# Direct Measurement of Strain-dependent Solid Surface Stress

## TL;DR

This study directly measures how solid surface stress in soft gels varies with strain, revealing a large surface modulus that influences solid mechanics at larger scales than previously thought.

## Contribution

It provides the first direct experimental evidence of strain-dependent surface stress in soft gels, confirming theoretical predictions for metals.

## Key findings

- Surface stress depends on strain via a surface modulus.
- Surface modulus in soft gels is much larger than zero-strain surface tension.
- Surface stresses can significantly influence solid mechanics at larger scales.

## Abstract

Surface stress, also known as surface tension, is a fundamental material property of any interface. However, measurements of solid surface stress in traditional engineering materials, such as metals and oxides, have proven to be very challenging. Consequently, our understanding relies heavily on untested theories, especially regarding the strain dependence of this property. Here, we take advantage of the high compliance and large elastic deformability of a soft polymer gel to directly measure solid surface stress as a function of strain. As anticipated by theoretical work for metals, we find that the surface stress depends on the strain via a surface modulus. Remarkably, the surface modulus of our soft gels is many times larger than the zero-strain surface tension. This suggests that surfaces stresses can play a dominant role in solid mechanics at much larger length scales than previously anticipated.