Analysis and Computation of Microstructure in Finite Plasticity

Abstract

We review aspects of pattern formation in plastically deformed single crystals, in particular as described in the investigation of a copper single crystal shear experiment in [DDMR09]. In this experiment, the specimen showed a band-like microstructure consisting of alternating crystal orientations. Such a formation of microstructure is often linked to a lack of convexity in the free energy describing the system. The specific parameters of the observed bands, namely the relative crystal orientation as well as the normal direction of the band layering, are thus compared to the predictions of the theory of kinematically compatible microstructure oscillating between low-energy states of the non-convex energy. We conclude that this theory is suitable to describe the experimentally observed band-like structure. Furthermore, we link these findings to the models used in studies of relaxation and evolution of microstructure.