Fifty years of Schallamach waves: From rubber friction to nanoscale fracture

TL;DR

This paper reviews 50 years of research on Schallamach waves, their role in rubber friction and nanoscale fracture, highlighting recent discoveries of solitary waves and dual waves, and connecting macroscopic and nanoscale phenomena.

Contribution

It provides a comprehensive review of Schallamach waves, introduces recent findings of solitary and dual waves, and links these phenomena across scales using continuum theory.

Findings

Identification of solitary Schallamach waves in specialized contacts

Discovery of a dual wave, the separation pulse, propagating oppositely

Application of continuum theory to describe wave behaviors across scales

Abstract

The question of how soft polymers slide against hard surfaces is of significant scientific interest, given its practical implications. Specifically, such sytems commonly show interesting stick-slip dynamics, wherein the interface moves intermittently despite uniform remote loading. \mt{The year 2021 marked the 50$^{th}$ anniversary of the publication of a seminal paper by Adolf Schallamach (\emph{Wear}, 1971)} that first revealed an intimate link between stick-slip and moving detachment waves, now called Schallamach waves. We place Schallamach's results in a broader context and review subsequent investigations of stick-slip, before discussing recent observations of solitary Schallamach waves. This variant is not observable in standard contacts so that a special cylindrical contact must be used to quantify its properties. The latter configuration also reveals the occurrence of a dual wave -- the so-called separation pulse -- that propagates in a direction opposite to Schallamach waves. We show how the dual wave and other, more general, Schallamach-type waves can be described using continuum theory, and provide pointers for future research. In the process, fundamental analogues of Schallamach-type waves emerge in nanoscale mechanics and interface fracture. The result is an on-going application of lessons learnt from Schallamach-type waves to better understand these latter phenomena.