A bibliometric overview of research on auxetic structures: Trends and patterns

Abstract

Auxetic structures have very interesting features compared to traditional structures and can also be used in the automotive industry thanks to their lightness and strength have attracted the attention of researchers in recent decades. The current study summarizes the contributions made by researchers from all over the world between 2002 and 2022 in the field of auxetic structures. Using the Scopus database, a bibliometric analysis was used to examine the scientific studies in the area. The analysis covered different characteristics of publications, including publication type, main study fields, journals, citations, authorship patterns, affiliations, and keywords. The bibliometric indicators showed that there were 2599 publications published by 5161 authors in 85 countries from 2002 to 2022. The results also showed that the publications produced came primarily from China, the United States, and the United Kingdom, and the publications produced from these countries accounted for 42.99% of all publications. In particular, the most productive author, country, institution, and journal are Grima JN, China, Ministry of Education China, and Composite Structures, respectively. This study has great value since it demonstrates how to research topics change from year to year and can predict future development trends.

Keywords

• Auxetic structures
• Bibexcel
• Bibliometric analysis
• Scopus
• VOSviewer

References

1. [1] Evans, KE. Auxetic polymers: a new range of materials. En-deavour. 1991;15:170–174. https://doi.org/10.1016/0160-9327(91)90123-S
2. [2] Brighenti R. Smart behaviour of layered plates through the use of auxetic materials. Thin-Walled Structures. 2014;84: 432–442. https://doi.org/10.1016/j.tws.2014.07.017
3. [3] Guo MF, Yang H, Ma L. Design and analysis of 2D double-U auxetic honeycombs. Thin-Walled Structures. 2020;155: 106915. https://doi.org/10.1016/j.tws.2020.106915
4. [4] Simpson J, Kazancı Z. Crushing investigation of crash boxes filled with honeycomb and re-entrant (auxetic) lattices. Thin-Walled Structures. 2020;150:106676. https://doi.org/10.1016/j.tws.2020.106676
5. [5] Wei L, Zhao X, Yu Q, Zhu G. A novel star auxetic honeycomb with enhanced in-plane crushing strength. Thin-Walled Struc-tures.2020;149:106623. https://doi.org/10.1016/j.tws.2020.106623
6. [6] Mohsenizadeh S, Alipour R, Shokri Rad M, Farokhi Nejad A, Ahmad Z. Crashworthiness assessment of auxetic foam-filled tube under quasi-static axial loading. Materials & Design. 2015;88:258–268. https://doi.org/10.1016/j.matdes.2015.08.152
7. [7] Tunay M, Cetin E. Energy absorption of 2D auxetic structures fabricated by fused deposition modeling. Journal of the Brazili-an Society of Mechanical Sciences and Engineering. 2023;45:500. https://doi.org/10.1007/s40430-023-04423-3
8. [8] Mazhnik E, Oganov AR. A model of hardness and fracture toughness of solids. Journal of Applied Physics. 2019;126:125109. https://doi.org/10.1063/1.5113622

9. [9] Donoghue JP, Alderson KL, Evans KE. The fracture toughness of composite laminates with a negative Poisson’s ratio. Physica Status Solidi (b). 2009;246:2011–2017. https://doi.org/10.1002/pssb.200982031
10. [10] Morin‐Martinez AA, Arcudia J, Zarate X, Cifuentes‐Quintal ME, Merino G. The quest for a bidirectional auxetic, elastic, and enhanced fracture toughness material: Revisiting the me-chanical properties of the the BeH2 monolayers. Journal of Computational Chemistry. 2022;44(3):248-255. https://doi.org/10.1002/jcc.26875
11. [11] Novak N, Krstulović-Opara L, Z. Ren Z, Vesenjak M. Com-pression and shear behaviour of graded chiral auxetic structures. Mechanics of Materials. 2020;148:103524. https://doi.org/10.1016/j.mechmat.2020.103524
