This thesis addresses finite element-based computational models for the biphasic analysis of hydrated soft tissues in physiological joints. The mixed velocity-pressure (vp) formulation of the linear biphasic theory is adopted to describe the hydrated soft tissue as a mixture of solid and fluid phases. The kinematic continuity conditions of the contact traction and fluid pressure are used as contact boundary conditions. An augmented Lagrangian biphasic contact framework is developed to enforce the biphasic contact constraint. The biphasic contact equations are implemented in commercial finite element software (COMSOL Multiphysics®, COMSOL, Inc., Burlington, MA). Solid mechanics in the Structural Mechanics Module and Darcy's Law in the Earth Science Module are used and coupled to obtain the linear biphasic equations. The Contact Pair feature is used to enforce contact constraint for the solid phase, and the Identity Pair feature is used to enforce fluid continuity constraint for the fluid phase. The accuracy of the implementation is verified using 2D axisymmetric and 3D problems, including indentation with a flat-ended indenter, indentation with a spherical-ended indenter, and contact of glenohumeral cartilage layers.

The augmented Lagrangian biphasic contact formulation is extended to finite sliding contact problems. Nonlinear stress and strain tensors are incorporated into the formulation. The accuracy of the sliding contact implementation is verified using an example problem of sliding contact between a rigid, impermeable indenter and a cartilage layer for which analytical solutions have been obtained. The new implementation's capability to handle a complex loading regime is verified by modeling plowing tests of the temporomandibular joint (TMJ) disc.

A theoretically-consistent biphasic finite element solution of the 2D axisymmetric human knee is developed. The interaction between the fluid and solid matrices of the soft tissues of the knee joint, the stress and strain distribution within the meniscus, and the changes in stress and strain distribution in the articular cartilage of the femur and tibia after meniscectomy are investigated.

Finally, a biphasic model of the 3D knee is developed. The geometry of the knee is based on MRI data, and the model includes cartilages, menisci, bones, and ligaments. A compressive force of 800N is applied to the knee in 0 degree of flexion followed by creep. The time-dependent contact behavior of the knee and the stress and fluid pressure distributions in the menisci and cartilages are investigated. The results of the 3D knee model show that the solid and fluid matrices of the soft tissue have different loadcarrying mechanisms and that the biphasic analysis is necessary for a complete understanding of the knee mechanics. The results of this study also show that the extension behavior of the menisci is essential for the load transmission.