The effects of chordwise pressure- and inertia-driven deformations on the power extraction potential of a kinematically constrained oscillating thin plate that undergoes a heaving and pitching motion are investigated. 2D fully coupled fluid-structure interaction simulations are performed at a Reynolds number of 1100 with thin flexible plates having a thickness over chord ratio of 1%. Three flexibility distributions are tested: a uniformly flexible plate as well as plates with only the rear part or the front part being flexible. The results are compared with those of rigid plates operating at the same conditions. Flexible plates show very promising results as they can extract up to more than twice the power of the corresponding rigid ones. The investigation of semi-flexible foils has highlighted the fact that considering a completely flexible foil with constant chordwise mechanical properties is likely not an optimal configuration. Indeed, different mechanisms are beneficial whether the front part or the rear part of the foil is flexible: pressure-driven deformations usually increase the performances of front flexible foils while inertia-driven deformations are beneficial to rear flexible foils. In cases involving weak fluid-structure interactions (e.g.: heavy plate in a light fluid), the resonance of the first deformation mode of the plate's tail or head may appear. It is observed that this phenomenon can either deteriorate or improve the performances of the flapping plate. In this context, the dimensionless flexibility appears to be a key factor as it is involved in the resonance phenomenon that turns out to greatly influence the flow field.