  A commensurate-incommensurate phase transition in bilayer graphene is
investigated in the framework of the Frenkel-Kontorova model extended to the
case of two interacting chains of particles. Analytic expressions are derived
to estimate the critical unit elongation of one of the graphene layers at which
the transition to the incommensurate phase takes place, the length and
formation energy of incommensurability defects (IDs) and the threshold force
required to start relative motion of the layers on the basis of
dispersion-corrected density functional theory calculations of the interlayer
interaction energy as a function of the relative position of the layers. These
estimates are confirmed by atomistic calculations using the DFT-D based
classical potential. The possibility to measure the barriers for relative
motion of graphene layers by the study of formation of IDs in bilayer graphene
is discussed.
