6. The Eigenfunction Virtual Fields Method

The Virtual Fields Method (VFM, Pierron and Grediac, 2012) is an inverse technique for computing mechanical properties of materials from full-field deformations obtained from techniques such as Digital Image Correlation (DIC). VFM is based on the principle of virtual work, which is a weak statement of the equations of motion. Central to VFM is the appropriate choice of virtual fields, which in prior work, have been assumed to be polynomials that are continuously differentiable, either piece-wise or over the entire domain of interest. In this work, we propose a new method for systematically identifying virtual fields by performing a principal component analysis (PCA) of the strain field measured from experiments. The virtual strain components to be used in VFM are then chosen to be the eigenfunctions so determined. In addition to being a physically meaningful set of virtual fields, such a choice exploits the orthogonality of the computed eigenfunctions while simultaneously eliminating computation of a large number of coefficients that define the virtual fields in prior approaches. In the case of linear elastic behaviour, we show that this new approach, named the Eigenfunction Virtual Fields Method (EVFM), leads to a compact system of equations that can be solved for the unknown material parameters.