RESEARCH PROGRESS IN AUXETIC MATERIALS AND STRUCTURES

Xin Ren; Xiangyu Zhang; Yimin Xie

doi:10.6052/0459-1879-18-381

Volume 51 Issue 3

Turn off MathJax

Article Contents

Article Navigation > Chinese Journal of Theoretical and Applied Mechanics > 2019 > 51(3): 656-689

Xin Ren, Xiangyu Zhang, Yimin Xie. RESEARCH PROGRESS IN AUXETIC MATERIALS AND STRUCTURES[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(3): 656-689. doi: 10.6052/0459-1879-18-381

Citation:

Xin Ren, Xiangyu Zhang, Yimin Xie. RESEARCH PROGRESS IN AUXETIC MATERIALS AND STRUCTURES[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(3): 656-689. doi: 10.6052/0459-1879-18-381

Xin Ren, Xiangyu Zhang, Yimin Xie. RESEARCH PROGRESS IN AUXETIC MATERIALS AND STRUCTURES[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(3): 656-689. doi: 10.6052/0459-1879-18-381

Citation:

PDF( 1758 KB)

RESEARCH PROGRESS IN AUXETIC MATERIALS AND STRUCTURES

doi: 10.6052/0459-1879-18-381

Xin Ren^{*2)
,
,},
Xiangyu Zhang^*,
Yimin Xie^{*†,;3)
,
,}

* College of Civil Engineering,Nanjing Tech University Nanjing Tech ,Nanjing 211816,China
† Center for Innovative Structures and Materials,School of Engineering,RMIT University,Melbourne 3001,Australia

Received Date: 2018-11-14
Publish Date: 2019-05-18

Abstract

Abstract

Auxetic materials and structures have special mechanical properties. In contrast to traditional materials, auxetic materials contract (expand) under uniaxial compression (tension). Auxetic materials have many desirable properties and are superior to traditional materials in terms of shear capacity, fracture resistance, energy absorption capacity and indentation resistance. Because of these excellent properties, auxetic materials are very promising in the fields of medical equipment, intelligent filters, intelligent sensors, protective equipment, aviation, navigation and national defense engineering, but the application and popularization of auxetic materials still face some challenges. In this paper, the domestic and foreign research results of auxetic materials are extensively reviewed and the latest progress of auxetic materials is introduced. Auxetic materials are roughly classified into the following four categories: natural auxetic materials, cellular auxetic materials, metallic auxetic materials, multi-material auxetics and auxetic composites. Internal structure, auxetic deformation mechanism and mechanical properties of each kind are discussed. Some excellent mechanical properties of auxetic materials are summarized and new inventions and applications of auxetic materials in various industries are introduced as well. In view of the fact that the actual application of auxetic materials are much less than the research theories and experimental results, this paper analyzes some shortcomings and the current challenges of auxetic materials, including high manufacturing cost, high porosity, insufficient bearing capacity and only suitable for small strain conditions. To promote the application of auxetics, the metallic auxetic materials are introduced in detail. The steps and methods for designing and fabricating 3D metallic auxetic materials are proposed as well.
- auxetics,
- negative Poisson's ratio,
- mechanical performance,
- metamaterials,
- structure

FullText(HTML)

References(1)

