A theoretical homogenized constitutive model formulation for matrix composite materials reinforced with curved fibers

A theoretical homogenized constitutive formulation to approximate the stiffness of reinforced composite with curved fibers is developed in this work. The theoretical model considers the stiffness contribution of the fibers taking into account their curvatures and spatial orientations. The variation of the geometry of the fibers is taken into account by means of a statistical distribution of their height and angle of orientation. In this way, it is possible to consider various scenarios, including the curvatures introduced by the manufacturing process. Comparisons of the elastic moduli obtained by 3D finite element analysis with the results of the present approach show good agreement. Finally, a parametric study that shows the effect of the main variables included in the proposed model is also presented.