Multi-displacement microstructure continuum modeling of anisotropic elastic metamaterials

Wave Motion

Volumn 49, Issue 3, 2012, Pages 411-426

  Liu, A P ^a,b   Zhu, R ^b   Liu, X N ^a,b   Hu, G K ^a   Huang, G L ^b  

^a BEIJING INSTITUTE OF TECHNOLOGY   (China)

^b University of Arkansas ^*  (United States)

Author keywords

Anisotropic mass density; Continuum; Metamaterial; Multi displacement; Wave propagation

Indexed keywords

ACOUSTICS; ANISOTROPY; CONTINUUM MECHANICS; DEFORMATION; DISPERSION (WAVES); METAMATERIALS; MICROSTRUCTURE; WAVE PROPAGATION;

ANISOTROPIC MASS DENSITIES; CONTINUUM; ELASTIC METAMATERIAL; FINITE ELEMENT SIMULATIONS; GOVERNING EQUATIONS; MICROSTRUCTURE CONTINUUM; MULTI-DISPLACEMENT; SIMPLIFIED PROCEDURE;

FINITE ELEMENT METHOD;

ACOUSTIC WAVE; ANISOTROPIC MEDIUM; BENCHMARKING; CYLINDER; DEFORMATION MECHANISM; FINITE ELEMENT METHOD; LEAD; MICROSTRUCTURE; RESONANCE; RUBBER; TWO-DIMENSIONAL MODELING; WAVE MODELING;

EID: 84862826697     PISSN: 01652125     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.wavemoti.2011.12.006     Document Type: Article

References (41)

