Surface Tension regularizes the Crack Singularity of Adhesive Contacts

TL;DR

This paper demonstrates that surface tension significantly influences the contact mechanics of stiff solids, regularizing the crack-like singularity at the contact edge and unifying global adhesion laws with local contact behavior.

Contribution

It introduces a universal self-similar structure at the contact edge governed by surface tension and elasticity, extending understanding beyond soft materials.

Findings

Surface tension regularizes the crack singularity in stiff solid contacts.

A universal self-similar structure emerges at the contact edge.

The theory unifies adhesion laws with local contact mechanics.

Abstract

The elastic and adhesive properties of a solid surface can be quantified by indenting it with a rigid sphere. Indentation tests are classically described by the JKR-law when the solid is very stiff, while recent work highlights the importance of surface tension for exceedingly soft materials. Here we show that surface tension plays a crucial role even for stiff solids: it regularizes the crack-like singularity at the edge of the contact. We find that the edge region exhibits a universal, self-similar structure that emerges from the balance of surface tension and elasticity. The similarity theory provides a complete description for adhesive contacts, reconciling the global adhesion laws and local contact mechanics.