Boundary and interface conditions in the relaxed micromorphic model: exploring finite-size metastructures for elastic wave control

TL;DR

This paper develops boundary and interface conditions for the relaxed micromorphic model, enabling accurate simulation of elastic wave scattering in finite-size metamaterials, and demonstrates its potential for designing wave-controlling metastructures.

Contribution

It introduces well-posed boundary conditions for the relaxed micromorphic model and validates its effectiveness in simulating finite-size metamaterials for elastic wave control.

Findings

The model accurately predicts scattering behavior across frequencies and angles.

It enables the design of metastructures for wave control and energy focusing.

The approach is computationally efficient for practical applications.

Abstract

In this paper, we establish well-posed boundary and interface conditions for the relaxed micromorphic model that are able to unveil the scattering response of fully finite-size metamaterials' samples. The resulting relaxed micromorphic boundary value problem is implemented in finite element simulations describing the scattering of a square metamaterial's sample whose side counts 9 unit cells. The results are validated against a direct finite element simulation encoding all the details of the underlying metamaterial's microstructure. The relaxed micromorphic model can recover the scattering metamaterial's behavior for a wide range of frequencies and for all possible angles of incidence, thus showing that it is suitable to describe dynamic anisotropy. Finally, thanks to the model's computational performances, we can design a metastructure combining metamaterials and classical materials in such a way that it acts as a protection device while providing energy focusing in specific collection points. These results open important perspectives for the short-term design of sustainable structures that can control elastic waves and recover energy.