Russian doll poroelasticity

n this thesis I solve three interconnected problems related to the understanding of cortical bone poroelasticity. The first and most basic problem addressed is the unconfined compression of a cylindrical annular disk of fluid-filled, porous, elastic solid between smooth, impermeable plates. The theory of anisotropic poroelastic materials is used to develop an analytical solution for this axisymmetric problem in which the plane of transverse isotropy is perpendicular to the cylindrical axis. A general solution is obtained from which the stress relaxation response is obtained. The solution to this boundary value problem is determined for three different boundary conditions on the pore pressure. These boundary conditions are (i) free fluid passage across the outer and inner cylindrical boundaries of the disk; (ii) free fluid passage across the outer cylindrical boundary and no flow across the inner boundary (i.e. zero pressure gradient); (iii) free fluid passage across the inner cylindrical boundary and no flow across the outer boundary. These solutions appeared in Gailani and Cowin (2008).;The second problem is to detail a design and execute an experimental method to measure the permeability of the lacunar-canalicular porosity (PLC) of bone tissue. The analytical solution of problem ;The two problems described are a prelude to constructing a more detailed model of the porous structure of osteonal cortical bone. This new porous structure model is said to be "nested" in the sense that smaller pore size porosity, the PLC, only interchanges interstitial bone fluid with the larger pore size porosity, the vascular porosity (PV). In the construction of the nested porosity model, called Russian doll poroelasticity, the analytical solution of problem...