A self-consistent approach for the acoustical modeling of vegetal wools. (17th March 2021) - Piégay, Clément; Glé, Philippe; Gourlay, Etienne; Gourdon, Emmanuel; Marceau, Sandrine
Highlights: Cylindrical self-consistent modelling of fibrous materials sound absorption properties. Biphasic cylindrical inclusion as representative elementary volume. Analytical relationships between microstructural parameters and macroscopic properties. Sound absorption modelling approach based on only two specific fibrous parameters. Cylindrical self-consistent modelling validation for the vegetal wools used in green buildings. Abstract: Vegetal wools have the capacity to store atmospheric carbon dioxyde, one of the main gases responsible for climate change. So, these insulating materials are used as key elements for green buildings. Moreover, vegetal wools present high sound absorption level performances contributing to the acoustic comfort of indoor living spaces. These properties are directly related to the morphology and the size of their vegetal fibres. Thus, to take their microstructural specificities into account for the modeling of their sound absorption properties, a micro-macro homogenization approach based on a cylindrical geometry is developed. This modeling method, based on a mix between Homogenization of Periodic Media ( H P M ) and Self-Consistent Method ( S C M ), is called S C M c y l . The macroscopic behaviour laws of materials are rigorously obtained by using H P M . Then, the S C M leads to the establishment of two possible analytical solutions (a velocity approach v and a pressure approach p ) under the fundamental assumption of the energy equivalence between a generic cylindrical inclusion, representative of the vegetal wools physical and geometrical properties at microscopic scale, and the homogeneous equivalent medium at the macroscopic scale. The two modeling approaches developed in this paper, S C M c y l − v and S C M c y l − p, can be used to determine the sound absorption of fibrous materials using only two parameters, an equivalent fibre radius value and the material porosity. Finally, these solutions are validated for the vegetal wools case by comparison with experimental measurements.