  We introduce a model of friction between two contacting (stationary or
co-sliding) rough surfaces, each comprising a random ensemble of polydisperse
hemispherical bumps. In the simplest version of the model, the bumps experience
on contact with each other only pairwise elastic repulsion and dissipative
drag. These minimal ingredients are sufficient to capture a static state of
jammed, interlocking contacting bumps, below a critical frictional force that
is proportional to the normal load and independent of the apparent contact
area, consistent with the Amontons-Coulomb laws of friction. However, they fail
to capture two widespread observations: (i) that the dynamic friction
coefficient (ratio of frictional to normal force in steady sliding) is a
roughly constant or slightly weakening function of the sliding velocity $U$, at
low $U$, with a non-zero quasistatic limit as $U\to 0$, and (ii) that the
static friction coefficient (ratio of frictional to normal force needed to
initiate sliding) increases ("ages") as a function of the time that surfaces
are pressed together in stationary contact, before sliding commences. To remedy
these shortcomings, we incorporate a single additional model ingredient: that
contacting bumps plastically nudge one another slightly sideways, above a
critical contact-contact load. With this additional insight, the model also
captures observations (i) and (ii).
