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On the Principle of a Geometric Mean of Even‐Rank Symmetric Tensors for Textured Polycrystals
Author(s) -
Matthies S.,
Humbert M.
Publication year - 1995
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s0021889894009623
Subject(s) - rank (graph theory) , orientation (vector space) , simple (philosophy) , function (biology) , bar (unit) , distribution (mathematics) , distribution function , geometric mean , tensor (intrinsic definition) , mathematics , physics , mathematical analysis , geometry , combinatorics , thermodynamics , philosophy , epistemology , evolutionary biology , meteorology , biology
A practicable and simple averaging procedure of even‐rank tensors is described, realizing an idea of Aleksandrov & Aizenberg [ Dokl. Akad. Nauk SSSR , (1967), 167 , 1028–1031]. It possesses the properties of a geometric mean, identically obeying the physical condition = . The orientation distribution function f ( g ) enters the calculations in the form of the well known arithmetic mean. The general case is completed by the consideration of specific (twice‐symmetric) fourth‐rank elastic tensors. Calculations with real and modelled orientation distributions lead to results close to those of much more complicated self‐consistent schemes.