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A Hybrid Micro–Macro–Model of Finite Plasticity with Discrete CODF–Textures
Author(s) -
Frankenreiter Ilona,
Rosato Daniele,
Miehe Christian
Publication year - 2009
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200910013
Subject(s) - anisotropy , plasticity , discretization , macroscopic scale , statistical physics , macro , crystal plasticity , multiscale modeling , finite strain theory , finite element method , computer science , materials science , mathematics , physics , mathematical analysis , optics , thermodynamics , chemistry , computational chemistry , quantum mechanics , composite material , programming language
We outline recent developments towards an efficient theoretical and algorithmic modeling of evolving crystal orientation microstructures in finite plasticity of polycrystals. We construct a framework for the description of grain texture induced anisotropy in planar polycrystals based on a hybrid micro‐macro modeling. On the macroscopic side this concerns a purely phenomenological setting of anisotropic finite plasticity based on evolving structural tensors accounting for the deformation‐induced macroscopic anisotropy. On the micro‐mechanical side, the macro‐model is linked with an accompanying microscopic plasticity model that accounts locally for microscopic structural changes in the form of grain re‐orientations. The model‐inherent scale bridging is accomplished by an evolving crystal orientation distribution function (CODF), which governs the evolution of the structural tensors. The evolution of the CODF is updated in a novel format based on the exploitation of two evolution equations in the Lagrangian setting. We discuss an efficient numerical implementation of evolving CODFs discretizing the orientation space. The new approach is compared with a Taylor model. The new model provides an efficient and fast computationally two‐scale approach for the prediction of the complex microstructures evolution in polycrystals. The capability of the proposed method is demonstrated by means of representative numerical examples. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)