Indentation, elasticity and surface tension

TL;DR

This paper discusses how classical elastic indentation models are insufficient at micro and nano scales where surface tension significantly influences mechanical response, highlighting the need for models that incorporate surface tension effects.

Contribution

It introduces the importance of including surface tension in elastic indentation models at small scales, addressing a gap in existing classical models.

Findings

Surface tension affects indentation response at sub-micron and millimeter scales.

Classical models like Hertz and Sneddon do not account for surface tension effects.

Incorporating surface tension can improve the accuracy of nanoindentation analysis.

Abstract

The classical models of Hertz, Sneddon and Boussinesq provide solutions for problems of indentation of a semi-infinite elastic massif by a sphere, a sphere or a cone and a flat punch. Although these models have been widely tested, it appears that at small scales and for flexible materials, surface tension can contribute to considerably to the mechanical response to indentation. The scales are typically those of the less than one micron for an elastomer and less than one millimetre for a gel. The exploitation of certain experimental results of microscopy or nanoindentation remain approximate due to the absence of models incorporating the effect of surface tension.