The propagation of one-dimensional transient elastic waves in woven-fabric composites

This article presents a study of transient elastic wave propagation in woven-fabric composites under dynamic loading. The analysis focuses on the unit cell of an orthogonal woven-fabric composite, which is composed of two sets of mutually orthogonal yarns of either the same fiber (non-hybrid fabric) or different fibers (hybrid fabric) in a matrix material. A one-dimensional analysis based upon the mosaic model and shear-lag approach has been developed to predict elastodynamic and elastostatic behavior. By using the technique of Laplace transforms, closed-form solutions of the dynamic displacements and dynamic stresses in each yarn, and the shearing stresses at the interfaces between adjacent yarns, are obtained in the transformed domain. Through numerical inversion of the Laplace transform, the wave-propagation solutions for these quantities can be obtained for any type of impact loading. Asymptotic formulae are given which describe the short-time behavior of the dynamic solutions. The stationary values of the dynamic solutions are identical to the corresponding static solutions which are also developed in this article. For any finite time, the dynamic solutions can be obtained by the numerical inversion of the Laplace transform. The results for a step uniform impact are presented as an example. (C) 1998 Elsevier Science Ltd. All rights reserved.