Computational homogenisation of acoustic metafoams

M.A. Lewińska; V.G. Kouznetsova; J.A.W. van Dommelen; M.G.D. Geers

doi:10.1016/j.euromechsol.2019.103805

Computational homogenisation of acoustic metafoams

M.A. Lewińska
, V.G. Kouznetsova
, J.A.W. van Dommelen (Corresponding author)
, M.G.D. Geers

Research output: Contribution to journal › Article › Academic › peer-review

10 Citations (Scopus)

217 Downloads (Pure)

Abstract

Acoustic metafoams are novel materials recently proposed for low frequency sound attenuation. The design of their microstructure is based on the combination of standard acoustic foams with locally resonant acoustic metamaterials. This results in improved sound attenuation properties due to the interaction between viscothermal dissipation effects and the local resonance effects at the pore level. In this paper, the non-standard behaviour of such a metafoam with a complex two-phase microstructure is analysed through a multiscale approach. The macroscopic problem is described by general balance equations and at the microscopic scale a detailed representation of the microstructure is considered. The frequency dependent effective properties are used to explain the extraordinary acoustic performance. The homogenisation approach is also validated using direct numerical simulations, showing that the homogenisation technique is adequate in modelling both viscothermal dissipation and the local resonance effect within the metafoam microstructure.

Original language	English
Article number	103805
Number of pages	9
Journal	European Journal of Mechanics. A, Solids
Volume	77
DOIs	https://doi.org/10.1016/j.euromechsol.2019.103805
Publication status	Published - 1 Sept 2019

Funding

The research leading to these results has received funding from the European Research Council under the European Union's Seventh Framework Programme ( FP7/2007–2013 )/ERC grant agreement no 339392. Appendix The macroscopic constitutive relations (14), (15), (16) and (17), using the Voigt notation, and taking into consideration the unit cell symmetries, are expressed as: (36) [ σ x x s σ y y s σ z z s σ y z s σ x z s σ x y s ɛ f ] = [ C 11 C 12 C 13 0 0 0 − Ψ 1 s f C 12 C 11 C 13 0 0 0 − Ψ 2 s f C 13 C 13 C 33 0 0 0 − Ψ 3 s f 0 0 0 C 44 0 0 0 0 0 0 0 C 44 0 0 0 0 0 0 0 C 66 0 − Ψ 1 s f − Ψ 2 s f − Ψ 3 s f 0 0 0 − S f ] [ ∂ u x s ∂ x ∂ u y s ∂ y ∂ u z s ∂ z ∂ u y s ∂ z ∂ u x s ∂ z ∂ u x s ∂ y p f ] , (37) [ f x s f y s f z s u x f u y f u z f ] = [ − ω 2 M 1 s 0 0 K 1 s f 0 0 0 − ω 2 M 1 s 0 0 K 1 s f 0 0 0 − ω 2 M 3 s 0 0 K 3 s f K 1 s f 0 0 ( ω 2 ρ 0 f ) − 1 K 1 f 0 0 0 K 1 s f 0 0 ( ω 2 ρ 0 f ) − 1 K 1 f 0 0 0 K 3 s f 0 0 ( ω 2 ρ 0 f ) − 1 K 3 f ] [ u x s u y s u z s ∂ p f ∂ x ∂ p f ∂ y ∂ p f ∂ z ] .

Keywords

Acoustic foams
Acoustic metamaterials
Computational homogenisation
Local resonance
Metafoams
Poro-elastic materials
Viscothermal dissipation

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10.1016/j.euromechsol.2019.103805

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title = "Computational homogenisation of acoustic metafoams",

abstract = "Acoustic metafoams are novel materials recently proposed for low frequency sound attenuation. The design of their microstructure is based on the combination of standard acoustic foams with locally resonant acoustic metamaterials. This results in improved sound attenuation properties due to the interaction between viscothermal dissipation effects and the local resonance effects at the pore level. In this paper, the non-standard behaviour of such a metafoam with a complex two-phase microstructure is analysed through a multiscale approach. The macroscopic problem is described by general balance equations and at the microscopic scale a detailed representation of the microstructure is considered. The frequency dependent effective properties are used to explain the extraordinary acoustic performance. The homogenisation approach is also validated using direct numerical simulations, showing that the homogenisation technique is adequate in modelling both viscothermal dissipation and the local resonance effect within the metafoam microstructure.",

keywords = "Acoustic foams, Acoustic metamaterials, Computational homogenisation, Local resonance, Metafoams, Poro-elastic materials, Viscothermal dissipation",

author = "M.A. Lewi{\'n}ska and V.G. Kouznetsova and \{van Dommelen\}, J.A.W. and M.G.D. Geers",

year = "2019",

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T1 - Computational homogenisation of acoustic metafoams

AU - Lewińska, M.A.

AU - Kouznetsova, V.G.

AU - van Dommelen, J.A.W.

AU - Geers, M.G.D.

PY - 2019/9/1

Y1 - 2019/9/1

N2 - Acoustic metafoams are novel materials recently proposed for low frequency sound attenuation. The design of their microstructure is based on the combination of standard acoustic foams with locally resonant acoustic metamaterials. This results in improved sound attenuation properties due to the interaction between viscothermal dissipation effects and the local resonance effects at the pore level. In this paper, the non-standard behaviour of such a metafoam with a complex two-phase microstructure is analysed through a multiscale approach. The macroscopic problem is described by general balance equations and at the microscopic scale a detailed representation of the microstructure is considered. The frequency dependent effective properties are used to explain the extraordinary acoustic performance. The homogenisation approach is also validated using direct numerical simulations, showing that the homogenisation technique is adequate in modelling both viscothermal dissipation and the local resonance effect within the metafoam microstructure.

AB - Acoustic metafoams are novel materials recently proposed for low frequency sound attenuation. The design of their microstructure is based on the combination of standard acoustic foams with locally resonant acoustic metamaterials. This results in improved sound attenuation properties due to the interaction between viscothermal dissipation effects and the local resonance effects at the pore level. In this paper, the non-standard behaviour of such a metafoam with a complex two-phase microstructure is analysed through a multiscale approach. The macroscopic problem is described by general balance equations and at the microscopic scale a detailed representation of the microstructure is considered. The frequency dependent effective properties are used to explain the extraordinary acoustic performance. The homogenisation approach is also validated using direct numerical simulations, showing that the homogenisation technique is adequate in modelling both viscothermal dissipation and the local resonance effect within the metafoam microstructure.

KW - Acoustic foams

KW - Acoustic metamaterials

KW - Computational homogenisation

KW - Local resonance

KW - Metafoams

KW - Poro-elastic materials

KW - Viscothermal dissipation

UR - https://www.scopus.com/pages/publications/85067614023

U2 - 10.1016/j.euromechsol.2019.103805

DO - 10.1016/j.euromechsol.2019.103805

M3 - Article

AN - SCOPUS:85067614023

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VL - 77

JO - European Journal of Mechanics. A, Solids

JF - European Journal of Mechanics. A, Solids

M1 - 103805

ER -

Computational homogenisation of acoustic metafoams

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