Finite Element Analysis of Precursors to Macroscopic Stick–Slip Motion in Elastic Materials: Analysis of Friction Test as a Boundary Value Problem

In this study, we apply the finite element method to investigate precursor to frictional sliding phenomena arising immediately prior to macroscopic stick–slip transitions in elastic bodies within the framework of a continuum theory. Using a numerical model that mimics an actual experimental system, we study the behavior of contact surface nodes to assess the influence of stiffness, driving velocity, initial conditions, and discretization conditions on the propagation characteristics of microscopic slips. In particular, we show that the initial distribution of frictional stress arising due to the Poisson effect has a significant effect on the propagation characteristics in slip regions. Next, based on the results of a finite element analysis of precursor phenomena that accounts for the influence of bulk compliance, we consider the determination of parameters in rate-dependent friction models. With regard to the behavior of sliding friction, we show that the relationship between friction tests and friction models is fundamentally different from the relationship between material tests and constitutive models for material deformation. We conclude that a proper understanding and classification of friction tests, friction models, and the relationship between these tests and boundary value problems are crucial ingredients in the application of computer-aided engineering techniques to sliding-friction phenomena; indeed, friction tests must ultimately be treated as boundary value problems.