Abstract
A combined experimental-numerical framework is presented in order to validate computations at the microscale. It is illustrated for a flat specimen with two holes, which is made of cast iron and imaged via in situ synchrotron laminography at micrometer resolution during a tensile test. The region in the reconstructed volume between the two holes is analyzed via Digital Volume Correlation (DVC) to measure displacement fields. Finite Element (FE) simulations, whose mesh is made consistent with the studied material microstructure, are driven by measured Dirichlet boundary conditions. Damage levels and gray level residuals for DVC measurements and FE simulations are assessed for validation purposes.
References
Kachanov, L.: Bull. SSR Acad. Sci. Division of Technical Sciences (in Russian) 8, 26 (1958)
Rabotnov, Y.: On the Equations of State for Creep, pp. 307–315. McMillan, New York, USA (1963)
Lemaitre, J.: A Course on Damage Mechanics. Springer-Verlag, Berlin (1992)
Cao, T.S., Maire, E., Verdu, C., Bobadilla, C., Lasne, P., Montmitonnet, P., Bouchard, P.O.: Comput. Mat. Sci. 84, 175 (2014)
Cao, T.S., Bobadilla, C., Montmitonnet, P., Bouchard, P.O.: J. Mat. Proc. Technol. 216, 385 (2015)
Gurson, A.: ASME J. Eng. Mat. Technol. 99, 2 (1977)
Needleman, A., Tvergaard, V.: J. Mech. Phys. Solids 32(6), 461 (1984)
Geers, M., De Borst, R., Peijs, T.: Compos. Sci. Tech. 59, 1569 (1999)
Claire, D., Hild, F., Roux, S.: C. R. Mécanique 330, 729 (2002)
Roux, S., Hild, F.: Exp. Mech. 48(4), 495 (2008)
Babout, L., Bréchet, Y., Maire, E., Fougères, R.: Acta Mat. 52(15), 4517 (2004)
Bouchard, P.O., Bourgeon, L., Lachapèle, H., Maire, E., Verdu, C., Forestier, R., Logé, R.: Mat. Sci. Eng. A 496(1–2), 223 (2008)
Ueda, T., Helfen, L., Morgeneyer, T.F.: Acta Mat. 78, 254 (2014)
Hannard, F., Pardoen, T., Maire, E., Le Bourlot, C., Mokso, R., Simar, A.: Acta Mat. 103, 558 (2016)
Morgeneyer, T., Taillandier-Thomas, T., Buljac, A., Helfen, L., Hild, F.: J. Mech. Phys. Solids 96, 550 (2016)
Morgeneyer, T., Besson, J., Proudhon, H., Starink, M., Sinclair, I.: Acta Mat. 57(13), 3902 (2009)
Tang, S., Kopacz, A.M., Chan O’Keeffe, S., Olson, G.B., Liu, W.K.: J. Mech. Phys. Solids 61(11), 2108 (2013)
Dong, M.J., Prioul, C., François, D.: Metall. Mat. Trans. A 28(11), 2245 (1997)
Hütter, G., Zybell, L., Kuna, M.: Eng. Fract. Mech. 144, 118 (2015)
Tomičević, Z., Kodvanj, J., Hild, F.: Eur. J. Mech. A/Solids 59, 140 (2016)
Zhang, K., Bai, J., François, D.: Int. J. Solids Struct. 36(23), 3407 (1999)
Bonora, N., Ruggiero, A.: Int. J. Solids Struct. 42(5–6), 1401 (2005)
Hütter, G., Zybell, L., Mühlich, U., Kuna, M.: Comput. Mat. Sci. 80, 61 (2013)
Hütter, G., Zybell, L., Kuna, M.: Int. J. Solids Struct. 51(3–4), 839 (2014)
Buljac, A., Shakoor, M., Neggers, J., Helfen, L., Bernacki, M., Bouchard, P.O., Morgeneyer, T.F., Hild, F.: Comput. Mech. 59(3), 419 (2017)
Helfen, L., Myagotin, A., Pernot, P., DiMichiel, M., Mikulík, P., Berthold, A., Baumbach, T.: Nucl. Inst. Meth. Phys. Res. B 563, 163 (2006)
Helfen, L., Morgeneyer, T., Xu, F., Mavrogordato, M., Sinclair, I., Schillinger, B., Baumbach, T.: Int. J. Mat. Res. 2012(2), 170 (2012)
Maurel, V., Helfen, L., N’Guyen, F., Köster, A., Di Michiel, M., Baumbach, T., Morgeneyer, T.: Scripta Mat. 66, 471 (2012)
Bull, D., Spearing, S., Sinclair, I., Helfen, L.: Compos. Part A 52, 62 (2013)
Reischig, P., Helfen, L., Wallert, A., Baumbach, T., Dik, J.: Appl. Phys. A 111, 983 (2013)
Bay, B., Smith, T., Fyhrie, D., Saad, M.: Exp. Mech. 39, 217 (1999)
Smith, T., Bay, B., Rashid, M.: Exp. Mech. 42(3), 272 (2002)
Bornert, M., Chaix, J., Doumalin, P., Dupré, J., Fournel, T., Jeulin, D., Maire, E., Moreaud, M., Moulinec, H.: Inst. Mes. Métrol. 4, 43 (2004)
Verhulp, E., van Rietbergen, B., Huiskes, R.: J. Biomech. 37(9), 1313 (2004)
Roux, S., Hild, F., Viot, P., Bernard, D.: Comp. Part A 39(8), 1253 (2008)
Rannou, J., Limodin, N., Réthoré, J., Gravouil, A., Ludwig, W., Baïetto, M., Buffière, J., Combescure, A., Hild, F., Roux, S.: Comp. Meth. Appl. Mech. Eng. 199, 1307 (2010)
