State-of-art of Metamaterials with Negative Poisson's Ratio

doi:10.3901/JME.2018.13.001

Abstract

Abstract: Since the concept of metamaterials is firstly proposed in the early 21st century, it has gradually developed into an important branch of new material technology. In recent years, dozens of metamaterials with diverse functions have emerged in endlessly in various fields. A comprehensive overview of metamaterials involved in acoustics, optics, thermology, mechanics and electromagnetics is stated. Focusing on metamaterials with negative Poisson's ratio, a research progress about the design of negative Poisson's ratio unit cells (including re-entrant structure, rotating polygons, chiral structure, etc.) is systematically reviewed in the perspective of their deformation mechanism. The thermal and acoustic metamaterials based on negative Poisson's ratio unit cells are detailed investigated from functional principles to basic properties. Prospects to the upcoming challenges and development trends of negative Poisson's ratio metamaterials are made.

Key words: cellular structure, compliant mechanism, metamaterial, negative Poisson's ratio

CLC Number:

TH112

YU Jingjun, XIE Yan, PEI Xu. State-of-art of Metamaterials with Negative Poisson's Ratio[J]. Journal of Mechanical Engineering, 2018, 54(13): 1-14.

References

[1] SMITH D R, PADILLA W J, VIER D C, et al. Composite medium with simultaneously negative permeability and permittivity[J]. Physical Review Letters, 2000, 84(18):4184-4187.
[2] KSHETRIMAYUM R S. A brief intro to metamaterials[J]. IEEE Potentials, 2005, 23(5):44-46.
[3] SHELBY R A, SMITH D R, NEMATNASSER S C, et al. Microwave transmission through a two-dimensional, isotropic, left-handed metamaterial[J]. Applied Physics Letters, 2001, 78(4):489-491.
[4] LIU Ruopeng, JI Chunlin, MOCK J J, et al. Broadband ground-plane cloak[J]. Science, 2009, 323(5912):366-369.
[5] YABLONOVITCH E, GMITTER T J, LEUNG K M. Photonic band structure:The face-centered-cubic case employing nonspherical atoms[J]. Physical Review Letters, 1991, 67(17):2295-2298.
[6] KHORASANINEJAD M, CHEN Weiting, DEVLIN R C, et al. Metalenses at visible wavelengths:Diffractionlimited focusing and subwavelength resolution imaging[J]. Science, 2016, 352(6290):1190-1194.
[7] 吴九汇,马富银,张思文,等. 声学超材料在低频减振降噪中的应用评述[J]. 机械工程学报, 2016, 52(13):68-78. WU Jiuhui, MA Fuyin, ZHANG Siwen, et al. Application of acoustic metamaterials in low-frequency vibration and noise reduction[J]. Journal of Mechanical Engineering, 2016, 52(13):68-78.
[8] LIU Zhengyou, ZHANG Xixiang, MAO Yiwei, et al. Locally resonant sonic materials[J]. Science, 2000, 289(5485):1734-1736.
[9] ZIGONEANU L, POPA B, CUMMER S A. Three-dimensional broadband omnidirectional acoustic ground cloak[J]. Nature Materials, 2014, 13(4):352-355.
[10] FAN C Z, GAO Y, HUANG J P. Shaped graded materials with an apparent negative thermal conductivity[J]. Applied Physics Letters, 2008, 92(25):251907.
[11] LI Jixi, GAO Yutang, HUANG J P. A bifunctional cloak using transformation media[J]. Journal of Applied Physics, 2010, 108(7):74504.
[12] NARAYANA S, SATO Y. Heat flux manipulation with engineered thermal materials[J]. Physical Review Letters, 2012, 108(21):214303.
[13] YU Xianglong, ZHOU Ji, LIANG Haiyi, et al. Mechanical metamaterials associated with stiffness, rigidity and compressibility:A brief review[J]. Progress in Materials Science, 2017, 94:114-173.
[14] BÜCKMANN T, THIEL M, KADIC M, et al. An elasto-mechanical unfeelability cloak made of pentamode metamaterials[J]. Nature Communications, 2014, 5:4130.
[15] SOKOLNIKOFF I S. Mathematical theory of elasticity[M]. Malabar:Krieger Publishing Company, 1983.
[16] AEH L. A Treatise on the mathematical theory of elasticity[M]. New York:Cambridge University Press, 1927.
[17] GUNTON D J, SAUNDERS G A. The Young's modulus and Poisson's ratio of arsenic, antimony and bismuth[J]. Journal of Materials Science, 1972, 7(9):1061-1068.
[18] LAKES R. Foam structures with a negative Poisson's ratio[J]. Science, 1987, 235(4792):1038-1040.
