The energy dissipation mechanism of graphene layers in commensurate contact is studied by molecular dynamics simulations.The commensurability between graphene layers is controlled by misfit angles between graphene layers or an in-plane strain applied to one of the graphene layers.We find that for small size graphene,the main energy dissipation is not caused by stick-slip.We propose two potential energy dissipation channels,the lattice distortion induced by the moiré superlattice structure and variation of entropy of the contacting landscape.Our results provide an insight into the energy dissipation mechanism of commensurate contact graphene.