Two-dimensional lattice models of the Peierls type

Two-dimensional discrete models are used to describe nonlinear interactions of 'atoms' within interface regions. An evolution algorithm is presented for a distribution of dislocations on a plane. Results of numerical simulations illustrate motion of a dislocation kink. A finite-thickness nonlinear interface is studied in two dimensions; it gives a further extension of the mathematical model to the analysis of contact problems with frictional interfaces.