A direct link between microstructure and acoustical macro-behaviour of real double porosity foams
Résumé
The acoustical macro-behaviour of mineral open-cell foam samples is modelled from microstructure morphology using a three-dimensional idealized periodic unit-cell (3D-PUC). The 3D-PUC is based on a regular arrangement of spheres, allowed to interpenetrate during the foaming process. Identification and dimensionning of the 3D-PUC is made from X-ray computed microtomography and fabrication process information. In addition, the 3D-PUC used allows to account for two scales of porosity: the interconnected network of bubbles (meso-porosity) and the inter-crystalline porosity of a gypsum matrix (micro-porosity). Transport properties of the micro- and the meso- scales are calculated from first principles and a hybrid micro-macro method is used in order to determine the frequency-dependent visco-thermal dissipation properties. The double porosity theory provides the visco-thermal coupling between the meso- and micro- scales [J. Acoust. Soc. Am. \textbf{114}, 7389 (2003)]. Finally, the results are successfully compared with experiments for two different mineral foam samples. The main originality of this work is to maintain a direct link between the microstructure morphology and the acoustical macro-behaviour all along the multi-scale modelling process, without any fitted parameter.
Domaines
Acoustique [physics.class-ph]
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