{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T08:16:54Z","timestamp":1772525814802,"version":"3.50.1"},"reference-count":49,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2025,7,11]],"date-time":"2025-07-11T00:00:00Z","timestamp":1752192000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,7,11]],"date-time":"2025-07-11T00:00:00Z","timestamp":1752192000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Adv. Model. and Simul. in Eng. Sci."],"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>The prediction of localized phenomena is still challenging. In particular, running an entirely consistent simulation with experimental observations is delicate. It is proposed that FE simulations on fine meshes be augmented with experimentally measured displacement fields based on the same fine mesh for consistency purposes. A new augmented DIC\/FE framework is proposed to allow fine meshes for both FE simulations and DIC analyses. A test case dealing with a biaxial experiment illustrates the feasibility of augmented analyses to capture strain localization due to damage although none of the two DIC\/FE computations alone would succeed. The effect of the coupling term between DIC and FE analyses is discussed. The present implementation accounts for the experimentally observed localized strain field due to damage.<\/jats:p>","DOI":"10.1186\/s40323-025-00296-4","type":"journal-article","created":{"date-parts":[[2025,7,11]],"date-time":"2025-07-11T07:48:28Z","timestamp":1752220108000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Augmented DIC and FE analyses: a two-field approach to damage localization"],"prefix":"10.1186","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4885-6732","authenticated-orcid":false,"given":"St\u00e9phane","family":"Roux","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5553-0066","authenticated-orcid":false,"given":"Fran\u00e7ois","family":"Hild","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,7,11]]},"reference":[{"key":"296_CR1","doi-asserted-by":"crossref","unstructured":"Sutton MA, McNeill SR, Helm JD, Chao YJ. Advances in two-dimensional and three-dimensional computer vision. In: Rastogi PK (editor) Photomechanics, vol. 77. Topics in applied physics. Berlin: Springer; 2000. pp. 323\u201372.","DOI":"10.1007\/3-540-48800-6_10"},{"key":"296_CR2","volume-title":"Image correlation for shape, motion and deformation measurements: basic concepts, theory and applications","author":"MA Sutton","year":"2009","unstructured":"Sutton MA, Orteu JJ, Schreier H. Image correlation for shape, motion and deformation measurements: basic concepts, theory and applications. New York: Springer; 2009."},{"key":"296_CR3","doi-asserted-by":"crossref","unstructured":"Sutton MA. Computer vision-based, noncontacting deformation measurements in mechanics: a generational transformation. Appl Mechan Rev. 2013;65(AMR\u201313\u20131009): 050802.","DOI":"10.1115\/1.4024984"},{"key":"296_CR4","doi-asserted-by":"crossref","unstructured":"Horn BKP, Schunck BG. Determining optical flow. Artif Intell. 1981;17:185\u2013203.","DOI":"10.1016\/0004-3702(81)90024-2"},{"key":"296_CR5","unstructured":"Lucas BD, Kanade T. An iterative image registration technique with an application to stereo vision. In: 7th international joint conference on artificial intelligence. 1981. pp. 674\u20139."},{"key":"296_CR6","first-page":"297","volume-title":"Handbook of computer vision and applications","author":"EP Simoncelli","year":"1999","unstructured":"Simoncelli EP. Bayesian multi-scale differential optical flow. In: J\u00e4hne B, Haussecker H, Geissler P, editors. Handbook of computer vision and applications, vol. 2. London: Academic Press; 1999. p. 297\u2013422."},{"issue":"3","key":"296_CR7","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1016\/0262-8856(83)90064-1","volume":"1","author":"MA Sutton","year":"1983","unstructured":"Sutton MA, Wolters WJ, Peters WH, Ranson WF, McNeill SR. Determination of displacements using an improved digital correlation method. Image Vis Comput. 