An asymptotic model for the deformation of a transversely isotropic, transversely homogeneous biphasic cartilage layer

TL;DR

This paper develops an asymptotic model to analyze the short-time deformation behavior of a transversely isotropic, transversely homogeneous biphasic cartilage layer, considering specific boundary conditions relevant to joint contact mechanics.

Contribution

It introduces a new asymptotic modeling approach for biphasic cartilage deformation accounting for anisotropy and homogeneity, with specific boundary assumptions.

Findings

Model accurately predicts initial cartilage deformation.

Highlights importance of anisotropic properties in cartilage mechanics.

Provides a foundation for future joint contact studies.

Abstract

In the present paper, an asymptotic model is constructed for the short-time deformation of an articular cartilage layer modeled as transversely isotropic, transversely homogeneous (TITH) biphasic material. It is assumed that the layer thickness is relatively small compared with the characteristic size of the normal surface load applied to the upper surface of the cartilage layer, while the bottom surface is assumed to be firmly attached to a rigid impermeable substrate. In view of applications to articular contact problems it is assumed that the interstitial fluid is not allowed to escape through the articular surface.