This dissertation work shows a novel approach for performing the theoretical analysis of the role of the viscous interstitial fluid phase within deformable porous media, under conditions of both sliding boundary contact and soft elastohydrodynamic lubrication. The lubrica tion mechanisms involved with deformable porous bearing materials remain a challenging engineering problem due to the special characteristics of the bearing material such as the surface deformation and the permeability of the bearing components, and the interactions between the solid and fluid phases of the material. Most of the previous theoretical work in this area has focused on fluid film lubrication of rigid porous bearings, with only a few studies which have addressed fluid film lubrication of deformable porous media. There are virtually no previous studies which have specifically addressed the sliding boundary contact of deformable porous media with viscous interstitial fluid. The complete analysis of such contact and lubrication behavior requires the development of proper boundary conditions at the interface of porous deformable media, and the solution of fundamental problems which pertain directly to sliding contact and lubrication. Such studies form the body of this work which, though applicable to general engineering bearings, pays special attention to articular cartilage, which is the porous deformable bearing material of human and animal diarthrodial joints.
The current research uses the framework of the linear biphasic theory proposed by Mow et al. . Frictional effects resulting from the viscosity of the interstitial fluid phase within the biphasic mixture are considered in great detail in this dissertation. Several problems are solved, including: 1) the general solution for sliding tractions on a porous deformable layer; 2) the interface boundary conditions for sliding contact of deformable porous media with viscous interstitial fluid; 3) 1-D canonical problems of sliding contact involving porous deformable layers of uniform thickness; and 4) 2-D sliding contact of a rigid impermeable cylinder against a porous deformable layer. It is found that the effects of the interstitial fluid viscosity are limited to thin boundary layers near the surface or substrate of the porous deformable material. Naturally, the frictional response at the contacting surfaces of porous deformable media is intimately related to these thin boundary layers. The results of these analyses suggest that such frictional responses are non-negligible under many circumstances, particularly when the permeability of the porous matrix is low or the viscosity of the interstitial fluid is high. For articular cartilage, the friction coefficient deriving from the viscosity of the interstitial fluid may be significant when the applied normal load is small compared to physiological loading conditions. Such findings provide cogent explanations for previously reported experimental results.
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