Micromechanical modeling of stress distribution in undulated composites under axial loading

The previously developed micromechanical model to predict the thermoelastic response of unidirectionally reinforced fibrous composites (Nayfeh and Abdelrahman, 1997) is extended for the case of undulated fiber reinforcement under axial loading. For the present purposes, the composite is modeled as a concentric cylindrical system laterally constrained such that it satisfies the periodicity condition of the unidirectionally reinforced composites. The field equations, combined with the interface, boundary and symmetry conditions, are first solved for the stress distribution in the system for cases involving straight fibers. Based upon local directions (slopes) of the undulated fibers, the linear transformation is used to obtain local stress distributions along the undulated fibers. The total stress field is found to be combinations of these local stresses and the inherent contributions obtained from the transformations of the normal loads along the undulated directions in the absence of reinforcement. The results of this modeling are compared with finite element computations for a variety of situations.