12. [12] Choi JB, Lakes RS. Non-linear properties of polymer cellular materials with a negative Poisson’s ratio. Journal of Materials Science. 1992;27:4678–4684. https://doi.org/10.1007/BF01166005
13. [13] Henyš, P, Vomáčko V, Ackermann M, Sobotka J, Solfronk P, Šafka J, Čapek L. Normal and shear behaviours of the auxetic metamaterials: homogenisation and experimental approaches. Meccanica. 2019;54:831–839. https://doi.org/10.1007/s11012-019-01000-8
14. [14] Coenen VL, Alderson KL. Mechanisms of failure in the static indentation resistance of auxetic carbon fibre laminates. Physi-ca Status Solidi (b). 2011;248:66–72. https://doi.org/10.1002/pssb.201083977
15. [15] Argatov II, Guinovart-Díaz R, Sabina FJ. On local indentation and impact compliance of isotropic auxetic materials from the continuum mechanics viewpoint. International Journal of Engi-neering Science. 2012;54:42–57. https://doi.org/10.1016/j.ijengsci.2012.01.010
16. [16] Lakes RS, Elms K. Indentability of Conventional and Nega-tive Poisson’s Ratio Foams. Journal of Composite Materials. 1993;27:1193–1202. https://doi.org/10.1177/002199839302701203
17. [17] Chekkal I, Bianchi M, Remillat C, Bécot F-X, Jaouen L, Scar-pa F. Vibro-Acoustic Properties of Auxetic Open Cell Foam: Model and Experimental Results. Acta Acustica united with Acustica. 2010;96:266–274. https://doi.org/10.3813/AAA.918276
18. [18] Eghbali P, Younesian D, Farhangdoust S. Enhancement of the low-frequency acoustic energy harvesting with auxetic resona-tors. Applied Energy. 2020;270:115217. https://doi.org/10.1016/j.apenergy.2020.115217
19. [19] Ye HF, Tao M, Zhang WZ. Modeling and Sound Insulation Performance Analysis of Two Honeycomb-hole Coatings. Journal of Physics: Conference Series. 2018;1016:012001. https://doi.org/10.1088/1742-6596/1016/1/012001
20. [20] Xie YM, Yang X, Shen J, Yan X, Ghaedizadeh A, Rong J, Huang X, Zhou S. Designing orthotropic materials for negative or zero compressibility. International Journal of Solids and Structures. 2014;51:4038–4051. https://doi.org/10.1016/j.ijsolstr.2014.07.024
21. [21] Grima JN, Caruana-Gauci R, Wojciechowski KW, Evans KE. Smart hexagonal truss systems exhibiting negative compressibil-ity through constrained angle stretching. Smart Materials and Structures. 2013;22:084015. https://doi.org/10.1088/0964-1726/22/8/084015
22. [22] Maruszewski TS, Wojciechowski KW. Anomalous defor-mation of constrained auxetic square. Review Advanced Mate-rial Science. 2010;23:169–174.
23. [23] Amin F, Ali MN, Ansari U, Mir M, Minhas MA, Shahid W. Auxetic Coronary Stent Endoprosthesis: Fabrication and Struc-tural Analysis. Journal of Applied Biomaterials & Functional Materials. 2015;13:127–135. https://doi.org/10.5301/jabfm.50002
24. [24] Akgun M, Eren R, Suvari F, Yurdakul T. Investigation of the effect of pique weave on auxetic performance and related fab-ric properties. The Journal of The Textile Insti-tute.2021;113(11):2369-2380. https://doi.org/10.1080/00405000.2021.1983978
25. [25] Critchley R, Corni I, Wharton JAA, Walsh FCC, Wood RJK, Stokes KR. A review of the manufacture, mechanical properties and potential applications of auxetic foams. Physica Status Sol-idi (b). 2013;250:1963–1982. https://doi.org/10.1002/pssb.201248550
26. [26] Ren X, Shen J, Tran P, Ngo TD, Xie YM. Auxetic nail: Design and experimental study. Composite Structures. 2018;184:288–298. https://doi.org/10.1016/j.compstruct.2017.10.013
27. [27] Zhang XY, Wang XY, Ren X, Xie YM, Wu Y, Zhou YY, Wang SL, Han CZ. A novel type of tubular structure with auxe-ticity both in radial direction and wall thickness. Thin-Walled Structures. 2021;163:107758. https://doi.org/10.1016/j.tws.2021.107758
