TY - GEN

T1 - Biphasic acoustic behavior of a non-periodic porous medium

AU - Gilbert, R. P.

AU - Panchenko, A.

AU - Vasilic, A.

PY - 2013/11/15

Y1 - 2013/11/15

N2 - 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 between a typical size of microstructural inhomogeneity and the macroscopic length scale 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 describes a biphasic, viscoelastic material with long-time history dependence. Homogenized system describes macroscopically anisotropic media and is more general than the Biot system.

AB - 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 between a typical size of microstructural inhomogeneity and the macroscopic length scale 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 describes a biphasic, viscoelastic material with long-time history dependence. Homogenized system describes macroscopically anisotropic media and is more general than the Biot system.

UR - http://www.scopus.com/inward/record.url?scp=84887385189&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84887385189&partnerID=8YFLogxK

U2 - 10.1061/9780784412992.234

DO - 10.1061/9780784412992.234

M3 - Conference contribution

AN - SCOPUS:84887385189

SN - 9780784412992

T3 - Poromechanics V - Proceedings of the 5th Biot Conference on Poromechanics

SP - 1981

EP - 1990

BT - Poromechanics V - Proceedings of the 5th Biot Conference on Poromechanics

T2 - 5th Biot Conference on Poromechanics, BIOT 2013

Y2 - 10 July 2013 through 12 July 2013

ER -