A Fourier-series-based Virtual Fields Method for the Identification of 2-D Stiffness and Traction Distributions

The virtual fields method (VFM) allows spatial distributions of material properties to be calculated from experimentally determined strain fields. A numerically efficient Fourier-series-based extension to the VFM (the F-VFM) has recently been developed, 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. However, the boundary conditions for the F-VFM are assumed to be well-defined, whereas in practice, the traction distributions on the perimeter of the region of interest are rarely known to any degree of accuracy. In the current paper, we therefore consider how the F-VFM theory can be extended to deal with the case of unknown boundary conditions. Three different approaches are proposed; their ability to reconstruct normalised stiffness distributions and traction distributions around the perimeter from noisy input strain fields is assessed through simulations based on a forward finite element analysis. Finally, a practical example is given involving experimental strain fields from a diametral compression test on an aluminium disc.