Simple contact mechanics model of the vertebrate cartilage

Abstract

We study a simple contact mechanics model of the vertebrate cartilage, which includes (bulk) osmotic effects. The surface roughness power spectrum of a pig cartilage is obtained from the measured surface topography. Using the Reynolds equations with fluid flow factors, calculated using the Persson contact mechanics theory and the Bruggeman effective medium theory, we show how the area of contact and the average interfacial separation change with time. We found that in most cases the contact area percolates, resulting in islands of confined fluid which carry most of the external load. Most importantly, we find that the pressure in the area of real contact is nearly independent of the external load, and well below 1 MPa. This allows the surfaces in the area of “real contact”, to be separated (at nanometer range separation distance) by osmotic repulsion, resulting in a very small (breakloose) friction force observed even after a long time of stationary contact.