Biot theory and its applications in bone acoustics and wave-ice interactions

• Main Author: Chen, Hua
• Format: Thesis
• Language: English
• Published: University of Delaware 2020
• Subjects: Sea ice
• Online Access: http://udspace.udel.edu/handle/19716/25000; https://doi.org/10.58088/zv61-dq98

Guyenne, Philippe Two applications of Biot poroelastic theory are studied, specifically applications in bone acoustics and wave--ice interactions. Cancellous bone can be described as an isotropic and homogeneous medium with constant material parameters. In a simplified case where both the bone sample and water tank are of infinite extent in the vertical direction, the exterior pressure field for a time--harmonic point source can be expressed in a series. The Helmholtz's equation is solved via contour integration of the Green’s function and the residue theorem, producing a semi-analytic solution valid for high frequencies. On the other hand, considering a setting closer to in vitro experiment, Biot’s equations for cancellous bone are coupled with a boundary integral equation for the water pressure. A numerical scheme is proposed to recover material parameters of cancellous bone in two dimensions. Numerous tests are performed for frequencies in the ultrasonic range, and the results show that such parameters as bone porosity can be determined with reasonable accuracy. ☐ For wave--ice interactions in marginal ice zone, a two--dimensional continuum model is proposed. It is based on a two--layer formulation where the floating sea ice is described as a homogeneous isotropic poroelastic material and the underlying ocean is viewed as a weakly compressible fluid. An analytic expression of dispersion relation is derived for traveling wave solutions of this coupled system. Extensive tests are conducted to examine the dependence of results on various parameters in both the porous and non--porous cases. Detailed comparison with existing models is provided, and good agreement on both wave dispersion and attenuation is found. In the porous case with friction, a non--monotonic behavior is observed for the attenuation rate as a function of frequency, which is reminiscent of the roll--over phenomenon that has been reported in field observations. University of Delaware, Department of Mathematical Sciences Ph.D.