Metamaterial shields for inner protection and outer tuning through a relaxed micromorphic approach

Abstract

In this paper, a coherent boundary value problem to model metamaterials' behavior based on the relaxed micromorphic model is established. This boundary value problem includes well-posed boundary conditions, thus disclosing the possibility of exploring the scattering patterns of finite-size metamaterials' specimens. Thanks to the simplified model's structure (few frequency-and angle-independent parameters), we are able to unveil the scattering metamaterial's response for a wide range of frequencies and angles of propagation of the incident wave. These results are an important stepping stone towards the conception of more complex large-scale meta-structures that can control elastic waves and recover energy.

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

“…We presented an inertia-augmented relaxed micromorphic model that enhances the model proposed in [1,2,37,38,39] via the addition of a term Curl Ṗ in the kinetic energy. We then used this model to describe the dynamical behavior of a labyrinthine metamaterial and compared its predictability when setting all curvature terms to zero, when setting only Curl Ṗ to zero and when considering the full model (including Curl P and Curl Ṗ ).…”

“…Table 1. Compared to Aluminium or Titanium, that we used for the metamaterials studied in [37,38,39], Polyethylene gives rise to lower wave speeds, thus allowing band-gap phenomena to appear at lower frequencies. A further lowering of the band-gap is obtained through the adoption of a labyrinth-type geometry, cf.…”

“…This model is based on the relaxed micromorphic model that we previously established [34,32,17,1,2] and has been augmented with a new inertia term accounting for coupled space-time derivatives of the micro-distortion tensor. The relaxed micromorphic model has extensively proven its efficacy in describing the broadband behavior of many infinite and finite-size metamaterials [1,2,37,38,39] and is extended in this paper so as to be able to account for negative group velocity which was not the case before. We will show that the proposed model is able to describe well the labyrinthine metamaterial's response for a large range of frequencies (going beyond the first band-gap) and wave numbers (approaching the size of the unit cell) and for all directions of propagation with a limited number of frequency-and scale-independent constitutive parameters.…”

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

“…This model is based on the relaxed micromorphic model that we previously established [49][50][51][52][53] and has been augmented with a new inertia term accounting for coupled space-time derivatives of the micro-distortion tensor. The relaxed micromorphic model has extensively proven its efficacy in describing the broadband behavior of many infinite and finitesize metamaterials [52][53][54][55][56] and is extended in this paper so as to be able to account for negative group velocity which was not the case before. We will show that the proposed model is able to describe well the labyrinthine metamaterial's response for a large range of frequencies (going beyond the first band gap) and wave numbers (approaching the size of the unit cell) and for all directions of propagation with a limited number of frequency-and scale-independent constitutive parameters.…”

Remarks on wave propagation in an acoustic metamaterial modeled as a relaxed micromorphic continuum

“…We propose to use an inertia-augmented relaxed micromorphic model. This model is based on the static relaxed micromorphic model [9,8,5] involving an additional macroscopic displacement field P ∈ R 3×3 and has been augmented with additional inertia terms accounting for coupled space-time derivatives of the micro-distortion tensor [1,2,10,11,12]. In this work, we present a guideline for the fitting procedure of this relaxed micromorphic model.…”