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Comparative Analysis of the Elastic Behavior of a Lamina Containing Wavy Fibers

TONY HONEIN, SERGE MAALOUF, GEORGE RAI, MICHEL NAJJAR

Abstract


In this paper we review and compare some of the analytical methods which have been proposed to predict the elastic behavior of a lamina containing wavy fibers. The earliest attempt in this regard may be traced to the work of Tabaddor et al. [1] who provided an explicit, but approximate, stress-strain relation of a lamina containing a wavy fiber and subjected to uniaxial loading. Their derivation is based on a closed-form equation worked out earlier by Tarnopolskii et al. [2] for the average longitudinal Young’s modulus of a lamina with a sinusoidal fiber. A major discrepancy between the results in [1] and more recent ones obtained by more exact, albeit numerical, approaches has been observed. The source of this discrepancy is identified to be a faulty assumption in [1]. We also review briefly methods based on complementary strain energy which may incorporate material nonlinearities into the already geometrically nonlinear response of a lamina with a wavy fiber. Finally, a novel method based on a simple idea is briefly discussed. It yields within the framework of infinitesimal deformations, an exact and explicit relation between stress and strain.


DOI
10.12783/asc2017/15296

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