Another extremely interesting topic in modern physics, which may be related to the study of friction, is the jamming transition. A granular material can flow through a pipe or it can jam. The transition is abrupt, and some scholars have claimed recently that it constitutes a phase transition. See, for example, a paper by G. Biroli “Jamming: A new kind of phase transition?” Nature Physics 3:222 (2007) . Physicists also claim that the jamming transition is similar to the mysterious (still not well-understood) glass transition.
Interestingly, the force is not distributed uniformly through the bulk of the material in jammed granular media. Instead, it forms “force chains.” These chains have been studied in 2D systems both experimentally (you need a grain which changes color when pressed to observe the chains visually) and by numerical simulations. O. Gendelman, Y. G. Pollack, I. Procaccia have also suggested a formalism to study the force chains.
T. S. Majmudar and R. P. Behringer, Contact force measurements and stress-induced anisotropy in granular materials, Nature (London) 435, 1079 (2005).
O. Gendelman, Y. G. Pollack, I. Procaccia, S. Sengupta, and J. Zylberg, What Determines the Static Force Chains in Stressed Granular Media? Phys. Rev. Lett. 116, 078001
As you can see, the chains form a somewhat random structure, which looks somewhat similar to what we see during the percolation (which is an archetypical model for the phase transitions and the emergence of a new behavior in various physical systems). However, whether there is indeed some deep similarity between the jamming and percolation, is not known at this point.
Why do I think that the jamming transition can be related to friction? Jamming belongs to the same class of phenomena as the plastic yield, onset of friction, and crack destabilization. The so-called jamming phase diagram (see, for example, Trappe et al., “Jamming phase diagram for attractive particles” Nature 411:772) is somewhat similar to the granular material failure phase diagram, about which I have already written recently in this blog, and which is of direct relevance to friction and the onset of rupture.
This would be a great topic to study, both theoretically, numerically, and experimentally, if somebody is interested to support such a research!