Collective behavior of viscoelastic sliders on a rigid rough surface
Srivatsan Hulikal (Caltech), Nadia Lapusta (Caltech), Kaushik Bhattacharya (California Institute of Technology)
Contact Mechanics
Tue 2:40 - 4:00
Barus-Holley 161
Friction plays an important role in phenomena in diverse fields of study, from biology to geology. The classical picture of friction consists of constant static/kinetic friction coefficients which linearly relate frictional and normal loads. Careful experiments show that the static friction coefficient increases with time while the kinetic friction coefficient depends on sliding velocity and an evolving “state” of the surface. Empirical rate-and-state (RS) friction laws proposed to model the results explain the frictional response of interfaces for a range of materials, from paper to rocks to metals. This universality is suggestive of common underlying physical processes governing the frictional response. However, a comprehensive micromechanical understanding of these phenomenological laws is lacking. Actual contact between two rough surfaces occurs only at a few spots known as asperities. The macroscopic frictional response is thought to be a result of the collective response of these contacts. We model each contact as a viscoelastic element (standard linear solid, SLS) and explore the collective behavior of an ensemble of such elements in contact with a rigid rough surface (Gaussian noise with exponential correlation). Assuming an asperity-scale friction law, we study the evolution of static/kinetic friction. Our results show that strengthening of static friction with time is observed only for a certain class of local friction laws. During sliding, we derive a Langevin equation for the evolution of force on an SLS. From the Langevin equation, we determine the ensemble behavior by deriving a Fokker-Planck equation and by performing Monte Carlo simulations. Results from velocity jump experiments show a behavior similar to that seen in experiments, with the probability density of forces serving as the internal state variable used in the RS laws. We make connection between parameters in our model, parameters in the RS laws and material/geometry of contacts.