1983;1(3):133\u20139.","journal-title":"Image Vis Comput"},{"issue":"25","key":"296_CR8","doi-asserted-by":"publisher","first-page":"232","DOI":"10.1007\/BF02325092","volume":"3","author":"TC Chu","year":"1985","unstructured":"Chu TC, Ranson WF, Sutton MA, Peters WH. Applications of digital-image-correlation techniques to experimental mechanics. Exp Mech. 1985;3(25):232\u201344.","journal-title":"Exp Mech"},{"key":"296_CR9","first-page":"420","volume-title":"12th international conference on experimental mechanics","author":"GB Broggiato","year":"2004","unstructured":"Broggiato GB. Adaptive image correlation technique for full-field strain measurement. In: Pappalettere C, editor. 12th international conference on experimental mechanics. Milan: McGraw Hill; 2004. p. 420\u20131."},{"issue":"34","key":"296_CR10","doi-asserted-by":"publisher","first-page":"7357","DOI":"10.1364\/AO.44.007357","volume":"44","author":"Y Sun","year":"2005","unstructured":"Sun Y, Pang J, Wong C, Su F. Finite-element formulation for a digital image correlation method. Appl Opt. 2005;44(34):7357\u201363.","journal-title":"Appl Opt"},{"key":"296_CR11","doi-asserted-by":"publisher","first-page":"789","DOI":"10.1007\/s11340-006-9824-8","volume":"46","author":"G Besnard","year":"2006","unstructured":"Besnard G, Hild F, Roux S. \u201cFinite-element\u201d displacement fields analysis from digital images: application to Portevin-Le Chatelier bands. Exp Mech. 2006;46:789\u2013803.","journal-title":"Exp Mech"},{"key":"296_CR12","volume-title":"Solutions of ill-posed problems","author":"AN Tikhonov","year":"1977","unstructured":"Tikhonov AN, Arsenin VY. Solutions of ill-posed problems. New York: Wiley; 1977."},{"key":"296_CR13","doi-asserted-by":"crossref","unstructured":"Leclerc H, P\u00e9ri\u00e9 JN, Roux S, Hild F. Integrated digital image correlation for the identification of mechanical properties. In: Gagalowicz A, Philips W (editors) MIRAGE 2009, vol. LNCS 5496. Berlin: Springer; 2009. pp. 161\u201371.","DOI":"10.1007\/978-3-642-01811-4_15"},{"issue":"6","key":"296_CR14","doi-asserted-by":"publisher","first-page":"631","DOI":"10.1002\/nme.2908","volume":"84","author":"J R\u00e9thor\u00e9","year":"2010","unstructured":"R\u00e9thor\u00e9 J. A fully integrated noise robust strategy for the identification of constitutive laws from digital images. Int J Numer Methods Eng. 2010;84(6):631\u201360.","journal-title":"Int J Numer Methods Eng"},{"issue":"7","key":"296_CR15","doi-asserted-by":"publisher","DOI":"10.1115\/1.4030457","volume":"82","author":"D Lindner","year":"2015","unstructured":"Lindner D, Mathieu F, Hild F, Allix O, Ha Minh C, Paulien-Camy O. On the evaluation of stress triaxiality fields in a notched titanium alloy sample via integrated DIC. J Appl Mech. 2015;82(7): 071014.","journal-title":"J Appl Mech"},{"issue":"5","key":"296_CR16","doi-asserted-by":"publisher","first-page":"12450","DOI":"10.1111\/str.12450","volume":"59","author":"J-E Dufour","year":"2023","unstructured":"Dufour J-E, Colantonio G, Bouvet C, P\u00e9ri\u00e9 J-N, Passieux J-C, Serra J. Monitoring structural scale composite specimens in a post-buckling regime: the integrated finite element stereo digital image correlation approach with geometrically non-linear regularization. Strain. 2023;59(5):12450.","journal-title":"Strain"},{"key":"296_CR17","doi-asserted-by":"crossref","unstructured":"Roux S, Hild F. 2.02\u2014Comprehensive full-field measurements via digital image correlation. In: Silberschmidt V (editor) Comprehensive mechanics of materials. 