Band gaps in the relaxed linear micromorphic continuum

TL;DR

This paper demonstrates that a simplified relaxed micromorphic model with only six parameters effectively predicts band-gaps in metamaterials with strong property contrasts, highlighting the role of the Cosserat couple modulus.

Contribution

The authors introduce a relaxed micromorphic model with fewer parameters that accurately describes band-gaps, emphasizing the significance of the Cosserat couple modulus in wave propagation.

Findings

Band-gaps are linked to the Cosserat couple modulus $$.

The model uses only 6 parameters instead of 18.

Band-gap onset occurs when $$ exceeds a threshold.

Abstract

In this note we show that the relaxed linear micromorphic model recently proposed by the authors can be suitably used to describe the presence of band-gaps in metamaterials with microstructures in which strong contrasts of the mechanical properties are present (e.g. phononic crystals and lattice structures). This relaxed micromorphic model only has 6 constitutive parameters instead of 18 parameters needed in Mindlin- and Eringen-type classical micromorphic models. We show that the onset of band-gaps is related to a unique constitutive parameter, the Cosserat couple modulus $\mu_{c}$ which starts to account for band-gaps when reaching a suitable threshold value. The limited number of parameters of our model, as well as the specific effect of some of them on wave propagation can be seen as an important step towards indirect measurement campaigns.