A new analytical model for calculation of stiffness of three-dimensional four-directional braided composites

The present paper represents a new analytical method for calculation of the stiffness of three-dimensional four-directional braided composites. In most previous works, the analytical approach had been largely neglected in the favor of the finite element model. Among those who have used the analytical model, the braided preform has been considered as made of one, or three, types of representative unit cells, while microscopic evidence of the microstructure of preforms reveals different configurations of the yarns in the interior, surface and corner regions of a braided preform. This paper presents a Multi-Unit Cell Model in which four kinds of unit cells, namely interior, interior surface, exterior surface and corner unit cells have been introduced as representative cells. Each type of unit cell in a braided composite possesses unique mechanical properties and has been considered as a uni-directional composite. Using rotation matrices, the angle between yarns and longitudinal direction has been incorporated in general coordinates of the model. Finally, using a volume averaging method, the total stiffness of the braided composite is calculated. The results are in good agreement with the available experimental data. The effect of braiding angle on the stiffness of braided composites is also examined.