Three-dimensional elastic behavior of undulating laminas in fiber composites

Analytical models have been developed in recent years for predicting the elastic properties of fiber reinforced composite laminates with undulated laminas, such as woven and filament wound composites. In these models, a representative volume element (RVE) is defined, assumptions about how strains or stresses vary throughout the RVE are made, and then the homogenized constitutive behavior of the RVE is calculated. The constitutive behavior has been modeled in the context of either two-dimensional plate behavior or three-dimensional continuum behavior. Of the latter genre, the few existing models capable of handling undulated laminas have not captured the full three-dimensional constitutive behavior, including all the out-of-plane couplings arising from the most general undulation configurations. Building on the existing models, the current investigation utilizes micromechanics to determine the three-dimensional stiffness at discrete stations along the length of an RVE containing an undulated lamina, and determines the overall RVE constitutive behavior by averaging either the stiffness or compliance along the length of the RVE, thus providing bounds on the material behavior. The new model is evaluated by comparison with existing models as well as experiments for laminates with and without undulations. Similarities and differences with previous models are discussed.