1st ed. Oxford: Elsevier; 2024. pp. 3\u201356.","DOI":"10.1016\/B978-0-323-90646-3.00021-6"},{"key":"296_CR18","doi-asserted-by":"publisher","first-page":"285","DOI":"10.3166\/ejcm.18.285-306","volume":"18","author":"J R\u00e9thor\u00e9","year":"2009","unstructured":"R\u00e9thor\u00e9 J, Roux S, Hild F. An extended and integrated digital image correlation technique applied to the analysis fractured samples. Eur J Comput Mech. 2009;18:285\u2013306.","journal-title":"Eur J Comput Mech"},{"issue":"6","key":"296_CR19","doi-asserted-by":"publisher","first-page":"531","DOI":"10.1002\/nme.4349","volume":"92","author":"JC Passieux","year":"2012","unstructured":"Passieux JC, P\u00e9ri\u00e9 JN. High resolution digital image correlation using proper generalized decomposition: PGD-DIC. Int J Numer Methods Eng. 2012;92(6):531\u201350.","journal-title":"Int J Numer Methods Eng"},{"key":"296_CR20","doi-asserted-by":"publisher","first-page":"330","DOI":"10.1177\/0309324713482457","volume":"48","author":"Z Tomi\u010devi\u0107","year":"2013","unstructured":"Tomi\u010devi\u0107 Z, Hild F, Roux S. Mechanics-aided digital image correlation. J Strain Anal Eng Design. 2013;48:330\u201343.","journal-title":"J Strain Anal Eng Design"},{"key":"296_CR21","unstructured":"Hansen PC. The L-curve and its use in the numerical treatment of inverse problems. In: Johnston P (editor) Computational inverse problems in electrocardiography. Advances in computational bioengineering series. Southampton: WIT Press; 2001. pp. 119\u201342."},{"key":"296_CR22","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijsolstr.2021.111223","volume":"234\u2013235","author":"A Rouwane","year":"2022","unstructured":"Rouwane A, Bouclier R, Passieux J-C, P\u00e9ri\u00e9 J-N. Architecture-driven digital image correlation technique (ADDICT) for the measurement of sub-cellular kinematic fields in speckle-free cellular materials. Int J Solids Struct. 2022;234\u2013235: 111223.","journal-title":"Int J Solids Struct"},{"issue":"4","key":"296_CR23","doi-asserted-by":"publisher","first-page":"479","DOI":"10.1007\/s11340-010-9407-6","volume":"51","author":"H Leclerc","year":"2011","unstructured":"Leclerc H, P\u00e9ri\u00e9 JN, Roux S, Hild F. Voxel-scale digital volume correlation. Exp Mech. 2011;51(4):479\u201390.","journal-title":"Exp Mech"},{"key":"296_CR24","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijmecsci.2023.108127","volume":"246","author":"A Zaplati\u0107","year":"2023","unstructured":"Zaplati\u0107 A, Vrgo\u010d A, Tomi\u010devi\u0107 Z, Hild F. Boundary condition effect on the evaluation of stress triaxiality fields. Int J Mech Sci. 2023;246: 108127.","journal-title":"Int J Mech Sci"},{"issue":"1","key":"296_CR25","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0022-5096(62)90024-8","volume":"10","author":"R Hill","year":"1962","unstructured":"Hill R. Acceleration waves in solids. J Mech Phys Solids. 1962;10(1):1\u201316.","journal-title":"J Mech Phys Solids"},{"key":"296_CR26","doi-asserted-by":"publisher","first-page":"371","DOI":"10.1016\/0022-5096(75)90001-0","volume":"23","author":"JW Rudnicki","year":"1975","unstructured":"Rudnicki JW, Rice JR. Conditions for localization of deformation in pressure-sensitive dilatant materials. J Mech Phys Solids. 1975;23:371\u201394.","journal-title":"J Mech Phys Solids"},{"key":"296_CR27","unstructured":"Rice JR. In: Koiter WT (editor) The localization of plastic deformations, pp. 207\u201320. Amsterdam: North-Holland; 1976."},{"issue":"3","key":"296_CR28","doi-asserted-by":"publisher","first-page":"327","DOI":"10.1002\/nme.1620170303","volume":"17","author":"S Pietruszczak","year":"1981","unstructured":"Pietruszczak S, Mr\u00f3z Z. Finite element analysis of deformation of strain-softening materials. Int J Numer Methods Eng. 1981;17(3):327\u201334.","journal-title":"Int J Numer Methods Eng"},{"issue":"3","key":"296_CR29","first-page":"381","volume":"111","author":"ZP Ba\u017eant","year":"1985","unstructured":"Ba\u017eant ZP, Belytschko TB. Wave propagation in a strain-softening bar:exact solution. J Eng Mech. 1985;111(3):381\u20139.","journal-title":"J Eng Mech"},{"key":"296_CR30","unstructured":"Hild F, Leclerc H, Roux S. Computer-implemented method for identifying mechanical properties by coupled correlation of images and mechanical modelling. Patent family WO2019166085A1, US2021003389A1, ES2911999T3, EP3759687A1. 2019. patents.google.com\/patent\/WO2019166085A1\/en."