Yes it has already widely discussed in the litterature and took into consideration for numerical modelling. This can be partly explained to the the surface roughness deformation when they are submitted to a press load and hence, to a lower friction coefficient.
A very quick search to give you an illustration:
Article On the Use of Advanced Friction Models for the Simulation of...
Yes, this is indeed the basis of Friction in Physics. Remember- Static and Kinetic friction !
So, when the body is at rest and as the load increases, friction is equal to the applied load till the body crosses the hinderance by starting acceleration. F= f in the static friction, F-f = m*a in the kinetic friction. These equations clearly shows that f