Experimental Mechanics

, Volume 58, Issue 5, pp 661–708 | Cite as

Digital Volume Correlation: Review of Progress and Challenges

  • A. Buljac
  • C. Jailin
  • A. Mendoza
  • J. Neggers
  • T. Taillandier-Thomas
  • A. Bouterf
  • B. Smaniotto
  • F. Hild
  • S. Roux


3D imaging has become popular for analyzing material microstructures. When time lapse series of 3D pictures are acquired during a single experiment, it is possible to measure displacement fields via digital volume correlation (DVC), thereby leading to 4D results. Such 4D analyses have been performed for almost two decades. The present paper aims at reviewing the achievements of and challenges faced by such measurement technique. Ex-situ and in-situ experiments are discussed. A general and unified DVC framework is introduced. Various sources of measurement bias and uncertainties are analyzed. The current challenges are studied and some propositions are given to address them.


DVC In-situ test Laminography Regularization Tomography Uncertainty quantification 



Different parts of the above mentioned examples were funded by Agence Nationale de la Recherche under the grants ANR-10-EQPX-37 (MATMECA), ANR-14-CE07-0034-02 (COMINSIDE), Saint Gobain, SAFRAN Aircraft Engines and SAFRAN Tech. It is a pleasure to acknowledge the support of BPI France within the DICCIT project, and ESRF for MA1006, MI1149, MA1631,MA1932, and ME1366 experiments.

Fruitful discussions with Profs. Olivier allix, Marc Bernacki, Claude Boccara, Pierre-Olivier Bouchard, Jean-Yves Buffière, Stephen Hall, Per-Lennart Larsson, Eric Maire, Cino Viggiani, and Drs. Jérôme Adrien, Edward Andó, Dominique Bernard, Xavier Brajer, René Gy, Lukas Helfen, Thilo Morgeneyer, Amir Nahas, Estelle Parra, Mehdi Rebai, Julien Schneider are acknowledged.


  1. 1.
    Adam J, Klinkmueller M, Schreurs G, Wieneke B (2013) Quantitative 3D strain analysis in analogue experiments simulating tectonic deformation integration of X-ray computed tomography and digital volume correlation techniques. J Struct Geology 55:127–149Google Scholar
  2. 2.
    Adrian RJ (2005) Twenty years of particle image velocimetry. Exper Fluid 39:159–169Google Scholar
  3. 3.
    Andò E, Hall S, Viggiani G, Desrues J, Bésuelle P (2012) Experimental micromechanics: grain-scale observation of sand deformation. Géotechnique Lett 2(3):107–112Google Scholar
  4. 4.
    Antoulas AC, Sorensen DC, Gugercin S (2001) A survey of model reduction methods for large-scale systems. Contemp Math 280:193–220MathSciNetzbMATHGoogle Scholar
  5. 5.
    Avril S, Bonnet M, Bretelle AS, Grédiac M, Hild F, Ienny P, Latourte F, Lemosse D, Pagano S, Pagnacco E, Pierron F (2008) Overview of identification methods of mechanical parameters based on full-field measurements. Exp Mech 48(4):381–402Google Scholar
  6. 6.
    Banhart J, Borbély A, Dzieciol K, Garcia-Moreno F, Manke I, Kardjilov N, Kaysser-Pyzalla AR, Strobl M, Treimer W (2010) X-ray and neutron imaging–complementary techniques for materials science and engineering: Dedicated to Professor Dr. H.-P. Degischer on the occasion of his 65th birthday. Int J Mater Res 101(9):1069–1079Google Scholar
  7. 7.
    Bar-Kochba E, Toyjanova J, Andrews E, Kim K-S, Franck C (2015) A fast iterative digital volume correlation algorithm for large deformations. Exp Mech 55(1):261–274Google Scholar
  8. 8.
    Baruchel J, Buffière JY, Maire E, Merle P, Peix G (eds) (2000) X-ray tomography in material sciences. Hermès Science, Paris (France)Google Scholar
  9. 9.
    Batenburg KJ, Sijbers J (2007) DART: A fast heuristic algebraic reconstruction algorithm for discrete tomography. In: IEEE International conference on image processing (ICIP 2007), vol 4, pp IV–133Google Scholar
  10. 10.
    Batenburg KJ, Sijbers J (2011) DART: a practical reconstruction algorithm for discrete tomography. IEEE Trans Image Process 20(9):2542–2553MathSciNetzbMATHGoogle Scholar
  11. 11.
    Bay B (2008) Methods and applications of digital volume correlation. J Strain Anal Eng Des 43(8):745–760Google Scholar
  12. 12.
    Bay B, Smith TS, Fyhrie DP, Saad M (1999) Digital volume correlation: three-dimensional strain mapping using X-ray tomography. Exp Mech 39(3):217–226Google Scholar
  13. 13.
    Beaurepaire E, Boccara AC, Lebec M, Blanchot L, Saint-Jalmes H (1998) Full-field optical coherence microscopy. Opt Lett 23(4):244–246Google Scholar
  14. 14.
    Benoit A, Guérard S, Gillet B, Guillot G, Hild F, Mitton D, Périé J-N, Roux S (2009) 3D analysis from micro-MRI during in situ compression on cancellous bone. J Biomechanics 42(14):2381–2386Google Scholar
  15. 15.
    Berek H, Ballaschk U, Aneziris CG, Losch K, Schladitz K (2015) The correlation of local deformation and stress-assisted local phase transformations in MMC foams. Mater Charact 107:139–148Google Scholar
  16. 16.
    Besnard G, Hild F, Roux S (2006) Finite-element displacement fields analysis from digital images: application to Portevin-Le Chatelier bands. Exp Mech 46:789–803Google Scholar
  17. 17.
    Bormann T, Schulz G, Deyhle H, Beckmann F, de Wild M, Kueffer J, Muench C, Hoffmann W, Mueller B (2014) Combining micro computed tomography and three-dimensional registration to evaluate local strains in shape memory scaffolds. Acta Biomater 10(2):1024–1034Google Scholar
  18. 18.
    Bornert M, Chaix J-M, Doumalin P, Dupré J-C, Fournel T, Jeulin D, Maire E, Moreaud M, Moulinec H (2004) Mesure tridimensionnelle de champs cinématiques par imagerie volumique pour l’analyse des matériaux et des matériaux et des structures. Instrumentation, Mesure, Métrologie 4:43–88Google Scholar
  19. 19.
    Borstnar G, Gillard F, Mavrogordato M, Sinclair I, Spearing SM (2016) Three-dimensional deformation mapping of mode I interlaminar crack extension in particle-toughened interlayers. Acta Mater 103:63–70Google Scholar
  20. 20.
    Bouterf A, Adrien J, Maire E, Brajer X, Hild F, Roux S (2016) Failure mechanisms of plasterboard in nail pull test determined by X-ray microtomography and digital Volume correlation. Exp Mech 56(8):1427–1437Google Scholar
  21. 21.
    Bouterf A, Adrien J, Maire E, Brajer X, Hild F, Roux S (2017) Identification of the crushing behavior of brittle foam from indentation to oedometric tests. J Mech Phys Solids 98:181–200Google Scholar
  22. 22.
    Bouterf A, Maire E, Roux S, Hild F, Brajer X, Gouillart E, Boller E (2018) Analysis of compaction in brittle foam with multiscale indentation tests. Mech Mat 118:22–30Google Scholar
  23. 23.
    Bouterf A, Roux S, Hild F, Adrien J, Maire E, Meille S (2014) Digital volume correlation applied to X-ray tomography images from spherical indentation tests on lightweight gypsum. Strain 50(5):444–453Google Scholar
  24. 24.