[19] CADDOCK B D, EVANS K E. Microporous materials with negative Poisson's ratios. I. Microstructure and mechanical properties[J]. Journal of Physics D:Applied Physics, 1989, 22(12):1877-1882.
[20] EVANS K E, CADDOCK B D. Microporous materials with negative Poisson's ratios. Ⅱ. Mechanisms and interpretation[J]. Journal of Physics D:Applied Physics, 1989, 22(12):1883-1887.
[21] MAY P R, FUSTER J M, HABER J, et al. Woodpecker drilling behavior. An endorsement of the rotational theory of impact brain injury[J]. Arch Neurol, 1979, 36(6):370-373.
[22] GIBSON L J, ASHBY M F. Cellular solids:Structure and properties[M]. New York:Cambridge University Press, 1997.
[23] ALMGREN R. An isotropic three-dimensional structure with Poisson's ratio=-1[J]. Journal of Elasticity, 1985, 15(4):427-430.
[24] LARSEN U D, SIGNUNG O, BOUWSTA S. Design and fabrication of compliant micromechanisms and structures with negative Poisson's ratio[J]. Journal of Microelectromechanical Systems, 1996, 6(2):99-106.
[25] GRIMA J N, GATT R, ALDERSON A, et al. On the potential of connected stars as auxetic systems[J]. Molecular Simulation, 2005, 31(13):925-935.
[26] KÖRNER C, LIEBOLDRIBEIRO Y. A systematic approach to identify cellular auxetic materials[J]. Smart Materials and Structures, 2015, 24(2):25013.
[27] WARMUTH F, OSMANLIC F, ADLER L, et al. Fabrication and characterisation of a fully auxetic 3D lattice structure via selective electron beam melting[J]. Smart Materials and Structures, 2017, 26(2):25013.
[28] SHOKRI Rad M, PRAWOTO Y, AHMAD Z. Analytical solution and finite element approach to the 3D re-entrant structures of auxetic materials[J]. Mechanics of Materials, 2014, 74:76-87.
[29] HENGSBACH S, LANTADA A D. Direct laser writing of auxetic structures:Present capabilities and challenges[J]. Smart Materials and Structures, 2014, 23(8):85033.
[30] MA Zhengdong. Three-dimensional auxetic structures and applications thereof:US, US7910193B2[P]. 2011-03-22.
[31] GRIMA J N, EVANS K E. Auxetic behavior from rotating squares[J]. Journal of Materials Science Letters, 2000, 19(17):1563-1565.
[32] GRIMA J N, FARRUGIA P, GATT R, et al. On the auxetic properties of rotating rhombi and parallelograms:A preliminary investigation[J]. Physica Status Solidi (b), 2008, 245(3):521-529.
[33] GRIMA J N, EVANS K E. Auxetic behavior from rotating triangles[J]. Journal of Materials Science, 2006, 41(10):3193-3196.
[34] EVANS K E, ALDERSON A. Rotation and dilation deformation mechanisms for auxetic behaviour in the α-cristobalite tetrahedral framework structure[J]. Physics and Chemistry of Minerals, 2001, 28(10):711-718.
[35] LAKES R. Deformation mechanisms in negative Poisson's ratio materials:Structural aspects[J]. Journal of Materials Science, 1991, 26(9):2287-2292.
[36] ALDERSON 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(7):1042-1048.
[37] ELIPE J C, LANTADA A. Comparative study of auxetic geometries by means of computer-aided design and engineering[J]. Smart Materials and Structures, 2012, 21(10):105004.
[38] GRIMA J N, GATT R, FARRUGIA P. On the properties of auxetic meta-tetrachiral structures[J]. Physica Status Solidi (b), 2008, 245(3):511-520.
[39] 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.
[40] HA C S, PLESHA M E, LAKES R S. Chiral three-dimensional isotropic lattices with negative Poisson's ratio[J]. Physica Status Solidi (b), 2016, 253(7):1243-1251.
[41] WU Lingling, LI Bo, ZHOU Ji. Isotropic negative thermal expansion metamaterials[J]. ACS Applied Materials & Interfaces, 2016, 8(27):17721-17727.
[42] FU Minghui, ZHENG Binbin, LI Weihua. A novel chiral three-dimensional material with negative Poisson's ratio and the equivalent elastic parameters[J]. Composite Structures, 2017, 176:442-448.
[43] ALDERSON A, EVANS K E. Modelling concurrent deformation mechanisms in auxetic microporous polymers[J]. Journal of Materials Science, 1997, 32(11):2797-2809.
[44] GRIMA J N, GATT R. Perforated sheets exhibiting negative Poisson's ratios[J]. Advanced Engineering Materials, 2010, 12(6):460-464.
[45] 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.
