Acoustic propagation in a random saturated medium: The monophasic case

Robert P. Gilbert, Alexander Panchenko, Ana Vasilic

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)2206-2214
Number of pages9
JournalMathematical Methods in the Applied Sciences
Issue number18
Publication statusPublished - Dec 2010


  • homogenization
  • mathematical biology
  • viscoelasticity

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)


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