Sodium-cooled fast reactors (SFRs) offer a promising alternative to conventional light-water technologies but present unique safety and design challenges. Among others, reactivity feedback effects associated to core deformations are significantly larger than in light-water r eactors. Their accurate evaluation is then a fundamental aspect of the safety analysis of fast reactors. In the past, these deformation effects were assessed assuming uniform radial and axial expansions of the c ore. This approach cannot be extended as easily to study more complex distortion patterns, such as core flowering and c ompaction. As a result, higher-fidelity approaches have been proposed in the fast reactor modeling community to deal with these non-uniformity effects. This work, building on the legacy of previous studies performed at EPFL, proposes a novel methodology aimed at addressing these challenges. Based on a higher-fidelity 3D mechanical analysis of the core deformations, it involves a new parametrization technique applicable to the low-computational-cost diffusion neutronics solver and allows to assess the deformation-induced reactivity feedback. The proposed methodology is described and the code developments necessary to its implementation in the multiphysics OpenFOAM-based code GeN-Foam are outlined. In order to verify the methodology, the European Sodium Fast Reactor ESFR-SMART is considered. First a set of single-physics simulations and of code-to-code comparisons is performed to conclude on the accuracy of the new methodology used. Then a fully-coupled multi-physics simulation is performed to capture the more complex core deformations that take place once the hot nominal power state is reached.