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 enable a direct evaluation across the entire computational domain, we develop a new Eulerian reformulation of the Lagrangian strain-based model by Arora et al. In contrast to previous approaches, the Eulerian formulation does not require simplifications and captures the full original model behavior. The resulting model can be applied to any converged CFD simulation due to one-way coupling with the fluid velocity field. We discuss the numerical treatment of the constitutive equations in a stabilized finite element context and validate the model in selected benchmark flows. The results highlight the model's advantages over existing methods. More complex test cases demonstrate the model's applicability to real-world devices. 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.