[46] GRIMA J N, GAT R, ELLUL B, et al. Auxetic behaviour in non-crystalline materials having star or triangular shaped perforations[J]. Journal of Non-Crystalline Solids, 2010, 356(37-40):1980-1987.
[47] TAYLOR M, FRANCESCONI L, GERENDAS M, et al. Low porosity metallic periodic structures with negative Poisson's ratio[J]. Advanced Materials, 2014, 26(15):2365-2370.
[48] OVERVELDE J T, SHAN S, BERTOLDI K. Compaction through buckling in 2D periodic, soft and porous structures:Effect of pore shape[J]. Advanced Materials, 2012, 24(17):2337-2342.
[49] RAVIRALA N, ALDERSON A, ALDERSON K L. Interlocking hexagons model for auxetic behaviour[J]. Journal of Materials Science, 2007, 42(17):7433-7445.
[50] 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.
[51] GASPAR N, REN X, SMITH C, et al. Novel honeycombs with auxetic behaviour[J]. Acta Materialia, 2005, 53(8):2439-2445.
[52] GRIMA J N, WILLIAMS J J, EVANS K E. Networked calix[4] arene polymers with unusual mechanical properties[J]. Chemical Communications, 2005(32):4065.
[53] GRIMA J N, WINCZEWSKI S, MIZZI L, et al. Tailoring graphene to achieve negative Poisson's ratio Properties[J]. Advanced Materials, 2015, 27(8):1455-1459.
[54] 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, 570:1-7.
[55] RODNEY D, GADOT B, MARTINEZ O R, et al. Reversible dilatancy in entangled single-wire materials[J]. Nature Materials, 2015, 15(1):72-77.
[56] VOCKE R D, KOTHERA C S, WOODS B K S, et al. Development and testing of a span-extending morphing wing[J]. Journal of Intelligent Material Systems and Structures, 2011, 22(9):879-890.
[57] JONES O. Cushioned earphones:US, US6412593B1[P]. 2002-06-02.
[58] TAKENAKA K. Negative thermal expansion materials:Technological key for control of thermal expansion[J]. Science and Technology of Advanced Materials, 2016, 13(1):13001.
[59] CRIBB J L. Shrinkage and thermal expansion of a two phase material[J]. Nature, 1968, 220:576-577.
[60] HAMMONDS K D, DOVE M T, GIDDY A P, et al. Rigid-unit phonon modes and structural phase transitions in framework silicates[J]. American Mineralogist, 1996, 81(9):1057-1079.
[61] LAKES R. Cellular solid structures with unbounded thermal expansion[J]. Journal of Materials Science Letters, 1996, 15(6):475-477.
[62] HA C S, HESTEKIN E, LI J, et al. Controllable thermal expansion of large magnitude in chiral negative Poisson's ratio lattices[J]. Physica Status Solidi (b), 2015, 252(7):1431-1434.
[63] QU Jingyuan, KADIC M, NABER A, et al. Micro-structured two-component 3D metamaterials with negative thermal-expansion coefficient from positive constituents[J]. Scientific Reports, 2017, 7:40643.
[64] SIGMUND O, TORQUATO S. Composites with extremal thermal expansion coefficients[J]. Applied Physics Letters, 1996, 69(21):3203.
[65] CHEN B C, SILVA E C, KIKUCHI N. Advances in computational design and optimization with application to MEMS[J]. International Journal for Numerical Methods in Engineering, 2001, 52(12):23-62.
[66] QI J, HALLORAN J W. Negative thermal expansion artificial material from iron-nickel alloys by oxide co-extrusion with reductive sintering[J]. Journal of Materials Science, 2004, 39(13):4113-4118.
[67] TAKEZAWA A, KOBASHI M, KITAMURA M. Porous composite with negative thermal expansion obtained by photopolymer additive manufacturing[J]. APL Materials, 2015, 3(7):76103.
[68] TAKEZAWA A, KOBASHI M. Design methodology for porous composites with tunable thermal expansion produced by multi-material topology optimization and additive manufacturing[J]. Composites Part B:Engineering, 2017, 131:21-29.
[69] JEFFERSON G, PARTHASARATHY T A, KERANS R J. Tailorable thermal expansion hybrid structures[J]. International Journal of Solids and Structures, 2009, 46(11-12):2372-2387.
[70] LIM T. Anisotropic and negative thermal expansion behavior in a cellular microstructure[J]. Journal of Materials Science, 2005, 40(12):3275-3277.
[71] STEEVE C A, LUCATO S L, HE M, et al. Concepts for structurally robust materials that combine low thermal expansion with high stiffness[J]. Journal of the Mechanics and Physics of Solids, 2007, 55(9):1803-1822.
