Layered elastic metamaterials, which simultaneously exhibit negative effective mass density and bulk modulus, can be obtained with a unit cell of multiphase materials. In this paper, a systematic method for the design of multiphase layered elastic metamaterials is presented, and single objective along with multiobjective optimization models are proposed. Using the multiobjective genetic algorithm, the topologies of the layered periodic unit cell are designed for target frequency band structures characterizing negative wavenumbers. These obtained metamaterials with periodic unit cells can exhibit a negative refractive index in several frequency spectrums. This will be a reference for the design of 2/3-D elastic/acoustic negative refraction metamaterials.

References

References
1.
Veselago
,
V. G.
,
1968
, “
The Electrodynamics of Substances With Simultaneously Negative Values of ε and μ
,”
Sov. Phys. Usp.
,
10
, pp.
509
514
.10.1070/PU1968v010n04ABEH003699
2.
Pendry
,
J. B.
,
Holden
,
A. J.
, and
Stewart
,
W. J.
,
1996
, “
Extremely Low Frequency Plasmons in Metallic Mesostructures
,”
Phys. Rev. Lett.
,
76
, pp.
4773
4476
.10.1103/PhysRevLett.76.4773
3.
Pendry
,
J. B.
,
Holden
,
A. J.
, and
Robbins
,
D. L.
1999
, “
Magnetism From Conductors and Enhanced Nonlinear Phenomena
,”
IEEE Trans Microwave Theory Tech.
,
47
, pp.
2075
2084
.10.1109/22.798002
4.
Shelby
,
R. A.
,
Smith
,
D. R.
, and
Schultz
,
S.
,
2001
, “
Experimental Verification of a Negative Index of Refraction
,”
Science
,
292
, pp.
77
79
.10.1126/science.1058847
5.
Liu
,
Z. Y.
,
Zhang
,
X. X.
,
Mao
,
Y. W.
,
Zhu
,
Y. Y.
,
Yang
,
Z. Y.
,
Chan
,
C. T.
, and
Sheng
,
P. W.
,
2000
, “
Locally Resonant Sonic Materials
,”
Science
,
289
, pp.
1734
1736
.10.1126/science.289.5485.1734
6.
Liu
,
Z. Y.
,
Chan
,
C. T.
, and
Sheng
,
P.
,
2005
, “
Analytic Model of Phononic Crystals With Local Resonances
,”
Phys. Rev. B
,
71
, p.
014103
.10.1103/PhysRevB.71.014103
7.
Fang
,
N.
,
Xi
,
D. J.
,
Xu
,
J. Y.
,
Ambati
,
M.
,
Srituravanich
,
W.
,
Sun
,
C.
, and
Zhang
,
X.
,
2006
, “
Ultrasonic Metamaterials With Negative Modulus
,”
Nature Mater.
,
5
, pp.
452
456
.10.1038/nmat1644
8.
Ding
,
Y. Q.
,
Liu
,
Z. Y.
,
Qiu
,
C. Y.
, and
Shi
,
J.
,
2007
, “
Metamaterial With Simultaneously Negative Bulk Modulus and Mass Density
,”
Phys. Rev. Lett.
,
99
, p.
093904
.10.1103/PhysRevLett.99.093904
9.
Deng
,
K.
,
Ding
,
Y. Q.
,
He
,
Z. J.
,
Zhao
,
H. P.
,
Shi
,
J.
, and
Liu
,
Z. Y.
,
2009
, “
Theoretical Study of Subwavelength Imaging by Acoustic Metamaterial Slabs
,”
J. Appl. Phys.
,
105
, p.
124909
.10.1063/1.3153976
10.
Pope
,
S. A.
, and
Daley
,
S.
,
2010
, “
Viscoelastic Locally Resonant Double Negative Metamaterials With Controllable Effective Density and Elasticity
,”
Phys. Lett. A
,
374
, pp.
4250
4255
.10.1016/j.physleta.2010.08.037
11.
Baz
,
A. M.
,
2010
, “
An Active Acoustic Metamaterial With Tunable Effective Density
,”
ASME J. Vibr. Acoust.
,
132
, p.
041011
.10.1115/1.4000983
12.
Liu
,
X. N.
,
Hu
,
G. K.
,
Huang
,
G. L.
, and
Sun
,
C. T.
,
2011
, “
An Elastic Metamaterial With Simultaneously Negative Mass Density and Bulk Modulus
,”
Appl. Phys. Lett.
,
98
, p.
