Homogenization of sound propagation in a deformable porous material based on microscopic viscous-thermal effects

Porous materials like acoustic foams can be used for shielding and their absorption abilities depend on the interaction of the acoustic wave and the complex microstructure. In this paper, a homogenization model is proposed to investigate the relation between the microstructure and the macroscopic properties. A numerical experiment is performed in the form of simulations of sound absorption tests on a porous material made from polyurethane. For simplicity, an idealized partially open cubic microstructure is adopted. The homogenization results are evaluated by comparison with Direct Numerical Simulations (DNS), showing a good performance of the approach for the studied porous material. By comparing the results, it is found that Biot's model with the parameters obtained from the homogenization approach predict a higher resonance frequency than the DNS, whereas a full homogenization modification improves the prediction due to the incorporation of the microscopic fluctuation.