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

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.