References

[1]	刘坚, 雷济荣, 夏百战. 基于Chebyshev展开的区间穿孔板超材料分析. 力学学报, 2017, 49(1): 137-148
[1]	(Liu Jian, Lei Jirong, Xia Baizhan.The interval analysis of multilayer-metamaterials with perforated apertures based on Chebyshev expansion. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(1): 137-148 (in Chinese))
[2]	Ren X, Das R, Tran P, et al.Auxetic metamaterials and structures: A review. Smart Materials and Structures, 2018, 27(2): 023001
[3]	Poirier JP.Introduction to the physics of the earth's interior. [PhD Thesis]. London: Cambridge University Press, 2000
[4]	Greaves GN, Greer AL, Lakes RS, et al.Poisson's ratio and modern materials. Nature Materials, 2011, 10(11): 823-837
[5]	Huang C, Chen L.Negative Poisson's ratio in modern functional Materials. Advanced Materials, 2016, 28(37): 8079-8096
[6]	Alderson A.A triumph of lateral thought. Chemistry & Industry, 1999, 10: 384-387
[7]	Lakes R.Foam structures with a negative Poisson's ratio. Science, 1987, 235: 1038-1040
[8]	Novak N, Vesenjak M, Ren Z.Auxetic cellular materials - A review. Journal of Mechanical Engineering, 2016(9): 485-493
[9]	Alderson A, Rasburn J, Simon AB.An auxetic filter: A tuneable filter displaying enhanced size selectivity or defouling properties. Industrial & Engineering Chemistry Research, 2000, 39(3): 654-665
[10]	Scarpa F.Auxetic materials for bioprostheses. Signal Processing Magazine, IEEE, 2008, 25(5): 128-126
[11]	Xu B, Arias F, Brittain ST, et al.Making negative Poisson's ratio microstructures by soft lithography. Advanced Materials, 1999, 11(14): 1186-1189
[12]	Zhang SL, Lai YC, He X, et al.Auxetic foam-based contact-mode triboelectric nanogenerator with highly sensitive self-powered strain sensing capabilities to monitor human body movement. Advanced Functional Materials, 2017, 27(25): 1616-1
[13]	Li Q, Kuang Y, Zhu M.Auxetic piezoelectric energy harvesters for increased electric power output. AIP Advances, 2017, 7(1): 2158-3226
[14]	Warmuth F.Fabrication and characterisation of a fully auxetic 3D lattice structure via selective electron beam melting. Smart Materials and Structures, 2017, 26(2): 025013
[15]	Grima JN, Jackson R, Alderson A, et al.Do zeolites have negative Poisson's ratios? Advanced Materials, 2000, 12(24): 1912-1918
[16]	Wang YC, Lakes R, Analytical parametric analysis of the contact problem of human buttocks and negative Poisson's ratio foam cushions. International Journal of Solids and Structures, 2002, 39(18): 4825-4838
[17]	Yanhong M.A nonlinear auxetic structural vibration damper with metal rubber particles. Smart Materials and Structures, 2013, 22(8): 084
[18]	Bertoldi K, Reis PM, Willshaw S, et al.Negative Poisson's ratio behavior induced by an elastic instability. Advanced Materials, 2010, 22(3): 361-366
[19]	Evans KE.Auxetic polymers. Membr. Technol, 2001, 137: 9
[20]	Love AEH.A Treatise on the Mathematical Theory of Elasticity. New York: Dover Publications, 1944
[21]	Ray H, Baughman JMS, Anvar A.Negative Poisson's ratios as a common feature of cubic metals. Nature, 1998, 392: 362
[22]	Keskar NR, Chelikowsky JR.Negative Poisson ratios in crystalline SiO$_2$ from first-principles calculations. Nature, 1992, 358(6383): 222-224
[23]	Wang H.$\delta $-Phosphorene: A two dimensional material with a highly negative Poisson's ratio. Nanoscale, 2017, 9(2): 850-855
[24]	Sanchez VC.Negative Poisson's ratios in siliceous zeolite MFI-silicalite. The Journal of Chemical Physics, 2008, 128(18): 184503
[25]	Kou LZ, Ma Y, Tang C, Auxetic and ferroelastic borophane: a novel 2D material with negative Possion's ratio and switchable dirac transport channels. Nano Letters, 2016, 16(12): 7910-7914
[26]	Qin H.Negative Poisson's ratio in rippled graphene. Nanoscale, 2017, 9(12): 4135-4142
[27]	Mortazavi B, Shahrokhi M, Makaremi M, et al.Anisotropic mechanical and optical response and negative Poisson's ratio in Mo$_{2}$C nanomembranes revealed by first-principles simulations. Nanotechnology, 2017, 28(11): 110705
[28]	Yu L, Yan Q, Ruzsinszky A.Negative Poisson's ratio in 1T-type crystalline two-dimensional transition metal dichalcogenides. Nature Communications, 2017, 8: 15224
[29]	Qin R, Zheng J, Zhu W, Sign-tunable Poisson's ratio in semi-fluorinated graphene. Nanoscale, 2017, 9(1): 128-133
[30]	Williams JL, Lewis JL.Properties and an anisotropic model of cancellous bone from the proximal tibial epiphysis. Journal of Biomechanical Engineering, 1982, 104(1): 50-56
[31]	Veronda DR, Westmann RA, Mechanical characterization of skin---Finite deformations. Journal of Biomechanics, 1970, 3(1): 111-124
[32]	Lees C, Vincent JF, Hillerton JE.Poisson's ratio in skin. Bio-medical Materials and Engineering, 1991, 1(1): 19-23
[33]	Baughman RH.Auxetic materials: Avoiding the shrink. Nature, 2003, 425(6959): 667-667
[34]	Wang N.Stem cell mechanics: Auxetic nuclei. Nat Mater, 2014, 13(6): 540-542
