Rate and Aging Time Dependent Static Friction of a Soft and Hard Solid Interface

TL;DR

This paper introduces a mathematical model for static friction between soft solids and hard surfaces, accounting for rate and aging effects, and aligns well with experimental data.

Contribution

It presents a novel population balance model that predicts static friction dependence on velocity and aging time for soft-hard interfaces.

Findings

Static friction stress varies logarithmically with pulling velocity.

Static friction stress varies logarithmically with aging time.

Model predictions agree with experimental observations.

Abstract

In this article, we present a mathematical model that answers a classical question concerning how much force, which is generally called static friction force, will it require to initiate the motion of a soft solid block such as gel, rubber or elastomer on a hard surface for instance glass surface. The model uses population balance of the bonds between the polymer chains of the soft solid and the hard surface to estimate rate and aging time dependent static friction. The model predicts that under certain range of the pulling velocity, the friction stress at the onset of sliding (static friction stress) varies as the logarithm of the pulling velocity, as well as the logarithm of the aging time. These predictions are consistent with the experimental observations.