Two-dimensional discrete models were used to describe the non-linear interactions of atoms within interface regions. An evolution algorithm was presented for a distribution of dislocations on a plane. The results of numerical simulations illustrated the motion of a dislocation kink. A finite-thickness non-linear interface was studied in 2 dimensions. It provided a further extension of the mathematical model to the analysis of contact problems with frictional interfaces.

Two-Dimensional Lattice Models of the Peierls Type. A.B.Movchan, R.Bullough, J.R.Willis: Philosophical Magazine, 2003, 83[5], 569-87