    Bowler AI, Drinkwater BW, Wilcox PD (2011) An investigation into the feasibility of internal strain measurement in solids by correlation of ultrasonic images. Proc the Royal Soc A-Math Phys Eng Sci 467 (2132):2247–2270Google Scholar
  25. 25.
    Brault R, Germaneau A, Dupré J-C, Doumalin P, Mistou S, Fazzini M (2013) In-situ analysis of laminated composite materials by X-ray micro-computed tomography and digital volume correlation. Exp Mech 53(7):1143–1151Google Scholar
  26. 26.
    Buffière J-Y, Maire E, Adrien J, Masse J-P, Boller E (2010) In situ experiments with X-ray tomography: an attractive tool for experimental mechanics. Exp Mech 50(3):289–305Google Scholar
  27. 27.
    Buffière JY, Maire E, Cloetens P, Lormand G, Fougères R (1999) Characterisation of internal damage in a MMCp using X-ray synchrotron phase contrast microtomography. Acta Mater 47(5):1613–1625Google Scholar
  28. 28.
    Buljac A (2017) Understanding, observation and quantification of ductile failure mechanisms via 3D imaging. PhD thesis, Université Paris-SaclayGoogle Scholar
  29. 29.
    Buljac A, Shakoor M, Neggers J, Bernacki M, Bouchard P-O, Helfen L, Morgeneyer TF, Hild F (2017) Numerical validation framework for micromechanical simulations based on synchrotron 3D imaging. Comput Mech 59(3):419–441zbMATHGoogle Scholar
  30. 30.
    Buljac A, Taillandier-Thomas T, Morgeneyer TF, Helfen L, Roux S, Hild F (2016) Slant strained band development during flat to slant crack transition in AA 2198 t8 sheet: in situ 3D measurements. Int J Fract 200(1-2):49–62Google Scholar
  31. 31.
    Buljac A, Trejo Navas V-M, Shakoor M, Bouterf A, Neggers J, Bernacki M, Bouchard P-O, Morgeneyer TF, Hild F (2017) On the Feasibility of Calibration of Elastoplastic Parameters at the Microscale via X-Ray Microtomography and Digital Volume Correlation for the Simulation of Ductile Damage. Submitted for publicationGoogle Scholar
  32. 32.
    Cai B, Karagadde S, Yuan L, Marrow TJ, Connolley T, Lee PD (2014) In situ synchrotron tomographic quantification of granular and intragranular deformation during semi-solid compression of an equiaxed dendritic Al-Cu alloy. Acta Mater 76:371–380Google Scholar
  33. 33.
    Cai B, Lee PD, Karagadde S, Marrow TJ, Connolley T (2016) Time-resolved synchrotron tomographic quantification of deformation during indentation of an equiaxed semi-solid granular alloy. Acta Mater 105:338–346Google Scholar
  34. 34.
    Candès EJ, Romberg J, Tao T (2006) Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans Inf Theory 52(2):489–509MathSciNetzbMATHGoogle Scholar
  35. 35.
    Champeney DC (1987) A handbook of Fourier theorems. Cambridge University Press, Cambridge (UK)zbMATHGoogle Scholar
  36. 36.
    Chen Y, Dall’Ara E, Sales E, Manda K, Wallace R, Pankaj P, Viceconti M (2017) Micro-CT based finite element models of cancellous bone predict accurately displacement once the boundary condition is well replicated: a validation study. J Mech Behav Biomed Mater 65:644–651Google Scholar
  37. 37.
    Chiang F-P, Mao L (2015) Development of interior strain measurement techniques using random speckle patterns. Meccanica 50(2):401–410Google Scholar
  38. 38.
    Chinesta F, Ammar A, Cueto E (2010) Recent advances and new challenges in the use of the proper generalized decomposition for solving multidimensional models. Arch Comput Meth Eng 17(4):327–350MathSciNetzbMATHGoogle Scholar
  39. 39.
    Choudhari C, Herblum R, Akens MK, Moore S, Hardisty M, Whyne CM (2016) Post-euthanasia micro-computed tomography-based strain analysis is able to represent quasi-static in vivo behavior of whole vertebrae. Proc Inst Mech Eng H J Eng Med 230(9):900–904Google Scholar
  40. 40.
    Colliat-Dangus JL, Desrues J, Foray P (1988) Triaxial testing of granular soil under elevated cell pressure. In: Donaghe RT, Chaney RC, Silver ML (eds) Advanced Triaxial Testing of Soil and Rock, volume STP 977. American Society for Testing and Materials, Philadelphia, pp 290–310Google Scholar
  41. 41.
    Cooley JW, Tuckey JW (1965) An algorithm for the machine calculation of complex fourier series. Math Comput 19(90):297–301MathSciNetzbMATHGoogle Scholar
  42. 42.
    Coudrillier B, Campbell IC, Read AT, Geraldes DM, Vo NT, Feola A, Mulvihill J, Albon J, Abel RL, Ethier CR (2016) Effects of peripapillary scleral stiffening on the deformation of the lamina cribrosa. Invest Ophthalmol Vis Sci 57(6):2666–2677Google Scholar
  43. 43.
    Coudrillier B, Geraldes DM, Vo NT, Atwood R, Reinhard C, Campbell IC, Raji Y, Albon J, Abel RL, Ethier CR (2016) Phase-contrast micro-computed tomography measurements of the intraocular pressure-induced deformation of the porcine lamina cribrosa. IEEE Trans Med Imaging 35(4):988–999Google Scholar
  44. 44.
    Dahdah N, Limodin N, El Bartali A, Witz J-F, Seghir R, Charkaluk E, Buffière J-Y (2016) Damage investigation in A319 aluminium alloy by X-ray tomography and digital Volume correlation during in situ high-temperature fatigue tests. Strain 52(4):324–335Google Scholar
  45. 45.
    Dall’Ara E, Barber D, Viceconti M (2014) About the inevitable compromise between spatial resolution and accuracy of strain measurement for bone tissue: a 3D zero-strain study. J Biomechanics 47(12):2956–2963Google Scholar
  46. 46.
    Danesi V, Tozzi G, Cristofolini L (2016) Application of digital volume correlation to study the efficacy of prophylactic vertebral augmentation. Clin Biomech 39:14–24Google Scholar
  47. 47.
    Davis GR, Elliot JC (2006) Artefacts in x-ray microtomography of materials. Mater Sci Eng 22(9):1011–1018Google Scholar
  48. 48.
    Desrues J, Andò E (2015) Strain localisation in granular media. C R Phys 16(1):26–36Google Scholar
  49. 49.
    Desrues J, Chambon R, Mokni M, Mazerolle F (1996) Void ratio evolution inside shear bands in triaxial sand specimens studied by computed tomography. Géotechnique 46(3):529–546Google Scholar
  50. 50.
    Desrues J, Viggiani G, Bésuelle P (eds) (2006) Advances in x-ray tomography for geomaterials. Wiley / ISTE, LondonGoogle Scholar
  51. 51.
    Donoho DL (2006) Compressed sensing. IEEE Trans Inf Theory 52(4):1289–1306MathSciNetzbMATHGoogle Scholar
  52. 52.
    Donoho DL, Maleki A, Montanari A (2011) The noise-sensitivity phase transition in compressed sensing. IEEE Trans Inf Theory 57(10):6920–6941MathSciNetzbMATHGoogle Scholar
  53. 53.
    Dubois A, Vabre L (2003) Ultrahigh-resolution OCT using white-light interference microscopy. In: Optical methods and optical coherence tomography in biomedicine VII, vol 4956. International Society for Optics and Photonics, pp 14–22Google Scholar
  54. 54.
