Bridging the Scales Between Discrete and Continuum Dislocation Models

We prove the many-particle limit passage of interacting particle systems described by gradient flows. The limiting equation is a gradient flow which describes the evolution of the particle density. Our proof methods rely on variational techniques such as G-convergence of the particle configuration energies and stability of gradient flows. The interacting particle systems under consideration model the motion of dislocations in metals. Since the collective motion of dislocations is the main driving force of plastic deformation of metals, we aim to contribute with our analysis to the current understanding of plasticity.