TY - JOUR

T1 - Homogenizing the acoustics of cancellous bone with an interstitial non-Newtonian fluid

AU - Gilbert, R. P.

AU - Panchenko, Alexander

AU - Vasilic, Ana

PY - 2011/2/15

Y1 - 2011/2/15

N2 - We study the problem of derivation of an effective model of acoustic wave propagation in a two-phase medium composed of a linear KelvinVoight viscoelastic solid and a shear-thinning non-Newtonian fluid. Bone tissue is an important example of such composite materials. The microstructure is modeled as a periodic arrangement of fluid-saturated pores inside the solid matrix. The ratio ε of the macroscopic length scale and the size of the microstructural periodicity cell is a small parameter of the problem. We employ two-scale convergence and some other weak convergence techniques to pass to the limit ε→0 in the nonlinear governing equations. The effective model is a two-velocity system for the effective velocity v̄ and a corrector velocity w. The latter describes the influence of the high-frequency oscillations on the effective wave propagation. The effective constitutive equation provides an explicit dependence of the effective stress on e(v̄)+ey(w).

AB - We study the problem of derivation of an effective model of acoustic wave propagation in a two-phase medium composed of a linear KelvinVoight viscoelastic solid and a shear-thinning non-Newtonian fluid. Bone tissue is an important example of such composite materials. The microstructure is modeled as a periodic arrangement of fluid-saturated pores inside the solid matrix. The ratio ε of the macroscopic length scale and the size of the microstructural periodicity cell is a small parameter of the problem. We employ two-scale convergence and some other weak convergence techniques to pass to the limit ε→0 in the nonlinear governing equations. The effective model is a two-velocity system for the effective velocity v̄ and a corrector velocity w. The latter describes the influence of the high-frequency oscillations on the effective wave propagation. The effective constitutive equation provides an explicit dependence of the effective stress on e(v̄)+ey(w).

KW - Bone mechanics

KW - Homogenization

KW - Non-Newtonian fluids

KW - Poroelastic media

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U2 - 10.1016/j.na.2010.06.053

DO - 10.1016/j.na.2010.06.053

M3 - Article

AN - SCOPUS:78650510262

VL - 74

SP - 1005

EP - 1018

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

SN - 0362-546X

IS - 4

ER -