Development of a finite element procedure of contact analysis for articular cartilage with large deformation based on the biphasic theory

Despite the importance of sliding contact in diarthrodial joints, the contact analysis algorithms presented over the past decade have been limited to cases of infinitesimal deformation and thus cannot reflect the real mechanical behavior of articular cartilage in daily life. In this study, a new finite element contact analysis approach allowing a large amount of sliding between articular cartilages is presented based on the biphasic theory, which is an effective model for articular cartilage. The geometric constraint condition and the continuity condition of the fluid phase on the contact surfaces are introduced by applying Lagrange multipliers. The formulation is carried out by transmitting the contact traction of the tissue and the hydrostatic pressure of the fluid phase equivalently between the contact surfaces by means of integrating virtual work due to contact over the contact area. The effectiveness of the proposed algorithm is verified by two numerical examples.