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' behaviour 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 metamaterial 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. This article is part of the theme issue ‘Wave generation and transmission in multi-scale complex media and structured metamaterials (part 1)’.

Multi-element Metamaterial’s Design Through the Relaxed Micromorphic Model

“…It has been largely shown that the bulk mechanical response of mechanical metamaterials can be effectively explored using an elastic-and inertia-augmented micromorphic model (reduced relaxed micromorphic model) which is able to describe the main metamaterials' fingerprint characteristics (anisotropy, dispersion, band-gaps, size-effects, etc. ), while keeping a reduced structure (free of unnecessary parameters) [3,43,44,83,100,101,102,109,112,113,114,115,135]. This model can be linked a posteriori to real metamaterials' microstructures via an inverse fitting procedure.…”

“…• Perfect interfaces. Both the displacement and the traction are continuous across a perfect interface [43,44,56,70,109,112,113,114,115,124].…”

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 [49–53] 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 [52–56] 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.…”

“…Table 1. Compared to aluminium or titanium, which we used for the metamaterials studied in literature [54–56], polyethylene gives rise to lower wave speeds, thus allowing band-gap phenomena to appear at lower frequencies.…”

Dispersive surface waves propagating through a continuous elastic medium with local rotation

“…Elastic metamaterials are new-age materials engineered to exhibit certain desired elastic properties which do not manifest in naturally occurring materials, including negative dynamic mass density [1], negative Poisson’s ratio [2], negative shear modulus [3,4], negative stiffness [5–7], or combinations of the aforementioned properties [8–11]. Elastic metamaterials have garnered great interest from the research community due to their potential applications in fields such as energy shielding [12,13], sound proofing [14–16], impact mitigation/shock absorption [17–20], and wave attenuation [21–23].…”