    Eastwood DS, Yufit V, Gelb J, Gu A, Bradley RS, Harris SJ, Brett DJL, Brandon NP, Lee PD, Withers PJ, Shearing PR (2014) Lithiation-induced dilation mapping in a lithium-ion battery electrode by 3D x-ray microscopy and digital volume correlation. Adv Energy Mater 4(4):1300506Google Scholar
  55. 55.
    Elliott JA, Windle AH, Hobdell JR, Eeckhaut G, Oldman RJ, Ludwig W, Boller E, Cloetens P, Baruchel J (2002) In-situ deformation of an open-cell flexible polyurethane foam characterised by 3d computed microtomography. J Mater Sci 37(8):1547–1555Google Scholar
  56. 56.
    Elsinga GE, Scarano F, Wieneke B, van Oudheusden BW (2006) Tomographic particle image velocimetry. Exp Fluids 41(6):933–947Google Scholar
  57. 57.
    Engl HW, Hanke M, Neubauer A (1996) Regularization of inverse problems. Kluwer, DordrechtzbMATHGoogle Scholar
  58. 58.
    Fedele R, Ciani A, Fiori F (2014) X-ray microtomography under loading and 3D-volume digital image correlation. A review. Fundamenta Informaticae 135(1-2):171–197MathSciNetzbMATHGoogle Scholar
  59. 59.
    Fedele R, Ciani A, Galantucci L, Bettuzzi M, Andena L (2013) A regularized, pyramidal multi-grid approach to global 3D-volume digital image correlation based on X-ray micro-tomography. Fundamenta Informaticae 125(3-4):361–376MathSciNetGoogle Scholar
  60. 60.
    Feldkamp LA, Davis LC, Kress JW (1984) Practical cone beam algorithm. J Opt Soc Am A1:612–619Google Scholar
  61. 61.
    Feng X, Hall MS, Wu M, Hui C-Y (2014) An adaptive algorithm for tracking 3D bead displacements: application in biological experiments. Measurement Sci Technol 25(5):055701Google Scholar
  62. 62.
    Figueroa Pilz F, Dowey PJ, Fauchille A-L, Courtois L, Bay B, Ma L, Taylor KG, Mecklenburgh J, Lee PD (2017) Synchrotron tomographic quantification of strain and fracture during simulated thermal maturation of an organic-rich shale, UK Kimmeridge Clay. J Geophys Res Solid Earth 122(4):2553–2564Google Scholar
  63. 63.
    Fila T, Jirousek O, Jung A, Kumpova I (2016) Identification of strain fields in pure Al and hybrid Ni/Al metal foams using X-ray micro-tomography under loading. Journal of Instrumentation, 11:C11017 NOVGoogle Scholar
  64. 64.
    Finegan DP, Tudisco E, Scheel M, Robinson JB, Taiwo OO, Eastwood S, Lee PD, Di Michiel M, Bay B, Hall S, Hinds G, Brett DJL, Shearing PR (2016) Quantifying Bulk Electrode Strain and Material Displacement within Lithium Batteries via High-Speed Operando Tomography and Digital Volume Correlation. Advan Sci 3(3):1500332Google Scholar
  65. 65.
    Fischer G, Nellesen J, Anar NB, Ehrig K, Riesemeier H, Tillmann W (2013) 3D analysis of micro-deformation in VHCF-loaded nodular cast iron by µCT. Mater Sci Eng A-Struct Mater Properties Microstructure Process 577:202–209Google Scholar
  66. 66.
    Flohr TG, McCollough CH, Bruder H, Petersilka M, Gruber K, Süss C, Grasruck M, Stierstorfer K, Krauss B, Raupach R et al (2006) First performance evaluation of a dual-source ct (dsct) system. Eur Radiol 16(2):256–268Google Scholar
  67. 67.
    Forsberg F, Mooser R, Arnold M, Hack E, Wyss P (2008) 3D micro-scale deformations of wood in bending Synchrotron radiation µCT data analyzed with digital volume correlation. J Struct Biol 164(3):255–262Google Scholar
  68. 68.
    Forsberg F, Siviour CR (2009) 3D deformation and strain analysis in compacted sugar using x-ray microtomography and digital volume correlation. Measurement Sci Technol 20(9):095703Google Scholar
  69. 69.
    Forsberg F, Sjodahl M, Mooser R, Hack E, Wyss P (2010) 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):47–60Google Scholar
  70. 70.
    Franck C, Hong S, Maskarinec SA, Tirrell DA, Ravichandran G (2007) Three-dimensional full-field measurements of large deformations in soft materials using confocal microscopy and digital volume correlation. Exp Mech 47(3):427–438Google Scholar
  71. 71.
    Fu J, Haghighi-Abayneh M, Pierron F, Ruiz PD (2016) Depth-resolved full-field measurement of corneal deformation by optical coherence tomography and digital volume correlation. Exp Mech 56(7):1203–1217Google Scholar
  72. 72.
    Fu J, Pierron F, Ruiz PD (2013) Elastic stiffness characterization using three-dimensional full-field deformation obtained with optical coherence tomography and digital volume correlation. J Biomed Opt 18(12):121512Google Scholar
  73. 73.
    Gates M, Gonzalez J, Lambros J, Heath MT (2015) Subset refinement for digital volume correlation numerical and experimental applications. Exp Mech 55(1):245–259Google Scholar
  74. 74.
    Gates M, Heath MT, Lambros J (2015) High-performance hybrid CPU and GPU parallel algorithm for digital volume correlation. Int J High Perform Comput Appl 29(1):92–106Google Scholar
  75. 75.
    Genet M, Lee LC, Kozerke S (2017) A continuum finite strain formulation of the equilibrium gap regularizer for finite element image correlation. CSMA
  76. 76.
    Germaneau A, Doumalin P, Dupré J-C (2007) 3D strain field measurement by correlation of volume images using scattered light recording of images and choice of marks. Strain 43(3):207–218Google Scholar
  77. 77.
    Germaneau A, Peyruseigt F, Mistou S, Doumalin P, Dupré J-C (2010) 3D mechanical analysis of aeronautical plain bearings validation of a finite element model from measurement of displacement fields by digital volume correlation and optical scanning tomography. Opt Lasers Eng 48(6):676–683Google Scholar
  78. 78.
    Gillard F, Boardman R, Mavrogordato M, Hollis D, Sinclair I, Pierron F, Browne M (2014) The application of digital volume correlation (DVC) to study the microstructural behaviour of trabecular bone during compression. J Mech Behav Biomed Mater 29:480–499Google Scholar
  79. 79.
    Gomes Perini LA, Passieux J-C, Périé J-N (2014) A multigrid PGD-based algorithm for volumetric displacement fields measurements. Strain 50(4):355–367Google Scholar
  80. 80.
    Gondrom S, Schropfer S (1999) Digital computed laminography and tomosynthesis — functional principles and industrial applications. J Nondestructive Testing Ultrasonics, 7(2)Google Scholar
  81. 81.
    Gondrom S, Zhou J, Maisl M, Reiter H, Kröning M, Arnold W (1999) X-ray computed laminography: an approach of computed tomography for applications with limited access. Nucl Eng Des 190(1):141–147Google Scholar
  82. 82.
    Grédiac M, Hild F (eds) (2012) Full-field measurements and identification in solid mechanics. ISTE/Wiley, LondonGoogle Scholar
  83. 83.
    Guillet J-P, Recur B, Frederique L, Bousquet B, Canioni L, Manek-Hönninger I, Desbarats P, Mounaix P (2014) Review of terahertz tomography techniques. J Infrared Millimeter Terahertz Waves 35 (4):382–411Google Scholar
  84. 84.
