Turboshaft engine fan blades are subject to high dynamic loads, particularly on new engine architectures such as Open Rotor. These loads can induce aeroelastic phenomena such as flutter or forced vibrations, which can lead to fatigue damage and potentially compromise the integrity of the engine. To reduce the fatigue stress experienced by these structures, external structural damping can be added to the blade with active or passive treatments. Constrained viscoelastic patches have been shown to be an effective passive damping treatment, relying on the energy dissipation capabilities of these materials while undergoing shear stresses. In this paper, an in-house numerical model based on previous studies is developed to predict the dynamic behavior of a slender fan blade with a constrained viscoelastic patch. This numerical model is validated through a confrontation with experimental test data. A particular interest is given to the elastomer and its material non-linear behavior, which had not been previously studied. This allows a better quantification of the efficiency of the damping treatment under various operating conditions, such as rotation speed and temperature to permit future patch optimization.