Development of a three-dimensional mixed variational model for woven composites. I. Mathematical formulation

Abstract

A mixed three-dimensional variational model has been derived for stress analysis of a representative volume element of woven fabric composites, based on the Reissner variational principle. In this model, each yarn is modeled as a homogeneous orthotropic (in its own material axes) medium, and the matrix regions that exist around the wavy yarns are also represented as separate regions in the model. In order to accurately predict the characteristic damage (crack initiation and its propagation), the equilibrium of stresses is satisfied pointwise everywhere in the model, and the yarn-interface stress compatibility is enforced in the model. The variational principle yields a set of second-order partial differential equations, which can numerically be solved by either by finite element or finite difference approaches. A solution procedure with representative results is given in an adjoining paper.