Flow-induced red blood cell damage (hemolysis) is a key factor in the design process of blood-handling medical devices, such as ventricular assist devices. The numerical prediction of this phenomenon is based on computational fluid dynamics (CFD) simulations. The most basic hemolysis models post-process the CFD results by directly applying empirical correlations to fluid stress (stress-based models). More recent models use the CFD results to explicitly resolve cell deformation (strain-based models). A disadvantage is that these models are typically written in a Lagrangian formulation, i.e., they require pathline tracking. To overcome this deficiency, we develop a new Eulerian model for red blood cell deformation. The model can be applied to any converged CFD simulation. In comparison to previous models, it provides a more accurate, robust and efficient way of predicting red blood cell deformation across the entire computational domain. The model equations are discretized using stabilized finite elements. We demonstrate the method's features in a realistic blood pump geometry and highlight the advantages over existing methods. Experiments in microchannels validate the model's predictive capabilities. The presented strain-based blood damage model allows for more accurate and efficient numerical biocompatibility analysis of prototypes. It thus holds great potential for the design process of future generations of medical devices.