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In this paper we describe the model of glide dislocation interaction with obstacles based on the planar curve dynamics. The dislocations are represented as smooth curves evolving in a slip plane according to the mean curvature motion law, and are mathematically described by the parametric approach. We enhance the parametric model by employing so called tangential redistribution of curve points to increase the stability during numerical computation. We developed additional algorithms for topological changes (i.e. merging and splitting of dislocation curves) enabling a detailed modelling of dislocation interaction with obstacles. The evolving dislocations are approximated as a moving piece-wise linear curves. The obstacles are represented as idealized circular areas of a repulsive stress. Our model is numerically solved by means of semi-implicit flowing finite volume method. We present results of qualitative and quantitative computational studies where we demonstrate the topological changes and discuss the effect of tangential redistribution of curve points on computational results.

This contribution deals with the numerical simulation of dislocation dynamics, their interaction, merging and changes in the dislocation topology. The glide dislocations are represented by parametrically described curves moving in slip planes. The simulation model is based on the numerical solution of the dislocation motion law belonging to the class of curvature driven curve dynamics. We focus on the simulation of the cross-slip of two dislocation curves where each curve evolves in a dierent slip plane. The dislocations evolve, under their mutual interaction and under some external force, towards each other and at a certain time their evolution continues outside slip planes. During this evolution the dislocations merge by the cross-slip occurs. As a result, there will be two dislocations evolving in three planes, two planes, and one plane where cross-slip occurred. The goal of our work is to simulate the motion of the dislocations and to determine the conditions under which the cross-slip occurs. The simulation of the dislocation evolution and merging is performed by improved parametric approach and numerical stability is enhanced by the tangential redistribution of the discretization points. where B is a drag coecient, and v(x, t) is the normal velocity of a dislocation at x ∈ Γ and time t. The term Lκ represents self-force expressed in the line tension approximation as the product of the line tension L and local curvature κ(x, t). The term τ app represents the local shear stress acting on the dislocation segment produced by the bulk elastic eld. The term τ int represents interaction force between dislocations. In our simulations, we consider the stress controlled regime where the applied stress in the channel is kept uniform. In the slip plane, the applied stress τ app is the same at each point of the line and for numerical computations we use τ app = const.The strain controlled regime analyzed in [3] could be an alternative. Parametric descriptionThe motion law (1.1) in the case of dislocation dynamics is treated by parameterization where the planar curve Γ (t) is described by a smooth time-dependent vector function X : S × I → R 2 , where S = [0, 1] is a xed interval for the curve parameter and I = [0, T ] is the (509)

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