  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 $\mu < 0.001$) 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
$\mu \approx 0.06$, 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 $\mu$ 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 $10~m/s$.
