KAUST-IAMCS Workshop on Multiscale Modeling, Advanced Discretization Techniques, and Simulation of Wave Propagation
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- King Abdullah University of Science and Technology (KAUST)
- Thuwal, Saudi Arabia
- Ana Vasilic, United Arab Emirates University (United Arab Emirates)
- Homogenizing Acoustic Wave Propagation Through a Two-Phase Medium
Authors
- Robert Gilbert, University of Delaware
- Alexander Panchenko, Washington State University
- Ana Vasilic, United Arab Emirates University (United Arab Emirates)
Abstract
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 the micro scale, equations describing effective behavior of material on the macro scale are derived via appropriate two-scale homogenization tools.