Constitutive laws for continuum dislocation dynamics

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In this project we aim at incorporating dislocation--dislocation interactions and dislocation reactions in the constitutive equations for continuum dislocation dynamics (CDD). A constitutive law for CDD defines the dependence of the average dislocation velocity on the current stress and dislocation state. The constitutive modeling shall be achieved in a double strategy combining a top down variational approach and bottom up methods built on discrete dislocation data. The variational methods are used to derive expressions for elastic interactions which capture, for example, strain gradient effects. The bottom up approach targets at classical strain hardening and uses statistical data on dislocation reactions and junction formation from discrete dislocation simulations. Moreover, dislocation multiplication resulting from dislocation reactions shall be incorporated in the constitutive law. The derived dislocation flux equations shall be incorporated in a finite-element code in order to compare the predictions to micro-experiments and discrete dislocation simulations.