Acoustic propagation in a random saturated medium: The monophasic case
Robert Pertsch Gilbert, Alexander Panchenko, Ana Vasilic · Mathematical Methods in the Applied Sciences · 2010
Abstract We study the problem of derivation of an effective model of acoustic wave propagation in a two‐phase, non‐periodic medium modeling a fine mixture of linear elastic solid and a viscous Newtonian fluid. Bone tissue is an important example of a composite material that can be modeled in this fashion. We extend known homogenization results for periodic geometries to the case of a stationary random, scale‐separated microstructure. The ratio ε of the macroscopic length scale and a typical size of the microstructural inhomogeneity is a small parameter of the problem. We employ stochastic two‐scale convergence in the mean to pass to the limit ε→0 in the governing equations. The effective model is a single‐phase viscoelastic material with long‐time history dependence. Copyright © 2010 John Wiley & Sons, Ltd.