Contact mechanics of adhesive beams. Part II: Low to high indentation

TL;DR

This paper extends a contact mechanics model to analyze the indentation of adhesive beams by a rigid punch, comparing theoretical, numerical, and classical contact models across different adhesive strengths.

Contribution

It introduces a coupled integral equation approach for adhesive beam indentation, incorporating boundary conditions and comparing results with finite element simulations and classical models.

Findings

Transition from Hertzian to JKR contact behavior with increasing adhesion

Validation of the integral equation model against FE simulations

Effect of adhesive strength on contact parameters

Abstract

In this article, we extended our approach, that is mentioned in part 1, to model the indentation of an adhesive beam by a rigid cylindrical punch. We considered clamped and simply supported beams for this study. We first modeled these beams as infinite length elastic layers which obey the kinetic and kinematic constraints imposed by the end supports. The adhesion effects are considered via the Dugdale-Barenblatt model based adhesive zone model. Solving the governing equations of this infinite layer along with its boundary conditions, we obtain a set of coupled Fredholm integral equations of first kind. These integral equations are then solved employing the collocation technique. The results obtained are then compared with finite element (FE) simulations and the previously published results for the non-adhesive case. We also obtained the results for the well-known Johnson-Kendall-Roberts (JKR) approximation of the contact. Finally we investigated the effect of various adhesive strengths on the contact parameters and showed the transition of the results from 'Hertzian' to 'JKR' approximation.