A Dynamical Effective Medium Theory for Elastic Metamaterials

TL;DR

This paper introduces a dynamical effective medium theory that predicts and explains the unusual wave propagation properties of elastic metamaterials near resonance frequencies, enabling design of materials with negative parameters and specific wave behaviors.

Contribution

The paper presents a new dynamical effective medium theory for elastic metamaterials that accurately predicts negative moduli and complex wave phenomena near resonances.

Findings

Negative bulk modulus, shear modulus, and mass density can be achieved.

Designs with large low-frequency band gaps are demonstrated.

Regions of negative refraction for different wave types are identified.

Abstract

We develop a dynamical effective medium theory to accurately predict the unusual properties of elastic metamaterials in two dimensions near the resonant frequencies. The theory shows that the effective bulk modulus, shear modulus, and mass density can be made negative by choosing proper resonant scatterers, leading to 8 possible types of wave propagation. The theory not only provides a convenient tool to search for various metamaterials with desired properties, but also gives a unified physical picture of these properties. Here we demonstrate two examples. One possesses large band gaps at low frequencies. The other exhibits two regions of negative refraction: one for both longitudinal and transverse waves and the other for longitudinal waves only.