[35]	Yamamoto T, Schiessel H.Chromatin gels are auxetic due to cooperative nucleosome assembly and disassembly dynamics. EPL, 2017, 118(2): 28003
[36]	Pagliara S.Auxetic nuclei in embryonic stem cells exiting pluripotency. Nat Mater, 2014, 13(6): 638-644
[37]	Yan Y, Yan L, Song LQ, et al.Pluripotent stem cell expansion and neural differentiation in 3-D scaffolds of tunable Poisson's ratio. Acta Biomaterialia, 2017, 49: 192-203
[38]	Christensen. Vibrant times for mechanical metamaterials. MRS Communications, 2015, FirstView: 1-10
[39]	Schaedler TA, Jacobsen AJ, Torrents A, et al.Ultralight metallic microlattices. Science, 2011, 334(6058): 962
[40]	Wang YC, Shen MW, Liao SM.Microstructural effects on the Poisson's ratio of star-shaped two-dimensional systems. Physica Status Solidi($B$) Basic Research, 2017, 254(12): 1770264
[41]	Gibson LJ, Ashby MF, Schajer GS, et al.The mechanics of two-dimensional cellular materials. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 1982, 382(1782): 25
[42]	Masters IG, Evans KE, Models for the elastic deformation of honeycombs. Composite Structures, 1996, 35(4): 403-422
[43]	Gibson LJ, Ashby MF.Cellular solids: Structure and properties. Oxford [etc.]: Pergamon, 1988
[44]	Larsen UD, Sigmund O, Bouwstra S.Design and fabrication of compliant micromechanisms and structures with negative Poisson's ratio. Journal of Microelectromechanical Systems, 1997, 6(2): 106
[45]	Grima JN.On the potential of connected stars as auxetic systems. Molecular Simulation, 2005, 31(13): 925-935
[46]	Hu YL.A review on auxetic structures and polymeric materials. Scientific Research and Essays, 2010
[47]	Saxena KK, Das R, Calius EP, Three decades of auxetics research-materials with negative Poisson's ratio: A review. Advanced Engineering Materials, 2016, 18(11): 1847-1870
[48]	Evans KE, Nkansah MA, Hutchinson IJ, Auxetic foams: Modelling negative Poisson's ratios. Acta Metallurgica et Materialia, 1994, 42(4): 1289-1294
[49]	Wang XT,. Mechanical properties of 3D re-entrant auxetic cellular structures. International Journal of Mechanical Sciences 2017, 131-132: 396-407
[50]	Yang L. Mechanical properties of 3D re-entrant honeycomb auxetic structures realized via additive manufacturing. International Journal of Solids and Structures, 2015, 69-70: 475-490
[51]	Fu MH, Chen Y, Hu LL, A novel auxetic honeycomb with enhanced in-plane stiffness and buckling strength. Composite Structures, 2017, 160: 574-585
[52]	Grima JN.Hexagonal honeycombs with zero Poisson's ratios and enhanced stiffness. Advanced Engineering Materials, 2010, 12(9): 855-862
[53]	Gao Q, Wang L, Zhou Z, et al.Theoretical, numerical and experimental analysis of three-dimensional double-V honeycomb. Materials and Design, 2018, 139: 380-391
[54]	Wang YL, Wang LM, Ma ZD, et al.Parametric analysis of a cylindrical negative Poisson's ratio structure. Smart Materials and Structures, 2016, 25(3): 35-38
[55]	Grima JN, Pierre SF, Ruben G, et al.On the auxetic properties of rotating rhombi and parallelograms: A preliminary investigation. Physica Status Solidi($B$), 2008, 245(3): 521-529
[56]	Grima JN, Evans KE.Auxetic behavior from rotating squares. Journal of Materials Science Letters, 2000, 19(17): 1563-1565
[57]	Grima JN, Evans KE.Auxetic behavior from rotating triangles. Journal of Materials Science, 2006, 41(10): 3193-3196
[58]	Joseph NG, Alderson A, Kenneth E.Negative Possion's ratio from rotating rectangles. Computational Methods in Science And Technology, 2004, 10(2): 8
[59]	Grima JN, Zammit V, Gatt R, et al.Auxetic behaviour from rotating semi-rigid units. Physica Status Solidi($B$), 2007, 244(3): 866-882
[60]	Alderson A, Evans KE.Rotation and dilation deformation mechanisms for auxetic behaviour in the $\alpha $-cristobalite tetrahedral framework structure. Physics and Chemistry of Minerals, 2001, 28(10): 711-718
[61]	Rafsanjani A, Pasini D, Bistable auxetic mechanical metamaterials inspired by ancient geometric motifs. Extreme Mechanics Letters, 2016, 9: 291-296
[62]	Lakes R.Deformation mechanisms in negative Poisson's ratio materials: structural aspects. Journal of Materials Science, 1991, 26(9): 2287-2292
[63]	Grima JN, Gatt R, Farrugia PS, On the properties of auxetic meta-tetrachiral structures. Physica Status Solidi($B$), 2008, 245(3): 511-520
[64]	Prall D, Lakes RS, Properties of a chiral honeycomb with a poisson's ratio of -1. International Journal of Mechanical Sciences, 1997, 39(3): 305-314
[65]	Mizzi L.Influence of translational disorder on the mechanical properties of hexachiral honeycomb systems. Composites Part B: Engineering, 2015, 80: 84-91
[66]	Ha CS, Plesha ME, Lakes RS.Chiral three-dimensional lattices with tunable Poisson's ratio. Smart Materials and Structures, 2016, 25(5): 054005
[67]	Lu ZX, Wang QS, Li X, et al.Elastic properties of two novel auxetic 3D cellular structures. International Journal of Solids and Structures, 2017, 124: 46-56