    Guvenilir A, Breunig TM, Kinney JH, Stock SR (1997) Direct observation of crack opening as a function of applied load in the interior of a notched tensile sample of al-li2090. Acta Mater 45:1977–1987Google Scholar
  85. 85.
    Hall S, Bornert M, Desrues J, Pannier Y, Lenoir N, Viggiani C, Bésuelle P (2010) Discrete and continuum analysis of localised deformation in sand using x-ray micro ct and volumetric digital image correlation. Géotechnique 60(5):315–322Google Scholar
  86. 86.
    Helfen L, Baumbach T, Mikulík P, Kiel D, Pernot P, Cloetens P, Baruchel J (2005) High-resolution three-dimensional imaging of flat objects by synchrotron-radiation computed laminography. Appl Phys Lett 86(7):071915Google Scholar
  87. 87.
    Helfen L, Myagotin A, Mikulík P, Pernot P, Voropaev A, Elyyan M, Di Michiel M, Baruchel J, Baumbach T (2011) On the implementation of computed laminography using synchrotron radiation. Rev Sci Instruments 82(063702)Google Scholar
  88. 88.
    Helfen L, Myagotin A, Rack A, Pernot P, Mikulík P, Di Michiel M, Baumbach T (2007) Synchrotron-radiation computed laminography for high-resolution three-dimensional imaging of flat devices. Phys Status Solidi (A) 204:2760–2765Google Scholar
  89. 89.
    Helfen L, Xu F, Suhonen H, Urbanelli L, Cloetens P, Baumbach T (2013) Nano-laminography for three-dimensional high-resolution imaging of flat specimens. J Instrum 8(05):C05006Google Scholar
  90. 90.
    Herman GT (1979) Correction for beam hardening in computed tomography. Phys Med Biol 24(1):81Google Scholar
  91. 91.
    Herman GT, Davidi R (2008) Image reconstruction from a small number of projections. Inverse Prob 24(045011)Google Scholar
  92. 92.
    Hild F, Bouterf A, Chamoin L, Mathieu F, Neggers J, Pled F, Tomičević Z, Roux S (2016) Toward 4D mechanical correlation. Advan Model Simul Eng Sci 3(17):1–26Google Scholar
  93. 93.
    Hild F, Bouterf A, Roux S (2015) Damage measurements via DIC from physical to mechanical damage. Int J Fract 191(1-2):77–105Google Scholar
  94. 94.
    Hild F, Fanget A, Adrien J, Maire E, Roux S (2011) Three-dimensional analysis of a tensile test on a propellant with digital volume correlation. Archives Mech 63(5-6):459–478Google Scholar
  95. 95.
    Hild F, Leclerc H, Roux S, Swiergiel N, Tomičević Z (2012) Circumventing the curse of resolution versus spatial resolution in digital image correlation from local to global and regularized approaches. In: IUTAM Symposium on advances of optical methods in experimental mechanicsGoogle Scholar
  96. 96.
    Hild F, Maire E, Roux S, Witz J-F (2009) Three dimensional analysis of a compression test on stone wool. Acta Mater 57:3310–3320Google Scholar
  97. 97.
    Hild F, Raka B, Baudequin M, Roux S, Cantelaube F (2002) Multi-scale displacement field measurements of compressed mineral wool samples by digital image correlation. Appl Opt, IP 41(32):6815–6828Google Scholar
  98. 98.
    Hild F, Roux S (2012) Comparison of local and global approaches to digital image correlation. Exp Mech 52(9):1503–1519Google Scholar
  99. 99.
    Hild F, Roux S (2012) Digital image correlation. In: Rastogi P, Hack E (eds) Optical Methods for Solid Mechanics. A Full-Field Approach. Wiley, Weinheim, pp 183–228Google Scholar
  100. 100.
    Hild F, Roux S, Bernard D, Hauss G, Rebai M (2013) On the use of 3D images and 3D displacement measurements for the analysis of damage mechanisms in concrete-like materials. In: Van Mier JGM, Ruiz G, Andrade C, Yu RC, Zhang XX (eds) FraMCoS-8, pp 1–11Google Scholar
  101. 101.
    Hill DLG, Batchelor PG, Holden M, Hawkes DJ (2001) Medical image registration. Phys Med Biol 46(3):R1Google Scholar
  102. 102.
    Hu Z, Du Y, Luo H, Zhong B, Lu H (2014) Internal deformation measurement and force chain characterization of mason sand under confined compression using incremental digital volume correlation. Exp Mech 54(9):1575–1586Google Scholar
  103. 103.
    Hu Z, Luo H, Bardenhagen SG, Siviour CR, Armstrong RW, Lu H (2015) Internal deformation measurement of polymer bonded sugar in compression by digital volume correlation of in-situ tomography. Exp Mech 55(1):289–300Google Scholar
  104. 104.
    Huang J, Pan X, Li S, Peng X, Xiong C, Fang J (2011) A digital volume correlation technique for 3-D deformation measurements of soft gels. Int J Appl Mech 3(2):335–354Google Scholar
  105. 105.
    Hussein AI, Mason ZD, Morgan EF (2013) Presence of intervertebral discs alters observed stiffness and failure mechanisms in the vertebra. J Biomechanics 46(10):1683–1688Google Scholar
  106. 106.
    Hussein AI, Morgan EF (2013) The effect of intravertebral heterogeneity in microstructure on vertebral strength and failure patterns. Osteoporos Int 24(3):979–989Google Scholar
  107. 107.
    Jackman TM, DelMonaco AM, Morgan EF (2016) Accuracy of finite element analyses of CT scans in predictions of vertebral failure patterns under axial compression and anterior flexion. J Biomechanics 49(2):267–275Google Scholar
  108. 108.
    Jackman TM, Hussein AI, Curtiss C, Fein PM, Camp A, De Barros L, Morgan EF (2016) Quantitative, 3D visualization of the initiation and progression of vertebral fractures under compression and anterior flexion. J Bone Miner Res 31(4):777–788Google Scholar
  109. 109.
    Jailin C, Bouterf A, Poncelet M, Roux S (2017) In situ µCT mechanical tests: fast 4D mechanical identification. Exp Mech 57(8):1327–1340Google Scholar
  110. 110.
    Jailin C, Buljac A, Bouterf A, Poncelet M, Hild F, Roux S (2018) Self-calibration for lab-µCT using space-time regularized projection-based DVC and model reduction. Meas Sci Tech 29:024003Google Scholar
  111. 111.
    Joffre T, Girlanda O, Forsberg F, Sahlen F, Sjodahl M, Gamstedt EK (2015) A 3D in-situ investigation of the deformation in compressive loading in the thickness direction of cellulose fiber mats. Cellulose 22(5):2993–3001Google Scholar
  112. 112.
    Johnson TRC, Nikolaou K, Wintersperger BJ, Leber AW, von Ziegler F, Rist C, Buhmann S, Knez A, Reiser MF, Becker CR (2006) Dual-source CT cardiac imaging: initial experience. Eur Radiol 16 (7):1409–1415Google Scholar
  113. 113.
    Kak AC, Slaney M (1988) Principles of computerized tomographic imaging. IEEE Press, New YorkzbMATHGoogle Scholar
  114. 114.
    Klein S, Staring M, Murphy K, Viergever MA, Pluim JPW (2010) ELASTIX: a toolbox for intensity-based medical image registration. IEEE Trans Med Imaging 29(1):196–205Google Scholar
  115. 115.
