Coupled systems mechanics

  • 제11권2호
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  • Pages.133-149
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  • 2022
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  • 2234-2184(pISSN)
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  • 2234-2192(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

DOI QR Code

Identifiability of Ludwik's law parameters depending on the sample geometry via inverse identification procedure

  • Zaplatic, Andrija (Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb) ;
  • Tomicevic, Zvonimir (Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb) ;
  • Cakmak, Damjan (Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb) ;
  • Hild, Francois (Univervisity Paris-Saclay, CentraleSupelec, ENS Paris-Saclay, CNRS, LMPS-Laboratoire de Mecanique Paris-Saclay)
  • 투고 : 2021.07.30
  • 심사 : 2021.11.22
  • 발행 : 2022.04.25
⟨ 이전 논문 다음 논문 ⟩

초록

The accurate prediction of elastoplasticity under prescribed workloads is essential in the optimization of engineering structures. Mechanical experiments are carried out with the goal of obtaining reliable sets of material parameters for a chosen constitutive law via inverse identification. In this work, two sample geometries made of high strength steel plates were evaluated to determine the optimal configuration for the identification of Ludwik's nonlinear isotropic hardening law. Finite element model updating(FEMU) was used to calibrate the material parameters. FEMU computes the parameter changes based on the Hessian matrix, and the sensitivity fields that report changes of computed fields with respect to material parameter changes. A sensitivity analysis was performed to determine the influence of the sample geometry on parameter identifiability. It was concluded that the sample with thinned gauge region with a large curvature radius provided more reliable material parameters.

키워드

과제정보

This work was performed within the FULLINSPECT project supported by the Croatian Science Foundation (UIP-2019-04-5460 Grant).