[68]	Fu M, Liu F, Hu L.A novel category of 3D chiral material with negative Poisson's ratio. Composites Science and Technology, 2018, 160: 111-118
[69]	Rossiter J, TakashimaK, Scarpa F, et al. Shape memory polymer hexachiral auxetic structures with tunable stiffness. Smart Materials and Structures, 2014, 23(4): 045007
[70]	Grima JN.Tailoring graphene to achieve negative Poisson's ratio properties. Advanced Materials, 2015, 27(8): 1455-1459
[71]	Javid F, Smith-Roberge E, Innes MC, et al.Dimpled elastic sheets: A new class of non-porous negative Poisson's ratio materials. Scientific Reports, 2015, 5(1): 18373
[72]	李笑, 李明. 折纸及其折痕设计研究综述. 力学学报, 2018, 50(3): 467-476
[72]	(Li Xiao, Li Ming.A review of origami and its crease design. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(3): 467-476 (in Chinese))
[73]	Liu SC, Lu GX, Chen Y, et al.Deformation of the Miura-ori patterned sheet. International Journal of Mechanical Sciences, 2015, 99: 130-142
[74]	Hou Y, Neville R, Scarpa F, et al.Graded conventional-auxetic Kirigami sandwich structures: Flatwise compression and edgewise loading. Composites Part B: Engineering, 2014, 59: 33-42
[75]	Neville RM, Scarpa F, Pirrera A.Shape morphing Kirigami mechanical metamaterials. Scientific Reports, 2016, 6: 31067
[76]	Chen YJ, Scarpa F, Remillat C, et al.Curved Kirigami SILICOMB cellular structures with zero Poisson's ratio for large deformations and morphing. Journal of Intelligent Material Systems and Structures, 2013, 25(6): 731-743
[77]	Zhang ZK, Hu H, Liu SR, et al.Study of an auxetic structure made of tubes and corrugated sheets. Physica Status Solidi($B)$, 2013, 250(10): 1996-2001
[78]	Grima JN, Gatt R.Perforated sheets exhibiting negative Poisson's ratios. Advanced Engineering Materials, 2010, 12(6): 460-464
[79]	于靖军, 谢岩, 裴旭. 负泊松比超材料研究进展. 机械工程学报, 2018, 54(13): 1-14
[79]	(Yu Jingjun, Xie Yan, Pei Xu.State-of-art of metamaterials with negative Poisson's ratio. Journal of Mechanical Engineering, 2018, 54(13): 1-14 (in Chinese))
[80]	Grima JN, Mizzi L, Azzopardi KM, et al.Auxetic perforated mechanical metamaterials with randomly oriented cuts. Advanced Materials, 2016, 28(2): 385-389
[81]	Tang Y, Yin J.Design of cut unit geometry in hierarchical kirigami-based auxetic metamaterials for high stretchability and compressibility. Extreme Mechanics Letters, 2017, 12: 77-85
[82]	Grima JN, Gatt R, Ellul B, et al.Auxetic behaviour in non-crystalline materials having star or triangular shaped perforations. Journal of Non-Crystalline Solids, 2010, 356(37-40): 1980-1987
[83]	Ravirala N, Alderson A, Alderson KL.Interlocking hexagons model for auxetic behaviour. Journal of Materials Science, 2007, 42(17): 7433-7445
[84]	Evans KE, Alderson A.Auxetic materials: Functional materials and structures from lateral thinking. Advanced Materials, 2000, 12(9): 617-628
[85]	Evans KE, Caddock BD.Microporous materials with negative Poisson's ratios. II. Mechanisms and interpretation. Journal of Physics D: Applied Physics, 1989, 22(12): 1883
[86]	Alderson A, Evans KE.Modelling concurrent deformation mechanisms in auxetic microporous polymers. Journal of Materials Science, 1997, 32(11): 2797-2809
[87]	Alderson KL, Alderson A, Smart G, et al.Auxetic polypropylene fibres: Part 1 - Manufacture and characterisation. Plastics, Rubber and Composites, 2002, 31(8): 344-349
[88]	Ravirala N, Alderson KL, Davies PJ, et al.Negative Poisson's ratio polyester fibers. Textile Research Journal, 2006, 76(7): 540-546
[89]	Miller W, Hook PB, Smith CW, et al.The manufacture and characterisation of a novel, low modulus, negative Poisson's ratio composite. Composites Science and Technology, 2009, 69(5): 651-655
[90]	Wright JR, Burns MK, Edward J, et al.On the design and characterisation of low-stiffness auxetic yarns and fabrics. Textile Research Journal, 2012, 82(7): 645-654
[91]	Miller W, Ren Z, Smith CW, et al.A negative Poisson's ratio carbon fibre composite using a negative Poisson's ratio yarn reinforcement. Composites Science and Technology, 2012, 72(7): 761-766
[92]	史炜, 杨伟, 李忠明等. 负泊松比材料研究进展. 高分子通报, 2003(6): 48-57
[92]	(Shi Wei, Yang Wei, Li Zhongming, et al.Advances in negative Poisson's ratio materials. Polymer Bulletin, 2003(6): 48-57 (in Chinese))
[93]	常玉萍, 程锡慧, 马丕波等. 具有负泊松比效应经编织物的制备及其力学性能. 纺织学报, 2015(8): 43-48
[93]	(Chang Yuping, Cheng Xihui, Ma Pibo, et al.Manufacture and mechanical properties of negative Poisson's ratio warp knitted fabrics. Journal of Textile Research, 2015(8): 43-48 (in Chinese))
[94]	Blaga M, Ciobanu AR, Pavko-Cuden A 等. 在电脑横机上编织负泊松比可折叠纬编针织结构. 国际纺织导报, 2014(6): 54-56
[94]	(Blaga M, Ciobanu AR, Pavko-Cuden A, et al. Production of foldable weft knitted structures with auxetic potential on electronic flat knitting machines. China Textile Leader, 2014(6): 54-56 (in Chinese))
