In this paper, we propose to use a second gradient, 3D orthotropic model for the characterization of the mechanical behavior of thick woven composite interlocks. Such second-gradient theory is seen to directly account for the out-of-plane bending rigidity of the yarns at the mesoscopic scale which is, in turn, related to the bending stiffness of the fibers composing the yarns themselves. The yarns' bending rigidity evidently affects the macroscopic bending of the material and this fact is revealed by presenting a three-point ...