Contact mechanics of adhesive beams. Part I: Moderate indentation

TL;DR

This paper models the contact mechanics of adhesive beams under moderate indentation using an adhesive zone approach, solving integral equations numerically, and compares predictions with experiments to understand adhesion effects.

Contribution

It introduces a novel adhesive zone model for beams, solving the contact problem with Chebyshev polynomial-based Galerkin method, and links to the JKR model as a special case.

Findings

Adhesive strength and support flexibility significantly affect contact behavior.

The model accurately predicts experimental results for various beam configurations.

The approach effectively models complex structural adhesives.

Abstract

We investigate the contact of a rigid cylindrical punch with an adhesive beam mounted on flexible end supports. Adhesion is modeled through an adhesive zone model. The resulting Fredholm integral equation of the first kind is solved by a Galerkin projection method in terms of Chebyshev polynomials. Results are reported for several combinations of adhesive strengths, beam thickness, and support flexibilities characterized through torsional and vertical translational spring stiffnesses. Special attention is paid to the important extreme cases of clamped and simply supported beams. The popular Johnson-Kendall-Roberts (JKR) model for adhesion is obtained as a limit of the adhesive zone model. Finally, we compare our predictions with preliminary experiments and also demonstrate the utility of our approach in modeling complex structural adhesives.