# Effects of stretching on the frictional stress of rubber

## TL;DR

This study experimentally investigates how in-plane surface stretching affects the frictional stress of PDMS rubber, revealing a proportional relationship between local frictional stress and stretch ratio, independent of contact geometry and direction.

## Contribution

It demonstrates that the local frictional stress on stretched rubber is proportional to the stretch ratio and independent of contact geometry and orientation, providing new insights into rubber friction behavior.

## Key findings

- Frictional stress is proportional to local stretch ratio.
- The relationship between frictional stress and stretch is independent of contact geometry.
- The stretch-dependence of friction is isotropic, not depending on the direction of stretching.

## Abstract

In this paper, we report on new experimental results on the effects of in-plane surface stretching on the friction of Poly(DiMethylSiloxane) (PDMS) rubber with smooth rigid probes. Friction-induced displacement fields are measured at the surface of the PDMS substrate under steady-state sliding. Then, the corresponding contact pressure and frictional stress distributions are determined from an inversion procedure. Using this approach, we show that the local frictional stress $\tau$ is proportional to the local stretch ratio $\lambda$ at the rubber surface. Additional data using a triangular flat punch indicate that $\tau(\lambda)$ relationship is independent on the contact geometry. From friction experiments using pre-stretched PDMS substrate, it is also found that the stretch-dependence of the frictional stress is isotropic, i.e. it does not depend on the angle between stretching and sliding directions. Potential physical explanations for this phenomenon are provided within the framework of Schallamach's friction model. Although the present experiments are dealing with smooth contact interfaces, the reported $\tau(\lambda)$ dependence is also relevant to the friction of statistically rough contact interfaces, while not accounted for in related contact mechanics models.