[95]	葛朝阳, 胡红. 一种新型三维负泊松比织物结构的压缩变形分析. 东华大学学报(自然科学版), 2014(5): 543-548
[95]	(Ge Zhaoyang, Hu Hong.Compression deformation analysis of an Innovative 3D fabric structure with Negative poisson's ratio. Journal of Donghua University (Natural Science), 2014 (5): 543-548 (in Chinese))
[96]	常玉萍, 马丕波, 钟文鑫等. 基于经编网眼结构的负泊松比织物设计. 纺织学报, 2016 (2): 44-49
[96]	(Chang Yuping, Ma Pibo, Zhong Wenxin, et al.Design of auxetic fabrics based on warp-knitted net structure. Journal of Textile Research, 2016 (2): 44-49 (in Chinese))
[97]	常玉萍, 马丕波. 基于网眼结构的负泊松比经编间隔织物模型及其拉伸性能. 纺织学报, 2017 (9): 59-65
[97]	(Chang Yuping, Ma Pibo.Model and tensile performance of negative Poisson's ratio warp-knitted spacer structures. Journal of Textile Research, 2017 (9): 59-65 (in Chinese))
[98]	马丕波, 常玉萍, 蒋高明. 负泊松比针织结构及其应用. 纺织导报, 2015(7): 47-50
[98]	(Ma Pibo, Chang Yuping, Jiang Gaoming.Knitted structures with negative Poisson's ratio. China Textile Leader, 2015(7): 47-50 (in Chinese))
[99]	杨智春, 邓庆田. 负泊松比材料与结构的力学性能研究及应用. 力学进展, 2011, 41(3): 335-350
[99]	(Yang Zhichun, Deng Qingtian.Mechanical property and application of materials and structures with nagative possion's ratio. Advances in Mechanics, 2011, 41(3): 335-350 (in Chinese))
[100]	Boakye A, Chang YP, Rafiu KR, et al.Design and manufacture of knitted tubular fabric with auxetic effect. Journal of the Textile Institute, 2017: 1-7
[101]	Ali M, Zeeshan M, Ahmed S, et al.Development and comfort characterization of 2D-Woven auxetic fabric for wearable and medical textile applications. Clothing and Textiles Research Journal, 2018, 36(3): 199-214
[102]	冯含笑, 魏孟媛, 薛文良等. 负泊松比纺织材料的研究现状与应用前景. 产业用纺织品, 2017(6): 1-5
[102]	(Feng Hanxiao, Wei Mengyuan, Xue Wenliang, et al.Research status and application prospect of negative Poission's ratio textile materials. Technical Textiles, 2017(6): 1-5 (in Chinese))
[103]	Smith CW, Grima JN, Evans KE.A novel mechanism for generating auxetic behaviour in reticulated foams: Missing rib foam model. Acta Materialia, 2000, 48(17): 4349-4356
[104]	Grima JN, Ravirala, Galea R, et al.Modelling and testing of a foldable macrostructure exhibiting auxetic behaviour. Physica Status Solidi($B)$, 2011, 248(1): 117-122
[105]	Gaspar N, Smith CW, Alderson A, et al.A generalised three-dimensional tethered-nodule model for auxetic materials. Journal of Materials Science, 2011, 46(2): 372-384
[106]	Dirrenberger J, Forest S, Jeulin D.Effective elastic properties of auxetic microstructures: anisotropy and structural applications. International Journal of Mechanics and Materials in Design, 2013, 9(1): 21-33
[107]	Pasternak E, Dyskin AV.Materials and structures with macroscopic negative Poisson's ratio. International Journal of Engineering Science, 2011, 52: 103-114
[108]	Rodney D, Gadot B, Martinez OR, et al.Reversible dilatancy in entangled single-wire materials. Nat Mater, 2016, 15(1): 72-77
[109]	Friis EA, Lakes RS, Park JB.Negative Poisson's ratio polymeric and metallic foams. Journal of Materials Science, 1988, 23(12): 4406-4414
[110]	Li D, Dong L, Lakes RS.The properties of copper foams with negative Poisson's ratio via resonant ultrasound spectroscopy. Physica Status Solidi($B)$, 2013, 250(10): 1983-1987
[111]	Zhang YN, Wu RQ, Schurter HM.Understanding of large auxetic properties of iron-gallium and iron-aluminum alloys. Journal of Applied Physics, 2010, 108(2): 023513
[112]	Schwerdtfeger J, Schury F, Stingl M, et al.Mechanical characterisation of a periodic auxetic structure produced by SEBM. Physica Status Solidi($B)$, 2012, 249(7): 1347-1352
[113]	Mitschke H, Schwerdtfeger J, Schury F, et al.Finding auxetic frameworks in periodic tessellations. Advanced Materials, 2011, 23(22-23): 2669-2674
[114]	Dirrenberger J, Forest S, Jeulin D.Elastoplasticity of auxetic materials. Computational Materials Science, 2012, 64: 57-61
[115]	Taylor M, Francesconi L, Gerendás M, et al.Low porosity metallic periodic structures with negative Poisson's ratio. Advanced Materials, 2014, 26(15): 2365-2370
[116]	Ren X, Shen JH, Ghaedizadeh A, et al.Experiments and parametric studies on 3D metallic auxetic metamaterials with tuneable mechanical properties. Smart Materials and Structures, 2015, 24(9): 95016
[117]	Ren X, Shen JH, Ghaedizadeh A, et al.A simple auxetic tubular structure with tuneable mechanical properties. Smart Materials and Structures, 2016, 25(6): 065012
[118]	Hiller J, Lipson H.Tunable digital material properties for 3D voxel printers. Rapid Prototyping Journal, 2010, 16(4): 241-247
[119]	Wang K, Chang YH, Chen YW, et al.Designable dual-material auxetic metamaterials using three-dimensional printing. Materials and Design, 2015, 67: 159-164
[120]	Vogiatzis P, Chen SK, Wang X, et al.Topology optimization of multi-material negative Poisson's ratio metamaterials using a reconciled level set method. CAD Computer Aided Design, 2017, 83: 15-32
