A Generalized Self-Consistent Mechanics Method for Solids Containing Elliptical Inclusions

[+] Author and Article Information
Y. Huang

Department of Mechanical Engineering-Engineering Mechanics, Michigan Technological University, Houghton, MI 49931

K. X. Hu

Corporate Manufacturing Research Center, Motorola, Schaumburg, IL 60196

J. Appl. Mech 62(3), 566-572 (Sep 01, 1995) (7 pages) doi:10.1115/1.2895982 History: Received April 15, 1993; Revised June 01, 1994; Online October 30, 2007


The determination of the effective moduli for a material containing elliptical inclusions is the objective of this paper. This is done by incorporating an inclusion/matrix/composite model into a general energy equivalence framework. Through the evaluation of the average strain in each individual inclusion, the current approach can handle the inclusion’s orientation dependency in a straightforward manner. The case of an in-plane isotropic distribution of elliptical inclusions is addressed in detail. For the case of reinforcements, or hard inclusions, the effect of the inclusion aspect ratio on in-plane effective moduli is small if the aspect ratio is larger than 0.5. For aspect ratios less than 0.3, the effective moduli increase dramatically, which implies that flat reinforcements are much more effective than traditional cylindrical reinforcements. It is also established that the generalized self-consistent method predicts a stronger dependence of effective moduli on the inclusion aspect ratio than does the Mori-Tanaka method, especially for shear moduli.

Copyright © 1995 by The American Society of Mechanical Engineers
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