A modified Mori-Tanaka method considering the doubly periodic distribution of inclusions

The strain concentration tensor for the inclusions in a two-phase composite is derived from the strain field integral equation based on the concept of the so called strain Green tensor. In contrast with the traditional Mori- Tanaka (MT) strain concentration tensor derived with the dilute method, such a strain concentration tensor includes a term related to the volume fraction and distribution of inclusions, whereby a modified Mori-Tanaka method considering the doubly periodic microstructural characteristics is developed. The traditional MT method has proven to be quite accurate in predicting the effective moduli of fiber reinforced composites with the hexagonal array of cylindrical fibers; however, it can not represent square symmetric effective properties of composites with a square array of fibers. The present method gets rid of such a drawback, and provides compact expressions for the effective stiffness and compliance tensors with the same self-consistency as the traditional MT method. A comparison with finite element calculations demonstrates the efficiency and accuracy of the present method.