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Locally resonant metamaterials have attracted a lot of interest in recent years thanks to their capability to manipulate elastic waves. They typically consist of periodically distributed resonant elements, e.g. soft inclusions in a stiff matrix, that interact with the propagating wave, leading to the formation of band gaps, which can be interpreted as an interval of negative homogenized mass.
When inclusions lack rotational symmetry, the homogenized mass density of the media becomes anisotropic and lead the formation of polarization bands. This allows the achievement of new capabilities in wave manipulation, such as selective wave polarization, mode conversion [1] and negative refraction [2].
Asymptotic homogenization has been proved to be a useful tool to characterize the dynamic properties of locally resonant metamaterials [3,4]. In this work, we make use of such a technique to study the role played by the mass anisotropy in the dispersion properties of the metamaterial, with particular emphasis on the formation of polarization bands. The possibility of selectively polarize and converting elastic waves is then discussed with the aid of some analytical and numerical examples.
[1] G. Ma et al., Polarization bandgaps and fluid-like elasticity in fully solid elastic metamaterials. Nature Communications 7, 2016.
[2] G. Bonnet and V. Monchiet, Negative refraction of elastic waves on a metamaterial with anisotropic local resonance. Journal of the Mechanics and Physics of Solids 169, 2022.
[3] C. Comi and J.J. Marigo, Homogenization approach and Bloch-Floquet theory for band-gap predictions in 2D locally resonant metamaterials. Journal of Elasticity 139, 2020
[4] D. Faraci et al., Wave polarization control in anisotropic locally resonant materials. Applied Sciences 13, 2023.