The physical mechanisms responsible for flame curvature evolution of a methane-air premixed flame attached to a bluff-body burner have been investigated using a high-fidelity flame-resolved three-dimensional simulation database. The contributions to the mean curvature generation due to the fluid flow motion and to a combination of flow and flame propagation induced strain rates have been analyzed in detail and dominant contributions in different zones (reactants, ame and products) of the flame have been identified. The effect of fluid flow on the mean curvature evolution is important on the unburned gas side, whereas the ame propagation dominates the mean curvature evolution in the reaction region and towards the hot products. The statistical contributions of the mean curvature transport equation have been analysed in terms of the iso-scalar surface geometry, characterized by the mean and Gauss curvatures. This information has subsequently been used to provide physical insights into the dominant mechanisms of curvature evolution for different flame topologies.</br> This project has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement No 706672 - ITPF.