The role of viscoelasticity on heterogeneous stress fields at frictional interfaces

We investigate the evolution of heterogeneous stress states along frictional in- terfaces. Using finite-element simulations, we model the occurrence of precur- sory slip sequences on a deformable-deformable as well as a deformable-rigid interface between two solids. Every interface rupture creates a stress concen- tration at its arrest position and erases the stress concentrations produced by previous slip events. While the interface is sticking perfectly between two slip events, erased stress concentrations reappear and survive several cycles of ruptures. Such reestablished stress concentrations are smaller than they were before the rupture. We show that the decrease rate of these stress concentrations is exponential with respect to the number of subsequent events and that the bulk viscoelasticity is at the origin of this history effect. During a slip event, the friction tractions at the interface change almost instantaneously, which leads, between two ruptures, to a relaxation-resembling viscous effect that restores the stress concentration. We describe the decrease rate analytically and highlight that it is proportional to the ratio of the viscous over the instantaneous Young’s moduli, and illustrate it by varying the material properties in our simulations.