Dislocation based Plasticity

Constitutive laws for continuum dislocation dynamics

In this project we aim at incorporating dislocation—dislocation interactions and dislocation reactions in the constitutive equations for continuum dislocation dynamics, CDD (Hochrainer et al. 2014)). 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 current project aims at the development of constitutive equations mostly for the very recent CDD based on the second order alignment tensor (Hochrainer, 2015). The reason is that the second order alignment tensor provides information on the directional distribution of all dislocations and not only of geometrically necessary as does the lowest order CDD theory (Hochrainer et al., 2014). This is for example important for understanding the dominance of given dislocation characters (e.g. braids of edge dislocations) in dislocation patterns. 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.




Total dislocation density (gray scale) and scaled main axes of dislocation alignment tensor in spontaneously developed dislocation structure. A dominant main axis indicates the prevailing of a dislocation character for statistically stored dislocations.




T. Hochrainer, S. Sandfeld, M. Zaiser, P. Gumbsch, 2014. Continuum dislocation dynamics: Towards a physical theory of crystal plasticity, J. Mech. Phys. Solids, 63, 167-178


T. Hochrainer, 2015. Multipole expansion of continuum dislocation dynamics in terms of alignment tensors, Philos. Mag., 95(12), 1321-1367.



Members :

Prof. Dr.-Ing. Thomas Hochrainer, Computation Material Modeling, University of Bremen
Alireza Ebrahimi, Computation Material Modeling, University of Bremen
Jason Marx, Computation Material Modeling, University of Bremen