1. School of Materials Science and Engineering, Tongji University, Shanghai 201804, China; 2. Shanghai Key Laboratory of R&D for Metallic Function Materials, Shanghai 201804, China
Abstract：Auxetic metamaterials and structures have excellent mechanical properties such as shear resistance, impact resistance, fracture resistance, energy absorption and vibration isolation, permeability variability, synclastic curvature in bending, etc. Auxetic metamaterials have broad application prospects in the fields of aerospace, navigation, mechanical automation, biomedicine, national defense and military and textile industry. Based on the deformation mechanism of auxetic metamaterials and structure, the physical models of re-entrant mechanism, rotating rigid mechanism, chiral/antichiral mechanism, fibril/nodule mechanism, miura-folded mechanism, buckling-induced mechanism, helical auxetic yarn structure were reviewed. These models can be widely applied in various engineering applications such as light laminated plates, fluid transportation and yarn to improve their properties. Finally, prospects to the upcoming challenges and progress trends of auxetic metamaterials and structures are made.It is pointed out that the application of negative Poisson’s ratio effect can help compensate the change of volume and area under the deformation of uniaxial loading. Then the shock resistance of turbine blade, antenna and car suction box can be improved. As a result, this review can provide benefits for the development of auxetic metamaterials.
[1] YU X L, ZHOU J, LIANG H Y, et al. Mechanical metamaterials associated with stiffness, rigidity and compressibility:a brief review[J]. Progress in Materials Science, 2018, 94:114-173. [2] 于靖军, 谢岩, 裴旭. 负泊松比超材料研究进展[J]. 机械工程学报, 2018, 54(13):1-14. YU J J, XIE Y, PEI X. State-of-art of metamaterials with negative Poisson's ratio[J]. Journal of Mechanical Engineering, 2018, 54(13):1-14. [3] 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[J]. 力学进展, 2011(3):335-350. YANG Z C, DENG Q T. Mechanical property and application of materials and structures with nagative Possion's ratio[J]. Advances in Mechanics, 2011(3):335-350. [4] YANG W, LI Z M, SHI W, et al. Review on auxetic materials[J]. Journal of Materials Science, 2004, 39:3269-3279. [5] LAKES R. Foam structures with a negative Poisson's ratio[J]. Science, 1987, 235:1038-1040. [6] NOVAK N, VESENJAK M, REN Z. Auxetic cellular materials-a review[J]. Journal of Mechanical Engineering, 2016(9):485-493. [7] HVEONHO C, DONGSIK S, KIM D N. Mechanics of auxetic materials. handbook of mechanics of materials[M]. Singapore:Springer, 2018:1-25. [8] 任鑫, 张相玉, 谢亿民. 负泊松比材料和结构的研究进展[J]. 力学学报. 2019, 51(3):656-689. REN X, ZHANG X Y, XIE Y M. Research progress in auxetic materials and structures[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(3):656-689. [9] KOLKEN H M A, ZADPOOR A A. Auxetic mechanical metamaterials[J]. RSC Advances, 2017, 7:5111-5129. [10] CHOI J B, LAKES R S. Non-linear properties of metallic cellular materialswith a negative Poisson's ratio[J]. Journal of Materials Science, 1992, 27(19):5375-5381. [11] DONOGHUE J P, ALDERSON K L, EVANS K E. The fracture toughness of composite laminates with a negative Poisson's ratio[J]. Physica Status Solidi (B), 2009, 246(9):2011-2017. [12] CHEKKAL I, BIANCHI M, REMILLAT C, et al. Vibro-acoustic properties of auxetic open cell foam:model and experimental results[J]. Acta Acustica United Acustica, 2010, 96:266-274. [13] 张梗林, 杨德庆.船舶宏观负泊松比蜂窝夹芯隔振器优化设计[J]. 振动与冲击, 2013, 32(22):68-72. ZHANG G L, YANG D Q. Optimization design of an auxetic honeycomb isolator in a ship[J]. Journal of Vibration and Shock, 2013, 32(22):68-72. [14] 张相闻, 杨德庆. 船用新型抗冲击隔振蜂窝基座[J]. 