NGUYEN, T.T. ... et al, 2013. Fourier-series-based virtual fields method for the identification of 2-D stiffness distributions. Presented at: Photomechanics 2013, 27th-29th May 2013, Montpellier, France.
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.