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.Comment: 20 pages, 13 figure