Effective-Property Characterization of Elastic Metamaterials for Advanced Wave Tailoring

Abstract

This work is mainly concerned with the development of a characterization methodology for determining the effective properties of anisotropic elastic metamaterials. Among the existing methods, the method using the scattering parameters of metamaterials has been known to be most efficient in electromagnetics owing to the robust performances. In the elastic regime, however, the conventional method using the scattering parameters cannot thoroughly characterize metamaterials due to the complex constitutive properties including the diagonal as well as the non-diagonal components in the stiffness tensor. Therefore, the method should be refined specifically for characterizing anisotropic elastic metamaterials. In order to achieve the goal, the improved version of the characterization method using scattering parameters is developed in this work. The proposed method works in the two steps: one is to determine the effective constitutive properties involved in the scattering parameters for normal incidences and the other is to determine the rest of the properties involved in the scattering parameters for oblique incidences. While the conventional method just yields the diagonal stiffness components even working only for the metamaterials having the material principal axes coinciding with the coordinate axes, the proposed method is shown to work for various types of metamaterials yielding the whole effective properties. By utilizing the developed characterization method, three types of novel elastic metamaterials are also proposed in this work and applied for the designs of elastic magnifying hyperlens, quasi-ideal mechanical bandpass filters, and wave mode converters, respectively. In order to design elastic magnifying hyperlens, metal-air-stratified metamaterials exhibiting an extremely anisotropy is used. Owing to the extreme property, the proposed hyperlens is shown to achieve high resolution images beyond the well-known diffraction limit, the fundamental limit for an imaging device. And, in order to design quasi-ideal mechanical bandpass filters, impedance-only-varying metamaterials are proposed and utilized for constructing effective impedance-varying phononic bandgap structures. The developed phononic bandgap structures are shown to exhibit quasi-ideal bandpass filter performances including a unity passband with the flat top, broad surrounding stopbands, and steep bandedges. Lastly, in order to design wave mode converters, the metamaterials exhibiting anomalous polarization characteristics are used. The developed mode converters are shown to robustly work for various environmental conditions while achieving the high conversion efficiencies.