A vanishing viscosity approach to the evolution of microstructures in finite plasticity



Material microstructures in finite single-slip crystal plasticity occur and evolve due to deformation. Their formation is not arbitrary, they tend to form structured spatial patterns. This hints at a universal underlying process. As in the approach of D. Kochmann and K. Hackl, we use a variational framework, focusing on the Lagrange functional to describe the evolving mircrostructure. We modify this approach by introducing a small smooth transition zone between the domains in order to improve the numerical treatment. We present explicit time-evolution equations for the volume fractions and the internal variables. We outline a numerical scheme. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)