Modeling a labyrinthine acoustic metamaterial through an inertia-augmented relaxed micromorphic approach

TL;DR

This paper introduces an inertia-augmented relaxed micromorphic model for acoustic metamaterials, enabling better dispersion curve fitting and the description of negative group velocity modes, which are crucial for negative refraction effects.

Contribution

The authors develop an enhanced relaxed micromorphic model with a Curl of velocity term, improving dispersion fitting and mode description in acoustic metamaterials.

Findings

Successfully fits dispersion curves of labyrinthine acoustic metamaterials.

Enables modeling of negative group velocity modes.

Provides more flexible asymptote behavior for different wave modes.

Abstract

We present an inertia-augmented relaxed micromorphic model that enriches the relaxed micromorphic model previously introduced by the authors via a term $\text{Curl}\dot{P}$ in the kinetic energy density. This enriched model allows us to obtain a good overall fitting of the dispersion curves while introducing the new possibility of describing modes with negative group velocity that are known to trigger negative refraction effects. The inertia-augmented model also allows for more freedom on the values of the asymptotes corresponding to the cut-offs. In the previous version of the relaxed micromorphic model, the asymptote of one curve (pressure or shear) is always bounded by the cut-off of the following curve of the same type. This constraint does not hold anymore in the enhanced version of the model. While the obtained curves' fitting is of good quality overall, a perfect quantitative agreement must still be reached for very small wavelengths that are close to the size of the unit cell.