Ana Vasilic, United Arab Emirates University

KAUST-IAMCS Workshop on Multiscale Modeling, Advanced Discretization Techniques, and Simulation of Wave Propagation

May 7-8, 2011

King Abdullah University of Science and Technology (KAUST)

Thuwal, Kingdom of Saudi Arabia

Homogenizing Acoustic Wave Propagation Through a Two-Phase Medium

This is a joint work with Robert P. Gilbert (University of Delaware) and Alexander Panchenko (Washington State University).

Homogenization techniques of obtaining averaged behavior of materials with multi-scale structure have a wide range of applications in biology, geo-sciences, and engineering. Here we focus on modeling acoustic properties of cancellous bone – the spongy, porous inner layer of bone filled with bone marrow and blood mixture. First, we model cancellous bone as a visco-elastic matrix with periodic microstructure filled with a sheer-thinning non-Newtonian fluid. As the cancellous bone structure is not exactly periodic, we also consider a randomly fissured domain with the associated random field being statistically homogeneous, with built-in scale separation. By considering the material properties at micro scale, equations describing effective behavior of material on macro scale are derived via appropriate two-scale homogenization tools.