Abstract
Since the turn of the century experimental solid mechanics has undergone major changes with the generalized use of images. The number of acquired data has literally exploded and one of today’s challenges is related to the saturation of mining procedures through such big data sets. With respect to digital image/volume correlation one of tomorrow’s pathways is to better control and master this data flow with procedures that are optimized for extracting the sought information with minimum uncertainties and maximum robustness. In this paper emphasis is put on various hierarchical identification procedures. Based on such structures a posteriori model/data reductions are performed in order to ease and make the exploitation of the experimental information far more efficient. Some possibilities related to other model order reduction techniques like the proper generalized decomposition are discussed and new opportunities are sketched.
Similar content being viewed by others
References
Sutton M, Orteu J, Schreier H (2009) Image correlation for shape, motion and deformation measurements: basic concepts, theory and applications. Springer, New York
Dufour JE, Hild F, Roux S (2015) Shape, displacement and mechanical properties from isogeometric multiview stereocorrelation. J Strain Anal 50(7):470
Baruchel J, Buffière J, Maire E, Merle P, Peix G (eds) (2000) X-Ray tomography in material sciences. Hermès Science, Paris
Maire E, Withers PJ (2014) Quantitative X-ray tomography. Int Mat Rev 59(1):1
Helfen L, Baumbach T, Mikulfk 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):071915
Helfen L, Myagotin A, Rack A, Pernot P, Mikulfk P, Di Michiel M, Baumbach T (2007) Synchrotron-radiation computed laminography for high-resolution three-dimensional imaging of flat devices. Phys Stat Sol 204:2760–2765
Benoit A, Guérard S, Gillet B, Guillot G, Hild F, Mitton D, Périé J, Roux S (2009) 3D analysis from micro-MRI during in situ compression on cancellous bone. J Biomech 42:2381–2386
Huang D, Swanson E, Lin C, Schuman J, Stinson W, Chang W, Hee M, Flotte T, Gregory K, Puliafito C, Fujimoto J (1991) Optical coherence tomography. Science 254(5035):1178–1181
Grédiac M, Hild F (eds) (2012) Full-field measurements and identification in solid mechanics. ISTE/Wiley, London
Oden J, Belytschko T, Fish J, Hughes T, Johnson C, Keyes D, Laub A, Petzold L, Srolovitz D, Yip S (2006) Simulation-based engineering sciences. Final report, NFS. www.nsf.gov/pubs/reports/sbes_final_report.pdf)
Carpiuc A (2015) Innovative tests for characterizing mixed-mode fracture of concrete: from pre-defined to interactive and hybrid tests. Ph.D. Thesis
Fayolle X, Calloch S, Hild F (2007) Controlling testing machines with digital image correlation. Exp Tech 31(3):57–63
Durif E, Réthoré J, Combescure A, Fregonese M, Chaudet P (2012) Controlling stress intensity factors during a fatigue crack propagation using digital image correlation and a load shedding procedure. Exp Mech 52:1021–1031
Fayolle X, Hild F (2013) Controlling stress intensity factor histories with digital images. Exp Mech 54:305–314
Darema F (2004) Dynamic data driven applications systems: a new paradigm for application simulations and measurements. Springer, Berlin
Sutton M (2013) Computer vision-based, noncontacting deformation measurements in mechanics: a generational transformation. Appl Mech Rev 65:050802
Sutton M, Hild F (2015) Recent advances and perspectives in digital image correlation. Exp Mech 55(1):1–8
Sutton MA, Li N, Joy D, Reynolds AP, Li X (2007) Scanning electron microscopy for quantitative small and large deformation measurements part i: sem imaging at magnifications from 200 to 10,000. Exp Mech 47(6):775–787
Teyssedre H, Roux S, Régnier G, Tracz A (2011) Filtering out slow-scan drifts in atomic force microscopy images. J Strain Anal 46(5):361–367
Han K, Ciccotti M, Roux S (2010) Measuring nanoscale stress intensity factors with an atomic force microscope. EuroPhys Lett 89(6):66003
Neggers J, Hoefnagels J, Hild F, Roux S, Geers M (2014) Direct stress-strain measurements from bulged membranes using topography image correlation. Exp Mech 54(5):717–727
Maynadier A, Poncelet M, Lavernhe-Taillard K, Roux S (2011) One-shot measurement of thermal and kinematic fields: infra-red image correlation (IRIC). Exp Mech 52(3):241–255
