# Contact of a spherical probe with a stretched rubber substrate

## TL;DR

This paper develops a theoretical model and conducts experiments to understand how a stretched neo-Hookean rubber substrate interacts with a spherical probe, predicting contact shape, load, and stiffness under various stretch ratios.

## Contribution

It introduces a new model for contact mechanics of stretched neo-Hookean substrates and validates it through experiments with silicone rubber, highlighting its accuracy below a stretch ratio of 1.25.

## Key findings

- Model accurately predicts contact behavior below stretch ratio 1.25
- Good agreement between theory and experiments for moderate stretches
- Deviations occur at higher stretch ratios due to material response differences

## Abstract

We report on a theoretical and experimental investigation of the normal contact of stretched neo-Hookean substrates with rigid spherical probes. Starting from a published formulation of surface Green's function for incremental displacements on a pre-stretched, neo-Hookean, substrate (L.H. Lee \textit{J. Mech. Phys. Sol.} \textbf{56} (2008) 2957-2971), a model is derived for both adhesive and non-adhesive contacts. The shape of the elliptical contact area together with the contact load and the contact stiffness are predicted as a function of the in-plane stretch ratios $\lambda_x$ and $\lambda_y$ of the substrate. The validity of this model is assessed by contact experiments carried out using an uniaxally stretched silicone rubber. for stretch ratio below about 1.25, a good agreement is observed between theory and experiments. Above this threshold, some deviations from the theoretical prediction are induced as a result of the departure of the mechanical response of the silicone rubber from the neo-Hokeean description embedded in the model.