The last decade has seen major advances in the experimental study of the onset of dynamic friction. Optical methods give access to the sliding interface before and during sliding onset, enabling characterisation of the local response to external shear. Treating the sliding interface as an extended system, experimentalists have probed the evolution of slip with high spatial resolution. Cameras operating at the order of 100 kHz have enabled direct study of the fast crack/rupture fronts associated with the transition from local pinning to shear displacement.
The spatiotemporal resolution goes beyond the phenomenological descriptions of the global frictional response, i.e. the net resistance to shear motion. Models of the friction of extended systems have a longstanding history in the earthquake community and as models of global friction motivated by the microscopic formation and breaking of contacts. Some of these models have been adapted to the study of sliding onset and investigated numerically. However, their quantitative predictive power has been poor.
In this thesis I study deterministic spring--block models of an elastic slider under dry friction. I apply Amontons--Coulomb friction at the block level. First, I study a one-dimensional model and investigate the length of precursors as a function of the driving force. Analytical expressions for point and uniform driving are found and shown to be in excellent agreement with simulation results. Qualitative agreement with experiments is demonstrated. The effect of a friction-induced torque is studied for uniform driving, and the output form the model is compared to a recently proposed theory.
I then study a two-dimensional model that includes the direction of sliding and the direction out of the sliding plane, the vertical. By comparison to the one-dimensional model, I show that successful prediction of the experimental results depends crucially on accurate representation of the forces associated with elastic deformations of the slider. This can be obtained in the two-dimensional model if realistic boundary conditions are applied.
The statics of sliding onset are the measures that correspond to the states the sliding system comes to rest in, for example the arrest point of a local slip zone, the interfacial shear and normal stress profiles and the length and number of precursors. The dynamics of sliding onset are the rapid time dynamics, for example the speed of the front of a growing slip zone. The statics are reproduced remarkably well in my two-dimensional model, while the dynamics still lack important features of the experimental results. This indicates that the statics depend only weakly on the dynamics, and that they could be studied independently of the fast time evolution. Conversely, the dynamics, although not reproducing the range of experimental observations, are shown to depend strongly on the local stresses and the details of the friction law, i.e. cannot be predicted independently of the statics.