Multi-scale Computational Design of Engineering Metamaterials. Application to Acoustic Insulation Cases

Computational design of engineering metamaterials (materials with engineered properties not found in nature) is a subject of increasing interest in computational mechanics. Additionally, additive manufacturing (3D printing) opens new ways to industrialization of metamaterials with optimized meso-scale topology. A computational framework, combining multiscale modeling, model order reduction and topological optimization of the meso scale is proposed for metamaterial design purposes.

Locally Resonant Acoustic Metamaterials (LRAM), are capable of stopping acoustic waves from propagating in frequency regions in the vicinity of their internal natural frequencies [1-2]. On this basis, the issue of numerically capturing the local resonance phenomena in a FE2 context is addressed. Several additional hypotheses based on scale separation are used to split the fully coupled micro-macro set of equations into a quasi-static and an inertial system [3]. These are then solved by considering a projection of the microscale equations into their natural modes, which allows for a low-cost computational treatment.


The incorporation of viscoelastic effects in the model proposed in [3], which manages to merge the attenuation bands associated to the multiple resonating frequencies into an extended larger range, is also assessed. Finality, topological optimization techniques are considered to design the resonating cells in order to maximize the band gap around a selected frequency.

As a representative example of application of the proposed approach, the design of a new kind of lightweight acoustic insulation panels, with the ability to attenuate noises in the low frequency range (below 5000 Hz) without the need of heavy pieces of very dense materials, is considered. Using the proposed methodology, the optimization of the acoustic performance of the panel, in terms of the acoustic transmission loss, is then performed.


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[2] A. Sridhar, V.G. Kouznetsova, M.G.D. Geers, Homogenization of locally resonant acoustic metamaterials towards an emergent enriched continuum, Comput. Mech. 57 (3) (2016) 423–435.

[3] D. Roca, O. Lloberas-Valls, J. Cante, J. Oliver. A computational multiscale homogenization framework accounting for inertial effects: application to acoustic metamaterials modelling. Comput. Methods Appl. Mech. Engrg. 330 (2018) 415–446