Hild F, Roux S (2012) Digital image correlation. Wiley, Weinheim
Réthoré J, Roux S, Hild F (2007) From pictures to extended finite elements: extended digital image correlation (X-DIC). C R Mécanique 335:131–137
Hild F, Roux S (2012) Comparison of local and global approaches to digital image correlation. Exp Mech 52(9):1503–1519
Tarantola A (1987) Inverse problems theory. Methods for data fitting and model parameter estimation. Elsevier, Southampton
Kaipio J, Somersalo E (2006) Statistical and computational inverse problems. Springer, New York
Mottershead J, Link M, Friswell M (2011) The sensitivity method in finite element model updating: a tutorial. Mech Syst Signal Proc 25(7):2275–2296
Leclerc H, Périé J, Roux S, Hild F (2009) Integrated digital image correlation for the identification of mechanical properties. Springer, Berlin, pp 161–171
Réthoré J (2010) A fully integrated noise robust strategy for the identification of constitutive laws from digital images. Int J Num Methods Eng 84(6):631–660
Mathieu F, Leclerc H, Hild F, Roux S (2015) Estimation of elastoplastic parameters via weighted FEMU and integrated-DIC. Exp Mech 55(1):105–119
Neggers J, Hoefnagels J, Geers M, Hild F, Roux S (2015) Time-resolved integrated digital image correlation. Int J Num Methods Eng 203(3):157–182
Hild F, Bouterf A, Chamoin L, Mathieu F, Neggers J, Pled F, Tomičević Z, Roux S (2016) Toward 4D mechanical correlation. Adv Mech Simul Eng Sci 47:495–503
Tikhonov A, Arsenin V (1977) Solutions of ill-posed problems. Wiley, New York
Lindner D, Mathieu F, Hild F, Allix O, Ha Minh C, Paulien-Camy O (2015) On the evaluation of stress triaxiality fields in a notched titanium alloy sample via integrated DIC. J Appl Mech 82(7):071014
Bertin M, Hild F, Roux S, Mathieu F, Leclerc H, Aimedieu P (2016) Integrated digital image correlation applied to elasto-plastic identification in a biaxial experiment. J Strain Anal 51(2):118–131
Chatterjee A (2000) An introduction to the proper orthogonal decomposition. Curr Sci 78(7):808
Maday Y, Ronquist EM (2004) The reduced basis element method: application to a thermal fin problem. SIAM J Sci Comput 26(1):240
Ladevèze P (2014) Separated representations and PGD-based model reduction. Springer, New York, pp 91–152
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 Methods Eng 17(4):327
Grepl M, Maday Y, Nguyen N, Patera A (2007) ESAIM. Modélisation mathématique et analyse numérique 41(3):575
Barrault M, Maday Y, Nguyen N, Patera A (2004) An ‘empirical interpolation’ method: application to efficient reduced-basis discretization o f partial differential equations. C R Acad Sci 339:667
Chaturentabut S, Sorensen D (2010) Nonlinear model reduction via discrete empirical interpolation. Soc Ind Appl Math 32(5):2737
Ryckelynck D (2009) Hyper-reduction of mechanical models involving internal variables. Int J Numer Methods Eng 77(1):75
Farhat C, Avery P, Chapman T, Cortial J (2014) Dimensional reduction of nonlinear finite element dynamic models with finite rotations and energy-based mesh sampling and weighting for computational efficiency. Int J Numer Methods Eng 98(9):625. doi:10.1002/nme.4668
Néron D, Ladevèze P (2012) In: ASME (ed) Proceedings of the 11th Biennial conference on engineering systems design and analysis (ESDA 2012)
Ladevèze P (1999) Nonlinear computational structural mechanics: new approaches and non-incremental methods of calculation. Mechanical engineering series. Springer, New York
Néron D, Boucard PA, Relun N (2015) Time-space PGD for the rapid solution of 3D nonlinear parametrized problems in the many-query context. Int J Numer Methods Eng 103(4):275
Relun N, Néron D, Boucard PA (2013) A model reduction technique based on the PGD for elastic-viscoplastic computational analysis. Comput Mech 51:83
Allix O, Vidal P (2002) A new multi-solution approach suitable for structural identification problems. Comput Methods Appl Mech Eng 191(1):2727
Mahnken R, Stein E (1996) Parameter identification for viscoplastic models based on analytical derivatives of a least-squares functional and stability investigations. Int J Plast 12(4):451
Constantinescu A, Tardieu N (2001) On the identification of elastoviscoplastic constitutive laws from indentation tests. Inverse Probl Eng 9:19