28. [28] Luo C, Han CZ, Zhang XY, Zhang XG, Ren X, Xie YM. De-sign, manufacturing and applications of auxetic tubular struc-tures: A review. Thin-Walled Structures. 2021;163:107682. https://doi.org/10.1016/j.tws.2021.107682
29. [29] Luo C, Ren X, Han D, Zhang XG, Zhong R, Zhang XY, Xie YM. A novel concrete-filled auxetic tube composite structure: Design and compressive characteristic study. Engineering Struc-tures. 2022;268:114759. https://doi.org/10.1016/j.engstruct.2022.114759
30. [30] Askari M, Hutchins DA, Thomas PJ, Astolfi L, Watson RL, Abdi M, Ricci M, Laureti S, Nie L, Freear S., Wildman R, Tuck C, Clarke M, Woods E, Clare AT. Additive manufacturing of metamaterials: A review. Additive Manufacturing. 2020;36:101562. https://doi.org/10.1016/j.addma.2020.101562
31. [31] Saxena K.K., Das R., Calius E.P., Three Decades of Auxetics Research − Materials with Negative Poisson’s Ratio: A Review. Advanced Engineering Materials. 2016;18:1847–1870. https://doi.org/10.1002/adem.201600053
32. [32] Liu Y., Hu H., A review on auxetic structures and polymeric materials. Scientific Research and Essays. 2010;5:1052–1063.
33. [33] Jiang W, Ren X, Wang SL, Zhang XG, Zhang XY, Luo C, Xie YM, Scarpa F, Alderson A, Evans EE. Manufacturing, charac-teristics and applications of auxetic foams: A state-of-the-art review. Composites Part B: Engineering. 2022;235:109733. https://doi.org/10.1016/j.compositesb.2022.109733
34. [34] Carneiro VH, Meireles J, Puga H, Auxetic materials — A re-view. Materials Science-Poland. 2013;31:561–571. https://doi.org/10.2478/s13536-013-0140-6
35. [35] Love AEH, A treatise on the mathematical theory of elasticity, Dover Publications, New York, 1944.
36. [36] Lakes R. Foam Structures with a Negative Poisson’s Ratio. Science. 1987;235:1038–1040. https://doi.org/10.1126/science.235.4792.1038
37. [37] Chan N, Evans KE. Fabrication methods for auxetic foams. Journal of Materials Science. 1997;32:5945–5953. https://doi.org/10.1023/A:1018606926094
38. [38] Scarpa F, Yates JR, Ciffo LG, Patsias S. Dynamic crushing of auxetic open-cell polyurethane foam, Proceedings of the Insti-tution of Mechanical Engineers. Part C: Journal of Mechanical Engineering Science. 2002;216:1153–1156. https://doi.org/10.1243/09544060232102938
39. [39] Bezazi A. Scarpa F. Mechanical behaviour of conventional and negative Poisson’s ratio thermoplastic polyurethane foams under compressive cyclic loading. International Journal of Fa-tigue. 2007;29:922–930. https://doi.org/10.1016/j.ijfatigue.2006.07.015
40. [40] Bezazi A, Scarpa F. Tensile fatigue of conventional and nega-tive Poisson’s ratio open cell PU foams. International Journal of Fatigue. 2009;31:488–494. https://doi.org/10.1016/j.ijfatigue.2008.05.005
41. [41] Bianchi M, Scarpa FL, Smith CW. Stiffness and energy dissi-pation in polyurethane auxetic foams. Journal of Materials Sci-ence. 2008;43:5851–5860. https://doi.org/10.1007/s10853-008-2841-5
42. [42] Bianchi M, Scarpa F, Banse M, Smith CW. Novel generation of auxetic open cell foams for curved and arbitrary shapes. Ac-ta Materialia. 2011;59:686–691. https://doi.org/10.1016/j.actamat.2010.10.006
43. [43] Grima JN, Gatt R, Alderson A, Evans KE. On the potential of connected stars as auxetic systems. Molecular Simulation. 2005;31:925–935. https://doi.org/10.1080/08927020500401139
44. [44] Grima JN, Gatt R, Ellul B, Chetcuti E. Auxetic behaviour in non-crystalline materials having star or triangular shaped perfo-rations. Journal of Non-Crystalline Solids. 2010;356:1980–1987. https://doi.org/10.1016/j.jnoncrysol.2010.05.074
