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A vanishing viscosity approach to the evolution of microstructures in finite plasticity
Author(s) -
Günther Christina,
Hackl Klaus
Publication year - 2012
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201210142
Subject(s) - plasticity , crystal plasticity , microstructure , finite volume method , statistical physics , finite strain theory , viscosity , deformation (meteorology) , mathematics , mechanics , classical mechanics , computer science , physics , materials science , thermodynamics , finite element method , metallurgy , meteorology
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)