Fourier-series-based virtual fields method for the identification of 2-D stiffness distributions

The Virtual Fields Method (VFM) is a powerful technique for the calculation of spatial distributions of material properties from experimentally-determined displacement fields. A Fourier-series-based extension to the VFM (the F-VFM) is presented here, in which the unknown stiffness distribution is parameterised in the spatial frequency domain rather than in the spatial domain as used in the classical VFM. We summarise here the theory of the F-VFM for the case of elastic isotropic thin structures with known boundary conditions. An efficient numerical algorithm based on the 2-D Fast Fourier Transform reduces the computation time by 3-4 orders of magnitude compared to a direct implementation of the F-VFM for typical experimental dataset sizes. Reconstruction of stiffness distributions with the FVFM has been validated on several stiffness distribution scenarios, one of which is presented here, in which a difference of about 0.5% was achieved between the reference and recovered stiffness distributions.