[121]	Alderson KL, Simkins VR, Coenen VL, et al.How to make auxetic fibre reinforced composites. Physica Status Solidi($B)$, 2005, 242(3): 509-518
[122]	Miki M, Murotsu Y.The peculiar behavior of the Poisson's ratio of laminated fibrous composites. JSME International Journal. Ser.1, Solid Mechanics, Strength of Materials, 1989, 32(1): 67-72
[123]	Milton GW.Composite materials with poisson's ratios close to -1. Journal of the Mechanics and Physics of Solids, 1992, 40(5): 1105-1137
[124]	Herakovich CT.Composite laminates with negative through-the-thickness Poisson's ratios. Journal of Composite Materials, 1984, 18(5): 447-455
[125]	Ghaznavi A, hariyat M. Non-linear layerwise dynamic response analysis of sandwich plates with soft auxetic cores and embedded SMA wires experiencing cyclic loadings. Composite Structures, 2017, 171: 185-197
[126]	Nkansah MA, Evans KE, Hutchinson IJ.Modelling the effects of negative Poisson's ratios in continuous-fibre composites. Journal of Materials Science, 1993, 28(10): 2687-2692
[127]	Zorzetto L, Ruffoni D.Re-entrant inclusions in cellular solids: From defects to reinforcements. Composite Structures, 2017, 176: 195-204
[128]	Zahra T, Dhanasekar M.Characterisation of cementitious polymer mortar-Auxetic foam composites. Construction and Building Materials, 2017, 147: 143-159
[129]	Hu JY, Zhou Y, Liu ZS, et al.Pattern switching in soft cellular structures and hydrogel-elastomer composite materials under compression. Polymers, 2017, 9(6): 229
[130]	Carneiro VH, Meireles J, Puga H.Auxetic materials-A review. Materials Science-Poland, 2013, 31(4): 561-571
[131]	Yang W, Li ZM, Shi W, et al.Review on auxetic materials. Journal of Materials Science, 2004, 39(10): 3269-3279
[132]	Lakes RS. Elms K.Indentability of conventional and negative Poisson's ratio foams. Journal of Composite Materials, 1993, 27(12): 1193-1202
[133]	Critchley R, Corni I, Wharton JA, et al.A review of the manufacture, mechanical properties and potential applications of auxetic foams. Physica Status Solidi($B)$, 2013, 250(10): 1963-1982
[134]	Yang S, Wang D, Gao RJ, et al.A comparative study of ballistic resistance of sandwich panels with aluminum foam and auxetic honeycomb cores. Advances in Mechanical Engineering, 2013(2): 496-500
[135]	Bezazi A, Boukharouba W, Scarpa F.Mechanical properties of auxetic carbon/epoxy composites: Static and cyclic fatigue behaviour. Physica Status Solidi($B)$, 2009, 246(9): 2102-2110
[136]	Choi JB, Lakes RS.Non-linear properties of metallic cellular materials with a negative Poisson's ratio. Journal of Materials Science, 1992, 27(19): 5375-5381
[137]	Donoghue JP, Alderson KL, Evans KE.The fracture toughness of composite laminates with a negative Poisson's ratio. Physica Status Solidi($B)$, 2009, 246(9): 2011-2017
[138]	Lim TC, Acharya UR.Longitudinal modulus of semi-auxetic unidirectional fiber composites. Journal of Reinforced Plastics and Composites, 2010, 29(10): 1441-1445
[139]	Yang S, Chalivendra VB, Kim YK.Fracture and impact characterization of novel auxetic Kevlar/Epoxy laminated composites. Composite Structures, 2017, 168: 120-129
[140]	Alderson A, Alderson KL, Chirima G, et al.The in-plane linear elastic constants and out-of-plane bending of 3-coordinated ligament and cylinder-ligament honeycombs. Composites Science and Technology, 2010, 70(7): 1034-1041
[141]	Alderson A, Rasburn J, Evans KE, et al.Auxetic polymeric filters display enhanced de-fouling and pressure compensation properties. Membrane Technology, 2001, 2001(137): 6-8
[142]	Alderson A, Rasburn J, Evans KE.Mass transport properties of auxetic (negative Poisson's ratio) foams. Physica Status Solidi($B)$, 2007, 244(3): 817-827
[143]	Grima JN. Auxtic Metamaterials. France: Strasbourg, 2010
[144]	Chen Q, Pugno NM.In-plane elastic buckling of hierarchical honeycomb materials. European Journal of Mechanics-A/Solids, 2012, 34: 120-129
[145]	May PR, Fuster JM, Haber J, et al.Woodpecker drilling behavior: An endorsement of the rotational theory of impact brain injury. Archives of Neurology, 1979, 36(6): 370-373
[146]	Imbalzano G, Tran P, Ngo TD, et al.A numerical study of auxetic composite panels under blast loadings. Composite Structures, 2016, 135: 339-352
[147]	Imbalzano G, Linforth S, Ngo TD, et al.Blast resistance of auxetic and honeycomb sandwich panels: Comparisons and parametric designs. Composite Structures, 2017, 183: 242-261
[148]	Strek T, Jopek H.Effective mechanical properties of concentric cylindrical composites with auxetic phase. Physica Status Solidi($B)$, 2012, 249(7): 1359-1365
[149]	Grujicic M, Galgalikar R, Snipes JS.Multi-physics modeling of the fabrication and dynamic performance of all-metal auxetic-hexagonal sandwich-structures. Materials and Design, 2013, 51: 113-130
[150]	Strek T, Jopek H, Bogdan T, et al.Computational analysis of sandwich-structured composites with an auxetic phase. Physica Status Solidi($B)$, 2014, 251(2): 354-366
