<p>Silicone-based polymers are recognized for their exceptional damping properties and ability to undergo large deformations. Their mechanical behavior can be characterized through a variety of experimental setups. Small-strain measurements at various frequencies and temperatures, as conducted in a dynamic thermo-mechanical analysis, provide storage and loss moduli. Tensile tests at large strain determine the elastic response, while experiments such as the ball-drop test characterize damping through the rebound resilience. Combining these different perspectives into a comprehensive material model for silicone-based polymers remains a challenging task and often requires numerical approaches to complement physical experiments. In this context, we present a finite element formulation specifically designed to simulate the ball-drop experiment, incorporating experimentally identified viscoelastic parameters into a nonlinear large-strain material model. Prony parameters obtained from small-strain dynamic thermo-mechanical analysis serve as the basis for our study. Large strains are captured via a multiplicative decomposition of the deformation gradient. The matrix exponential is used to consistently incorporate logarithmic viscous strains into the constitutive model. The model is thermodynamically consistent and rooted in the Clausius-Duhem inequality. A distinctive feature of our formulation is the spatial discretization of the internal viscous strains using tensor-valued finite elements, which allows the evolution laws to be expressed in weak form. Through numerical studies, we analyze the sensitivity of the rebound behavior to imperfections and geometric variations. We identify potential sources of discrepancies with respect to previously reported experimental observations, including frictional contact and three-dimensional effects such as eccentric impacts, which break the assumption of axisymmetric deformation.</p>