Research Article
Oct 1980
Graded and Perfect Disorder in Random Media Elasticity
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VIEW THE REPLYPublication: Journal of the Engineering Mechanics Division
Volume 106, Issue 5
Abstract
The basic problem considered concerns the calculation of effective elastic moduli of a random elastic medium such as a polycrystalline aggregate or a disordered composite, given some statistical information about its microstructure. A rigorous formal general solution is obtained as a Neumann-type series of multiple integrals which contain the statistical information in terms of n-point correlation functions of increasing order n. The integrals can be calculated provided the medium is highly disordered. To describe the disorder in a quantitative fashion, the concept of graded and perfect (=maximum) disorder is introduced. Rigorous bounds of nth order are derived for the effective elastic moduli of random media which are classified as disordered of grade n. The effective elastic moduli of the perfectly disordered medium concide in rigor with the well-known self-consistent moduli.
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Published In
Journal of the Engineering Mechanics Division
Volume 106 • Issue 5 • October 1980
Pages: 889 - 914
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© 1980 American Society of Civil Engineers.
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Published in print: Oct 1980
Published online: Feb 3, 2021
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Ekkehart Kröner
Prof. of Theoretical and Applied Physics; Institut fur Theoretische und Angewandte Physik der Universitat und Max-Planck Institut für Metallforschung, Stuttgart, West Germany
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