    Kobayashi M, Toda H, Kawai Y, Ohgaki T, Uesugi K, Wilkinson DS, Kobayashi T, Aoki Y, Nakazawa M (2008) High-density three-dimensional mapping of internal strain by tracking microstructural features. Acta Mater 56(10):2167–2181Google Scholar
  116. 116.
    Krupa K, Bekiesińska-Figatowska M (2015) Artifacts in magnetic resonance imaging. Pol J Radiol 80:93Google Scholar
  117. 117.
    Kullback S (1959) Information theory and statistics. Wiley, New-YorkzbMATHGoogle Scholar
  118. 118.
    Lachambre J, Réthoré J, Weck A, Buffière J-Y (2015) Extraction of stress intensity factors for 3D small fatigue cracks using digital volume correlation and x-ray tomography. Int J Fatigue 71:3–10Google Scholar
  119. 119.
    Ladevèze P (2014) PGD In linear and nonlinear computational solid mechanics. In: Separated representations and PGD-based model reduction. Springer, pp 91–152Google Scholar
  120. 120.
    Leclerc H, Neggers J, Mathieu F, Hild F, Roux S (2015) Correli 3.0. Agence pour la Protection des Programmes, IDDN.FR.001.520008.000. S. P.2015.000.31500Google Scholar
  121. 121.
    Leclerc H, Périé J-N, Hild F, Roux S (2012) Digital volume correlation: what are the limits to the spatial resolution?. Mech Industry 13(6):361–371Google Scholar
  122. 122.
    Leclerc H, Périé J-N, Roux S, Hild F (2011) Voxel-scale digital volume correlation. Exp Mech 51(4):479–490Google Scholar
  123. 123.
    Leclerc H, Roux S, Hild F (2015) Projection savings in CT-based digital volume correlation. Exp Mech 55(1):275–287Google Scholar
  124. 124.
    Lecomte-Grosbras P, Réthoré J, Limodin N, Witz J-F, Brieu M (2015) Three-dimensional investigation of free-edge effects in laminate composites using x-ray tomography and digital volume correlation. Exp Mech 55(1):301–311Google Scholar
  125. 125.
    Lemaitre J (1992) A course on damage mechanics. Springer, BerlinzbMATHGoogle Scholar
  126. 126.
    Lenoir N, Bornert M, Desrues J, Bésuelle P, Viggiani G (2007) Volumetric digital image correlation applied to x-ray microtomography images from triaxial compression tests on argillaceous rock. Strain 43:193–205Google Scholar
  127. 127.
    Leplay P, Réthoré J, Meille S, Baietto M-C, Adrien J, Chevalier J, Maire E (2013) Three-dimensional analysis of an in situ double-torsion test by x-ray computed tomography and digital volume correlation. Exp Mech 53(7):1265–1275Google Scholar
  128. 128.
    Lesman A, Notbohm J, Tirrel DA, Ravichandran G (2014) Contractile forces regulate cell division in three-dimensional environments. J Cell Biol 205(2):155–162Google Scholar
  129. 129.
    Lim KY, Henderson JT, Neu CP (2013) Cell and tissue deformation measurements: texture correlation with third-order approximation of displacement gradients. J Biomechanics 46(14):2490–2496Google Scholar
  130. 130.
    Limodin N, Réthoré J, Adrien J, Buffière J-Y, Hild F, Roux S (2011) Analysis and artifact correction for volume correlation measurements using tomographic images from a laboratory x-ray Source. Exp Mech 51(6):959–970Google Scholar
  131. 131.
    Limodin N, Réthoré J, Buffière J-Y, Hild F, Roux S, Ludwig W, Rannou J, Gravouil A (2010) Influence of closure on the 3D propagation of fatigue cracks in a nodular cast iron investigated by X-ray tomography and 3D Volume correlation. Acta Mater 58(8):2957–2967Google Scholar
  132. 132.
    Limodin N, Réthoré J, Buffière JY, Gravouil A, Hild F, Roux S (2009) Crack closure and stress intensity factor measurements in nodular graphite cast iron using 3D correlation of laboratory X ray microtomography images. Acta Mater 57(14):4090–4101Google Scholar
  133. 133.
    Liu L, Morgan EF (2007) Accuracy and precision of digital volume correlation in quantifying displacements and strains in trabecular bone. J Biomechanics 40(15):3516–3520Google Scholar
  134. 134.
    Ludwig W, Buffière J-Y, Savelli S, Cloetens P (2003) Study of the interaction of a short fatigue crack with grain boundaries in a cast Al alloy using X-ray microtomography. Acta Mater 51(3):585–598Google Scholar
  135. 135.
    Ludwik P (1909) Elemente der technologischen Mechanik. Verlag Von Julius Springer Leipzig (Germany)Google Scholar
  136. 136.
    Madi K, Tozzi G, Zhang QH, Tong J, Cossey A, Au A, Hollis D, Hild F (2013) Computation of full-field displacements in a scaffold implant using digital volume correlation and finite element analysis. Med Eng Phys 35(9):1298–1312Google Scholar
  137. 137.
    Mae BA (2003) The revolution in medical imaging. Rosen Pub. Group, New YorkGoogle Scholar
  138. 138.
    Maes F, Collignon A, Vandermeulen D, Marchal G, Suetens P (1997) Multimodality image registration by maximization of mutual information. IEEE Trans Med Imaging 16(2):187–198Google Scholar
  139. 139.
    Mahalanobis PC (1936) On the generalised distance in statistics. In: Proceedings of the National Institute of Sciences of India, pp 49–55Google Scholar
  140. 140.
    Maintz JBA, Viergever MA (1998) A survey of medical image registration. Med Image Anal 2(1):1–36Google Scholar
  141. 141.
    Maire E, Buffière J-Y, Salvo L, Blandin JJ, Ludwig W, Létang J-M (2001) On the application of x-ray microtomography in the field of materials science. Adv Eng Mater 3(8):539–546Google Scholar
  142. 142.
    Maire E, Le Bourlot C, Adrien J, Mortensen A, Mokso R (2016) 20-Hz x-ray tomography during an in situ tensile test. Int J Fract 200(1):3–12Google Scholar
  143. 143.
    Maire E, Withers PJ (2014) Quantitative x-ray tomography. Int Mater Rev 59(1):1–43Google Scholar
  144. 144.
    Makitalo M, Foi A (2013) Optimal inversion of the generalized anscombe transformation for poisson-gaussian noise. IEEE Trans Image Process 22(1):91–103MathSciNetzbMATHGoogle Scholar
  145. 145.
    Malfroy Camine V, Rudiger HA, Pioletti DP, Terrier A (2016) Full-field measurement of micromotion around a cementless femoral stem using micro-CT imaging and radiopaque markers. J Biomechanics 49(16):4002–4008Google Scholar
  146. 146.
    Marrow TJ, Mostafavi M, Hashimoto T, Thompson GE (2014) A quantitative three-dimensional in situ study of a short fatigue crack in a magnesium alloy. Int J Fatigue 66:183–193Google Scholar
  147. 147.
    Maskarinec SA, Franck C, Tirrell DA, Ravichandran G (2009) Quantifying cellular traction forces in three dimensions. Proc Natl Acad Sci USA 106(52):22108–22113Google Scholar
  148. 148.
    Mathieu F, Hild F, Roux S (2012) Identification of a crack propagation law by digital image correlation. Int J Fatigue 36:146–154Google Scholar
  149. 149.
    Mathieu F, Leclerc H, Hild F, Roux S (2015) Estimation of elastoplastic parameters via weighted FEMU and integrated-DIC. Exp Mech 55(1):105–119Google Scholar
  150. 150.