Bouterf, A., Roux, S., Hild, F., Adrien, J., Maire, E.: Strain 50(5), 444 (2014)
Hild, F., Bouterf, A., Chamoin, L., Mathieu, F., Neggers, J., Pled, F., Tomičević, Z., Roux, S.: Adv. Mech. Simul. Eng. Sci. 3(1), 1 (2016)
Zhang, Y., Bajaj, C., Sohn, B.S.: Comput. Meth. Appl. Mech. Eng. 194(48–49), 5083 (2005)
Young, P.G., Beresford-West, T.B.H., Coward, S.R.L., Notarberardino, B., Walker, B., Abdul-Aziz, A.: Phil. Trans. A 366(1878), 3155 (2008)
Osher, S., Sethian, J.A.: J. Comput. Phys. 79(1), 12 (1988)
Kimmel, R., Shaked, D., Kiryati, N., Bruckstein, A.M.: Comput. Vis. Image Underst. 62(3), 382 (1995)
Sukumar, N., Chopp, D., Moës, N., Belytschko, T.: Comput. Meth. Appl. Mech. Eng. 190(46–47), 6183 (2001)
Roux, E., Bernacki, M., Bouchard, P.O.: Comput. Mat. Sci. 68, 32 (2013)
Quan, D.L., Toulorge, T., Marchandise, E., Remacle, J.F., Bricteux, G.: Comp. Meth. Appl. Mech. Eng. 268, 65 (2014)
Shakoor, M., Scholtes, B., Bouchard, P.O., Bernacki, M.: Appl. Math. Model. 39(23–24), 7291 (2015)
Shakoor, M., Bouchard, P.O., Bernacki, M.: Int. J. Num. Meth. Eng. 109(4), 555 (2017)
Weck, A., Wilkinson, D.: Acta Materialia 56(8), 1774 (2008)
Myagotin, A., Voropaev, A., Helfen, L., Hänschke, D., Baumbach, T., Trans, I.E.E.E.: Image Process. 22(12), 5348 (2013)
Vogelgesang, M., Farago, T., Morgeneyer, T.F., Helfen, L., dos Santos Rolo, T., Myagotin, A., Baumbach, T.: J. Synchrotron Rad. 23, 1254 (2016)
Besnard, G., Hild, F., Roux, S.: Exp. Mech. 46, 789 (2006)
Hild, F., Roux, S.: Exp. Mech. 52(9), 1503 (2012)
Xu, F., Helfen, L., Baumbach, T., Suhonen, H.: Optics Exp. 20, 794 (2012)
Morgeneyer, T., Helfen, L., Mubarak, H., Hild, F.: Exp. Mech. 53(4), 543 (2013)
Limodin, N., Rthor, J., Adrien, J., Buffire, J., Hild, F., Roux, S.: Exp. Mech. 51(6), 959 (2011)
Leclerc, H., Périé, J., Hild, F., Roux, S.: Mech. Indust. 13, 361 (2012)
Roux, E., Shakoor, M., Bernacki, M., Bouchard, P.O.: Model. Simul. Mat. Sci. Eng. 22(7), 075001 (2014)
Shakoor, M., Bernacki, M., Bouchard, P.O.: Eng. Fract. Mech. 147, 398 (2015)
Schindelin, J., Arganda-Carreras, I., Frise, E., Kaynig, V., Longair, M., Pietzsch, T., Preibisch, S., Rueden, C., Saalfeld, S., Schmid, B., Tinevez, J.Y., White, D.J., Hartenstein, V., Eliceiri, K., Tomancak, P., Cardona, A.: Nature Meth. 9(7), 676 (2012)
Schneider, C.A., Rasband, W.S., Eliceiri, K.W.: Nature Meth. 9(7), 671 (2012)
Boffi, D., Brezzi, F., Demkowicz, L.F., Durán, R.G., Falk, R.S., Fortin, M.: Mixed Finite Elements, Compatibility Conditions, and Applications. Lecture Notes in Mathematics, vol. 1939. Springer, Berlin (2008)
Wagoner, R.H., Chenot, J.L.: Metal Forming Analysis. Cambridge University Press (2001)
Leclerc, H., Neggers, J., Mathieu, F., Roux, S., Hild, F.: Correli 3.0. IDDN.FR.001.520008.000.S.P.2015.000.31500, Agence pour la Protection des Programmes, Paris, France (2015)
Acknowledgements
This work was performed within the COMINSIDE project funded by the French Agence Nationale de la Recherche (ANR-14-CE07-0034-02 grant). We also acknowledge the European Synchrotron Radiation Facility for provision of beamtime at beamline ID15, experiment ME 1366. It is also a pleasure to acknowledge the support of BPI France (“DICCIT” project), and of the Carnot M.I.N.E.S institute (“CORTEX” project). M. Kuna and L. Zybell from IMFD, TU Freiberg, are thanked for materials supply and machining as well as for scientific discussions.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this chapter
Cite this chapter
Buljac, A. et al. (2018). Experimental-Numerical Validation Framework for Micromechanical Simulations. In: Sorić, J., Wriggers, P., Allix, O. (eds) Multiscale Modeling of Heterogeneous Structures. Lecture Notes in Applied and Computational Mechanics, vol 86. Springer, Cham. https://doi.org/10.1007/978-3-319-65463-8_8
Download citation
DOI: https://doi.org/10.1007/978-3-319-65463-8_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-65462-1
Online ISBN: 978-3-319-65463-8
eBook Packages: EngineeringEngineering (R0)