Multi-point Scattering Measurements for Effective Property Extraction from Metamaterials with Skin Effects

TL;DR

This paper introduces a multi-point scattering measurement method to accurately extract effective properties of heterogeneous metamaterials, accounting for boundary effects and enabling characterization without internal field knowledge.

Contribution

It presents a novel experimental approach that distinguishes skin and interior region properties, improving the accuracy of effective property extraction in metamaterials.

Findings

Effective parameters converge with increased unit cells or ambient media modulus.

Skin and interior regions exhibit different responses affecting parameter extraction.

Method successfully reproduces scattering for various slab thicknesses and conditions.

Abstract

Scattering experiments can be leveraged to extract the effective properties of a heterogeneous metamaterial slab based on multi-point measurements in surrounding media. In this technique, two measurements are made in the ambient media on each side of a finite thickness micro-structured slab to decompose incoming and outgoing waves. The method is applied to an example with locally resonant micro-structured inclusions while paying close attention to parameters that influence the extracted material parameters. It is observed that the extracted overall parameters converge to limiting values when the number of unit cells across the slab thickness or ambient media modulus are increased. Dependence of extracted material parameters on the number of cells through thickness or ambient media properties are attributed to the different response of boundary (skin) and interior cells. A method is presented which represents a finite array with different effective properties for the skin regions vs. the interior regions with great success in reproducing the scattering for different slab thicknesses, and through which the interior regions properties become independent of ambient media properties. In stop bands with lower material loss, challenges arise that are associated with extremely small transmission. The assumption of continuity in transmission phase is enforceable to remove phase ambiguity, although in certain cases (associated with nearly lossless specimens) this assumption appears to fail. In such cases, interference from coupled shear modes may lead to apparent higher longitudinal transmission within the stop band. This work provides a proof of concept for the development of an experimental methodology capable of extracting the effective properties and dispersion behavior of heterogeneous mechanical metamaterials without any knowledge of the internal fields.