Due to complex structure of aortic valve (AV) leaflets and its strong interaction with the blood flow field, realistic and accurate modeling of the valve deformations comes with many challenges. In this study, we aimed to investigate the effect of AV material properties on the valve deformations, by implementing different non-linear properties of the AV leaflets in three different material models. In the computations, we captured the dynamics between the leaflet deformations and blood flow field variations by using an iterative implicit fluid-structure interaction (FSI) approach. By comparison of the FSI simulation results of these three models, the effects of hyperelasticity and anisotropy on the valve deformations have been studied in detail. The simulation results reveal the fact that the material characteristics strongly affect the deformation characteristics of the leaflets in the systolic phase. The material anisotropy stabilizes the leaflet movements during the systolic phase, which helps decreasing the flutters of the leaflets during the peak jet blood flow. Similarly, it has been observed that the hyperelastic behavior yields an increase in the valve opening area during systolic phase which prevents the risk of excessive work of the heart due to high pressure difference. Furthermore, simulation results indicate that the stress levels in hyperelastic model are much lower, compared to the stress levels in linear elastic one. This suggests that the non-linear material character of the leaflets decreases the risk of calcification.