Fiber reinforced composite materials have been applied widely to many structures, because they have some advantages like easy handling, high specific strength, etc. The numerical method like finite element method has been applied to design and to evaluate the material properties and behavior as the development of Computer Aided Engineering. It is very difficult to calculate with accuracy not only in structural scale but also in detail material scale (for example, the order of fiber diameter) by the traditional FEM, becausecompositematerials like woven fabric composites have the geometrical complexityand the large difference between above mentioned scales. The development of multi-scale analysis method is one of the major topics in computational mechanics. Mesh superpositionis one of multi-scale analysis methods and is an effective method to solve the problems which have the large difference between the structure scale and the reinforcement scale. We have expanded the finite element mesh superposition method with 3 scales and have defined as M3 (Macro-Meso-Micro) method. In this paper, we have proposed a new approach method combined with M3 method and homogenized method to obtain the mechanical properties and to simulate the behavior of woven fabric composites. In addition, the elastic-plastic mechanics and the damage mechanics have been introduced into M3 method to investigate the effects of matrix-crack on the structural and material properties. From the numerical results, it is revealed that it is very useful for the evaluation of mechanical properties of composite materials.