振动与冲击, 2015, 34(10):40-45. ZHANG X W, YANG D Q. A novel marine impact resistance and vibration isolation cellular base[J]. Journal of Vibration and Shock, 2015, 34(10):40-45. [15] ZHANG X W, YANG D Q. Numerical and experimental studies of a light-weight auxetic cellular vibration isolation base[J]. Shock and Vibration, 2016, 9:1-16. [16] WANG Z Y, HU H. Auxetic materials and their potential applications in textiles[J]. Textile Research Journal, 2014, 84(15):1600-1611. [17] EVANS K E, ALDERSON A. Auxetic materials:functional materials and structures from lateral thinking[J]. Advanced Materials, 2000, 12:617-628. [18] CARNEIRO V H, MEIRELES J, PUGA H. Auxetic materials-a review[J]. Materials Science-Poland, 2013, 31(4):561-571. [19] CRESPO J, FRANCISCO J M. A continuum approach for the large strain finite element analysis of auxetic materials[J]. International Journal of Mechanical Sciences, 2018, 135:441-457. [20] YANG L, HARRYSSON O, WEST H, et al. Mechanical properties of 3D re-entrant honeycomb auxetic structures realized via additive manufacturing[J]. International Journal of Solids and Structures, 2015, 69/70:475-490. [21] CARNEIRO V H, PUGA H. Axisymmetric auxetics[J]. Composite Structures, 2018, 195:232-248. [22] HU L L, LUO Z R, ZHANG Z Y, et al. Mechanical property of re-entrant anti-trichiral honeycombs under large deformation[J]. Composites:Part B, 2019, 163:107-120. [23] WANG H, LU Z X, YANG Z Y, et al. A novel re-entrant auxetic honeycomb with enhanced in-plane impact resistance[J]. Composite Structures, 2019, 8:758-770. [24] KIM J, SHIN D, YOO D S, et al. Regularly configured structures with polygonal prisms for three-dimensional auxetic behavior[J]. Proceedings of the Royal Society A, 2017, 473(2202):20160926. [25] LAKES R. Deformation mechanisms in negative Poisson's ratio materials:structural aspects[J]. Journal of Materials Science, 1991, 26(9):2287-2292. [26] GRIMA J N, GATT R, FARRUGIA P S, et al. On the properties of auxetic meta-tetrachiral structures[J]. Physica Status Solidi (b), 2008, 245(3):511-520. [27] ALDERSON A, EVANS K E. Modelling concurrent deformation mechanisms in auxetic microporous polymers[J]. Journal of Materials Science, 1997, 32(11):2797-2809. [28] MAHADEVAN L, RICA S. Self-organized origami[J]. Science, 2005, 307:1740. [29] LAKES R. Deformation mechanisms in negative Poisson's ratio materials:structural aspects[J]. Journal of Materials Science, 1991, 26(9):2287-2292. [30] JAVID F, LIU J, SHIM J, et al. Mechanics of instability-induced pattern transformations in elastomeric porous cylinders[J]. Journal of the Mechanics and Physics of Solids, 2016, 96:1-17. [31] SAXENA K K, DAS R, CALIUS E P. Three decades of auxetics research-materials with negative Poisson's ratio:a review[J]. Advanced Engineering Materials, 2016, 18(11):1847-1870. [32] GRIMA J N, GATT R, ALDERSON A. On the potential of connected stars as auxetic systems[J]. Molecular Simulation, 2005, 13:923-934. [33] LI Y, OLA H, HARVEY W, et al. Mechanical properties of 3D re-entrant honeycomb auxetic structures realized via additive manufacturing[J]. International Journal of Solids and Structures, 2015, 69/70:475-490. [34] GRIMA J N, GATT R, ALDERSON A, et al. On the auxetic properties of rotating rectangles' with different connectivity[J]. Journal of the Physical Society of Japan, 2005, 74:2866-2867. [35] ALSERSON A, ALDERSON K L, ATTARD D, et al. Elastic constants of 3-, 4- and 6-connected chiral and anti-chiral honeycombs subject to uniaxial in-plane loading[J]. Composites Science and Technology, 2010, 70:1042-1048. [36] CHAN S H, MICHAEL E. P, RODERIC S L. Chiral three-dimensional isotropic lattices with negative Poisson's ratio[J]. Physics Status Solidi B, 2016, 253(7):1243-125. [37] EVANS K E, CADDOCK B D. Microporous materials with negative Poisson's ratios Ⅱ. mechanismsand interpretation[J]. Journal of Physics D, 1989, 22:1877-1883. [38] HE C, LIU P, GRIFFIN A C. Toward negative Poisson ratio polymers through molecular design[J]. Macromolecules, 1998, 31:3145-3147. [39] LV C, KRISHNARAJU D, KONJEVOD G, et al. Origami based mechanical metamaterials[J]. Scientific Reports, 2014, 