RESUMEN

In this work we discuss the convergence of an approximation scheme for the solution, near an attractor, of a discontinuous dynamical system arising in the theory of dislocations in crystalline solids. It is well known that dislocations can move only along a finite number of crystallographic directions: in two dimensions, the resulting trajectories are piecewise rectilinear paths. However, in special situations such as near an attractor, dislocations are forced to move along curved paths: we characterize this class of motions as fine mixtures of crystallographic motions, using the notion of generalized curves due to Young, and we explicitly compute the parametrized measure associated to a sequence of polygonals. The result is then used to motivate a simple numerical scheme and show that it is physically consistent. Numerical simulations based on this scheme are also presented and discussed. Key words. dislocation motion, dislocations and cracks, force on a dislocation, Young measures