On the use of PGD to deal with large scale FE-based DIC problems
Résumé
A new FE DIC method based on the PGD (Proper Generalized Decomposition) is proposed. The unknown displacement is then sought as a sum of products of separated dimensions functions. When introduced in the formulation of the brightness conservation, this interpolation yields a set of mono-dimensional problems that can be made independent. The method involves only 1D meshes and the resolution of 1D finite element problems. An algorithm that builds successive best rank-one approximations is proposed and integrated into the nonlinear iterations of the correlation problem. With the method proposed herein, the number of elements in each dimension has much less impact on the computational cost. This method is therefore a good candidate to go down in resolution or to deal with large scale DIC problems. The proposed PGD approach is compared with a standard FE method for both 2D and 3D problems (Q4 or C8).