    McDonald S, Withers PJ (2014) Combining x-ray microtomography and three-dimensional digital volume correlation to track microstructure evolution during sintering of copper powder. J Strain Anal Eng Des 49(4):257–269Google Scholar
  151. 151.
    Mendoza A, Roux S, Schneider J, Parra E (2017) Extraction of topological differences in woven composite materials. In: 7Th conference on industrial computed tomographyGoogle Scholar
  152. 152.
    Mendoza A, Roux S, Schneider J, Parra E, Obert E (2017) Unwrapping textile fabric. In: 3Rd international conference on tomography of materials and structuresGoogle Scholar
  153. 153.
    Moore EH (1920) On the reciprocal of the general algebraic matrix. Bull Am Math Soc 2(26):394–395Google Scholar
  154. 154.
    Morandi P, Brémand E, Doumalin P, Germaneau A, Dupré J-C (2014) New optical scanning tomography using a rotating slicing for time-resolved measurements of 3D full field displacements in structures. Opt Lasers Eng 58:85–92Google Scholar
  155. 155.
    Morgeneyer TF, Helfen L, Mubarak H, Hild F (2013) 3D digital Volume Correlation of synchrotron radiation laminography images of ductile crack initiation an initial feasibility study. Exp Mech 53(4):543–556Google Scholar
  156. 156.
    Morgeneyer TF, Taillandier-Thomas T, Buljac A, Helfen L, Hild F (2016) On strain and damage interactions during tearing: 3D in situ measurements and simulations for a ductile alloy (AA2139-T3). J Mech Phys Solids 96:550–571Google Scholar
  157. 157.
    Morgeneyer TF, Taillandier-Thomas T, Helfen L, Baumbach T, Sinclair I, Roux S, Hild F (2014) In situ 3-D observation of early strain localization during failure of thin Al alloy (2198) sheet. Acta Mater 69:78–91Google Scholar
  158. 158.
    Mortazavi F, Ghossein E, Levesque M, Villemure I (2014) High resolution measurement of internal full-field displacements and strains using global spectral digital volume correlation. Opt Lasers Eng 55:44–52Google Scholar
  159. 159.
    Mostafavi M, Baimpas N, Tarleton E, Atwood R, McDonald S, Korsunsky AM, Marrow TJ (2013) Three-dimensional crack observation, quantification and simulation in a quasi-brittle material. Acta Mater 61(16):6276–6289Google Scholar
  160. 160.
    Mostafavi M, Bradley R, Armstrong DEJ, Marrow TJ (2016) Quantifying yield behaviour in metals by x-ray nanotomography. Sci Report 6:34346Google Scholar
  161. 161.
    Mostafavi M, Collins DM, Cai B, Bradley R, Atwood R, Reinhard C, Jiang X, Galano M, Lee PD, Marrow TJ (2015) Yield behavior beneath hardness indentations in ductile metals, measured by three-dimensional computed x-ray tomography and digital volume correlation. Acta Mater 82:468–482Google Scholar
  162. 162.
    Mostafavi M, McDonald S, Cetinel H, Mummery PM, Marrow TJ (2013) Flexural strength and defect behaviour of polygranular graphite under different states of stress. Carbon 59:325–336Google Scholar
  163. 163.
    Nahas A, Bauer M, Roux S, Boccara AC (2013) 3D static elastography at the micrometer scale using full field OCT. Biomed Opt Express 4(10):2138–2149Google Scholar
  164. 164.
    Neggers J, Allix O, Hild F, Roux S (2018) Big data in experimental mechanics and model order reduction: today’s challenges and tomorrow’s opportunities. Arch Comput Meth Eng 25(1):143–164MathSciNetzbMATHGoogle Scholar
  165. 165.
    Nguyen TT, Yvonnet J, Bornert M, Chateau C (2016) Initiation and propagation of complex 3D networks of cracks in heterogeneous quasi-brittle materials: direct comparison between in situ testing-microCT experiments and phase field simulations. J Mech Phys Solids 95:320–350Google Scholar
  166. 166.
    Novelline RA (2018) Squire’s fundamentals of radiology. Harvard University Press, CambridgeGoogle Scholar
  167. 167.
    Palanca M, Cristofolini L, Dall’Ara E, Curto M, Innocente F, Danesi V, Tozzi G (2016) Digital volume correlation can be used to estimate local strains in natural and augmented vertebrae: an organ-level study. J Biomechanics 49(16):3882–3890Google Scholar
  168. 168.
    Palanca M, Tozzi G, Cristofolini L, Viceconti M, Dall’Ara E (2015) Three-dimensional local measurements of bone strain and displacement: comparison of three digital volume correlation approaches. J Biomechanical Eng-Trans ASME 137(7):071006Google Scholar
  169. 169.
    Pan B, Wang B, Wu D, Lubineau G (2014) An efficient and accurate 3D displacements tracking strategy for digital volume correlation. Opt Lasers Eng 58:126–135Google Scholar
  170. 170.
    Pan B, Wu D, Wang Z (2012) Internal displacement and strain measurement using digital volume correlation: a least-squares framework. Measure Sci Technol, 23(4)Google Scholar
  171. 171.
    Parker KJ, Doyley MM, Rubens DJ (2011) Corrigendum 1: imaging the elastic properties of tissue: the 20 year perspective. Phys Med Biol 56(2):513Google Scholar
  172. 172.
    Parker KJ, Doyley MM, Rubens DJ (2011) Imaging the elastic properties of tissue: the 20 year perspective. Phys Med Biol 56(1):R1Google Scholar
  173. 173.
    Parker KJ, Doyley MM, Rubens DJ (2012) Corrigendum 2: imaging the elastic properties of tissue: the 20 year perspective. Phys Med Biol 57(16):5359Google Scholar
  174. 174.
    Passieux J-C, Périé J-N (2012) High resolution digital image correlation using proper generalized decomposition: PGD-DIC. Int J Numer Methods Eng 92(6):531–550MathSciNetzbMATHGoogle Scholar
  175. 175.
    Passieux J-C, Périé J-N, Salaün M (2015) A dual domain decomposition method for finite element digital image correlation. Int J Numer Methods Eng 102(10):1670–1682MathSciNetzbMATHGoogle Scholar
  176. 176.
    Patterson BM, Cordes NL, Henderson K, Mertens JCE, Clarke AJ, Hornberger B, Merkle A, Etchin S, Tkachuk A, Leibowitz M, Trapp D, Qiu W, Zhang B, Bale H, Lu X, Hartwell R, Withers PJ, Bradley RS (2016) In situ laboratory-based transmission x-ray microscopy and tomography of material deformation at the nanoscale. Exp Mech 56(9):1585–1597Google Scholar
  177. 177.
    Paz-Garcia JM, Taiwo OO, Tudisco E, Finegan DP, Shearing PR, Brett DJL, Hall S (2016) 4D analysis of the microstructural evolution of Si-based electrodes during lithiation time-lapse x-ray imaging and digital volume correlation. J Power Sources 320:196–203Google Scholar
  178. 178.
    Penrose R (1956) On best approximate solutions of linear matrix equations. Math Proc Camb Philos Soc 52 (1):17–19zbMATHGoogle Scholar
  179. 179.
    Petersilka M, Bruder H, Krauss B, Stierstorfer K, Flohr TG (2008) Technical principles of dual source CT. Eur J Radiol 68(3):362–368Google Scholar
  180. 180.
    Pierron F, McDonald S, Hollis D, Fu J, Withers PJ, Alderson A (2013) Comparison of the mechanical behaviour of standard and auxetic foams by x-ray computed tomography and digital volume correlation. Strain 49(6):467–482Google Scholar
  181. 181.
