A Three-Dimensional Constitutive Theory for Fiber Composite Laminated Media

[+] Author and Article Information
R. M. Christensen

Department of Applied Science, University of California, and Lawrence Livermore National Laboratory, Livermore, CA 94550

E. Zywicz

Lawrence Livermore National Laboratory, Ceramics and Composite Section, Livermore, CA 94550

J. Appl. Mech 57(4), 948-955 (Dec 01, 1990) (8 pages) doi:10.1115/1.2897666 History: Received August 04, 1989; Revised February 05, 1990; Online March 31, 2008


A three-dimensional elastic constitutive theory is developed for application to fiber composite laminated media. The lamina level constitutive relationship is a specific subset of general, transversely isotropic media behavior. This special class of lamina behavior permits the development of an exact lamination procedure for systems assembled from a single lamina type. The three-dimensional constitutive form for the laminate is determined in terms of the subscale lamina properties and the orientations of each lamina. The extension of this specific constitutive relationship to general transversely isotropic lamina involves separation of the five lamina-scale properties into fiber-dominated versus matrix-dominated classifications and the development of a generalized averaging procedure for the matrix-dominated properties. The resulting three-dimensional constitutive/lamination theory is evaluated through comparisons between exact solutions, using data bases appropriate for graphite and glass epoxy systems in quasi-isotropic layups. The theory remains highly effective through the transition from thin laminate to thick laminate behavior and even beyond that through the transition from thick laminate behavior to fully and strongly three-dimensional elastic behavior. The generalized averaging procedure for the matrix-dominated properties produces variations in results that are the same or less than the variations in results due to the experimental uncertainty in the matrix-dominated properties themselves. The theory is fairly simple and extremely versatile in its application.

Copyright © 1990 by The American Society of Mechanical Engineers
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