, Desai S (2019) A comprehensive review of additive manufacturing (3D printing):processes, applications and future potential. Am J Appl Sci 16:244-272
232. Zareiyan B, Khoshnevis B (2017) Automation in construction interlayer adhesion and strength of structures in contour crafting-effects of aggregate size, extrusion rate, and layer thickness. Autom Constr 81:112-121
233. Bourell DL (2016) Perspectives on additive manufacturing. Annu Rev Mater Res 46:1-18
234. Tran J (2015) The law and 3D printing. UIC J Inf Technol Priv Law. https://doi.org/10.2139/ssrn.2581775

[1]	Wei-Jun Zhu, Guo-Qiang Tian, Yang Lu, Kai Miao, Di-Chen Li. Leaching improvement of ceramic cores for hollow turbine blades based on additive manufacturing [J]. Advances in Manufacturing, 2019, 7(4): 353-363.
[2]	Saroj Kumar Padhi, S. S. Mahapatra, Rosalin Padhi, Harish Chandra Das. Performance analysis of a thick copper-electroplated FDM ABS plastic rapid tool EDM electrode [J]. Advances in Manufacturing, 2018, 6(4): 442-456.
[3]	Yu Dong, Jamie Milentis, Alokesh Pramanik. Additive manufacturing of mechanical testing samples based on virgin poly (lactic acid) (PLA) and PLA/wood fibre composites [J]. Advances in Manufacturing, 2018, 6(1): 71-82.