Microstructure-based numerical modeling of foams for acoustic shielding

In this paper, a numerical homogenization approach is proposed to obtain isotropic Biot's parameters based on the microstructure of an porous material. It is assumed that a macroscopic point can be represented by a microscopic Representative Volume Element (RVE) consisting of the solid and the fluid. The macroscopic properties are controlled by Biot's equations and the RVE is governed by linearized balance equations for momentum and linear constitutive laws. With suitable boundary conditions, the micro-macro relation is formulated based on consistency of energy. Then, Biot's parameters are calculated through the response of the RVE. By following this new homogenization approach, examples with simple microstructures are given and simulations of two sound absorption experiments are conducted by using Biot's equations. The results are compared with Direct Numerical Simulations and it shows a favourable performance of this new approach compared to the alternative Transfer Matrix Method.