Research Papers

Multi-Objective Optimization of Layered Elastic Metamaterials With Multiphase Microstructures

[+] Author and Article Information
Weikai Xu

Key Laboratory of Liaoning Province for Composite Structural Analysis of Aerocraft and Simulation,
Shenyang Aerospace University,
Shenyang 110136, China
e-mail: weikaixu@gmail.com

Wei Wang

School of Civil Engineering,
Shenyang Jianzhu University,
Shenyang 110168, China

Tianzhi Yang

Department of Astronautics,
Shenyang Aerospace University,
Shenyang 110136, China

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received April 30, 2012; final manuscript received February 21, 2013; published online June 6, 2013. Assoc. Editor: Massimo Ruzzene.

J. Vib. Acoust 135(4), 041010 (Jun 06, 2013) (6 pages) Paper No: VIB-12-1132; doi: 10.1115/1.4023900 History: Received April 30, 2012; Revised February 21, 2013

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.

Copyright © 2013 by ASME
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Veselago, V. G., 1968, “The Electrodynamics of Substances With Simultaneously Negative Values of ε and μ,” Sov. Phys. Usp., 10, pp. 509–514. [CrossRef]
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. [CrossRef] [PubMed]
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. [CrossRef]
Shelby, R. A., Smith, D. R., and Schultz, S., 2001, “Experimental Verification of a Negative Index of Refraction,” Science, 292, pp. 77–79. [CrossRef] [PubMed]
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. [CrossRef] [PubMed]
Liu, Z. Y., Chan, C. T., and Sheng, P., 2005, “Analytic Model of Phononic Crystals With Local Resonances,” Phys. Rev. B, 71, p. 014103. [CrossRef]
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. [CrossRef]
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. [CrossRef] [PubMed]
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. [CrossRef]
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. [CrossRef]
Baz, A. M., 2010, “An Active Acoustic Metamaterial With Tunable Effective Density,” ASME J. Vibr. Acoust., 132, p. 041011. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Fredkin, D. R., and Ron, A., 2002, “Effectively Left-Handed (Negative Index) Composite Material,” Appl. Phys. Lett., 81, pp. 1753–1755. [CrossRef]
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.
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. [CrossRef]
Wu, R. X., 2005, “Effective Negative Refraction Index in Periodic Metal-Ferrite-Metal Film Composite,” J Appl. Phys., 97, p. 076105. [CrossRef]
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. [CrossRef]
Bendsoe, M. P., and Sigmund, O., 1999, “Material Interpolation Schemes in Topology Optimization,” Arch. Appl. Mech., 69, pp. 635–654. [CrossRef]
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. [CrossRef]
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. [CrossRef]


Grahic Jump Location
Fig. 1

The sketch of the unit cell

Grahic Jump Location
Fig. 2

Case I: (a) the optimal topological configuration of the result (half of the cell), (b) the dispersion curves, (c) bulk modulus, and (d) mass density

Grahic Jump Location
Fig. 3

The Pareto diagram of the multiobjective design

Grahic Jump Location
Fig. 4

Case II: (a) the topological configuration of the design selected from the Pareto front (half of the cell), (b) the dispersion curves, (c) bulk modulus, and (d) mass density



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