Generation and evolution of inelastic microstructures - an overview

In this paper we give an overview on the modeling of inelastic microstructures using variational methods. We start by discussing the underlying variational principles for inelastic materials, derive evolution equations for internal variables, and introduce the concept of condensed energy. As a mathematical prerequisite we review the variational calculus of nonconvex potentials and the notion of relaxation. We use these instruments in order to study the initiation of plastic microstructures. Here we focus on a model of single-slip crystal plasticity. Afterwards we move on to model the evolution of microstructures. We introduce the concept of essential microstructures and the corresponding relaxed energies and dissipation potentials, and derive evolution equations for microstructure parameters. We then present a numerical scheme by means of which the microstructure development can be computed, and show numerical results for particular examples