The mechanical equilibrium of soft solids with surface elasticity

TL;DR

This paper investigates how surface elasticity influences the mechanical behavior of soft solids, revealing its role in stiffening surfaces, regularizing singularities, and impacting phenomena like wetting and adhesion.

Contribution

It develops a boundary condition framework for surface elasticity, demonstrating its effects on surface response and singularity regularization in soft materials.

Findings

Surface elasticity stiffens the surface response at small length-scales.

It regularizes displacement singularities in line force problems.

Implications for wetting, adhesion, and friction phenomena.

Abstract

Recent experiments have shown that surface stresses in soft materials can have a significant strain-dependence. Here we explore the implications of this surface elasticity to show how, and when, we expect it to arise. We develop the appropriate boundary condition, showing that it simplifies significantly in certain cases. We show that surface elasticity's main role is to effectively stiffen a solid surface's response to in-plane tractions, in particular at length-scales smaller than a characteristic elastocapillary length. We also investigate how surface elasticity effects the Green's-function problem of a line force on a flat, linear-elastic substrate. There are significant changes to this solution, especially in that the well-known displacement singularity is regularised. This raises interesting implications for soft phenomena like wetting contact lines, adhesion and friction. Finally, we discuss open questions, future directions, and close ties with existing fields of research.