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A Minimum Problem Defining Effective Isotropic Elastic Properties
Author(s) -
Böhlke T.,
Bertram A.
Publication year - 2000
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.20000801481
Subject(s) - isotropy , elasticity (physics) , crystallite , orientation (vector space) , mathematics , mathematical analysis , statistical physics , materials science , geometry , physics , optics , composite material , metallurgy
The paper discusses a special aspect of averages approximating the elastic properties of polycrystalline aggregates with a uniform orientation distribution. It is shown that the well known isotropic estimations by Voigt and Reuss and a recently suggested geometric mean of the local elasticity tensors minimize their distances to the single crystal elasticity tensors as well as to the corresponding volume averages. In this analysis, only the influence of the grain orientation distribution on the macroscopic response is considered.