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Effect of Load Path on Parameter Identification for Plasticity Models Using Bayesian Methods

  • Ehsan AdeliEmail author
  • Bojana Rosić
  • Hermann G. Matthies
  • Sven Reinstädler
Chapter
  • 33 Downloads
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 137)

Abstract

To evaluate the cyclic behavior under different loading conditions using the kinematic and isotropic hardening theory of steel, a Chaboche viscoplastic material model is employed. The parameters of a constitutive model are usually identified by minimization of the distance between model response and experimental data. However, measurement errors and differences in the specimens lead to deviations in the determined parameters. In this article the Chaboche model is used and a stochastic simulation technique is applied to generate artificial data which exhibit the same stochastic behavior as experimental data. Then the model parameters are identified by applying an estimation using Bayes’s theorem. The Gauss–Markov–Kalman filter using functional approximation is introduced and employed to estimate the model parameters in the Bayesian setting. Identified parameters are compared with the true parameters in the simulation, and the efficiency of the identification method is discussed. At the end, the effect of the load path on the parameter identification is investigated.

Keywords

Steel hardening theory Chaboche viscoplastic material model Parameter identification Stochastic simulation technique Bayesian methods Gauss–Markov—Kalman filter 

Notes

Acknowledgement

This work is partially supported by the DFG through GRK 2075.

References

  1. 1.
    Miller, A.: An inelastic constitutive model for monotonic, cyclic, and creep deformation: part I—equations development and analytical procedures. J. Eng. Mater. Technol. 98(2), 97–105 (1976)CrossRefGoogle Scholar
  2. 2.
    Krempl, E., McMahon, J.J., Yao, D.: Viscoplasticity based on overstress with a differential growth law for the equilibrium stress. Mech. Mater. 5, 35–48 (1986)CrossRefGoogle Scholar
  3. 3.
    Korhonen, R.K., Laasanen, M.S., Toyras, J., Lappalainen, R., Helminen, H.J., Jurvelin, J.S.: Fibril reinforced poroelastic model predicts specifically mechanical behavior of normal, proteoglycan depleted and collagen degraded articular cartilage. J Biomech 36, 1373–1379 (2003)CrossRefGoogle Scholar
  4. 4.
    Aubertin, M., Gill, D.E., Ladanyi, B.: A unified viscoplastic model for the inelastic flow of alkali halides. Mech. Mater. 11, 63–82 (1991)CrossRefGoogle Scholar
  5. 5.
    Chan, K.S., Bodner, S.R., Fossum, A.F., Munson, D.E.: A constitutive model for inelastic flow and damage evolution in solids under triaxial compression. Mech. Mater. 14, 1–14 (1992)CrossRefGoogle Scholar
  6. 6.
    Chaboche, J.L., Rousselier, G.: On the plastic and viscoplastic constitutive equations—part 1: rules developed with internal variable concept. J. Press. Vessel Technol. 105, 153–158 (1983)CrossRefGoogle Scholar
  7. 7.
    Chaboche, J.L., Rousselier, G.: On the plastic and viscoplastic constitutive equations—part 2: application of internal variable concepts to the 316 stainless steel. J. Press. Vessel Technol. 105, 159–164 (1983)CrossRefGoogle Scholar
  8. 8.
    Kłosowski, P., Mleczek, A.: Parameters’ identification of Perzyna and Chaboche viscoplastic models for aluminum alloy at temperature of 120C. Eng. Trans. 62(3), 291–305 (2014)Google Scholar
  9. 9.
    Gong, Y., Hyde, C., Sun, W., Hyde, T.: Determination of material properties in the Chaboche unified viscoplasticity model. J. Mater. Des. Appl. 224(1), 19–29 (2010)Google Scholar
  10. 10.
    Harth, T., Lehn, J.: Identification of material parameters for inelastic constitutive models using stochastic methods. GAMM-Mitt. 30(2), 409–429 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Chan, K.S., Bodner, S.R., Lindholm, U.S.: Phenomenological modelling of hardening and thermal recovery in metals. J. Eng. Mater. Technol. 110, 1–8 (1988)CrossRefGoogle Scholar
  12. 12.
    Velde, J.: 3D Nonlocal Damage Modeling for Steel Structures under Earthquake Loading. Department of Architecture, Civil Engineering and Environmental Sciences University of Braunschweig—Institute of Technology (2010)Google Scholar
  13. 13.
    Matthies, H.G.: Stochastic finite elements: computational approaches to stochastic partial differential equations. J. Appl. Math. Mech. 88, 849–873 (2008)MathSciNetzbMATHGoogle Scholar
  14. 14.
    Matthies, H.G.: Uncertainty quantification with stochastic finite elements. Encyclopedia of computational mechanics. In: Stein, E., de Borst, R., Hughes, T.R.J. (eds.) Wiley, Chichester (2007)Google Scholar
  15. 15.
    Matthies, H.G., Zander, E., Rosić, B.V., Litvinenko, A.: Parameter estimation via conditional expectation: a Bayesian inversion. J. Adv. Model. Simul. Eng. Sci. 3(24), (2016)Google Scholar
  16. 16.
    Rosić, B.V., Litvinenko, A., Pajonk, O., Matthies, H.G.: Sampling-free linear Bayesian update of polynomial chaos representations. J. Comput. Phys. 231(17), 5761–5787 (2012)MathSciNetzbMATHCrossRefGoogle Scholar
  17. 17.
    Matthies, H.G., Zander, E., Rosić, B.V., Litvinenko, A., Pajonk, O.: Inverse problems in a Bayesian setting. J. Comput. Methods Solids Fluids 41, 245–286 (2016)CrossRefGoogle Scholar
  18. 18.
    Rosić, B.V., Matthies, H.G.: Identification of properties of stochastic elastoplastic systems. In: Computational Methods in Stochastic Dynamics, pp. 237–253 (2013)Google Scholar

Copyright information

© National Technology & Engineering Solutions of Sandia, and The Editor(s), under exclusive license to Springer Nature Switzerland AG  2020

Authors and Affiliations

  • Ehsan Adeli
    • 1
    Email author
  • Bojana Rosić
    • 1
  • Hermann G. Matthies
    • 1
  • Sven Reinstädler
    • 2
  1. 1.Institute of Scientific ComputingTechnische Universität BraunschweigBraunschweigGermany
  2. 2.Institute of Structural AnalysisTechnische Universität BraunschweigBraunschweigGermany

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