참고문헌

  1. Ahmed, S.T., Aguib, S., Toufik, T., Noureddine, C. and Ahmed, C. (2019), "Effects of the geometrical parameters of the core on the mechanical behavior of sandwich honeycomb panel", Couple. Syst. Mech., 8(6), 473-488. https://doi.org/10.12989/csm.2019.8.6.473.
  2. Bertin, M., Hild, F. and 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. https://doi.org/10.1111/str.12178.
  3. Bertin, M., Hild, F. and Roux, S. (2017), "On the identifiability of Hill-1948 plasticity model with a single biaxial test on very thin sheet", Strain, 53(5), e12233, https://doi.org/10.1111/str.12233.
  4. Bertin, M., Hild, F., Roux, S., Mathieu, F., Leclerc, H. and Aimedieu, P. (2016), "Integrated digital image correlation applied to elastoplastic identification in a biaxial experiment", J. Strain Anal. Eng. Des., 51(2), 118-131. https://doi.org/10.1177/0309324715614759.
  5. Besnard, G., Hild, F. and Roux, S. (2006), ""Finite-element" displacement fields analysis from digital images: Application to Portevin-Le Chatelier bands", Exp. Mech., 46(6), 789-803. https://doi.org/10.1007/s11340-006-9824-8.
  6. Claire, D., Hild, F. and Roux, S. (2004), "A finite element formulation to identify damage fields: The equilibrium gap method", Int. J. Numer. Meth. Eng., 61(2), 189-208. https://doi.org/10.1002/nme.1057.
  7. Cooreman, S., Lecompte, D., Sol, H., Vantomme, J. and Debruyne, D. (2008), "Identification of mechanical material behavior through inverse modeling and DIC", Conf. Proc. Soc. Exp. Mech. Ser., 65(4), 421-433. https://doi.org/10.1007/s11340-007-9094-0.
  8. Geymonat, G., Hild, F. and Pagano S. (2002), "Identification of elastic parameters by displacement field measurement", Comptes Rendus Mecanique, 330, 403-408. https://doi.org/10.1016/S1631-0721(02)01476-6.
  9. Grediac, M. and Pierron F. (2006), "Applying the virtual fields method to the identification of elasto-plastic constitutive parameters", Int. J. Plast., 22(4), 602-627. https://doi.org/10.1016/j.ijplas.2005.04.007.
  10. Guery, A., Hild, F., Latourte, F. and Roux, S. (2016), "Identification of crystal plasticity parameters using DIC measurements and weighted FEMU", Mech. Mater., 100, 55-71. https://doi.org/10.1016/j.mechmat.2016.06.007.
  11. Hild, F. and Roux, S. (2012), "Comparison of local and global approaches to digital image correlation", Exp. Mech., 52(9), 1503-1519. https://doi.org/10.1007/s11340-012-9603-7.
  12. Kavanagh, K.T. and Clough, R.W. (1971), "Finite element applications in the characterization of elastic solids", Int. J. Solid. Struct., 7(1), 11-23. https://doi.org/10.1016/0020-7683(71)90015-1.
  13. Leclerc, H., Neggers, J., Mathieu, F.., Hild, F. and Roux, S. (2015), Correli 3.0, Agence Pour la Protection des Programmes, Paris, France, IDDN.FR.001.520008.000.S.P.2015.000.31500.
  14. Lecompte, D., Smits, A., Sol, H., Vantomme, J. and Van Hemelrijck, D. (2007), "Mixed numerical-experimental technique for orthotropic parameter identification using biaxial tensile tests on cruciform specimens", Int. J. Solid. Struct., 44(5), 1643-1656. https://doi.org/10.1016/j.ijsolstr.2006.06.050.
  15. Lindner, D., Mathieu, F., Hild F., Alix, O., Minh, C.H. and Paulien-Camy, O. (2015), "On the evaluation of stress triaxiality fields in a notched titanium alloy sample via integrated digital image correlation", J. Appl. Mech.-T., ASME, 82(7), 1-10. https://doi.org/10.1115/1.4030457.
  16. Ludwik, P. (1909), Elemente der Technologischen Mechanik, Verlag von Julius Springer, Berlin, Germany.
  17. Martins, J.M.P., Andrade-Campos, A. and Thuilier, S. (2018), "Comparison of inverse identification strategies for constitutive mechanical models using full-field measurements", Int. J. Mech. Sci., 145, 330-345. https://doi.org/10.1016/j.ijmecsci.2018.07.013.
  18. Mathieu, F., Leclerc, H., Hild, F. and Roux, S. (2015), "Estimation of elastoplastic parameters via weighted FEMU and integrated-DIC", Exp. Mech., 55, 105-1129. https://doi.org/10.1007/s11340-014-9888-9.
  19. Nam Do, X., Ibrahimbegovic, A. and Brancherie, D. (2015), "Combined hardening and localized failure with softening plasticity in dynamics", Couple. Syst. Mech., 4(2), 115-136. https://doi.org/10.12989/csm.2015.4.2.115.
  20. Neggers, J., Mathieu, F., Hild, F., Roux, S. and Swiergiel, N. (2017), "Improving full-field identification using progressive model enrichments", Int. J. Solid. Struct., 118(7), 213-223. https://doi.org/10.1016/j.ijsolstr.2017.03.013.
  21. Passieux, J.C., Bugarin, F., David, C., Perie, J.N. and Robert, L. (2015), "Multiscale displacement field measurement using digital image correlation: Application to the identification of elastic properties", Exp. Mech., 5, 121-137. https://doi.org/10.1007/s11340-014-9872-4.
  22. Prates, P.A., Pereira, A.F.G., Oliveira, M.C. and Fernandes, J.V. (2019), "Analytical sensitivity matrix for the inverse identification of hardening parameters of metal sheets", Eur. J. Mech. A Solid., 75, 205-215. https://doi.org/10.1016/j.euromechsol.2019.01.010.
  23. Prates, P.A., Pereira, A.F.G., Sakharova, N.A., Oliveira, M.C. and Fernandes, J.V. (2016), "Inverse strategies for identifying the parameters of constitutive laws of metal sheets", Adv. Mater. Sci. Eng., 2016, 1-18. https://doi.org/10.1155/2016/4152963.
  24. Roux, S. and Hild, F. (2020), "Optimal procedure for the identification of constitutive parameters from experimentally measured displacement fields", Int. J. Solid. Struct., 184(2), 14-23. https://doi.org/10.1016/j.ijsolstr.2018.11.008.
  25. Sutton, M.A., Orteu, J.J. and Schreier, H.W. (2009), Image Correlation for Shape, Motion and Deformation Measurements, Springer, New York, USA.
  26. Tarantola, A. (1987), Inverse Problems Theory. Methods for Data Fitting and Model Parameter Estimation, Elsevier Applied Science, Southampton, UK.
  27. Tisza, M. (2005), "Numerical modeling and simulation in sheet metal forming academic and industrial perspectives", Mater. Sci. Forum, 473-474, 407-414. https://doi.org/10.4028/www.scientific.net/msf.473-474.407.
  28. Tomicevic, Z., Hild, F. and Roux, S. (2013), "Mechanics-aided digital image correlation", J. Strain Anal. Eng. Des., 48(5), 330-343. https://doi.org/10.1177/0309324713482457.
  29. Tomicevic, Z., Kodvanj, J. and Hild, F. (2016a), "Characterization of the nonlinear behavior of nodular graphite cast iron via inverse identification: Analysis of uniaxial tests", Eur. J. Mech. A Solid., 59, 140-154. https://doi.org/10.1016/j.euromechsol.2016.02.010.
  30. Tomicevic, Z., Kodvanj, J. and Hild, F. (2016b), "Characterization of the nonlinear behavior of nodular graphite cast iron via inverse identification: Analysis of biaxial tests", Eur. J. Mech. A Solid., 59, 195-209. https://doi.org/10.1016/j.euromechsol.2016.02.010.