Unit-cell variability and micro-macro modeling of polyurethane acoustic foams

This paper investigates the impact of the irregular microgeometry of polyurethane acoustic foam on the macroscopic acoustic behavior predicted by a unit-cell model. Two semi-empirical unit-cell models coupled to a rigorous sensitivity analysis technique are used for this purpose. In these models, the porous material is idealized as a packing of a periodic unit-cell (PUC) representative of the disordered network that constitutes the porous frame. The non-acoustic parameters involved in the classical Johnson-Champoux-Allard model are derived from characteristic properties of the PUC and semi-empirical relationships. However, due to the large complexity of the foam microgeometry, the measurements of the main unit-cell properties can be subjected to an important variability mainly related to bulk inhomogeneity, microstructural irregularities, and limitations of the used measurement methods. A global sensitivity analysis is performed on these two models in order to investigate how the variability associated with the measured PUC characteristics affects the models outputs. This allows identification of the possible limitations of a unit-cell micro-macro approach. The sensitivity analysis mainly shows that for moderately and highly reticulated polyurethane foams, the strut length parameter is the key parameter since it greatly impacts three important non-acoustic parameters and causes large uncertainty on the sound absorption coefficient even if its measurement variability is moderate. For foams with a slight inhomogeneity and anisotropy, a micro-macro model associated to cell size measurements should be preferred.