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Solid friction at high sliding velocities: an explicit 3D dynamical SPH approach

We present realistic 3D numerical simulations of elastic bodies sliding on top of each other in a regime of velocities ranging from meters to tens of meters per second using the so-called Smoothed Particle Hydrodynamics (SPH) method. Our investigations are restricted to regimes of pressure and roughness where only elastic deformations occur between asperities at the contact surface between the slider block and the substrate. In this regime, solid friction is due to the generation of vibrational radiations which are subsequently damped out. We study periodic commensurate and incommensurate asperities and various types of disordered surfaces. We report the evidence of a transition from zero (or non-measurable $μ< 0.001$) friction to a finite friction as the normal pressure increases above about $10^6~Pa$. For larger normal pressures (up to $10^9~Pa$), we find a remarkably universal value for the friction coefficient $μ\approx 0.06$, which is independent of the internal dissipation strength over three order of magnitudes, and independent of the detailled nature of the slider block-substrate interactions. We find that disorder may either decrease or increase $μ$ due to the competition between two effects: disorder detunes the coherent vibrations of the asperties that occur in the periodic case, leading to weaker acoustic radiation and thus weaker damping. On the other hand, large disorder leads to stronger vibration amplitudes at local asperities and thus stronger damping. Our simulations have confirmed the existence of jumps over steps or asperities of the slider blocks occurring at the largest velocities studied ($10~m/s$). These jumps lead to chaotic motions similar to the bouncing-ball problem. We find a velocity strengthening with a doubling of the friction coefficient as the velocity increases from $1~m/s$ to $10~m/s$.