[151]	Alderson A, Alderson KL.Auxetic materials. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 2007, 221(4): 565-575
[152]	Heo H, Ju J, Kim DM.Compliant cellular structures: Application to a passive morphing airfoil. Composite Structures, 2013, 106: 560-569
[153]	Jacobs S, Coconnier C, DiMaio D, et al. Deployable auxetic shape memory alloy cellular antenna demonstrator: Design, manufacturing and modal testing. Smart Materials and Structures, 2012, 21(7): 075013
[154]	Prawoto Y.Seeing auxetic materials from the mechanics point of view: A structural review on the negative Poisson's ratio. Computational Materials Science, 2012, 58: 140-153
[155]	Avellaneda M, Swart PJ.Calculating the performance of 1--3 piezoelectric composites for hydrophone applications: An effective medium approach. The Journal of the Acoustical Society of America, 1998, 103(3): 1449-1467
[156]	Nakamura M.Fundamental properties of intermetallic compounds. MRS Bulletin, 2013, 20(8): 33-39
[157]	Ali MN, Rehman IU.An auxetic structure configured as oesophageal stent with potential to be used for palliative treatment of oesophageal cancer: Development and in vitro mechanical analysis. Journal of Materials Science: Materials in Medicine, 2011, 22(11): 2573-2581
[158]	Ali MN, Busfield JC, Rehman I.Auxetic oesophageal stents: structure and mechanical properties. Journal of Materials Science: Materials in Medicine, 2014, 25(2): 527-553
[159]	Kuribayashi K, Tsuchiya K, You Z, et al.Self-deployable origami stent grafts as a biomedical application of Ni-rich TiNi shape memory alloy foil. Materials Science and Engineering: $A$, 2006, 419(1-2): 131-137
[160]	Kuribayashi K, You Z.Deployable stent. Google Patents, 2006
[161]	Ley TJ.Stent configurations. Google Patents, 2002
[162]	Burriesci G, Bergamasco G.Annuloplasty prosthesis with an auxetic structure. Google Patents, 2011
[163]	Jiang Y, Liu Z, Matsuhisa N, et al.Auxetic mechanical metamaterials to enhance sensitivity of stretchable strain sensors. Advanced Materials, 2018, 30(12): 0935-9648
[164]	Gatt R, Mizzi L, Azzopardi JI, et al.Hierarchical auxetic mechanical metamaterials. Scientific Reports, 2015, 5: 8395
[165]	Bhullar SK, Ahmed JKF, Jun MBG.Design and fabrication of stent with negative Poisson's ratio. International Journal of Mechanical, Aerospace,Industrial and Mechatronics Engineering, 2014(2): 213-219
[166]	Janus-Michalska M, Jasinska D, Smardzewski J.Comparison of contact stress distribution for foam seat and seat of auxetic spring skeleton. International Journal of Applied Mechanics and Engineering, 2013, 18(1): 18
[167]	Foster L, Peketi P, Allen T, et al.Application of auxetic foam in sports helmets. Applied Sciences Switzerland, 2018, 8(3): 354
[168]	Alderson K, Alderson A, Anand S, et al.Auxetic warp knit textile structures. Physica Status Solidi($B)$, 2012, 249(7): 1322-1329
[169]	葛朝阳. 三维负泊松比织物结构的设计制造和变形机理研究. [博士论文]. 上海:东华大学, 2014
[169]	(Ge Zhaoyang.Design, manufacture and deformation mechanism of a three-dimensuional structure with negative Possion's ratio. [PhD Thesis]. Shanghai: Donghua University, 2014 (in Chinese))
[170]	亓昌, 安文姿, 杨姝. 负泊松比安全带织带乘员碰撞保护性能的FE仿真. 汽车安全与节能学报, 2013, 4(3): 215-222
[170]	(Qi Chang, An Wenzi, Yang Shu.FE simulation of the occupant crash protection performance of the negative Poisson's ratio seat belt webbing. Journal of Automotive Safety and Energy, 2013, 4(3): 215-222 (in Chinese))
[171]	Avellaneda M, Swart PJ.Calculating the performance of 1-3 piezocomposites for hydrophone applications: An effective medium approach. Journal of the Acoustica1 Society of America, 1998, 103: 1449-1467
[172]	Baughman RH, Shacklette JM, Zakhidov AA, et al.Negative Poisson's ratios as a common feature of cubic metals. Nature, 1998, 392: 362-365
[173]	黄春阳, 唐山, 彭向和. 超弹性薄膜与可压缩基底双层结构表面失稳分析. 力学学报, 2017, 49(4): 758-762
[173]	(Huang Chunyang, Tang Shan, Peng Xianghe.Study of surface instability about hyperelastic films on auxetic substrates under compression. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(4): 758-762 (in Chinese))
[174]	Choi JB.Design of a fastener based on negative Poisson's ratio foam. Cellular Polymers, 1991, 10: 8
[175]	Grima JN, Gatt R.A novel chemo-mechanical process for making auxetic foams and for their reconversion to conventional form. [PhD Thesis]. University of Malta, 2009
[176]	Ren X, Shen JH, Tran P, et al.Auxetic nail: Design and experimental study. Composite Structures, 2018, 184: 288-298
[177]	Nakamura M.Fundamental properties of intermetallic cornpounds. MRS Bulletin, 1995, 20(8): 33-39
[178]	颜芳芳, 徐晓东. 负泊松比柔性蜂窝结构在变体机翼中的应用. 中国机械工程, 2012(5): 542-546
[178]	(Yan Fangfang, Xu Xiaodong.Negative Poisson's ratio honeycomb structure and its applications in structure design of morphing aircraft. China Mechanical Engineering, 2012(5): 542-546 (in Chinese))
