基于弹性力学的超构材料
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摘要
近年来以微结构为基本构造单元的人工超构材料,由于具有自然材料所不具备的可设计的奇异物性,在材料学、声学、光学、电磁学以及信息能源等领域具有巨大的发展潜力.超构材料的研究脱胎于电磁超构材料,但是近年来在声学、热学、静电、静磁学以及弹性力学领域取得了飞跃的发展,大大拓展了超构材料的研究领域.借助Milton图重点阐述了基于弹性力学的新型超构材料的超常特性及其主要类别:例如具有负的质量密度和负弹性模量的声学超构材料,具有负泊松比的拉胀超构材料,具有剪切模量G=0的反胀超构材料,以及高强度的超轻材料等新奇的人工超构材料.不仅如此,还结合变换力学着重描述了声波和弹性波在这类弹性力学超构材料中的传播特性,以及详细阐述了负弹性参数超构材料界面的声表面波的特征及其物理效应.最后结合弹性力学超构材料在我国的研究现状,对利用弹性力学超构材料和声波超构材料操纵弹性波和声波的传播以及开发设计新型弹性力学超构材料等问题作了总结与展望,希望推进此类材料在诸多研究领域的应用.
In recent years, artificial metamaterials base on micro structures are showing huge development potential in fields of materials science, acoustics, seismology and information technologies, due to their devisable physical singularities which do not exist in natural materials. The study of metamaterial was born out of electromagnetic metamaterial. Nowadays, metamaterials have achieved a big leap forward with developments in the fields of acoustic, thermal, static, static magnetic and elastic mechanics, which greatly expand their study fields. With the help of a Milton graph, we focus on the extraordinary characteristics of novel elastic mechanics-based metamaterials and their species, such as acoustic metamaterials with negative mass density and elastic modulus, auxetic metamaterials with negative Poisson's ratio, inverse bulging metamaterials with shear modulus G=0 and ultra-light materials with high strength. In addition, combining with the transform mechanical, this paper focuses on the propagation characteristics of acoustic and elastic waves in this elastic mechanics metamaterial and then elaborated the characteristics and physical effects of surface acoustic waves in the interface of metamaterials with negative elasticity parameters. Finally, we make a summary and prospect of the development of metamaterials combining with the elastic mechanics metamaterial research condition in China, such as metamaterial and acoustic metamaterial operating acoustic and elastic wave propagation using the elastic mechanics, design and development of a new type of elastic mechanics metamaterial. We hope this will help to accelerate the application of this metamaterial in many research fields.
In recent years, artificial metamaterials base on micro structures are showing huge development potential in fields of materials science, acoustics, seismology and information technologies, due to their devisable physical singularities which do not exist in natural materials. The study of metamaterial was born out of electromagnetic metamaterial. Nowadays, metamaterials have achieved a big leap forward with developments in the fields of acoustic, thermal, static, static magnetic and elastic mechanics, which greatly expand their study fields. With the help of a Milton graph, we focus on the extraordinary characteristics of novel elastic mechanics-based metamaterials and their species, such as acoustic metamaterials with negative mass density and elastic modulus, auxetic metamaterials with negative Poisson's ratio, inverse bulging metamaterials with shear modulus G=0 and ultra-light materials with high strength. In addition, combining with the transform mechanical, this paper focuses on the propagation characteristics of acoustic and elastic waves in this elastic mechanics metamaterial and then elaborated the characteristics and physical effects of surface acoustic waves in the interface of metamaterials with negative elasticity parameters. Finally, we make a summary and prospect of the development of metamaterials combining with the elastic mechanics metamaterial research condition in China, such as metamaterial and acoustic metamaterial operating acoustic and elastic wave propagation using the elastic mechanics, design and development of a new type of elastic mechanics metamaterial. We hope this will help to accelerate the application of this metamaterial in many research fields.
引文
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28 Lv C,Krishnaraju D,Konjevod G,et al.Origami based Mechanical Metamaterials.Sci Rep,2014,4,doi:10.1038/srep05979
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34 Li X F,Ni X,Feng L A,et al.Tunable unidirectional sound propagation through a sonic-crystal-based acoustic diode.Phys Rev Lett,2011,106:084301
35 Ambati M,Fang N,Sun C,et al.Surface resonant states and superlensing in acoustic metamaterials.Phys Rev B,2007,75:195447
36 Zhao D G,Liu Z Y,Qiu C Y,et al.Surface acoustic waves in two-dimensional phononic crystals:Dispersion relation and the eigenfield distribution of surface modes.Phys Rev B,2007,76:144301
37 Zhou Y,Lu M H,Feng L,et al.Acoustic surface evanescent wave and its dominant contribution to extraordinary acoustic transmission and collimation of sound.Phys Rev Lett,2010,104:164301
38 Layman C N,Naify C J,Martin T P,et al.Highly anisotropic elements for acoustic pentamode applications.Phys Rev Lett,2013,111:024302
39 Cheng W,Wang J J,Jonas U,et al.Observation and tuning of hypersonic bandgaps in colloidal crystals.Nat Mater,2006,5:830–836
