Contact problem for a thin elastic layer with variable thickness: Application to sensitivity analysis of articular contact mechanics

TL;DR

This paper develops an asymptotic model to analyze how small variations in cartilage layer thickness affect joint contact mechanics, providing explicit solutions and optimization criteria for better understanding and minimizing non-uniformity effects.

Contribution

It introduces a four-term asymptotic expansion for contact displacement in layered elastic models, extending previous 2D results and offering an optimization approach for cartilage thickness.

Findings

Derived explicit asymptotic solutions for contact displacement.

Identified criteria to optimize cartilage layer thickness.

Demonstrated the impact of thickness variations on joint force-displacement.

Abstract

In the framework of the recently developed asymptotic models for tibio-femoral contact incorporating frictionless elliptical contact interaction between thin elastic, viscoelastic, or biphasic cartilage layers, we apply an asymptotic modeling approach for analytical evaluating the sensitivity of crucial parameters in joint contact mechanics due to small variations in the thicknesses of the contacting cartilage layers. The four term asymptotic expansion for the normal displacement at the contact surface is explicitly derived, which recovers the corresponding solution obtained previously for the 2D case in the compressible case. It was found that to minimize the influence of the cartilage thickness non-uniformity on the force-displacement relationship, the effective thicknesses of articular layers should be determined from a special optimization criterion.