A homogenization approach for characterization of the fluid-solid coupling parameters in Biot׳s equations for acoustic poroelastic materials

In this paper, a homogenization method is proposed to obtain the parameters of Biot׳s poroelastic theory from a multiscale perspective. It is assumed that the behavior of a macroscopic material point can be captured through the response of a microscopic Representative Volume Element (RVE) consisting of both a solid skeleton and a gaseous fluid. The macroscopic governing equations are assumed to be Biot׳s poroelastic equations and the RVE is governed by the conservation of linear momentum and the adopted linear constitutive laws under the isothermal condition. With boundary conditions relying on the macroscopic solid displacement and fluid pressure, the homogenized solid stress and fluid displacement are obtained based on energy consistency. This homogenization framework offers an approach to obtain Biot׳s parameters directly through the response of the RVE in the regime of Darcy׳s flow where the pressure gradient is dominating. A numerical experiment is performed in the form of a sound absorption test on a porous material with an idealized partially open microstructure that is described by Biot׳s equations where the parameters are obtained through the proposed homogenization approach. The result is evaluated by comparison with Direct Numerical Simulations (DNS), showing a superior performance of this approach compared to an alternative semi-phenomenological model for estimating Biot׳s parameters of the studied porous material.