Abstract
The homogenization method is applied to evaluate the effective elastic moduli of damaged materials containing periodically distributed micro elliptical cracks. The microscopic equations of the homogenization method are solved by the superposition method. First part of this paper presents the development of the superposition method with finite element solution of an uncracked solid and the VNA analytical solution for an elliptical crack subject to arbitrary crack-face loading. The superposition method makes it possible to solve elliptical crack problems by using relatively coarse regular mesh pattern which does not describe the shapes of the elliptical cracks. Second part presents the adaption of the superposition method to the homogenization method. By using the developed method, we can evaluate not only macroscopic effective elastic moduli of the damaged materials but also microscopic behavior such as microscopic stress fields and stress intensity factors of the elliptical cracks. The developed method was used to solve the various types of damaged materials.
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