Self-Similarity of Friction Laws

TL;DR

This paper investigates how friction laws behave across different scales in spring-block models, revealing that Coulomb's law remains scale invariant while other laws do not.

Contribution

It demonstrates the scale invariance of Coulomb's friction law in mesoscopic to macroscopic models and clarifies conditions for other laws' invariance.

Findings

Coulomb law is always scale invariant in the models

Other proposed laws are only invariant under specific conditions

Provides insight into the multiscale behavior of friction laws

Abstract

The change of the friction law from a mesoscopic level to a macroscopic level is studied in the spring-block models introduced by Burridge-Knopoff. We find that the Coulomb law is always scale invariant. Other proposed scaling laws are only invariant under certain conditions.}