},{"key":"296_CR31","unstructured":"Hild F, Roux S. Digital image correlation. In: Hack E, editor. Rastogi P. Optical methods for solid mechanics. A full-field approach. Weinheim: Wiley-VCH; 2012. p. 183\u2013228."},{"key":"296_CR32","doi-asserted-by":"publisher","first-page":"160","DOI":"10.1111\/j.1475-1305.2008.00592.x","volume":"45","author":"YQ Wang","year":"2009","unstructured":"Wang YQ, Sutton MA, Bruck HA, Schreier HW. Quantitative error assessment in pattern matching: effects of intensity pattern noise, interpolation, strain and image contrast on motion measurements. Strain. 2009;45:160\u201378.","journal-title":"Strain"},{"issue":"9","key":"296_CR33","doi-asserted-by":"publisher","first-page":"1503","DOI":"10.1007\/s11340-012-9603-7","volume":"52","author":"F Hild","year":"2012","unstructured":"Hild F, Roux S. Comparison of local and global approaches to digital image correlation. Exper Mech. 2012;52(9):1503\u201319.","journal-title":"Exper Mech"},{"issue":"13\/16","key":"296_CR34","doi-asserted-by":"publisher","first-page":"1968","DOI":"10.1016\/j.cma.2006.10.005","volume":"196","author":"P Feissel","year":"2007","unstructured":"Feissel P, Allix O. Modified constitutive relation error identification strategy for transient dynamics with corrupted data: the elastic case. Comput Meth Appl Mech Eng. 2007;196(13\/16):1968\u201383.","journal-title":"Comput Meth Appl Mech Eng"},{"key":"296_CR35","doi-asserted-by":"publisher","first-page":"228","DOI":"10.1007\/978-3-662-02761-5","volume-title":"A course on damage mechanics","author":"J Lemaitre","year":"1992","unstructured":"Lemaitre J. A course on damage mechanics. Berlin: Springer; 1992. p. 228."},{"issue":"9","key":"296_CR36","doi-asserted-by":"publisher","first-page":"805","DOI":"10.2514\/8.3664","volume":"23","author":"MJ Turner","year":"1956","unstructured":"Turner MJ, Clough RW, Martin HC, Topp LJ. Stiffness and deflection analysis of complex structures. J Aeronaut Sci. 1956;23(9):805\u201323.","journal-title":"J Aeronaut Sci"},{"issue":"2","key":"296_CR37","doi-asserted-by":"publisher","first-page":"380","DOI":"10.2514\/3.2874","volume":"3","author":"RJ Guyan","year":"1965","unstructured":"Guyan RJ. Reduction of stiffness and mass matrices. AIAA J. 1965;3(2):380\u2013380.","journal-title":"AIAA J"},{"issue":"2","key":"296_CR38","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1002\/nme.1057","volume":"61","author":"D Claire","year":"2004","unstructured":"Claire D, Hild F, Roux S. A finite element formulation to identify damage fields: the equilibrium gap method. Int J Num Methods Eng. 2004;61(2):189\u2013208.","journal-title":"Int J Num Methods Eng"},{"issue":"2","key":"296_CR39","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1177\/1056789506064940","volume":"16","author":"D Claire","year":"2007","unstructured":"Claire D, Hild F, Roux S. Identification of a damage law by using full-field displacement measurements. Int J Damage Mech. 2007;16(2):179\u201397.","journal-title":"Int J Damage Mech"},{"issue":"4","key":"296_CR40","doi-asserted-by":"publisher","first-page":"495","DOI":"10.1007\/s11340-007-9103-3","volume":"48","author":"S Roux","year":"2008","unstructured":"Roux S, Hild F. Digital image mechanical identification (DIMI). Exp Mech. 2008;48(4):495\u2013508.","journal-title":"Exp Mech"},{"issue":"4","key":"296_CR41","doi-asserted-by":"publisher","first-page":"381","DOI":"10.1007\/s11340-008-9148-y","volume":"48","author":"S Avril","year":"2008","unstructured":"Avril S, Bonnet M, Bretelle AS, Gr\u00e9diac M, Hild F, Ienny P, Latourte F, Lemosse D, Pagano S, Pagnacco E, Pierron F. Overview of identification methods of mechanical parameters based on full-field measurements. Exp Mech. 2008;48(4):381\u2013402.","journal-title":"Exp Mech"},{"issue":"10","key":"296_CR42","doi-asserted-by":"publisher","first-page":"1512","DOI":"10.1061\/(ASCE)0733-9399(1987)113:10(1512)","volume":"113","author":"G Pijaudier-Cabot","year":"1987","unstructured":"Pijaudier-Cabot G, Bazant ZP. Nonlocal damage theory. ASCE J Eng Mech. 1987;113(10):1512\u201333.","journal-title":"ASCE