251907
.10.1063/1.3597651
13.
Yang
,
J. J.
,
Huang
,
M.
,
Yang
,
C. F.
, and
Cai
,
G. H.
,
2011
, “
A Metamaterial Acoustic Concentrator With Regular Polygonal Cross Section
,”
ASME J. Vibr. Acoust.
,
133
(
6
), p.
061016
.10.1115/1.4004678
14.
Li
,
J.
,
Fok
,
L.
,
Yin
,
X.
,
Bartal
,
G.
, and
Zhang
,
X.
,
2009
, “
Experimental Demonstration of an Acoustic Magnifying Hyperlens
,”
Nature Mater.
,
8
, pp.
931
934
.10.1038/nmat2561
15.
Xu
,
W. K.
, and
Wang
,
W.
,
2012
, “
Single-Negative Properties Based on the Bandgaps of One-Dimensional Phononic Crystal
,”
Appl. Mech. Mater.
,
105–107
, pp.
279
282
.10.4028/www.scientific.net/AMM.105-107.279
16.
Hussein
,
M. I.
,
Hulbert
,
G. M.
, and
Scott
,
R. A.
,
2006
, “
Dispersive Elastodynamics of 1D Banded Materials and Structures: Analysis
,”
J. Sound Vib.
,
289
, p.
779
806
.10.1016/j.jsv.2005.02.030
17.
Nemat-Nasser
,
S.
, and
Srivastava
,
A.
,
2011
, “
Negative Effective Dynamic Mass-Density and Stiffness: Micro-Architecture and Phononic Transport in Periodic Composites
,”
AIP Adv.
,
1
, p.
041502
.10.1063/1.3675939
18.
Hussein
,
M. I.
,
Hamza
,
K.
, and
Hulbert
,
G. M.
,
2006
, “
Multiobjective Evolutionary Optimization of Periodic Layered Materials for Desired Wave Dispersion Characteristics
,”
Struct. Multidiscip. Optim.
,
31
, pp.
60
75
.10.1007/s00158-005-0555-8
19.
Fredkin
,
D. R.
, and
Ron
,
A.
,
2002
, “
Effectively Left-Handed (Negative Index) Composite Material
,”
Appl. Phys. Lett.
,
81
, pp.
1753
1755
.10.1063/1.1505119
20.
Wang
,
D.
,
Fan
,
Z. X.
,
Huang
,
J. B.
, and
Wang
,
Y. J.
,
2006
, “
Symmetrical Periods Used as Matching Layers in Multilayer Thin Film Design
,”
Chin. Opt. Lett.
,
4
, pp.
675
677
.
21.
Wang
,
Z. G.
,
Lee
,
S. H.
,
Kim
,
C. K.
,
Park
,
C. M.
,
Nahm
,
K.
, and
Nikitov
,
S. A.
,
2008
, “
Effective Medium Theory of the One-Dimensional Resonance Phononic Crystal
,”
J. Phys.: Condens. Matter.
,
20
, p.
055209
.10.1088/0953-8984/20/5/055209
22.
Wu
,
R. X.
,
2005
, “
Effective Negative Refraction Index in Periodic Metal-Ferrite-Metal Film Composite
,”
J Appl. Phys.
,
97
, p.
076105
.10.1063/1.1883718
23.
Smith
,
D. R.
,
Vier
,
D. C.
,
Koschny
,
T.
, and
Soukoulis
,
C. M.
,
2005
, “
Electromagnetic Parameter Retrieval From Inhomogeneous Metamaterials
,”
Phys. Rev. E
,
71
, p.
036617
.10.1103/PhysRevE.71.036617
24.
Bendsoe
,
M. P.
, and
Sigmund
,
O.
,
1999
, “
Material Interpolation Schemes in Topology Optimization
,”
Arch. Appl. Mech.
,
69
, pp.
635
654
.10.1007/s004190050248
25.
Depine
,
R. A.
, and
Lakhtakia
,
A.
,
2004
, “
A New Condition to Identify Isotropic Dielectric-Magnetic Materials Displaying Negative Phase Velocity
,”
Microwave Opt. Technol. Lett.
,
41
, pp.
315
316
.10.1002/mop.20127
26.
Deb
,
K.
,
Pratap
,
A.
,
Agarwal
,
S.
, and
Meyarivan
,
T.
,
2002
, “
A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II
,”
IEEE Trans. Evol. Comput.
,
6
, pp.
182
197
.10.1109/4235.996017
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