    Popescu DP, Choo-Smith L-P, Flueraru C, Mao Y, Chang S, Disano J, Sherif S, Sowa MG (2011) Optical coherence tomography: fundamental principles, instrumental designs and biomedical applications. Biophys Rev 3(3):155–169Google Scholar
  182. 182.
    Prell D, Kyriakou Y, Kalender WA (2009) Comparison of ring artifact correction methods for flat-detector CT. Phys Med Biol 54(12):3881Google Scholar
  183. 183.
    Rahmani B, Ghossein E, Villemure I, Levesque M (2014) In-situ mechanical properties identification of 3D particulate composites using the virtual fields method. Int J Solids Struct 51(18):3076–3086Google Scholar
  184. 184.
    Rannou J, Limodin N, Réthore J, Gravouil A, Ludwig W, Baietto-Dubourg M-C, Buffière J-Y, Combescure A, Hild F, Roux S (2010) Three dimensional experimental and numerical multiscale analysis of a fatigue crack. Comput Methods Appl Mech Eng 199(21-22):1307–1325zbMATHGoogle Scholar
  185. 185.
    Ren M, Liang J, Wei B (2016) Accurate B-spline-based 3-D interpolation scheme for digital volume correlation. Rev Sci Instruments 87(12):125114Google Scholar
  186. 186.
    Réthoré J, Hild F, Roux S (2007) Shear-band capturing using a multiscale extended digital image correlation technique. Comput Methods Appl Mech Eng 196(49-52):5016–5030zbMATHGoogle Scholar
  187. 187.
    Réthoré J, Hild F, Roux S (2008) Extended digital image correlation with crack shape optimization. Int J Numer Methods Eng 73(2):248–272MathSciNetzbMATHGoogle Scholar
  188. 188.
    Réthoré J, Limodin N, Buffière J-Y, Hild F, Ludwig W, Roux S (2011) Digital volume correlation analyses of synchrotron tomographic images. J Strain Anal Eng Des 46(7):683–695Google Scholar
  189. 189.
    Réthoré J, Roux S, Hild F (2009) An extended and integrated digital image correlation technique applied to the analysis fractured samples. European J Comput Mech 18:285–306zbMATHGoogle Scholar
  190. 190.
    Réthoré J, Roux S, Hild F (2011) Optimal and noise-robust extraction of fracture mechanics parameters from kinematic measurements. Eng Fracture Mech 78(9):1827–1845Google Scholar
  191. 191.
    Réthoré J, Tinnes J-P, Roux S, Buffière J-Y, Hild F (2008) Extended three-dimensional digital image correlation (X3D-DIC). Comptes Rendus Mécanique 336:643–649zbMATHGoogle Scholar
  192. 192.
    Roberts BC, Perilli E, Reynolds KJ (2014) Application of the digital volume correlation technique for the measurement of displacement and strain fields in bone: a literature review. J Biomechanics 47(5):923–934Google Scholar
  193. 193.
    Roeder BA, Kokini K, Robinson JP, Voytik-Harbin SL (2004) Local, three-dimensional strain measurements within largely deformed extracellular matrix constructs. J Biomechanical Eng-Trans ASME 126 (6):699–708Google Scholar
  194. 194.
    Rohlfing T, Maurer CR, Bluemke DA, Jacobs MA (2003) Volume-preserving nonrigid registration of MR breast images using free-form deformation with an incompressibility constraint. IEEE Trans Med Imaging 22 (6):730–741Google Scholar
  195. 195.
    Roux S, Hild F (2006) Stress intensity factor measurements from digital image correlation: post-processing and integrated approaches. Int J Fract 140(1-4):141–157zbMATHGoogle Scholar
  196. 196.
    Roux S, Hild F, Viot P, Bernard D (2008) Three-dimensional image correlation from x-ray computed tomography of solid foam. Compos Part A Appl Sci Manuf 39(8):1253–1265Google Scholar
  197. 197.
    Roux S, Réthoré J, Hild F (2009) Digital image correlation and fracture: an advanced technique for estimating stress intensity factors of 2D and 3D cracks. J Phys D Appl Phys 42:214004Google Scholar
  198. 198.
    Rueckert D, Sonoda LI, Hayes C, Hill DLG, Leach MO, Hawkes DJ (1999) Nonrigid registration using free-form deformations: application to breast MR images. IEEE Trans Med Imaging 18(8):712–721Google Scholar
  199. 199.
    Salvo L, Cloetens P, Maire E, Zabler S, Blandin J-J, Buffière JY, Ludwig W, Boller E, Bellet D, Josserond C (2003) X-ray micro-tomography an attractive characterisation technique in materials science. Nuclear Instruments and Method Phys Res Section B: Beam Interact Mater and Atoms 200:273–286Google Scholar
  200. 200.
    Saucedo-Mora L, Mostafavi M, Khoshkhou D, Reinhard C, Atwood R, Zhao S, Connolly B, Marrow TJ (2016) Observation and simulation of indentation damage in a SiC-SiC fibre ceramic matrix composite. Finite Elem Anal Des 110:11–19Google Scholar
  201. 201.
    Saucedo-Mora L, Zou C, Lowe T, Marrow TJ (2017) Three-dimensional measurement and cohesive element modelling of deformation and damage in a 2.5-dimensional woven ceramic matrix composite. Fatigue Fract Eng Mater Struct 40(5):683–695Google Scholar
  202. 202.
    Scarano F (2013) Tomographic PIV: principles and practice. Meas Sci Technol 24(1):012001Google Scholar
  203. 203.
    Schneider J, Leclerc H, Hild F, Roux S (2015) Method for characterising a part. Patent, WO2015092212 A1Google Scholar
  204. 204.
    Schoenberg IJ (1946) Contributions to the problem of approximation of equidistant data by analytic functions. Part A. Q Appl Math 4:45–99Google Scholar
  205. 205.
    Shakoor M, Buljac A, Neggers J, Hild F, Morgeneyer TF, Helfen L, Bernacki M, Bouchard P-O (2017) On the choice of boundary conditions for micromechanical simulations based on 3D imaging. Int J Solids Struct 112:83–96zbMATHGoogle Scholar
  206. 206.
    Smith TS, Bay B, Rashid MM (2002) Digital volume correlation including rotational degrees of freedom during minimization. Exp Mech 42(3):272–278Google Scholar
  207. 207.
    Stock SR (2008) Recent advances in x-ray microtomography applied to materials. Int Mater Rev 53(3):129–181Google Scholar
  208. 208.
    Studholme C, Hill DLG, Hawkes DJ (1996) Automated 3-D registration of MR and CT images of the head. Med Image Anal 1(2):163–175Google Scholar
  209. 209.
    Sukjamsri C, Geraldes DM, Gregory T, Ahmed F, Hollis D, Schenk S, Amis A, Emery R, Hansen U (2015) Digital volume correlation and micro-CT: an in-vitro technique for measuring full-field interface micromotion around polyethylene implants. J Biomechanics 48(12):3447–3454Google Scholar
  210. 210.
    Sur F, Grédiac M (2015) Measuring the noise of digital imaging sensors by stacking raw images affected by vibrations and illumination flickering. SIAM J Imag Sci 8(1):611–643MathSciNetzbMATHGoogle Scholar
  211. 211.
    Sutton MA, Orteu JJ, Schreier H (2009) Image correlation for shape, motion and deformation measurements: basic concepts, theory and applications. Springer, New YorkGoogle Scholar
  212. 212.
    Taillandier-Thomas T, Roux S, Hild F (2016) Soft route to 4D tomography. Phys Rev Lett 117 (2):025501MathSciNetGoogle Scholar
  213. 213.
