Three-dimensional contact of transversely isotropic transversely homogeneous cartilage layers: A closed-form solution

Abstract

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.

A multiscale model for anisotropic damage and hysteresis in biodegradable polymers

“…The main contribution of this work is a multiscale constitutive model which is able to predict, with only five physically motivated parameters, a wide range of phenomena and deformation classes. Numerous biological materials are constituted by a network of stiff macromolecules, e.g.. collagen, immersed into a soft incompressible extracellular matrix (see [15,16]). This enables outstanding mechanical properties which, as in this work, can be explained via a multiscale approach.…”

Atomic force microscopy-based indentation of cells: modelling the effect of a pericellular coat

“…Finally, we note that any effects of adhesion (at the indenter/brush interface) and time-dependent deformation of both cell body [50] and brush layer [51] are neglected (indentation models for thin viscoelastic and biphasic layers have been developed in [52][53][54]), and thus, the modelling framework is applicable for quasi-static indentation only.…”

On nonlinear dilatational strain gradient elasticity

“…It has also to be remarked that the proposed model has also a strong relation to the so-called generalized models of continuum with scalar (one-dimensional) microstructure by Capriz [17] or Eringen [52,53], see also [23,64,94,104,106]. So it can be used for various applications to material modelling of pressure sensitive materials as those studied in [95,131] or to study some phenomena of phase transitions occurring in solid materials [69,110].…”