Acoustic propagation in a random saturated medium: The monophasic case

✍ Scribed by Robert P. Gilbert; Alexander Panchenko; Ana Vasilic

• Publisher: John Wiley and Sons
• Year: 2010
• Tongue: English
• Weight: 163 KB
• Volume: 33
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/mma.1360

✦ Synopsis

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.