In the present work, we propose a novel lumped-parameter model for the description of the aortic valve dynamics, including elastic effects associated to the leaflets' curvature. The introduction of a lumped-parameter model based on momentum balance entails an easier calibration of the parameter models, that are instead typically numerous in phenomenological-based models. This model is coupled with 3D Navier-Stokes equations describing the blood flow, where the valve surface is represented by a resistive method, and valve leaflets velocity is taken into consideration. The resulting reduced fluid-structure interaction problem has a computational cost that is comparable with the solution of a prescribed-motion fluid dynamics problem. A SUPG-PSPG stabilized finite element scheme is adopted for the discretization of the coupled problem, and the computational results show the suitability of the system in representing the leaflets motion, the blood flow in the ascending aorta, and the pressure jump across the leaflets.