J Eng Mech"},{"issue":"2","key":"296_CR43","first-page":"345","volume":"115","author":"J Mazars","year":"1989","unstructured":"Mazars J, Pijaudier-Cabot G. Continuum damage theory, application to concrete. J Eng Mech. 1989;115(2):345\u201365.","journal-title":"J Eng Mech"},{"key":"296_CR44","doi-asserted-by":"publisher","first-page":"3391","DOI":"10.1002\/(SICI)1097-0207(19961015)39:19<3391::AID-NME7>3.0.CO;2-D","volume":"39","author":"R Peerlings","year":"1996","unstructured":"Peerlings R, Borst R, Brekelmans W, Vree J. Gradient-enhanced damage for quasi-brittle materials. Int J Num Methods Eng. 1996;39:3391\u2013403.","journal-title":"Int J Num Methods Eng"},{"key":"296_CR45","doi-asserted-by":"publisher","first-page":"1319","DOI":"10.1016\/S0022-5096(98)00034-9","volume":"46","author":"GA Francfort","year":"1998","unstructured":"Francfort GA, Marigo JJ. Revisiting brittle fracture as an energy minimization problem. J Mech Phys Solids. 1998;46:1319\u201342.","journal-title":"J Mech Phys Solids"},{"key":"296_CR46","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.87.045501","volume":"87","author":"A Karma","year":"2001","unstructured":"Karma A, Kessler DA, Levine H. Phase-field model of mode III dynamic fracture. Phys Rev Lett. 2001;87: 045501.","journal-title":"Phys Rev Lett"},{"key":"296_CR47","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1007\/s10659-007-9107-3","volume":"91","author":"B Bourdin","year":"2008","unstructured":"Bourdin B, Francfort GA, Marigo JJ. The variational approach to fracture. J Elast. 2008;91:5\u2013148.","journal-title":"J Elast"},{"issue":"10","key":"296_CR48","doi-asserted-by":"publisher","first-page":"1273","DOI":"10.1002\/nme.2861","volume":"83","author":"C Miehe","year":"2010","unstructured":"Miehe C, Welschinger F, Hofacker M. Thermodynamically consistent phase-field models of fracture: variational principles and multi-field FE implementations. Int J Num Methods Eng. 2010;83(10):1273\u2013311.","journal-title":"Int J Num Methods Eng"},{"key":"296_CR49","doi-asserted-by":"publisher","first-page":"383","DOI":"10.1007\/s00466-014-1109-y","volume":"55","author":"M Ambati","year":"2015","unstructured":"Ambati M, Gerasimov T, De Lorenzis L. A review on phase-field models of brittle fracture and a new fast hybrid formulation. Comput Mech. 2015;55:383\u2013405.","journal-title":"Comput Mech"}],"container-title":["Advanced Modeling and Simulation in Engineering Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s40323-025-00296-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1186\/s40323-025-00296-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s40323-025-00296-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,7]],"date-time":"2025-09-07T05:06:43Z","timestamp":1757221603000},"score":1,"resource":{"primary":{"URL":"https:\/\/amses-journal.springeropen.com\/articles\/10.1186\/s40323-025-00296-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7,11]]},"references-count":49,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2025,12]]}},"alternative-id":["296"],"URL":"https:\/\/doi.org\/10.1186\/s40323-025-00296-4","relation":{},"ISSN":["2213-7467"],"issn-type":[{"value":"2213-7467","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,7,11]]},"assertion":[{"value":"6 June 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 May 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 July 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Not applicable.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethics approval and consent to participate"}},{"value":"Not applicable.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for publication"}},{"value":"Not applicable.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Materials availability"}},{"value":"Not available.","order":5,"name":"Ethics","group":{"name":"EthicsHeading","label":"Code availability"}},{"value":"The authors have no conflict of interest to declare.","order":6,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"16"}}