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In-Plane Semi-Linear Cloaks with Arbitrary Shape

  • Dengke Guo
  • Zheng ChangEmail author
  • Gengkai Hu
Article
  • 26 Downloads

Abstract

Soft materials with semi-linear strain energy function can be used as smart transformation media to manipulate elastic waves via finite pre-deformation. However, the intrinsic constraints involved in such materials limit the shapes of transformation devices to very simple cases. In this work, combining theoretical and numerical analyses, we report an approach of achieving the in-plane elastodynamic cloak with arbitrary shape. We demonstrate that with the appropriate out-of-plane stretch applied on the semi-linear material, cloaking effect can be achieved for both P- and SV-waves in the symmetric plane of a 3D domain, and the performance of the cloak with arbitrary cross section can be guaranteed for relatively small in-plane rotation. In addition, we propose an empirical formula to predict the deformation limit of the cloaks with semi-linear materials. This work may stimulate the experimental research on soft-matter-based transformation devices. Potential applications can be anticipated in nondestructive testing, structure impact protection, biomedical imaging and soft robotics.

Keywords

Elastic waves Cloak Hyperelasticity Semi-linear Arbitrary shape 

Notes

Acknowledgements

The authors are grateful to Dr. Yi Chen for valuable discussions. This work was supported by the National Natural Science Foundation of China (Grant Nos. 11472044, 11521062, 11602294, 11632003) and the Chinese Universities Scientific Fund (Grant No. 2019TC134).

References

  1. 1.
    Pendry JB, Schurig D, Smith DR. Controlling electromagnetic fields. Science. 2006;312(5781):1780–2.MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Leonhardt U. Optical conformal mapping. Science. 2006;312(5781):1777–80.MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Chen T, Weng CN, Chen JS. Cloak for curvilinearly anisotropic media in conduction. Appl Phys Lett. 2008;93(11):114103.CrossRefGoogle Scholar
  4. 4.
    Zhang S, Genov DA, Sun C, Zhang X. Cloaking of matter waves. Phys Rev Lett. 2008;100(12):123002.CrossRefGoogle Scholar
  5. 5.
    Schurig D, Mock JJ, Justice BJ, Cummer SA, Pendry JB, Starr AF, Smith DR. Metamaterial electromagnetic cloak at microwave frequencies. Science. 2006;314(5801):977–80.CrossRefGoogle Scholar
  6. 6.
    Norris AN. Acoustic cloaking theory. Proc R Soc A Math Phys Eng Sci. 2008;464(2097):2411.MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Norris AN, Shuvalov AL. Elastic cloaking theory. Wave Motion. 2011;48(6):525–38.MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Chen HY, Chan CT. Acoustic cloaking in three dimensions using acoustic metamaterials. Appl Phys Lett. 2007;91(18):183518.CrossRefGoogle Scholar
  9. 9.
    Chen Y, Zheng MY, Liu XN, Bi YF, Sun ZY, Xiang P, Yang J, Hu GK. Broadband solid cloak for underwater acoustics. Phys Rev B. 2017;95(18):180104.CrossRefGoogle Scholar
  10. 10.
    Hu J, Chang Z, Hu GK. Approximate method for controlling solid elastic waves by transformation media. Phys Rev B. 2011;84(20):201101.CrossRefGoogle Scholar
  11. 11.
    Liu ZY, Zhang XX, Chan CT, Sheng P. Locally resonant sonic materials. Science. 2000;289(5485):1734–6.CrossRefGoogle Scholar
  12. 12.
    Zhu R, Yasuda H, Huang GL, Yang JK. Kirigami-based elastic metamaterials with anisotropic mass density for subwavelength flexural wave control. Sci Rep. 2018;8(1):483.CrossRefGoogle Scholar
  13. 13.
    Liu XN, Hu GK, Huang GL, Sun CT. An elastic metamaterial with simultaneously negative mass density and bulk modulus. Appl Phys Lett. 2011;98(25):251907.CrossRefGoogle Scholar
  14. 14.
    Cheng Y, Zhou XM, Hu GK. Broadband dual-anisotropic solid metamaterials. Sci Rep. 2017;7(1):13197.CrossRefGoogle Scholar
  15. 15.
    Norris AN, Parnell WJ. Hyperelastic cloaking theory: transformation elasticity with pre-stressed solids. Proc R Soc A Math Phys Eng Sci. 2012;468(2146):2881–903.MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Chen HY, Chan CT, Sheng P. Transformation optics and metamaterials. Nat Mater. 2010;9:387.CrossRefGoogle Scholar
  17. 17.
    Li J, Pendry JB. Hiding under the carpet: a new strategy for cloaking. Phys Rev Lett. 2008;101(20):203901.CrossRefGoogle Scholar
  18. 18.
    Chang Z, Hu J, Hu GK. Controlling elastic waves with isotropic materials. Appl Phys Lett. 2011;98(12):121904.CrossRefGoogle Scholar
  19. 19.
    Hu J, Zhou XM, Hu GK. Design method for electromagnetic cloak with arbitrary shapes based on Laplace’s equation. Opt Express. 2009;17(15):13070.CrossRefGoogle Scholar
  20. 20.
    Chang Z, Zhou XM, Hu J, Hu GK. Design method for quasi-isotropic transformation materials based on inverse Laplace’s equation with sliding boundaries. Opt Express. 2010;18(6):6089–96.CrossRefGoogle Scholar
  21. 21.
    Chang Z, Guo HY, Li B, Feng XQ. Disentangling longitudinal and shear elastic waves by neo-Hookean soft devices. Appl Phys Lett. 2015;106(16):161903.CrossRefGoogle Scholar
  22. 22.
    Parnell WJ. Nonlinear pre-stress for cloaking from antiplane elastic waves. Proc R Soc A Math Phys Eng Sci. 2012;468(2138):563–80.MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Parnell WJ, Norris AN, Shearer T. Employing pre-stress to generate finite cloaks for antiplane elastic waves. Appl Phys Lett. 2012;100(17):171907.CrossRefGoogle Scholar
  24. 24.
    Guo DK, Chen Y, Chang Z, Hu GK. Longitudinal elastic wave control by pre-deforming semi-linear materials. J Acoust Soc Am. 2017;142(3):1229–35.CrossRefGoogle Scholar
  25. 25.
    Ogden RW. Incremental statics and dynamics of pre-stressed elastic materials. In: Destrade M, Saccomandi G, editors. Waves in nonlinear pre-stressed materials. Vienna: Springer; 2007. p. 1–26.Google Scholar
  26. 26.
    Brun M, Guenneau S, Movchan AB. Achieving control of in-plane elastic waves. Appl Phys Lett. 2009;94(6):061903.CrossRefGoogle Scholar
  27. 27.
    Chang Z, Guo DK, Feng XQ, Hu GK. A facile method to realize perfectly matched layers for elastic waves. Wave Motion. 2014;51(7):1170–8.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics 2019

Authors and Affiliations

  1. 1.Key Laboratory of Dynamics and Control of Flight Vehicle, Ministry of Education, School of Aerospace EngineeringBeijing Institute of TechnologyBeijingChina
  2. 2.College of ScienceChina Agricultural UniversityBeijingChina

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