Unveiling Extreme Anisotropy in Elastic Structured Media

TL;DR

This paper demonstrates how high frequency homogenisation theory can predict and confirm extreme anisotropy in elastic structured media, enabling precise control of wave modes through effective medium properties.

Contribution

It applies a novel asymptotic homogenisation approach to elastic waves, revealing a transition from positive definite to indefinite tensors and corresponding mode behavior.

Findings

Confirmed a spectral region with dramatic tensor switch from positive definite to indefinite

Identified two distinct highly anisotropic modes with small frequency shifts

Validated theoretical predictions through time-domain experiments

Abstract

Periodic structures can be engineered to exhibit unique properties observed at symmetry points, such as zero group velocity, Dirac cones and saddle points; identifying these, and the nature of the associated modes, from a direct reading of the dispersion surfaces is not straightforward, especially in three-dimensions or at high frequencies when several dispersion surfaces fold back in the Brillouin zone. A recently proposed asymptotic high frequency homogenisation theory is applied to a challenging time-domain experiment with elastic waves in a pinned metallic plate. The prediction of a narrow high-frequency spectral region where the effective medium tensor dramatically switches from positive definite to indefinite is confirmed experimentally; a small frequency shift of the pulse carrier results in two distinct types of highly anisotropic modes. The underlying effective equation mirrors this behaviour with a change in form from elliptic to hyperbolic exemplifying the high degree of wave control available and the importance of a simple and effective predictive model.