4:5979. [40] BOUAZIZ O, MASSE J P, ALLAIN S, et al. Compression of crumpled aluminum thin foils and comparison with other cellular materials[J]. Materials Science and Engineering:A, 2013, 570:1-17. [41] BERTOLDI K, BOYCE M C, DESCHANEL S, et al. Mechanics of deformation-triggered pattern transformations and superelastic behavior in periodic elastomeric structures[J]. Journal of the Mechanics and Physics of Solids, 2008, 56:2642-2668. [42] SHIM J, PERDIGOU C, CHEN E R, et al. Buckling-induced encapsulation of structured elastic shells under pressure[J]. Proceedings of the National Academy of Sciences of the United States of America, 2012, 109:5978-5983. [43] MILLER W, HOOK P B, SMITH C W, et al. The manufacture and characterisation of a novel, low modulus, negative Poisson's ratio composite[J]. Composite Science Technology, 2009, 69:651-655. [44] GRIMA J N, RAVIRALA, GALEA R, et al. Modelling and testing of a foldable macrostructure exhibiting auxetic behaviour[J]. Physica Status Solidi (b), 2011, 248(1):117-122. [45] RAVIRALA N, ALDERSON A, ALDERSON K L. Interlocking hexagons model for auxetic behaviour[J]. Journal of Materials Science, 2007, 42(17):7433-7445. [46] SMITH C W, GRIMA J N, EVANS K E. A novel mechanism for generating auxetic behaviour in reticulated foams:missing rib foam model[J]. Acta Materialia, 2000, 48(17):4349-4356. [47] GASPAR N, SMITH C W, ALDERSON A, et al. A generalised three-dimensional tethered-nodule model for auxetic materials[J]. Journal of Materials Science, 2011, 46(2):372-384. [48] DIRRENBERGER J, FOREST S, JEULIN D. Effective elastic properties of auxetic microstructures:anisotropy and structural applications[J]. International Journal of Mechanics and Materials in Design, 2013, 9(1):21-33. [49] GRIMA J N, GATT R. Perforated sheets exhibiting negative Poisson's ratios[J]. Advanced Engineering Materials, 2010, 12(6):460-464. [50] MIZZI L, AZZOPARDI K M, ATTARD D, et al. Auxetic metamaterials exhibiting giant negative Poisson's ratios[J]. Physica Status Solidi-rapid Research Letters, 2015, 9(7):425-430. [51] BAUGHMAN R H, SHACKLETTE J M, ZAKHIDOV A A, et al. Negative Poisson's ratios as a common feature of cubic metals[J]. Nature, 1998, 392:362-365. [52] 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[J]. 中国机械工程, 2012(5):542-546. YAN F F, XU X D. Negative Poisson's ratio honeycomb structure and its applications in structure design of morphing aircraft[J]. China Mechanical Engineering, 2012(5):542-546. [53] JACOBS S, COCONNIER C, DIMIAIO D, et al. Deployable auxetic shape memory alloy cellular antenna demonstrator:design, manufacturing and modal testing[J]. Smart Materials and Structures, 2012, 21(7):075013. [54] 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[J]. 汽车安全与节能学报, 2013, 4(3):215-222. QI C, AN W Z, YANG S. FE simulation of the occupant crash protection performance of the negative Poisson's ratio seat belt webbing[J]. Journal of Automotive Safety and Energy, 2013, 4(3):215-222. [55] AVELLANEDA M, SWART P J. Calculating the performance of 1-3 piezocomposites for hydrophone applications:an effective medium approach[J]. Journal of the Acoustica1 Society of America, 1998, 103:1449-1467. [56] ZHOU G, MA Z D, LI G Y, et al. Design optimization of a novel NPR crash box based on multi-objective genetic algorithm[J]. Struct Multidisc Optim, 2016, 54:673-684. [57] 马丕波, 常玉萍, 蒋高明. 负泊松比针织结构及其应用[J]. 纺织导报, 2015, 7:47-50. MA P B, CHANG Y P, JIANG G M. Knitted structures with negative Poisson's ratio[J]. China Textile Leader, 2015, 7:47-50. [58] SAXENA K K, DAS R, CALIUS E P. Three decades of auxetics research-materials with negative Poisson's ratio:a review[J]. Advanced Engineering Materials, 2016, 18(11):1847-1870. [59] ALI M, ZEESHAN M, AHMED S, et al. Development and comfort characterization of 2D-woven auxetic fabric for wearable and medical textile applications[J]. Clothing and Textiles Research Journal, 2018, 36(3):199-214.
2021, Vol. 49 
