  We present classical molecular dynamics calculations of the behavior of
copper and gold nanoparticles on a graphene sheet, sheared with a constant
applied force $F_{\rm a}$. The force $F_{\rm s}$ acting on the particle from
the substrate depends on the material of the nanoparticles (Au or Cu), and
exhibits a sawtooth dependency on time, which we attribute to local
commensurability between the metal nanoparticle surface atomic positions with
the graphene lattice. The time-averaged value of $F_{\rm s}$ (the friction
force) acting on Au nanoparticles increases linearly with the contact area,
having slopes close to the experimentally observable ones. A qualitative model
is proposed to explain the observed results.