    Taillandier-Thomas T, Roux S, Morgeneyer TF, Hild F (2014) Localized strain field measurement on laminography data with mechanical regularization. Nuclear Instruments & Methods Phys Res Section B-Beam Interact Mater Atoms 324:70–79Google Scholar
  214. 214.
    Tikhonov AN, Arsenin VY (1977) Solutions of ill-posed problems. Wiley, New YorkzbMATHGoogle Scholar
  215. 215.
    Toda H, Maire E, Aoki Y, Kobayashi M (2011) Three-dimensional strain mapping using in situ X-ray synchrotron microtomography. J Strain Anal Eng Des 46(7):549–561Google Scholar
  216. 216.
    Toda H, Sinclair I, Buffière J-Y, Maire E, Khor KH, Gregson P, Kobayashi T (2004) A 3d measurement procedure for internal local crack driving forces via synchrotron x-ray microtomography. Acta Mater 52:1305–1317Google Scholar
  217. 217.
    Tomičević Z, Hild F, Roux S (2013) Mechanics-aided digital image correlation. J Strain Anal Eng Des 48:330–343Google Scholar
  218. 218.
    Tomičević Z, Kodvanj J, Hild F (2016) Characterization of the nonlinear behavior of nodular graphite cast iron via inverse identification-analysis of uniaxial tests. Eur J Mech A Solids 59:140–154Google Scholar
  219. 219.
    Tozzi G, Danesi V, Palanca M, Cristofolini L (2016) Elastic full-field strain analysis and microdamage progression in the vertebral body from digital volume correlation. Strain 52(5):446–455Google Scholar
  220. 220.
    Tozzi G, Zhang Q-H, Tong J (2014) Microdamage assessment of bone-cement interfaces under monotonic and cyclic compression. J Biomechanics 47(14):3466–3474Google Scholar
  221. 221.
    Tran H, Doumalin P, Delisée C, Dupré J-C, Malvestio J, Germaneau A (2013) 3D mechanical analysis of low-density wood-based fiberboards by x-ray microcomputed tomography and digital volume correlation. J Mater Sci 48(8):3198–3212Google Scholar
  222. 222.
    Truesdell C, Noll W (1965) The non-linear field theories of mechanics, volume III/3. Springer, BerlinzbMATHGoogle Scholar
  223. 223.
    Tudisco E, Hall S, Charalampidou EM, Kardjilov N, Hilger A, Sone H (2015) Full-field measurements of strain localisation in sandstone by neutron tomography and 3D-volumetric digital image correlation. Phys Procedia 69:509–515Google Scholar
  224. 224.
    Tudisco E, Jailin C, Mendoza A, Tengattini A, Andò E, Hall S, Viggiani G, Hild F, Roux S (2017) An extension of digital volume correlation for multimodality image registration. Meas Sci Technol 28 (9):095401Google Scholar
  225. 225.
    Vajda I (1989) Theory of statistical inference and information, vol 11, Kluwer Academic Publishers, NorwellGoogle Scholar
  226. 226.
    Van Aarle W, Palenstijn WJ, De Beenhouwer J, Altantzis T, Bals S, Batenburg KJ, Sijbers J (2015) The ASTRA toolbox: a platform for advanced algorithm development in electron tomography. Ultramicroscopy 157:35–47Google Scholar
  227. 227.
    van den Elsen PA, Pol EJD, Viergever MA (1993) Medical image matching: a review with classification. IEEE Eng Med Biol Mag 12(1):26–39Google Scholar
  228. 228.
    Van Gompel G, Van Slambrouck K, Defrise M, Batenburg KJ, de Mey J, Sijbers J, Nuyts J (2011) Iterative correction of beam hardening artifacts in CT. Med Phys 38(S1):S36–S49Google Scholar
  229. 229.
    Verhulp E, van Rietbergen B, Huiskes R (2004) A three-dimensional digital image correlation technique for strain measurements in microstructures. J Biomechanics 37(9):1313–1320Google Scholar
  230. 230.
    Vertyagina Y, Mostafavi M, Reinhard C, Atwood R, Marrow TJ (2014) In situ quantitative three-dimensional characterisation of sub-indentation cracking in polycrystalline alumina. J Eur Ceram Soc 34 (12):3127–3132Google Scholar
  231. 231.
    Wan K, Yang P (2015) Expanded digital volume correlation for ex situ applications. Measure Sci Technol 26(9)Google Scholar
  232. 232.
    Wang B, Pan B, Tao R, Lubineau G (2017) Systematic errors in digital volume correlation due to the self-heating effect of a laboratory x-ray CT scanner. Meas Sci Technol 28(5):055402Google Scholar
  233. 233.
    Wang L, Limodin N, El Bartali A, Witz J-F, Seghir R, Buffière J-Y, Charkaluk E (2016) Influence of pores on crack initiation in monotonic tensile and cyclic loadings in lost foam casting a319 alloy by using 3D in-situ analysis. Mater Sci Eng A 673:362–372Google Scholar
  234. 234.
    Wang T, Jiang Z, Kemao Q, Lin F, Soon SH (2016) GPU accelerated digital volume correlation. Exp Mech 56(2):297–309Google Scholar
  235. 235.
    Wells WM, Viola P, Atsumi H, Nakajima S, Kikinis R (1996) Multi-modal volume registration by maximization of mutual information. Med Image Anal 1(1):35–51Google Scholar
  236. 236.
    Withers PJ (2007) X-ray nanotomography. Mater Today 10(12):26–34Google Scholar
  237. 237.
    Xu F, Helfen L, Baumbach T, Suhonen H (2012) Comparison of image quality in computed laminography and tomography. Opt Express 20:794–806Google Scholar
  238. 238.
    Xu S, Grande-Allen KJ (2010) The evolution of the field of biomechanics through the lens of experimental mechanics. Exp Mech 50(6):667–682Google Scholar
  239. 239.
    Yang Z, Ren W, Sharma R, McDonald S, Mostafavi M, Vertyagina Y, Marrow TJ (2017) In-situ x-ray computed tomography characterisation of 3D fracture evolution and image-based numerical homogenisation of concrete. Cem Concr Compos 75:74–83Google Scholar
  240. 240.
    Yeni YN, Wu B, Huang L, Oravec D (2013) Mechanical loading causes detectable changes in morphometric measures of trabecular structure in human cancellous bone. J Biomechanical Eng-Trans ASME 135 (5):54505Google Scholar
  241. 241.
    Zauel R, Yeni YN, Bay B, Dong XN, Fyhrie DP (2006) Comparison of the linear finite element prediction of deformation and strain of human cancellous bone to 3D digital volume correlation measurements. J Biomechanical Eng-Trans ASME 128(1):1–6Google Scholar
  242. 242.
    Zhu M-L, Zhang Q-H, Lupton C, Tong J (2016) Spatial resolution and measurement uncertainty of strains in bone and bone-cement interface using digital volume correlation. J Mech Behav Biomed Mater 57:269–279Google Scholar
  243. 243.
    Zhuge X, Palenstijn WJ, Batenburg KJ (2016) TVR-DART: a more robust algorithm for discrete tomography from limited projection data with automated gray value estimation. IEEE Trans Image Process 25 (1):455–468MathSciNetGoogle Scholar
  244. 244.
    Zitová B, Flusser J (2003) Image registration methods: a survey. Image Vis Comput 21(11):977–1000Google Scholar

Copyright information

© Society for Experimental Mechanics 2018

Authors and Affiliations

  1. 1.Laboratoire de Mécanique et Technologie (LMT), ENS Paris-Saclay, CNRSUniversity of Paris-SaclayCachanFrance

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