1. Hu X., Chan C.T., Zi J. Two-dimensional sonic crystals with Helmholtz resonators. Phys. Rev. E 2005, 71:055601(R).
2. Hu X., Chan C.T. Refraction of water waves by periodic cylinder arrays. Phys. Rev. Lett. 2005, 95:154501.
3. Liu Z., Zhang X., Mao Y., Zhu Y.Y., Yang Z., Chan C.T., Sheng P. Locally resonant sonic materials. Science 2000, 289:1734-1736.
4. Yang S., Page J.H., Liu Z., Cowan M.L., Chan C.T., Sheng P. Ultrasound tunneling through 3D phononic crystals. Phys. Rev. Lett. 2002, 88:104301.
5. Hou Z., Fu X., Liu Y. Calculational method to study the transmission properties of phononic crystals. Phys. Rev. B 2004, 70:014304.
6. Fang N., Xi D., Xu J., Ambati M., Srituravanich W., Sun C., Zhang X. Ultrasonic metamaterials with negative modulus. Nature Mater. 2006, 5:452-456.
7. Gonella S., To A.C., Liu W.K. Interplay between phononic bandgaps and piezoelectric microstructures for energy harvesting. J. Mech. Phys. Solids 2009, 57:621-633.
8. Liu X.N., Hu G.K., Huang G.L., Sun C.T. Wave propagation characterization and design of two-dimensional elastic chiral metacomposite. J. Vib. Acoust. 2011, 330.
9. Kafesaki M., Economou E.N. Multiple scattering theory for 3D periodic acoustic composites. Phys. Rev. B 1999, 60:11993.
10. Hu X., Ho K.M., Chan C.T., Zi J. Homogenization of acoustic metamaterials of Helmholtz resonators in fluid. Phys. Rev. B 2008, 77:172301.
11. Sheng P. Introduction to Wave Scattering, Localization, and Mesoscopic Phenomena 1995, Academic, San Diego.
12. Liu Z., Chan C.T., Sheng P. Analytic model of phononic crystals with local resonances. Phys. Rev. B 2005, 71:014103.
13. Mei J., Liu Z., Wen W., Sheng P. Effective mass density of fluid-solid composites. Phys. Rev. Lett. 2006, 96:024301.
14. Wu Y., Lai Y., Zhang Z.Q. Effective medium theory for elastic metamaterials in two dimensions. Phys. Rev. B 2007, 76:205313.
15. Yang Z., Mei J., Yang M., Chan N.H., Sheng P. Membrane-type acoustic metamaterial with negative dynamic mass. Phys. Rev. Lett. 2008, 101:204301.
16. Zhou X.M., Hu G.K. Analytic model of elastic metamaterials with local resonances. Phys. Rev. B 2009, 79:195109.
17. Ding Y., Liu Z., Qiu C., Shi J. Metamaterial with simultaneously negative bulk modulus and mass density. Phys. Rev. Lett. 2007, 99:093904.
18. Imhof M.G. Multiple multipole expansions for elastic scattering. J. Acoust. Soc. Am. 1996, 100:2969-2979.
19. Wang G., Wen X., Wen J., Shao L., Liu Y. Two-dimensional locally resonant phononic crystals with binary structures. Phys. Rev. Lett. 2004, 93:154302.
20. Khelif A., Deymier P.A., Djafari-Rouhani B., Vasseur J.O., Dobrzynski L. Two-dimensional phononic crystal with tunable narrow pass band: application to a waveguide with selective frequency. J. Appl. Phys. 2003, 94:1308.
21. Torrent D., Sánchez-Dehesa J. Anisotropic mass density by two-dimensional acoustic metamaterials. New J. Phys. 2008, 10:023004.
22. Ao X., Chan C.T. Far-field image magnification for acoustic waves using anisotropic acoustic metamaterials. Phys. Rev. E 2008, 77:025601.
23. Willis J.R. Exact effective relations for dynamics of a laminated body. Mech. Mater. 2009, 41:385-393.
24. Willis J.R. Effective constitutive relations for waves in composites and metamaterials. Proc. R. Soc. A 2011, 10.1098/rspa.2010.0620.
25. Shuvalov A.L., Kutsenko A.A., Norris A.N., Poncelet O. Effective Willis constitutive equations for periodically stratified anisotropic elastic media. Proc. R. Soc. A 2011, 467:1749-1769.
26. Nemat-Nasser S., Willis J.R., Srivastava A., Amirkhizi A.V. Homogenization of periodic elastic composites and locally resonant sonic materials. Phys. Rev. B 2011, 83:104103.
27. Hirsekorn M., Delsanto P.P. Elastic wave propagation in locally resonant sonic material: comparison between local interaction simulation approach and modal analysis. J. Appl. Phys. 2006, 99:124912.
28. Gu Y., Luo X., Ma H. Low frequency elastic wave propagation in two dimensional locally resonant phononic crystal with asymmetric resonator. J. Appl. Phys. 2009, 105:044903.
29. Wozniak Cz. Refined macro-dynamics of periodic structures. Arch. Mech. 1993, 45:295-304.
30. Milton G.W., Willis J.R. On modifications of Newton's second law and linear continuum elastodynamics. Proc. R. Soc. A 2007, 463:855-880.
31. Milton G.W. New metamaterials with macroscopic behavior outside that of continuum elastodynamics. New J. Phys. 2007, 9:359.
32. Alibert J.J., Seppecher P., Dell'Isola F. Truss modular beams with deformation energy depending on higher displacement gradients. Math. Mech. Solids 2003, 8:51-73.
33. E. Cosserat, F. Cosserat, Théorie des corps déformables, A. Hermann et Fils, Paris, 1909.
34. Eringen A.C., Suhubi E.S. Nonlinear theory of simple micro-elastic solids-I. Int. J. Eng. Sci. 1964, 2:189-203.
35. Toupin R.A. Elastic materials with couple-stresses. Arch. Ration. Mech. Anal. 1962, 11:385-414.
36. Eringen A.C. Microcontinuum Field Theories I: Foundations and Solids 1999, Springer-Verlag, New York.
37. Mindlin R.D. Micro-structure in linear elasticity. Arch. Ration. Mech. Anal. 1964, 16:51-78.
38. Sun C.T., Achenbach J.D., Herrmann G. Continuum theory for a laminated medium. J. Appl. Mech. 1968, 53:467-475.
39. Huang G.L., Sun C.T. Continuum modeling of solids with micro/nanostructures. Philos. Mag. 2007, 87:3689-3707.
40. Zhu R., Huang H.H., Huang G.L., Sun C.T. Microstructure continuum modeling of an elastic metamaterial. Int. J. Eng. Sci. 2011, 49:1477-1485.
41. Barber J.R. Elasticity 2010, Springer, Dordrecht. third ed.