A review on wave propagation modeling in band-gap metamaterials via enriched continuum models

TL;DR

This paper reviews the relaxed micromorphic model's unique ability among enriched continuum models to accurately describe band-gaps in non-local metamaterials, highlighting its effectiveness in modeling micro-macro vibrational coupling.

Contribution

It demonstrates that the relaxed micromorphic model is the only non-local continuum model capable of describing band-gaps without micro-macro coupling, and compares its effectiveness with other models.

Findings

The relaxed micromorphic model uniquely accounts for band-gaps in metamaterials.

Adding gradient inertia enables other models to describe band-gap onset.

The relaxed micromorphic model effectively describes multiple band-gaps.

Abstract

In the present contribution we show that the relaxed micromorphic model is the only non-local continuum model which is able to account for the description of band-gaps in metamaterials for which the kinetic energy accounts separately for micro and macro-motions without considering a micro-macro coupling. Moreover, we show that when adding a gradient inertia term which indeed allows for the description of the coupling of the vibrations of the microstructure to the macroscopic motion of the unit cell, other enriched continuum models of the micromorphic type may allow the description of the onset of band-gaps. Nevertheless, the relaxed micromorphic model proves to be yet the most effective enriched continuum model which is able to describe multiple band-gaps in non-local metamaterials.