Phonon band structures of the three dimensional latticed pentamode metamaterials

Guan Wang,Lin Zhang,Zhuo Xu,Li Jin

doi:10.1063/1.4977715

Guan Wang, Lin Zhang + Show 2 more

Open Access

https://doi.org/10.1063/1.4977715

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Abstract

The artificially designed three-dimensional (3D) pentamode metamaterials have such an extraordinary characteristic that the solid materials behave like liquids. Meanwhile, the ideal structure of the pentamode metamaterials arranges in the same way as that of the diamond crystals. In the present research, we regard three types of pentamode metamaterials derived from the 3D crystal lattices as research objects. The phonon band structures of the candidate pentamode structures are calculated by using the finite element method (FEM). We illustrate the relation between the ratio of the bulk modulus B and the shear modulus G of different combinations of D and d. Finally, we find out the relationship between the phonon band structure and the structure parameters. It is useful for generating the phonon band structure and controlling elastic wave propagation.

Highlights

In recent years, there has been much research on designing the artificial composite materials with peculiar features which are not available in the natural materials
This strong localized resonance is responsible for the appearance of negative effective parameters,[14,15] negative index of refraction,[16,17] and some unexpected properties, including invisible cloaking[18] and dark acoustic metamaterials.[19]
The double cones length h=16.15 μm is chosen as the basic unit parameter

Summary

Introduction

There has been much research on designing the artificial composite materials with peculiar features which are not available in the natural materials. This means that the incident elastic (or acoustic) wave at a certain frequency range does not propagate in the designed composite medium.[3,4,5,6,7] Several applications have been suggested, such as acoustic absorption,[8] phononic crystal waveguides and filters,[9,10] and acoustic frequency selective devices.[11] The concept and the designed structure of the photonic metamaterials are important developments in the propagation of EM waves.[12,13] Most of photonic metamaterials are based on the periodic artificial structures, whose unit cell has a strong localized resonance This strong localized resonance is responsible for the appearance of negative effective parameters,[14,15] negative index of refraction,[16,17] and some unexpected properties, including invisible cloaking[18] and dark acoustic metamaterials.[19]

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Conclusion