40 Ma G C,Yang M,Xiao S W,et al.Acoustic metasurface with hybrid resonances.Nat Mater,2014,13:873–878
2 Kushwaha M S,Halevi P,Dobrzynski,et al.Acoustic band-structure of periodic elastic composites.Phys Rev Lett,1993,71:2022–2025
3 Ao X Y,Chan C T.Complex band structures and effective medium descriptions of periodic acoustic composite systems.Phys Rev B,2009,80:235118
4 Liu Z Y,Zhang X X,Mao Y W,et al.Locally resonant sonic materials.Science,2000,289:1734–1736
5 Lu M H,Zhu S N,Ming N B.Negative birefraction of acoustic wave in a sonic crystal.Nat Mater,2007,6:744–748
6 Zhang S,Xia C G,Fang N.Broadband acoustic cloak for ultrasound waves.Phys Rev Lett,2011,106:024301
7 Berryman J G.Long-wavelengh propagation in composite elastic media I.Spherical inclusions.Acoust Soc Am,1980,68:1809–1819
8 Park J W,Park B,Kim D,et al.Determination of effective mass density and modulus for resonant metamaterials.J Acoust Soc Am,2012,132 :2793–2799
9 Lee S H,Park C M,Seo Y M,et al.Composite acoustic medium with simultaneously negative density and modulus.Phys Rev Lett,2010,104:054301
10 Fleury R,Alu A.Extraordinary sound transmission through density-near-zero ultranarrow channels.Phys Rev Lett,2013,111:055501
11 Liang Z X,Li J S.Extreme acoustic metamaterial by coiling up space.Phys Rev Lett,2012,108:114301
12 Silva A,Monticone F,Castaldi G,et al.Performing mathematical operations with metamaterials.Science,2014,343:160–163
13 Zigoneanu L,Popa B I,Starr A F,et al.Design and measurements of a broadband two-dimensional acoustic metamaterial with anisotropic effective mass density.J Appl Phys,2011,109:054906
14 Popa B I,Cummer S A.Homogeneous and compact acoustic ground cloaks.Phys Rev B,2011,83:224304
15 Zhu J,Christensen J,Jung J,et al.A holey-structured metamaterial for acoustic deep-subwavelength imaging.Nature Phys,2011,7:52–55
16 Li J S,Fok L,Yin X B,et al.Experimental demonstration of an acoustic magnifying hyperlens.Nat Mater,2009,8:931–934
17 Liu Z Y,Chan C T,Sheng P.Analytic model of phononic crystals with local resonances.Phys Rev B,2005,71:014103
18 Baz A.The structure of an active acoustic metamaterial with tunable effective density.New J Phys,2009,11:123010
19 Milton G W.Composite materials with poisson’s ratios close to-1.J Mech Phys Solids,1992,40:1105–1137
20 Kadic M,Buckmann T,Stenger N,et al.On the practicability of pentamode mechanical metamaterials.Appl Phys Lett,2012,100:191901
21 Lakes R.Foam structures with a negative poissons ratio.Science,1987,235:1038–1040
22 Buckmann T,Schittny R,Thiel M,et al.On three-dimensional dilational elastic metamaterials.New J Phys,2014,16:033032
23 Babaee s,Shim J,Weaver J C,et al.3D soft metamaterials with negative poisson's ratio.Adv Mater,2013,25:5044–5049
24 Paulose J,Chen B G,Vincenzo V.Topological modes bound to dislocations in mechanical metamaterials.Ar Xiv preprint 2014,ar Xiv:1406.3323
25 Schaedler T A,Jacobsen A J,Torrents A,et al.Ultralight metallic microlattices.Science,2011,334:962–965
26 Mecklenburg M,Schuchardt A,Mishra Y K,et al.Aerographite:Ultra lightweight,flexible nanowall,carbon microtube material with outstanding mechanical performance.Adv Mater,2012,24:3486–3490
27 Florijn B,Coulais C,Hecke V M.Programmable mechanical metamaterials.Ar Xiv preprint,2014,ar Xiv:1407.4273
28 Lv C,Krishnaraju D,Konjevod G,et al.Origami based Mechanical Metamaterials.Sci Rep,2014,4,doi:10.1038/srep05979
29 Yang S X,Page J H,Liu Z Y,et al.Ultrasound tunneling through 3D phononic crystals.Phys Rev Lett,2002,88:104301
30 Zhang X D,Liu Z Y.Extremal transmission and beating effect of acoustic waves in two-dimensional sonic crystals.Phys Rev Lett,2012,101:174301
31 Huang X Q,Lai Y,Hang Z H,et al.Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials.Nat Mater,2011,10:582–586
32 Torrent D,Sanchez-Dehesa J.Anisotropic mass density by radially periodic fluid structures.Phys Rev Lett,2010,105:174301
33 Liang B,Guo X S,Tu J.An acoustic rectifier.Nat Mater,2010,9:989–992
34 Li X F,Ni X,Feng L A,et al.Tunable unidirectional sound propagation through a sonic-crystal-based acoustic diode.Phys Rev Lett,2011,106:084301
35 Ambati M,Fang N,Sun C,et al.Surface resonant states and superlensing in acoustic metamaterials.Phys Rev B,2007,75:195447
36 Zhao D G,Liu Z Y,Qiu C Y,et al.Surface acoustic waves in two-dimensional phononic crystals:Dispersion relation and the eigenfield distribution of surface modes.Phys Rev B,2007,76:144301
37 Zhou Y,Lu M H,Feng L,et al.Acoustic surface evanescent wave and its dominant contribution to extraordinary acoustic transmission and collimation of sound.Phys Rev Lett,2010,104:164301
38 Layman C N,Naify C J,Martin T P,et al.Highly anisotropic elements for acoustic pentamode applications.Phys Rev Lett,2013,111:024302
39 Cheng W,Wang J J,Jonas U,et al.Observation and tuning of hypersonic bandgaps in colloidal crystals.Nat Mater,2006,5:830–836
40 Ma G C,Yang M,Xiao S W,et al.Acoustic metasurface with hybrid resonances.Nat Mater,2014,13:873–878