Numerical procedures are frequently required to examine the behavior of biological systems because of the geometry, boundary conditions, and/or material characteristics involved. The finite elem ent m ethod was applied here to the biphasic theory via the principle of virtual work to establish a numerical routine for analyses of articular cartilage behavior. The matrix equations that resulted contained displacements of the solid matrix (u) and true fluid pressure (p) as the unknown variables at the element nodes. Both the small strain, linear representation and the large strain theory, encompassing material and geometric nonlinearities, were incorporated. The time-dependent characteristics inherent to two-phase m aterials forced discretization in the time as well as the spatial domain, and thus solutions were obtained at discrete time points. The necessary algorithms and com puter code were developed for the analysis of two-dimensional plane strain, plane stress, and axially symmetric cases.

To determ ine the biomechanical properties of articular cartilage necessary for the finite elem ent analyses, two methods of repairing damaged articular surfaces, transplantation of osteochondral shell allografts and of chondrogenic autografts, were studied. The experimental evaluation of normal and repair tissue properties concluded that repair cartilage possesses a lower stiffness and higher perm eability than normal tissue.

The u-p finite elem ent numerical procedure demonstrated excellent agreem ent with available closed-form and numerical solutions for the configurations of confined compression and unconfined compression under small strains, and for confined compression under large strains. The behavior of a repair surface to an imposed static compressive load at the surface was then evaluated. The consequence of a decreased stiffness, decreased Poisson’s ratio and increased perm eability for the repair tissue was an increase in shear along the interface, which could have implications in the ability of the repair tissue to attach to the adjacent, normal cartilage. The finite elem ent solutions of the unconfined compression configuration under nonlinear conditions dem onstrated differences from the linear solutions due to the nonlinear effects of the large strain constitutive laws and strain-dependent properties.