45. [45] Wang H, Lu Z, Yang Z, Li X. A novel re-entrant auxetic hon-eycomb with enhanced in-plane impact resistance. Composite Structures. 2019;208:758–770. https://doi.org/10.1016/j.compstruct.2018.10.024
46. [46] Guo M-F, Yang H, Ma L. 3D lightweight double arrow-head plate-lattice auxetic structures with enhanced stiffness and en-ergy absorption performance. Composite Structures. 2022;290:115484. https://doi.org/10.1016/j.compstruct.2022.115484
47. [47] Lan X, Meng L, Zhao J, Wang Z. Mechanical properties and damage characterizations of 3D double-arrowhead auxetic structure with high-relative-density realized via selective laser melting. European Journal of Mechanics-A/Solids. 2021;90:104386. https://doi.org/10.1016/j.euromechsol.2021.104386
48. [48] Chen Y-L, Wang X-T, Ma L. Damping mechanisms of CFRP three-dimensional double-arrow-head auxetic metamaterials. Polymer Testing. 2020;81:106189. https://doi.org/10.1016/j.polymertesting.2019.106189
49. [49] Wang X-T, Wang B, Wen Z-H, Ma L. Fabrication and me-chanical properties of CFRP composite three-dimensional dou-ble-arrow-head auxetic structures. Composites Science and Technology. 2018;164:92–102. https://doi.org/10.1016/j.compscitech.2018.05.014
50. [50] Qiao JX, Chen CQ. Impact resistance of uniform and func-tionally graded auxetic double arrowhead honeycombs. Interna-tional Journal of Impact Engineering. 2015;83:47–58. https://doi.org/10.1016/j.ijimpeng.2015.04.005
51. [51] Zhang Z, Wen Q, Li P, Hu H. Application of double arrow-head auxetic honeycomb structure in displacement measure-ment. Sensors and Actuators A: Physical. 2022;333:113218. https://doi.org/10.1016/j.sna.2021.113218
52. [52] Gibson, LJ, Ashby, MF, Schajer, GS, Robertson, CI. The me-chanics of two-dimensional cellular materials. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences. 1982;382:25–42. https://doi.org/10.1098/rspa.1982.0088
53. [53] Masters IG, Evans KE. Models for the elastic deformation of honeycombs. Composite Structures. 1996;35:403–422. https://doi.org/10.1016/S0263-8223(96)00054-2
54. [54] Hu LL, Zhou MZ, Deng H. Dynamic crushing response of auxetic honeycombs under large deformation: Theoretical anal-ysis and numerical simulation. Thin-Walled Structures. 2018;131:373–384. https://doi.org/10.1016/j.tws.2018.04.020
55. [55] Hu LL, Zhou MZ, Deng H. Dynamic indentation of auxetic and non-auxetic honeycombs under large deformation. Compo-site Structures. 2019;207:323–330. https://doi.org/10.1016/j.compstruct.2018.09.066
56. [56] Kolken HMA, Zadpoor AA, Auxetic mechanical metamateri-als. RSC Advances. 2017;7:5111–5129. https://doi.org/10.1039/C6RA27333E
57. [57] Gaspar N, Ren XJ, Smith CW, Grima JN, Evans KE. Novel honeycombs with auxetic behaviour. Acta Materialia. 2005;53:2439–2445. https://doi.org/10.1016/j.actamat.2005.02.006
58. [58] Smith CW, Grima J, Evans KE. A novel mechanism for gen-erating auxetic behaviour in reticulated foams: missing rib foam model. Acta Materialia. 2000;48:4349–4356. https://doi.org/10.1016/S1359-6454(00)00269-X
59. [59] Najafi M, Ahmadi H, Liaghat G. Experimental investigation on energy absorption of auxetic structures. Mater Today Pro-ceedings. 2021;34:350–355. https://doi.org/10.1016/j.matpr.2020.06.075
60. [60] Grima JN, Evans KE. Auxetic behavior from rotating triangles. Journal of Materials Science. 2006;41:3193–3196. https://doi.org/10.1007/s10853-006-6339-8
61. [61] Grima JN, Alderson A, Evans, KE. Negative poisson’s ratios from rotationg rectangles. Comput Methods Sci Technol. 2004;10:137–145. https://doi.org/10.12921/cmst.2004.10.02.137-145
62. [62] Grima JN, Evans KE. Auxetic behavior from rotating squares. Journal of Materials Science Letters. 2000;19:1563–1565.
