Indentation of a two-dimensional bonded elastic layer with surface tension

TL;DR

This paper explores how surface tension influences the indentation behavior of a bonded elastic layer at micro-/nano-scale, revealing increased hardness and altered contact pressure distribution, with practical load-contact width relations.

Contribution

It introduces a theoretical and numerical framework for analyzing surface tension effects on elastic layer indentation, including a generalized explicit load-contact width relationship.

Findings

Surface tension significantly increases elastic layer hardness.

Contact pressure distribution is notably affected by surface tension.

Derived explicit relationship between load and contact half-width.

Abstract

Surface tension is a prominent factor for the deformation of solids at micro-/nano-scale. This paper investigates the effects of surface tension on the two-dimensional contact problems of an elastic layer bonded to the rigid substrate. Under the plane strain assumption, the elastic field induced by a uniformly distributed pressure within a finite width is formulated by applying the Fourier integral transform, and the limiting process leading to the solutions for a line force brings the requisite surface Greens function. For the indentation of an elastic layer by a rigid cylinder, the corresponding singular integral equation is derived, and subsequently solved by using an effective numerical method based on Gauss-Chebyshev quadrature formula. It is found from the theoretical and numerical results that the existence of surface tension strongly enhances the hardness of the elastic layer and significantly affects the distribution of contact pressure, when the size of contact region is comparable to the elastocapillary length. In addition, an approximated relationship between external load and half-width of contact is generalized in an explicit and concise form, which is useful and convenient for practical applications.