A Regularized, Pyramidal Multi-grid Approach to Global 3D-Volume Digital Image Correlation Based on X-ray Micro-tomography

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 * 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 362 R. Fedele, et al. / A Regularized, Pyramidal Multi-grid Approach to Global Digital Image CorrelationNewton 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.

Computational prediction of strain-dependent diffusion of transcription factors through the cell nucleus

“…Future work will concern the mathematical modeling of the nuclear membrane and modifications in nuclear envelope diffusivity through the changes in the nuclear pore complex, the analytical dependence of diffusivity on local volumetric strain and possibly other field variables (such as the molar concentration), and the analysis of cultured cells through digital image correlation (Fedele et al. 2013a , b ) of suitable time sequences of confocal images, in order to develop finite element model updating procedures (Fedele 2015 ).…”

Global 2D digital image correlation for motion estimation in a finite element framework: a variational formulation and a regularized, pyramidal, multi‐grid implementation

“…Finally, the bulk deformation of a specimen, opaque to natural light, can be estimated through 3D-volume DIC algorithms on the basis of truly three-dimensional tomographic images at different loading steps, achieved by synchrotron radiation or advanced X-ray laboratory sources, see e.g. [4][5][6][7]. 740 R. FEDELE, L. GALANTUCCI AND A. CIANI In this paper, focus is posed on 2D DIC methodology as an effective tool to reconstruct the in-plane deformation of a loaded specimen, even in the presence of kinematic discontinuities due to fracture processes.…”

Performance Analysis of Micro-Grid Based On Measurement and Processing Different Electrical Quantities

“…In the event that this cannot be attained, it the overall level of reliability of the grid is compromised. In line with such an aspect, we can add that there is always the need to evaluate the extent to which a grid can be applied or used within a given area [6]. This is usually beneficial in that it goes a very long way towards the quantification of the manner in which the performance of micro-grid systems is impacted by the optimal placement of capacitors.…”