Analysis of the directionality on periodic materials

TL;DR

This paper introduces a new measure for anisotropy in periodic materials based on their dynamic dispersion surfaces, providing a more comprehensive understanding of directionality beyond static properties.

Contribution

It presents a novel anisotropy measure derived from dispersion surfaces, applicable to various phenomena including elastodynamics, enhancing analysis of directional properties in metamaterials.

Findings

The measure captures bulk directionality from dispersion surfaces.

Results demonstrate applicability to elastodynamics.

Method extends analysis beyond static approximations.

Abstract

There is an increasing interest in the study of metamaterials and periodic materials across disciplines. These are anisotropic and their properties present directionality. For example, the wave speed depends on the propagation direction. Furthermore, they are heterogeneous, and their directionality depends on their spectra. Common approaches to describe anisotropy have been used in the large-wavelength approximation corresponding to static properties. Here we present an anisotropy measure based on the dynamic behavior. It receives dispersion surfaces from Bloch analyses and outputs a curve/surface with bulk directionality encoded on it. We present results for elastodynamics, but it is applicable to other phenomena.