Amirouche N., Bécot F., Sgard F.

Porous materials are commonly used as passive devices for the noise control in building and automotive industries. It has been shown recently that the double porosity concept may be used to increase the acoustic absorption of high resistivity porous materials. For instance, a second scale of porosity (meso-porosity) is obtained by manufacturing perforations in a porous substrate (mico-porosity). The improvement is observed in a frequency band which depends on the shape and on the distribution of the perforations. Acoustic performances of these materials can be predicted using finite element methods (FEM). These approaches allow to describe correctly the system's geometry at low frequencies. However, the strong variations of the field in the vicinity of the perforations requires a very fine mesh and therefore a very large number of unknowns To overcome the computational limitations inherent to FE modeling, it is proposed here to examine the application of the Multi-scales Finite Element Method (MsFEM) for studying the acoustic performances of double porosity materials. Using this method, the porous medium can be described using two geometric scales : the mesoscopic scale (unresolved scale) and the macroscopic one (resolved scale). The idea is to solve the finite element problem at the resolved scale using the shape functions which are solutions of the 'standard' finite element problem at the unresolved scale. Considering a porous medium having a rigid and motionless skeleton, this approach is validated by comparisons with the results from a 'standard' FEM model using linear shape functions.