The first part of the paper proposed a semi-analytical method for the tridimensional thermal-elastic-plastic contact between two hemispherical asperities. The algorithm has been described for both the load-driven (ld) and the displacement-driven (dd) formulations, and validated through a nano-indentation test simulation. The way to consider rolling and sliding motion of the contacting bodies consists of solving the elastic-plastic contact at each time step while upgrading the geometries as well as the hardening state along the moving directions. The derivations concerning the interference calculation at each step of the sliding process are then shown, and an application to the tugging between two spherical asperities in simple sliding (dd formulation) is made. The way to project the forces in the global reference is outlined, considering the macro-projection due to the angle between the plane of contact and the sliding direction, and the micro-projection due to the pile-up induced by the permanent deformation of the bodies due to their relative motion. Finally a load ratio is introduced and results are qualitatively compared to a two-dimensional FEM analysis presented elsewhere.

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