[72] STEEVES C A, MMERCER C, ANTINUCCI E, et al. Experimental investigation of the thermal properties of tailored expansion lattices[J]. International Journal of Mechanics and Materials in Design, 2009, 5(2):195-202.
[73] YAMAMOTO N, GDOUTOS E, TODA R, et al. Thin films with ultra-low thermal expansion[J]. Advanced Materials, 2014, 26(19):3076-3080.
[74] WEI Kai, CHEN Haosen, PEI Yongmao, et al. Planar lattices with tailorable coefficient of thermal expansion and high stiffness based on dual-material triangle unit[J]. Journal of the Mechanics and Physics of Solids, 2016, 86:173-191.
[75] HOPKINS J B, SONG Y, LEE H, et al. Polytope sector-based synthesis and analysis of microstructural architectures with tunable thermal conductivity and expansion[J]. Journal of Mechanical Design, 2016, 138(5):51401.
[76] WANG Qingming, JACKSON J A, GE Qi, et al. Lightweight mechanical metamaterials with tunable negative thermal expansion[J]. Physical Review Letters, 2016, 117(17).
[77] KUSHWAHA M S, HALEVI P, DOBRZYNSKI L, et al. Acoustic band structure of periodic elastic composites[J]. Physical Review Letters, 1993, 71(13):2022-2025.
[78] SCARPA F, TOMLINSON G. Theoretical characteristics of the vibration of sandwich plates with in-plane negative Poisson's ratio values[J]. Journal of Sound and Vibration, 2000, 230(1):45-67.
[79] RUZZENE M, SCARPA F. Control of wave propagation in sandwich beams with auxetic core[J]. Journal of Intelligent Material Systems and Structures, 2003, 14(7):443-453.
[80] RUZZENE M, SCARPA F, SORANNA F. Wave beaming effects in two-dimensional cellular structures[J]. Smart Materials and Structures, 2003, 12(3):363-372.
[81] RUZZENE M. Vibration and sound radiation of sandwich beams with honeycomb truss core[J]. Journal of Sound and Vibration, 2004, 277(4-5):741-763.
[82] GONELLA S, RUZZENE M. Analysis of in-plane wave propagation in hexagonal and re-entrant lattices[J]. Journal of Sound and Vibration, 2008, 312(1-2):125-139.
[83] 黄毓,刘书田. 二维格栅材料带隙特性分析与设计[J]. 力学学报, 2011, 43(2):316-329. HUANG Yu, LIU Shutian. Analysis and design of two dimensional lattice materials with band-gap characteristics[J]. Chinese Journal of Theoretical and Applied Mechanics, 2011, 43(2):316-329.
[84] MENG Junmiao, DENG Zichen, ZHANG Kai, et al. Band gap analysis of star-shaped honeycombs with varied Poisson's ratio[J]. Smart Materials and Structures, 2015, 24(9):95011.
[85] KRÖDEL S, DELPERO T, BERGAMINI A, et al. 3D auxetic microlattices with independently controllable acoustic band gaps and quasi-static elastic moduli[J]. Advanced Engineering Materials, 2014, 16(4):357-363.
[86] WARMUTH F, KRÖDEL C. Phononic band gaps in 2D quadratic and 3D cubic cellular structures[J]. Materials, 2015, 8(12):8327-8337.
[87] SPADONI A, RUZZENE M. Structural and acoustic behavior of chiral truss-core beams[J]. Journal of Vibration and Acoustics, 2006, 128(5):616.
[88] 徐时吟,黄修长,华宏星. 六韧带手性结构的能带特性[J]. 上海交通大学学报, 2013, 47(2):167-172. XU Shiyin, HUANG Xiuchang, HUA Hongxing. Study on the band structure of hexagonal chiral Structures[J]. Journal of Shanghai Jiaotong University, 2013, 47(2):167-172.
[89] DONG Haowen, WANG Yuesheng, WANG Yuefeng, et al. Reducing symmetry in topology optimization of two-dimensional porous phononic crystals[J]. AIP Advances, 2015, 5(11):117149.
[90] 严珠妹. 含手性谐振单元声子晶体的带隙和传输特性研究[D]. 北京:北京交通大学, 2016. YAN Zhumei. Bandgap and propagation properties of phononic crystals with chirally resonant units[D]. Beijing:Beijing Jiaotong University, 2016.
[91] BILLON K, ZAMPETAKIS I, SCARPA F, et al. Mechanics and band gaps in hierarchical auxetic rectangular perforated composite metamaterials[J]. Composite Structures, 2017, 160:1042-1050.
[92] 于靖军,郝广波,陈贵敏,等. 柔性机构及其应用研究进展[J]. 机械工程学报, 2015, 51(13):53-68. YU Jingjun, HAO Guangbo, CHEN Guimin, et al. State-of-arts of compliant mechanisms and their applicaitons[J]. Journal of Mechanical Engineering,2015, 51(13):53-68.
[93] FAN Xiqiu, ZHANG Honghai, WANG Xuefeng, et al. Nanoimprint lithography technology with automatic alignment[J]. Chinese Journal of Mechanical Engineering, 2007, 20(3):1-5.