Keywords: woven composites, Mori-Tanaka method, homogenization, orientation averaging, finite element method, optimization, porosity.

Woven composites, i.e. composites reinforced with mutually interlaced systems of unidirectional fiber tows, belong to the most progressive material systems with applications ranging from the strengthening of civil engineering structures to the design of biocompatible medical implants. This type of reinforcement offers a number of advantages including the possibility of forming complex shapes, increased stiffness for a multi-dimensional loading and high damage tolerance.

Modeling of woven composites, however, presents a significant challenge even for the linear elastic case due to the complex three-dimensional geometry of these material systems. With an increasing level of sophistication, the models for the determination of overall properties include modified rule of mixtures, approaches based on classical laminate theories (CLT) and fully detailed three-dimensional finite element method (FEM) simulations. It is generally accepted that the last class of models is the most accurate one when provided with reliable geometrical information.

The disadvantage of the FEM-based approach is, however, a high cost associated with the analysis, not only in terms of computational time but especially when accounting for the generation of three-dimensional finite element meshes. The approaches based on CLT theories are, on the other hand, relatively easy to implement and provide a reasonable approximation of in-plane elastic moduli. Therefore, a procedure based on a reasonable compromise between the accuracy of the FEM-based modeling and the simplicity of traditional CLT-based methods is on demand.

In the present contribution, we propose an effective media theory-based model for the evaluation of effective properties of plain weave fabric composites. To keep the possibility of incorporating imperfections in the tow paths, the Mori-Tanaka theory, formulated for the matrix composites stiffened with a family of ellipsoidal inclusions, is used as the point of departure. The shape of the "equivalent" ellipsoid, modeling the collective reinforcing effect of the fiber tows, is determined by matching the results of the approximate model with extensive FEM-based computations for a wide range of geometrical and material parameters.

The methodology is exemplified on an analysis of real-world carbon-carbon woven composites characterized by a histogram of tow angle inclinations. In the last part of the contribution, an appropriate methodology allowing for the treatment composites with multi-scale porosity is briefly discussed.

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