Frictional contact of two spheres for arbitrary 2D loading

Overview & Synopsis

Frictional interaction of two elastic spheres is a fundamental problem of contact mechanics. The tangential displacement depends on the normal and tangential force in a complicated and, in general, hysteretic way. We analyze in detail the key memory characteristic of the system (the traction distribution in the contact zone) and write out analytical solutions in various loading regimes. Then, a general scheme of memory organization is established that enables to describe all possible regimes in a universal way. The result is a computer-assisted general solution to the problem.