63. [63] Grima JN, Farrugia P-S, Gatt R, Attard D. On the auxetic properties of rotating rhombi and parallelograms: A preliminary investigation. Phys Status Solidi(b). 2008;245:521–529. https://doi.org/10.1002/pssb.200777705
64. [64] Gatt R, Mizzi L, Azzopardi JI, Azzopardi KM, Attard D, Casha A, Briffa J, Grima JN. Hierarchical auxetic mechanical metamaterials. Scientific Reports. 2015;5:1–6. https://doi.org/10.1038/srep08395
65. [65] Kelvin WTB. The molecular tactics of a crystal, Clarendon Press; 1894.
66. [66] A. Alderson A, Alderson KL, Attard D, Evans KE, Grima JN, Gatt R, Miller W, Ravirala N, Smith CW, Zied K. Elastic con-stants of 3-, 4- and 6-connected chiral and anti-chiral honey-combs subject to uniaxial in-plane loading. Composites Science and Technology. 2010;70:1042–1048. https://doi.org/10.1016/j.compscitech.2009.07.009
67. [67] Hu LL, Luo ZR, Zhang ZY, Lian MK, Huang LS. Mechanical property of re-entrant anti-trichiral honeycombs under large de-formation. Composites Part B: Engineering. 2019;163:107–120. https://doi.org/10.1016/j.compositesb.2018.11.010
68. [68] Mousanezhad D, Haghpanah B, Ghosh R, Hamouda AM, Nayeb-Hashemi H, Vaziri A. Elastic properties of chiral, anti-chiral, and hierarchical honeycombs: A simple energy-based approach. Theoretical and Applied Mechanics Letters. 2016;6:81–96. https://doi.org/10.1016/j.taml.2016.02.004
69. [69] Ha CS, Plesha ME, Lakes RS. Chiral three-dimensional lattices with tunable Poisson’s ratio. Smart Materials and Structures. 2016;25:054005. https://doi.org/10.1088/0964-1726/25/5/054005
70. [70] Gatt R, Attard D, Farrugia P-S, Azzopardi KM, Mizzi L, Brin-cat J-P, Grima JN. A realistic generic model for anti-tetrachiral systems. Phys Status Solidi (b). 2013;250:2012–2019. https://doi.org/10.1002/pssb.201384246
71. [71] Grima JN, Gatt R, Farrugia P-S. On the properties of auxetic meta-tetrachiral structures. Phys Status Solidi(b). 2008;245:511–520. https://doi.org/10.1002/pssb.200777704
72. [72] Jiang Y, Li Y. 3D Printed Auxetic Mechanical Metamaterial with Chiral Cells and Re-entrant Cores. Scientific Reports. 2018;8:2397. https://doi.org/10.1038/s41598-018-20795-2
73. [73] Wu W, Qi D, Liao H, Qian G, Geng L, Niu Y, Liang J. De-formation mechanism of innovative 3D chiral metamaterials. Scientific Reports. 2018;8:12575. https://doi.org/10.1038/s41598-018-30737-7
74. [74] Ebrahimi H, Mousanezhad D, Nayeb-Hashemi H, Norato J, Vaziri A. 3D cellular metamaterials with planar anti-chiral to-pology. Materials & Design. 2018;145:226–231. https://doi.org/10.1016/j.matdes.2018.02.052
75. [75] Liu S, Lu G, Chen Y, Leong YW. Deformation of the Miura-ori patterned sheet. International Journal of Mechanical Scienc-es. 2015;99:130–142. https://doi.org/10.1016/j.ijmecsci.2015.05.009
76. [76] Lv C, Krishnaraju D, Konjevod G, Yu H, Jiang H. Origami based Mechanical Metamaterials. Scientific Reports. 2015,4: 5979. https://doi.org/10.1038/srep05979
77. [77] Bertoldi K, Vitelli V, Christensen J, Van Hecke M. Flexible mechanical metamaterials. Nature Reviews Materials. 2017;2:17066. https://doi.org/10.1038/natrevmats.2017.66
78. [78] Eidini M. Zigzag-base folded sheet cellular mechanical met-amaterials. Extreme Mechanics Letters. 2016;6:96–102. https://doi.org/10.1016/j.eml.2015.12.006
79. [79] De Bellis N. Bibliometrics and citation analysis: from the sci-ence citation index to cybermetrics. Scarecrow press; 2009.
