A one-dimensional mesoscopic spring block model with Amontons-Coulomb friction is introduced in order to investigate if some features of recent friction experiments can be understood. Our results suggest that the model too simple to reproduce the main features of the experiment. A two dimensional model and a different local friction law is needed.
In order to test the latter, a two dimensional quasi-static discrete element method is developed to find the tangential loading curve of a thin surface layer. A single asperity is modeled as a semi-circle, in agreement with Hertz and Cattaneo-Mindlin theory. A scaling behavior of the shear stiffness of an asperity with the compression and the dynamic friction coefficient is found, and used to develop a theoretical model for the shear strength of a rough surface assuming elastic independence of asperities.
The discrete element method is further used to model a self affine surface and a gradient percolation surface. Our results suggest that the qualitative behavior of the shear stiffness for the self affine surface is in agreement with the theory, while the behavior of the gradient percolation surface is not.