A New Parameter Identification Approach by Experimental Design and Multiple Regressions Method: Application to the Elastoplastic Damage Constitutive Law of a Steel Thin Parts

Abstract:

In this paper, a new procedure for the identification of constitutive elastoplastic models coupled with an isotropic damage variable under large strains is presented. It is a statistical approach used for experimental characterization and identification based on a design of experiments of numerical simulations of mechanical characterization tests. The parameters for a reference material are determined by multiple linear regression as a function of shape indices.The material of reference is mild steel E24; it was characterized in a series of tensile tests of thin plate specimens. The Swift hardening law coupled with an isotropic damage variable that was identified by introducing in the established formulations shape indexes extracted from the experimental tension/elongation curves.The number of simulations required for the identification of the parameters of the reference material is roughly 18% of the number required by the inverse method (simplex).

• Periodical: Advanced Materials Research (Volume 1099)
• Pages: 71-79
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.1099.71
• Online since: April 2015
• Authors: M.T. Nasri, Slimani Faouzi, Mohammed Ali Rezgui*, M. Ayadi, Abel Cherouat
• Keywords: Damage, Hardening, Multiple Linear Regression, Parameter Identification, Swift Model

References

[1] Pijaudier‐Cabot, G., Bažant, Z. (1987), J Eng Mech 113(10), 1512. doi: 10. 1061/(ASCE) 0733-9399(1987)113: 10(1512).

DOI: 10.1061/(asce)0733-9399(1987)113:10(1512)

[2] Ghouati, O., Gelin, J.C. (1998), J Mater Process Technol 80–81, 560. doi: 10. 1016/S0924-0136(98)00159-9.

[3] Flores, P. (2005), Development of experimental equipment and identification procedures for sheet metal constitutive laws. [Ph.D. Thesis], University of Liege, Belgium.

[4] Cooreman, S., Lecompte, D., Sol, H., Vantomme, J., Debruyne, D. (2007), International Journal of Solids and Structures 44(13), 4329. doi: 10. 1016/j. ijsolstr. 2006. 11. 024.

DOI: 10.1016/j.ijsolstr.2006.11.024

[5] Feng, X.T., Yang, C. (2001), Comput Methods Appl Mech Eng 190(45), 5957. doi: 10. 1016/S0045-7825(01)00207-9.

[6] Huber, N., Tsakmakis, C. (2001), Comput Methods Appl Mech Eng 191(3–5), 353. doi: 10. 1016/S0045-7825(01)00278-X.

[7] Papadrakakis, M., Lagaros, N.D. (2002), Comput Methods Appl Mech Eng 191(32), 3491. doi: 10. 1016/S0045-7825(02)00287-6.

[8] Nelder, J.A., Mead, R. (1965), Comput J 7(4), 308. doi: 10. 1093/comjnl/7. 4. 308.

[9] Ayadi, M., Cherouat, A., Slimani, F., Rezgui, M.A., Zghal, A. (2011), Appl Mech Mater 62, 37. doi: 10. 4028/www. scientific. net/AMM. 62. 37.

DOI: 10.4028/www.scientific.net/amm.62.37

[10] Bonnet, M., Constantinescu, A. (2005), Inverse probl 21(2), R1. doi: 10. 1088/0266-5611/21/2/R01.

[11] Avril, S., Bonnet, M., Bretelle, A.S., Grediac, M., Hild, F., Ienny, P., Latourte, F., Lemosse, D., Pagano, S., Pagnacco, E., Pierron, F. (2008), Exp Mech 48(4), 381. doi: 10. 1007/s11340-008-9148-y.

DOI: 10.1007/s11340-008-9148-y

[12] Ramault, C., Makris, A., Sol, H., Van Hemelrijck, D., Lecompte, D., Lamkanfi, E. (2009).

[13] Montgomery, D.C. (2006), Design and analysis of experiments, 5th, ed Wiley, New York.

[14] Ayadi, M., Rezgui, M.A., Cherouat, A., Slimani, F., Nasri, T.M. (2009), Mec Ind 10(06), 503. doi: 10. 1051/meca/2010009.

[15] Cherouat, A., Ayadi, M., Rezgui, M.A. (2011), Int J Comput Methods Eng Sci Mech 12(3), 114. doi: 10. 1080/15502287. 2011. 564268.