80. [80] Yaoyang X, Boeing WJ. Mapping biofuel field: A bibliometric evaluation of research output. Renewable and Sustainable En-ergy Reviews. 2013;28:82–91. https://doi.org/10.1016/j.rser.2013.07.027
81. [81] Du H, Li N, Brown MA, Peng Y, Shuai Y. A bibliographic analysis of recent solar energy literatures: The expansion and evolution of a research field. Renewable Energy. 2014;66:696–706. https://doi.org/10.1016/j.renene.2014.01.018
82. [82] van Eck NJ, Waltman L. Software survey: VOSviewer, a computer program for bibliometric mapping. Scientometrics. 2010;84:523–538. https://doi.org/10.1007/s11192-009-0146-3
83. [83] Thompson MK, Moroni G, Vaneker T, Fadel G, Campbell RI, Gibson I, Bernard A, Schulz J, Graf P, Ahuja B, Martina F. De-sign for Additive Manufacturing: Trends, opportunities, consid-erations, and constraints. CIRP Annals. 2016;65:737–760. https://doi.org/10.1016/j.cirp.2016.05.004
84. [84] Chen Z, Li Z, Li J, Liu C, Lao C, Fu Y, Liu C, Li Y, Wang P, He Y, 3D printing of ceramics: A review. Journal of the Euro-pean Ceramic Society. 2019;39:661–687. https://doi.org/10.1016/j.jeurceramsoc.2018.11.013
85. [85] Zhang Y, Wang S, Ji G, A Comprehensive Survey on Particle Swarm Optimization Algorithm and Its Applications. Mathemat-ical Problems in Engineering. 2015;2015:931256. https://doi.org/10.1155/2015/931256
86. [86] Ren X, Das R, Tran P, Ngo TD, Xie YM, Auxetic metamateri-als and structures: a review. Smart Materials and Structures. 2018;27:023001. https://doi.org/10.1088/1361-665X/aaa61c
87. [87] Körner C. Additive manufacturing of metallic components by selective electron beam melting - a review. International Materi-als Reviews. 2016;61:361–377. https://doi.org/10.1080/09506608.2016.1176289
88. [88] Gong H, Rafi K, Gu H, Janaki Ram GD, Starr T, Stucker B. Influence of defects on mechanical properties of Ti–6Al–4V components produced by selective laser melting and electron beam melting. Materials & Design. 2015;86:545–554. https://doi.org/10.1016/j.matdes.2015.07.147
89. [89] Babaee S, Shim J, Weaver JC, Chen ER, Patel N, Bertoldi K. 3D Soft Metamaterials with Negative Poisson’s Ratio. Ad-vanced Materials. 2013;25:5044–5049. https://doi.org/10.1002/adma.201301986
90. [90] Jiang J.W, Park HS. Negative poisson’s ratio in single-layer black phosphorus. Nature Communications. 2014;5:4727. https://doi.org/10.1038/ncomms5727
91. [91] Bückmann T, Stenger N, Kadic M, J. Kaschke J, Frölich A, Kennerknecht T., Eberl C., Thiel M., Wegener M., Tailored 3D Mechanical Metamaterials Made by Dip-in Direct-Laser-Writing Optical Lithography. Advanced Materials. 2012;24:2710–2714. https://doi.org/10.1002/adma.201200584
92. [92] Yu X, Zhou J, Liang H, Jiang Z, Wu L, Mechanical metamate-rials associated with stiffness, rigidity and compressibility: A brief review. Progress in Materials Science. 2018;94:114–173. https://doi.org/10.1016/j.pmatsci.2017.12.003