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

• Autorzy: Fedele R. , Ciani A. , Galantucci L. , Bettuzzi M. , Andena L.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

cellular materials; Ill-posed Inverse Problems; Tychonoff regularization; Volume Digital Image Correlation

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2013
• Tom: Vol. 125, nr 3/4
• Strony: 361--376
• Opis fizyczny: Bibliogr. 22 poz., fot., rys., wykr.

Twórcy

autor

Fedele R.

• Dept. of Structural Engineering, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milan, Italy

autor

Ciani A.

• Dept. of Structural Engineering, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milan, Italy

autor

Galantucci L.

• Dept. of Structural Engineering, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milan, Italy

autor

Bettuzzi M.

• Dept. of Physics, University of Bologna, and INFN, Viale Berti Pichat 6/2, 40127 Bologna, Italy

autor

Andena L.

• Dept. of Chemistry, Material and Chemical Engineering ”Giulio Natta”, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milan, Italy

Bibliografia

• [1]. Avalle, A., Belingardi, G., Montanini, R.: Characterization of polymeric structural foams under compressive impact loading by means of energy-absorption diagram, Int. J. Impact Engn., 25, 2001, 455-472.
• [2]. Bay, B., Smith, T., Fyhrie, D., Saad, M.: Digital volume correlation: three-dimensional strain mapping using X-ray tomography, Experimental Mechanics, 39, 1999, 217-226.
• [3]. Bettuzzi, M., Brancaccio, R., Morigi, M., Gallo, A., Strolin, S., Casali, F., Lamanna, E., Ariij, M.: CT imaging of the internal human ear: Test of a high resolution scanner, Nucl. Instr. Meth. Phys. Res. A, 640, 2011, S60-S64.
• [4]. Bolzon, G., Fedele, R., Maier, G.: Parameter identification of a cohesive crack model by Kalman Filter, Comp. Meth. Appl. Mech. Eng., 191, 2002, 2947-2871.
• [5]. Bonnet, M., Frangi, A.: Analyse des solides deformables par la methode des elements finis, Les Editions de l’Ecole Polytechnique, Palaiseau (France), 2006.
• [6]. Bornert, M., Vales, F., Gharbi, H., Minh, D. N.: Multiscale full-field strain measurements for micromechanical investigations of the hydromechanical behaviour of clayey rocks, Strain, 46, 2010, 33-46.
• [7]. Briggs, W., Henson, V., McCormick, S.: A multigrid tutorial, SIAM Society of Industrial and Applied Mathematics, Philadelphia, PA, USA (2nd Edition), 2000.
• [8]. Buffiere, J., Maire, E., Adrien, J., Masse, J., Boller, E.: In situ experiments with X-ray tomography: an attractive tool for experimental mechanics, Exp. Mech., 50, 2010, 289-305.
• [9]. Espinosa, H., Hild, F., Eds.: IUTAM Symposium on Full-field Measurements and Identification in Solid Mechanics Cachan, France 4-8 July 2011, vol. 4 of Procedia IUTAM, Elsevier B.V., Dordrecht, The Netherlands, 2012.
• [10]. Fedele, R., Maier, G., Whelan, M.: Calibration of local constitutive models through measurements at the macroscale in heterogeneous media, Comp. Meth. Appl. Mech. Engn., 195(37), 2006, 4971-4990.
• [11]. Fedele, R., Raka, B., Hild, F., Roux, S.: Identification of adhesive properties in GLARE laminates by Digital Image Correlation, J. Mech. Phys. Solids, 57(7), 2009, 1003-1016.
• [12]. Fornberg, B.: Generation of finite difference formulas on arbitrarily spaced grids, Mathematics of Computation, 51(184), 1988.
• [13]. Forsberg, F., Sjdahl, M., Mooser, R., Hack, E., Wyss, P.: Full Three-Dimensional Strain Measurements on Wood Exposed to Three-Point Bending: Analysis by Use of Digital Volume Correlation Applied to Synchrotron Radiation Micro-Computed Tomography Image Data, Strain, 46(1), 2010,47-60.
• [14]. Gibson, L., Ashby, M.: Cellular solids. Structure and properties, Cambridge Solid State Science Series, Cambridge, UK (2nd Edition), 1999.
• [15]. Kak, A., Slaney, M.: Principles of Computerized Tomographic Imaging, Society of Industrial and Applied Mathematics, Philadelphia, PA, USA, 2001.
• [16]. Leclerc, H., Perie, J., Roux, S., Hild, F.: Voxel-Scale Digital Volume Correlation, Exp. Mech., 51(4), 2011, 479-490.
• [17]. Martz, H., Logan, C., Schneberk, D., Shull, P.: X-ray imaging: Fundamentals, Industrial Techniques and Applications, CRC Press, Taylor and Francis Group, London, UK (in press), 2013, ISBN 9780849397721.
• [18]. Pan, B., Wu, D., Wang, Z.: Internal displacement and strain measurement using digital volume correlation: a least-squares framework, Meas. Sci. Technol., 23(4), 2012, 1-13.
• [19]. Rethore, J., Hild, F., Roux, S.: Shear-band capturing using a multiscale extended digital image correlation technique, Comp. Meth. Appl. Mech. Engn., 196, 2007, 5016-5030.
• [20]. Russell, W.: Polynomial interpolation schemes for internal derivative distribution on structured grids, Appl Numer. Math,, 17, 1995, 129-171.
• [21]. Sutton, M., Orteu, J., Schreier, H.: Image correlation for shape, motion and deformation measurements, Springer-Verlag, Heidelberg, 2009.
• [22]. Valoroso, N., Fedele, R.: Characterization of a cohesive-zone model describing damage and de-cohesion at bonded interfaces. Sensitivity analysis and pseudo-experimental parameter identification, Int. J. Solids Struct., 47(13), 2010, 1666-1677.