Pore-scale bending and membrane effects in permeo-elastic media
Résumé
Permeo-elastic media are permeable media whose pore fluid network is connected and their solid frame is made of a stiff skeleton onto which highly flexible thin films are fixed. In this work, we investigate acoustic wave propagation in permeo-elastic media accounting for pore-scale membrane and bending effects in the films. To this end, it is used the two-scale asymptotic homogenisation method to derive upscaled models, asymptotic analyses to disclose the different wave propagation regimes, and the finite element method to solve the local fluid-structure interaction boundary-value problems arising from homogenisation. The study evidences the salient acoustic features of permeo-elastic media and shows that these may significantly depart from those of conventional porous media due to the interplay of the elastic and kinetic energy of the films with the viscous and kinetic energy of the fluid. It is concluded that the control of membrane and bending effects may lead to a useful way of tuning the atypical effective acoustical properties of permeo-elastic media.