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The behavior of plain woven fabric composites is studied using three-dimensional finite elements which allows detailed modeling of the geometric complexities and spatial material variations within the fabric. Damages in the composite constituents viz. yarn and pure matrix are modeled on a continuum basis and related to their material constitutive behavior. The 3D constitutive laws describing pure matrix and yarn behavior are developed using a damage mechanics based approach with the dissipated energy density as the damage parameter. The strain energy dissipation (SED) concept is employed to describe the damage state and current stiffnesses of the weave constituents. A progressive failure analysis of plain woven fabrics subjected to tension and in-plane shear is carried out considering both geometric and material nonlinearities. The initiation and progression of damage within the fabric is investigated and the significant damage mechanisms outlined.