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Effective Flow Potentials for Anisotropic Polycrystals
Author(s) -
Tsotsova Rumena,
Böhlke Thomas
Publication year - 2009
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200910131
Subject(s) - anisotropy , scalar (mathematics) , a priori and a posteriori , representation (politics) , flow (mathematics) , minification , balanced flow , tensor (intrinsic definition) , distribution function , crystallite , orientation (vector space) , function (biology) , mathematical analysis , statistical physics , mathematics , physics , materials science , pure mathematics , geometry , mathematical optimization , thermodynamics , optics , philosophy , epistemology , politics , political science , law , evolutionary biology , biology , metallurgy
Abstract In this paper a micromechanically based flow potential for anisotropic fcc polycrystals is derived that takes into account the crystallite orientation distribution function (codf) in terms of tensorial texture coefficients. The effective flow potential is based on a representation theorem for anisotropic scalar functions depending on a 2nd‐order tensor. A priori unknown functions in the representation are determined by defining and solving explicitly a minimization problem over SO(3). Important analytical properties of the coefficient matrix of the minimization problem are discussed. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)