Abstract
We study the effect of a long-range correlated scale-invariant random pinning force on the motion and friction properties of an elastically driven asperity in a quasistatic regime. It is shown that when the elastic coupling is weak, the macroscopic dynamic behavior of the asperity can be described as elasto-plastic with a perfectly plastic plateau. The plastic plateau corresponds to statistically stationary sliding. The macroscopic friction behavior arises from the competition between reversible and irreversible motion due to the multiplicity of equilibrium positions. This introduces a history-dependent behavior, with marked memory effects over a characteristic length scale which is computed. This well-defined length scale is compared to the usual ``memory length'' considered in friction experiments. We also analyze the hardening behavior and the hysteretic behavior in radial and cyclic loadings.
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