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.

Theory for diffusive and ballistic air leakage and its application to suction cups

“…This is due to the high contact pressure in the region r * < r < r * + l(t), which increases the transfer of the plastisizer to the PMMA surface as compared to the contact region r * + l(t) < r < r 1 , where the contact pressure is much smaller. This pressure-induced increase in the transfer of fluid (or mobile molecules) from a solid to the surface of a counter material is well known in the context of soft-PVC, and also know for other fluid filled materials, e.g., the cartilage of the human joints [38][39][40].…”

A coupled contact model of cartilage lubrication in the mixed-mode regime under static compression

“…By comparison, it is reasonable to assume that under a static compression case (i.e., two-legged stance) which is investigated in this study, the entrainment speed and shear rate would be at low level, and hence a relatively higher viscosity may be assumed. In light of this, 1 Pa•s is adopted as the base case to be consistent with previous study [15]. In addition, a parametric study is performed in Section 3.3.1 to discuss the lubrication effect of different viscosity values.…”

“… For simplicity, the viscosity of synovial fluid is assumed to be constant (i.e., using 1 Pa•s as the base case as per assumptions made in previous studies [7], [15]).…”

Cartilage rehydration: The sliding-induced hydrodynamic triggering mechanism

“…Here, the draining process due to static loading is modelled by using the FEM software package Abaqus v. 2017 [29][30] [31]. Let us observe that, at this stage, we neglect the role played by the roughness: indeed, the micro-squeeze occurring due to the static loading [32] [33] does not provide qualitatively significant variation to the loading problem solution in terms of stress/strain distribution, of contact pressures and, ultimately, of the entire biphasic mechanics. Consequently, as reported in Figure 2a, by reproducing a contact configuration mimicking the typical experimental setup [34], we model a smooth cartilage cylindrical punch in contact with a flat disk assumed to be perfectly rigid.…”