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

A mixed three-dimensional variational model has been derived for stress ana lysis 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 mat rix regions that exist around the wavy yarns are also represented as separa te 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 stre ss compatibility is enforced in the model. The variational principle yields a set of second-order partial differential equations, which can numericall y be solved by either by finite element or finite difference approaches. A solution procedure with representative results is given in an adjoining pap er. (C) 2001 Elsevier Science Ltd. All rights reserved.