Affiliations: Dept. of Structural Engineering, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milan, Italy. [email protected] | Dept. of Physics, University of Bologna, and INFN, Viale Berti Pichat 6/2, 40127 Bologna, Italy | Dept. of Chemistry, Material and Chemical Engineering ”Giulio Natta”, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milan, Italy
Note: [] The Authors kindly acknowledge: (i) the support provided by CARIPLO Foundation to the Project titled: ”Innovative metal-ceramic joints for high and ultra-high temperature applications (UHT)” (Grant n. 2010-0432, Call for Scientific and technological research on advanced materials); (ii) the support provided by Politecnico di Milano to the project ”CINEMAT” (2010, 5 per mille Young researcher Call). Address for correspondence: Piazza Leonardo da Vinci n. 32, 20133 Milan, Italy
Abstract: In this study a robust strategy for 3D-Volume Digital Image Correlation (DIC) is presented, apt to provide accurate kinematic measurements within a loaded sample on the basis of three-dimensional digital images by X-ray computed micro-tomography. In the framework of a Galerkin, finite element discretization of the displacement field, the inverse problem of estimating 3D motion inside the bulk material is solved recursively on a hierarchical family of grids, linked by suitable restriction and prolongation operators. Such structured grids are defined over an image pyramid, which is generated starting from the raw tomographic reconstructions by a reiterated application of average filters and sub-sampling operators. To achieve robust estimates of the underlying displacement fields, multi-grid cycles are performed ascending and descending along the pyramid in a selected sequence. At each scale, the least-square matching function for DIC is enriched by means of a penalty term in the spirit of Tychonoff regularization, including as a priori information the estimate achieved at the previous grid and transferred to the current scale. For each grid only one Newton iteration can be considered, implying important time savings. Results are presented concerning a laboratory X-ray micro-tomography experiment on a polymeric foam sample, subjected to loading by an apparatus ad-hoc realized.
