Friction laws from dimensional-analysis point of view

TL;DR

This paper derives the logarithmic dependence of friction laws on slip velocity and state variables using dimensional analysis, challenging the assumption that thermal activation processes are the sole explanation.

Contribution

It introduces a dimensional analysis approach to derive friction laws, showing that their form does not necessarily imply thermal activation processes.

Findings

Friction coefficient's dependence on slip velocity and state variables can be derived without physical process assumptions.

Logarithmic dependence is not mandatory if multiple state variables share the same dimension.

The approach offers a new perspective on the theoretical basis of friction laws.

Abstract

Friction laws, which are a key to the understanding of the diversity of earthquakes, are considered theoretically. Using dimensional analysis, the logarithmic dependence of the friction coefficient on the slip velocity and the state variable is derived without any knowledge of the underlying physical processes on the frictional surface. This is based on a simple assumption that the friction coefficient is expressed as the difference from a reference state. Therefore, the functional form of the rate and state dependent friction law itself does not necessarily mean that thermal activation processes dominate friction. It is also shown that, if there are two (or more) state variables having the same dimension, we need not assume the logarithmic dependence on the state variables.