## 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.

Original language | English |
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Pages (from-to) | 2206-2214 |

Number of pages | 9 |

Journal | Mathematical Methods in the Applied Sciences |

Volume | 33 |

Issue number | 18 |

DOIs | |

Publication status | Published - Dec 2010 |

## Keywords

- homogenization
- mathematical biology
- viscoelasticity

## ASJC Scopus subject areas

- Mathematics(all)
- Engineering(all)