[179]	吴秉鸿, 张相闻, 杨德庆. 负泊松比超材料隔振基座的实船应用分析. 船舶工程, 2018(2): 55-62
[179]	(Wu Binghong, Zhang Xiangwen, Yang Deqing.Real ship application analysis of vibration isolation base made by auxetic metamaterials. Ship Engineering, 2018 (2): 55-62 (in Chinese))
[180]	杨德庆, 马涛, 张梗林. 舰艇新型宏观负泊松比效应蜂窝舷侧防护结构. 爆炸与冲击, 2015(2): 243-248
[180]	(Yang Deqing, Ma Tao, Zhang Genglin.A novel auxetic broadside defensive structure for naval ships. Explosion and Shock Waves, 2015(2): 243-248 (in Chinese))
[181]	韦璇, 马玉璞, 孙社营. 舰船声隐身技术和材料的发展现状与展望. 舰船科学技术, 2006(6): 22-27
[181]	(Wei Xuan, Ma Yupu, Sun Sheying.The present status and prospect of acoustic stealth techniques and materials on warships. Ship Science and Technology, 2006 (6): 22-27 (in Chinese))
[182]	杨呜波, 阳霞, 李忠明等. 负泊松比材料的结构与性能. 高分子材料科学与工程, 2001(6): 15-18,24
[182]	(Yang Mingbo, Yang Xia, Li Zhongming, et al.The Structure and properties of the material with negative Possion's ratio. Polymer Materials Science & Engineering, 2001(6): 15-18,24 (in Chinese))
[183]	Liu YP, Hu H, Lam JKC.Negative Poisson's ratio weft-knitted fabrics. Textile Research Journal, 2010, 80(9): 856-863
[184]	孔凡臣, 孙建伟, 张邦成等. 基于四杆曲柄滑块机构的可展机构设计. 长春工业大学学报, 2018(1): 1-7
[184]	(Kong Fanchen, Sun Jianwei, Zhang Bangcheng, et al.Design of deployable mechanisms based on four-bar slider-crank mechanism. Journal of Changchun University of Technology, 2018(1): 1-7 (in Chinese))
[185]	Mori O, Sawada H, Funase R, et al.First solar power sail demonstration by IKAROS. Transactions of the Japan Society for Aeronautical & Spaceences Space Technology Japan, 2010, 8(27): 25-31
[186]	Tsuda Y, Mori O, Funase R, et al.Flight status of IKAROS deep space solar sail demonstrator. Acta Astronautica, 2011, 69(9-10): 833-840
[187]	O J.Cushioned earphones. US: US6412593B1, 2002
[188]	Zhengdong M.Three-dimensional auxetic structures and applications thereof. US: US7910193B2, 2011
[189]	Bianchi M, Scarpa F, Smith CW.Shape memory behaviour in auxetic foams: Mechanical properties. Acta Materialia, 2010, 58(3): 858-865
[190]	Hassan MR, Scarpa F, Ruzzene M. Smart shape memory alloy chiral honeycomb. Materials Science and Engineering, 2008, 481-482: 654-657
[191]	Sun Y, Pugno N.Hierarchical fibers with a negative poisson's ratio for tougher composites. Materials, 2013, 6(2): 699-712
[192]	Tang YC, Lin GJ, Han L, et al.Design of hierarchically cut hinges for highly stretchable and reconfigurable metamaterials with enhanced strength. Advanced Materials, 2015, 27(44): 7181-7190
[193]	Billon K, Zampetakis I, Scarpa F.Mechanics and band gaps in hierarchical auxetic rectangular perforated composite metamaterials. Composite Structures, 2017, 160: 1042-1050
[194]	Ren X, Shen JH, Ghaedizadeh A, et al.Numerical simulations of 3D metallic auxetic metamaterials in both compression and tension. Applied Mechanics and Materials, 2016, 846: 565-570
[195]	Bertoldi K.Harnessing instabilities to design tunable architected cellular materials//Annual Review of Materials Research, 2017: 51-61
[196]	Wu JL, Luo Z, Li H.Level-set topology optimization for mechanical metamaterials under hybrid uncertainties. Computer Methods in Applied Mechanics and Engineering, 2017, 319: 414-441
[197]	Clausen A, Wang FW, Jensen JS, et al.Topology optimized architectures with programmable Poisson's ratio over large deformations. Advanced Materials, 2015, 27(37): 5523-5527
[198]	Bruggi M, Zega V, Corigliano A.Synthesis of auxetic structures using optimization of compliant mechanisms and a micropolar material model. Structural and Multidisciplinary Optimization, 2017, 55(1): 1-12
[199]	Wang ZP, Poh LH, Dirrenberger J, et al.Isogeometric shape optimization of smoothed petal auxetic structures via computational periodic homogenization. Computer Methods in Applied Mechanics and Engineering, 2017, 323: 250-271
[200]	Xie YM, Steven GP.A simple evolutionary procedure for structural optimization. Computers & Structures, 1993, 49(5): 885-896
[201]	Xie YM, Steven GP.Basic evolutionary structural optimization, in Evolutionary Structural Optimization. London: Springer, 1997: 12-29
[202]	Yang XY, Xie YM.Bidirectional evolutionary method for stiffness optimization. AIAA Journal, 1999, 37(11): 1483-1488
[203]	Huang X, Xie YM.Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite Elements in Analysis and Design, 2007, 43(14): 1039-1049
[204]	Ai L, Gao XL.Metamaterials with negative Poisson's ratio and non-positive thermal expansion. Composite Structures, 2017, 162: 70-84
[205]	Ng CK, Saxena KK, Das R, et al.On the anisotropic and negative thermal expansion from dual-material re-entrant-type cellular metamaterials. Journal of Materials Science, 2017, 52(2): 899-912
[206]	Hewage T, Alderson A, Alderson KL.Double-negative mechanical metamaterials displaying simultaneous negative stiffness and negative Poisson's ratio properties. Adv Mater, 2016, 28(46): 10323-10332