An analytical method for rolling contact of articular cartilages in diarthrodial joint

An analytical method is presented to investigate the stresses and strains in the cartilage layers of diarthrodial joint under rolling contact. Each cartilage layer in contact is assumed to be biphasic, composed of a linear elastic solid phase and a Newtonian viscous fluid, whereas the subchondral bone is simplified as a rigid body. The contact range of two cartilage layers is discretized, where the surface tractions are piecewise given. A Galerkin-penalty method is applied to form the finite element formulation for the cartilage layers. The surface tractions, stresses and strains in the cartilage layers are then obtained. for each time step with a numerical procedure of rolling contact. Results show that the interstitial fluid plays a fundamental role in the distributions of the stresses and strains in the cartilage, The normal solid stress reaches its maximum on the cartilage-subchondral bone interface. The coefficient of friction at the contact surface has a great effect on the tangential traction while it has little effect on the normal traction. The difference of rolling velocity between the two cartilage layers has an increasing effect on the tangential traction as the coefficient of friction increases.