  Inhomogeneity and anisotropy play a crucial role in attributing articular
cartilage its properties. The frictionless contact model constructed here
consists in two thin biphasic transversely isotropic transversely homogeneous
(TITH) cartilage layers firmly attached onto rigid substrates and shaped as
elliptic paraboloids of different radii. Using asymptotic techniques, a
solution to the deformation problem of such material has been recently obtained
extending previous ones referred to homogeneous materials. The layer itself is
thin in comparison with the size of the contact area and the observed time is
shorter than the hydrogel characteristic time. The emerging three-dimensional
contact problem is solved in closed-form and numerical benchmarks for constant
and oscillating loads are given. The results are shown in terms of contact
pressure and approach of the bones. The latter is derived to be directly
proportional to the contact area. Existing experimental data are reinterpreted
in view of the current model formulation. Comparisons are made with existing
solutions for homogeneous biphasic materials in order to underline the
functional importance of inhomogeneity in spreading the contact pressure
distribution across the contact area. Particular attention is paid to the
applicability of the retrieved formulas for interpreting measurements of in
vivo experiments. Future directions are also prospected.
