On the validity of the method of reduction of dimensionality: area of contact, average interfacial separation and contact stiffness

TL;DR

This paper critically evaluates the effectiveness of the 1D elastic foundation model in contact mechanics, showing it fails to accurately predict contact area and separation due to neglecting long-range elastic interactions.

Contribution

The study demonstrates the limitations of the 1D mapping approach in contact mechanics, highlighting the importance of long-range elastic coupling for accurate predictions.

Findings

1D elastic foundation model fails qualitatively in contact predictions

Long-range elastic coupling is crucial for accurate contact mechanics

Comparison with numerical results shows the model's limitations

Abstract

It has recently been suggested that many contact mechanics problems between solids can be accurately studied by mapping the problem on an effective one dimensional (1D) elastic foundation model. Using this 1D mapping we calculate the contact area and the average interfacial separation between elastic solids with nominally flat but randomly rough surfaces. We show, by comparison to exact numerical results, that the 1D mapping method fails even qualitatively. We also calculate the normal interfacial stiffness $K$ and compare it with the result of an analytical study. We attribute the failure of the elastic foundation model to the neglect of the long-range elastic coupling between the asperity contact regions.