Homogenization of the macroscopic stiffness of 2D triaxially braided composites: Roles of the local stiffness model and undulating average scheme

This work investigates a two-level homogenization of the macroscopic stiffness of the 2DTBC with emphasizes on the roles of the local stiffness model and undulating average scheme. The effective elastic property of the braid yarn is rigorously derived by an energy method instead of intuitive mathematical average methods in the literature. General formulations of the compliance and stiffness undulating average schemes have been obtained, which are proven to be reduced to the simple mathematical average methods in certain cases. Validated with different experiments, it is unexpected to find out that the prediction combined with the simple rule of mixture and stiffness undulating average scheme yields the most consistent agreement with experimental results after the overall assessment of all the in-plane engineering elastic constants under various braiding conditions.