Analysis of the unilateral contact problem for biphasic cartilage layers with an elliptic contact zone and accounting for the tangential displacements

TL;DR

This paper investigates a 3D unilateral contact problem for biphasic cartilage layers with elliptic contact zones, incorporating both normal and tangential displacements, and derives approximate relationships between contact parameters.

Contribution

It introduces a novel model accounting for tangential displacements in biphasic cartilage contact problems and derives asymptotic and first-order approximation solutions.

Findings

Established exact relationships between contact approach and pressure characteristics.

Derived asymptotic expressions for contact pressure integrals.

Formulated a first-order approximation problem for the contact analysis.

Abstract

A three-dimensional unilateral contact problem for articular cartilage layers attached to subchondral bones shaped as elliptic paraboloids is considered in the framework of the biphasic cartilage model. The main novelty of the study is in accounting not only for the normal (vertical), but also for tangential vertical (horisontal) displacements of the contacting surfaces. Exact general relationships have been established between the contact approach and some integral characteristics of the contact pressure, including the contact force. Asymptotic representations for the contact pressure integral characteristics are obtained in terms of the contact approach and some integral characteristics of the contact zone. The main result is represented by the first-order approximation problem.