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For millions of years, insects have showcased unmatched aerodynamic performance in various flight conditions. They stably hover, adapt to very different flight conditions and perform extreme aerobatic manoeuvres. A key feature is that insects can use their flexible wings to modulate the aerodynamic forces, increasing their flight efficiency. However, the aeroelastic benefits remain partially unexplored for different ranges of dynamic flapping motions. A complete understanding could help design flapping wing micro air vehicles that exploit nature's full potential better. This work presents an open-source, high-fidelity, Fluid-Structure Interaction solver (FSI) to simulate flapping and deforming wings. The FSI environment couples the Computational Structural Mechanics (CSM) software Kratos Multiphysics with the Computational Fluid Dynamics (CFD) software OpenFOAM thanks to the coupling code CoCoNuT. The CSM solves the non-linear structural equations of the flexible wings, modelled with the finite element method and shell elements. The CFD computes the aerodynamic forces generated by the deformed wings in laminar flow conditions. The simulation relies on the finite volume method and the deformable overset technique with innovative interpolation boundary conditions to prevent grid degradation when the wings experience large motion and deformation. Finally, an IQNI algorithm couples the flow and structure solver. The developments are validated on a 2D foil and exploited on 3D elliptical wings, revealing the aerodynamic influence of flexibility for a wide range of flapping motions.