Frictional dissipation and stored energy in combined slip and sliding of two spherical grains

Abstract

The frictional dissipation and energy stored in two spherical grains are investigated analytically for the sliding or combined slip-sliding regimes for the experimentally-typical cases of testing. The analytical formulae are proposed for the explicit and approximate predictions of the work of driving force, kinetic, dissipated and stored energies. Controlling the energy balance, a mathematical insight is also attained into the evolution and redistribution of these quantities over the contact interfaces. It is demonstrated that the total frictional dissipation expended by the moving sphere can be analytically represented as a sum of frictional dissipation given at each contact interface. It also provides for the geometrical construction of the reference contact paths using the overlap approach for contact interaction of two spheres of the same material. The rate of dissipation is expressed in terms of the relative contact zone velocities of two spheres.