An analytical solution to the adhesive cylindrical indentation of a compressible elastic thin layer

ABSTRACT

A simple analytical method based on the Kerr-type model is proposed to extend the well-known Johnson-Kendall-Roberts (JKR) model to the adhesive contact between a rigid cylinder and a compressible elastic thin layer under plane strain. The Kerr-type model provides a linear differential relation between the contact pressure and the normal deflection of the upper surface of the layer, whose lower surface is either bonded or sliding on a rigid substrate. With the aid of Betti’s reciprocal theorem, several easy-to-use explicit formulas are obtained for the relations between the indentation force, the indentation depth and the contact width, and the pressure distribution inside the contact zone and the pull-off force are determined. Reasonable agreement of the predicted results with existing numerical results shows that the present analytical model can capture the adhesive effects on the cylindrical indentation of a compressible elastic thin layer on a rigid substrate.

KEYWORDS:

• Adhesion
• JKR model
• Kerr-type model
• cylindrical indentation
• elastic layer

Acknowledgment

This work is supported by the National Natural Science Foundation of China (11802043), the Fundamental Research Funds for the Central Universities (2019CDXYHK0001); and the NSERC (Natural Science & Engineering Research Council) of Canada (NSERC-RGPIN204992).

Additional information

Funding

This work is supported by the National Natural Science Foundation of China (11802043), the Fundamental Research Funds for the Central Universities (2019CDXYHK0001); and the NSERC (Natural Science & Engineering Research Council) of Canada (NSERC-RGPIN204992).