Nadal E, Chinesta F, Diez P, Fuenmayor F, Deniac F (2015) Real time parameter identification and solution reconstruction from experimental data using the proper generalized decomposition. Comput Methods Appl Mech Eng 296:113
Vitse M, Néron D, Boucard PA (2014) Virtual charts of solutions for parametrized nonlinear equations. Comput Mech 54(6):1529
Gomes Perini L, Passieux JC, Périé JN (2014) A multigrid PGD-based algorithm for volumetric displacement fields measurements. Strain 50(4):355
Passieux JC, Périé JN (2012) High resolution digital image correlation using proper generalized decomposition: PGD-DIC. Int J Num Methods Eng 92(6):531
Besnard G, Leclerc H, Roux S, Hild F (2012) Analysis of image series through global digital image correlation. J Strain Anal 47(4):214
J. Neggers, F. Mathieu, S. Roux, F. Hild, in Photomechanics (2015)
Neggers J, Mathieu F, Roux S, Hild F (2017) Reducing full-field identification cost by using Quasi-Newton methods. Springer, New York, pp 135–140
Kononen J, Bubendorf L, Kallionimeni A, Bärlund M, Schraml P, Leighton S, Torhorst J, Mihatsch MJ, Sauter G, Kallionimeni OP (1998) Tissue microarrays for high-throughput molecular profiling of tumor specimens. Nat Med 4(7):844–847
Sundberg SA (2000) High-throughput and ultra-high-throughput screening: solution-and cell-based approaches. Curr Opin Biotechnol 11(1):47
Corbett PT, Leclaire J, Vial L, West KR, Wietor JL, Sanders JK, Otto S (2006) Dynamic combinatorial chemistry. Chem Rev 106(9):3652–3711
Sarikaya M, Tamerler C, Jen AKY, Schulten K, Baneyx F (2003) Molecular biomimetics: nanotechnology through biology. Nat Mater 2(9):577–585
Bertin MBR, Hild F, Roux S (2016) Optimization of a cruciform specimen geometry for the identification of constitutive parameters based upon full-field measurements. Strain 52(4):307–323
Allix O, Feissel P, Nguyen H (2005) Identification strategy in the presence of corrupted measurements. Eng Comput 22(5–6):487–504
Beaubier B, Dufour J, Hild F, Roux S, Lavernhe-Taillard S, Lavernhe-Taillard K (2014) AD-based calibration and shape measurement with stereoDIC. Exp Mech 54(3):329
Dufour JE, Beaubier B, Hild F, Roux S (2015) CAD-based displacement measurements with stereo-DIC. Exp Mech 55(9):1657
Limodin N, Réthoré J, Adrien J, Buffière J, 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
Dufour J, Hild F, Roux S (2014) Integrated digital image correlation for the evaluation and correction of optical distortions. Opt Lasers Eng 56:121–133
Leclerc H, Roux S, Hild F, Leclerc H, Roux S, Hild F (2015) Projection savings in CT-based digital volume correlation. Exp Mech 55(1):275–287
Taillandier-Thomas T, Roux S, Hild F (2016) Soft route to 4D tomography. Phys Rev Lett 117(2):025501
Neggers J, Mathieu F, Hild F, Roux S, Swiergiel N (2017) Improving full-field identification using progressive model enrichments. Int J Solids Struct 203:157–182
Hild F, Bouterf A, Roux S (2015) Damage measurements via DIC. Int J Fract 191(1):77
Hild F, Raka B, Baudequin M, Roux S, Cantelaube F (2002) Multiscale displacement field measurements of compressed mineral-wool samples by digital image correlation. Appl Opt 41(32):6815–6828
Peherstorfer B, Willcox K (2015) Dynamic data-driven reduced-order models. Comput Methods Appl Mech Eng 291:21
Kirchdoerfer T, Ortiz M (2016) Data-driven computational mechanics. Comput Methods Appl Mech Eng 304:81–101
Ibanez R, Abisset-Chavanne E, Aguado JV, Gonzalez D, Cueto E, Chinesta F (2017) kPCA-Based parametric solutions within the PGD framework. Arch Comput Methods Eng. doi:10.1007/s11831-016-9173-4
Germain P, Nguyen Q, Suquet P (1983) Continuum thermodynamics. J Appl Mech 50:1010
Lemaitre J, Chaboche J (1990) Mechanics of solid materials. Cambridge University Press, Cambridge
Acknowledgements
It is a pleasure to acknowledge the support of BPI France within the “DICCIT” project.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
On behalf of all authors, the corresponding author states that there is no conflict of interest.
Rights and permissions
About this article
Cite this article
Neggers, J., Allix, O., Hild, F. et al. Big Data in Experimental Mechanics and Model Order Reduction: Today’s Challenges and Tomorrow’s Opportunities. Arch Computat Methods Eng 25, 143–164 (2018). https://doi.org/10.1007/s11831-017-9234-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11831-017-9234-3