Local elastodynamic stresses in the unit cell of a woven fabric composite

A theoretical study of the local elastodynamic stresses of woven fabric com posites under dynamic loadings is presented in this article. The analysis f ocuses on the unit cell of an orthogonal woven fabric composite, which is c omposed of two sets of mutually orthogonal yarns of either the same fiber ( nonhybrid fabric) or different fibers (hybrid fabric) in a matrix material. Using the mosaic model for simplifying woven fabric composites and a shear lag approach to account for the inter-yam deformation, a one-dimensional a nalysis has been developed to predict the local elastodynamic and elastosta tic behavior. The initial and boundary value problems are formulated and th en solved using Laplace transforms. Closed form solutions of the dynamic di splacements and stresses in each yarn and the bond shearing stresses at the interfaces between adjacent yarns are obtained in the time domain for any type of in-plane impact loadings. When time tends to infinity, the dynamic solutions approach to their corresponding static solutions, which are also developed in this article. Solutions of certain special cases are identical to those reported in the literature. Lastly, the dynamic stresses and bond shearing stresses of plain weave composites subjected to step uniform impa cts are presented and discussed as an example of the general analytical mod el.