Instabilities in frictional sliding: From Schallamach waves to locomoting invertebrates

Intermittent motion, called stick-slip, is a friction instability that commonly occurs during relative sliding of two elastic solids. In adhesive polymer contacts, where elasticity and interface adhesion are strongly coupled, stick-slip arises due to the propagation of slow detachment waves at the interface. Here we analyze two distinct detachment waves moving parallel (Schallamach wave) and antiparallel (separation wave) to applied remote sliding. Both waves cause slip in the same direction, travel at speeds much lesser than any elastic wave speed, and are therefore describable using the same perturbative elastodynamic framework with identical boundary conditions. Our calculations reveal a close correspondence between moving detachment waves and bimaterial interface cracks, including the nature of the singularity and the functional forms of the stresses. Based on this correspondence, and coupled with a fracture analogy for dynamic friction, we develop a phase diagram showing domains of possible occurrence of stick-slip via detachment waves vis-á-vis steady interface sliding. We also describe an Ising-like lattice analogue of this system, discuss the nature of the associated transition from stick to slip at the interface, and establish similarities with other phenomena in geophysics and invertebrate locomotion. We close with some comments about the possibility of dynamic interface waves, propagating at speeds comparable to elastic wave speeds in the two slid solids.