A link between microstructure evolution and macroscopic response in
elasto-plasticity: formulation and numerical approximation of the
higher-dimensional Continuum Dislocation Dynamics theory
Micro-plasticity theories and models are suitable to explain and predict
mechanical response of devices on length scales where the influence of the
carrier of plastic deformation - the dislocations - cannot be neglected or
completely averaged out. To consider these effects without resolving each
single dislocation a large variety of continuum descriptions has been
developed, amongst which the higher-dimensional continuum dislocation dynamics
(hdCDD) theory by Hochrainer et al. (Phil. Mag. 87, pp. 1261-1282) takes a
different, statistical approach and contains information that are usually only
contained in discrete dislocation models. We present a concise formulation of
hdCDD in a general single-crystal plasticity context together with a
discontinuous Galerkin scheme for the numerical implementation which we
evaluate by numerical examples: a thin film under tensile and shear loads. We
study the influence of different realistic boundary conditions and demonstrate
that dislocation fluxes and their lines' curvature are key features in
small-scale plasticity
