Modeling wave propagation and boundary effects in acoustic metamaterials by a relaxed micromorphic continuum
Please login to view abstract download link
Exploring the dynamical response of mechanical metamaterials in the framework of elastic propagation has gathered increasing attention in the last decades. In order to describe elastic wave propagation in metamaterials, i.e. solids with heterogeneities or microstructure, it is necessary to consider non-local or enriched models. The relaxed micromorphic model (RMM) [1, 2, 3] proposed here can describe these effects as a continuous material with enriched kinematics. One of the most important micro-mechanical effects is the appearance of band gaps for which waves at given frequencies cannot propagate through the material. We have shown in previous papers [1, 2, 3] that the relaxed micromorphic model can describe the bulk behavior of mechanical metamaterials. Things become more complicated when considering finite-size metamaterial blocks for which boundary effects may play a major role, e.g. due to the reduced size of the block itself. In these cases, the relaxed micromorphic model framework must be enriched to account for these boundary effects. We will show how the concept of boundary forces can be used to address the modeling of finite-size metamaterial specimens in the context of micromorphic elasticity. References [1] A. Madeo, P. Neff, I.-D. Ghiba, P. Placidi and G. Rosi, "Wave propagation in relaxed micromorphic continua: modeling metamaterials with frequency band-gaps". Continuum Mechanics and Thermodynamics, 27.4 (2015). Pp. 551–570. [2] M.V. d’Agostino, G. Barbagallo, I.-D. Ghiba, B. Eidel, P. Neff and A. Madeo, "Effective description of anisotropic wave dispersion in mechanical band-gap metamaterials via the relaxed micromorphic model". Journal of Elasticity, 139.2 (2020). Pp. 299–329. [3] J. Voss, G. Rizzi, P. Neff and A. Madeo, "Modeling a labyrinthine acoustic metamaterial through an inertia-augmented relaxed micromorphic approach". Mathematics and Mechanics of Solids, 28(10) (2023). Pp. 2177–2201.