Homogenization method based on eigenvector expansions

On the basis of the eigenvector expansions, in the present paper a homogenization method is presented to evaluate the macromechanical properties of any kind of woven fabric composites. In this homogenization method, there are two kinds of finite elements with different scales. Different from the conventional homogenization method, which evaluates the homogenized elastic moduli for a heterogeneous unit cell, the present homogenization method evaluates the homogenized stiffness matrix of the heterogeneous unit cell of composite materials directly based on the eigenvector expansions, and in the homogenized stiffness matrix the diagonal elements are different. The advantage of doing it in this manner is that the homogenized stiffness matrix can depict the local geometry and material architecture within the unit cell in much more detail than the overall homogeneous elastic moduli. Two numerical examples of three-dimensional orthogonal woven fabric composites are given to illustrate the effectiveness of the method and to compare the results obtained by both methods. The first example is about the comparisons between the stiffness matrix obtained by the present homogenization method and that by the conventional homogenization method. The second example is about the comparisons among the frequencies by three different methods. Since the finite element method is adopted during numerical analysis, it is easy to extend the applications of this method to any kind of composite materials with more complicated geometry and material architecture.