The normal stress effect and equilibrium friction coefficient of articular cartilage under steady frictional shear

During creep or stress relaxation, articular cartilage exhibits a time-dependent friction coefficient which has been shown to reach an equilibrium value, μeq, as the tissue deformation equilibrates. This study investigates the frictional properties of articular cartilage explants under steady frictional shear and constant compressive strain after the tissue reaches stress-relaxation equilibrium. The two parameters measured are the normal force and frictional torque, from which the friction coefficient was then calculated. It is shown in this experimental study that: (1) Under a prescribed infinitesimal compressive strain, cartilage supports higher compressive normal stress under steady shear than it does in the absence of frictional shear. Furthermore, the normal stress increases with increasing sliding velocity, resulting in a velocity-dependent value of μeq. The observed normal stress effectively increases the compressive stiffness of cartilage by a factor up to 3.1. (2) Under a prescribed steady frictional shear both the normal stress and frictional shear stress increase, though not proportionally, with increasing compressive strain, producing a decreasing friction coefficient. (3) This velocity-dependent normal stress effect is also shown to result, at least partly, from intrinsic properties of cartilage. The normal stress effect has not been previously reported for articular cartilage, and represents an intriguing mechanical response not commonly encountered in solids, though common in non-Newtonian fluids.