Yld2004-18p anisotropy parameter identification using ann models and variance-based input selection
Salam Ebrahim ABRAR, Lee Kinsey BRAD, Ha JINJIN
Abstract. Artificial neural networks (ANNs) are employed in this study as an inverse analysis method to identify the anisotropy parameters of the Yld2004-18p yield function, using the heterogeneous deformation field generated during hole expansion (HE) tests. Strain components extracted from various locations on the blank in numerical HE simulations form the training dataset. Two ANN models are developed: the first utilizes strain components from all extraction locations as inputs, while the second employs a variance-based input selection strategy, focusing only on strain components with higher variance. The proposed models are applied to AA6022-T4, and the identified anisotropy parameters are evaluated by comparing r-values, normalized stresses in various stress states, and yield loci analytically calculated using the ANN-predicted parameters.
Keywords
Anisotropic Yield Function, Artificial Neural Networks, Inverse Analysis
Published online 5/7/2025, 10 pages
Copyright © 2025 by the author(s)
Published under license by Materials Research Forum LLC., Millersville PA, USA
Citation: Salam Ebrahim ABRAR, Lee Kinsey BRAD, Ha JINJIN, Yld2004-18p anisotropy parameter identification using ann models and variance-based input selection, Materials Research Proceedings, Vol. 54, pp 1605-1614, 2025
DOI: https://doi.org/10.21741/9781644903599-173
The article was published as article 173 of the book Material Forming
Content from this work may be used under the terms of the Creative Commons Attribution 3.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
References
[1] S. Darzi, B.L. Kinsey, J. Ha, Reforming toolpath effect on deformation mechanics in double-sided incremental forming, International Journal of Mechanical Sciences 280 (2024) 109548. https://doi.org/10.1016/j.ijmecsci.2024.109548
[2] V. Cvitanić, F. Vlak, Ž. Lozina, A finite element formulation based on non-associated plasticity for sheet metal forming, International Journal of Plasticity 24 (2008) 646–687. https://doi.org/10.1016/j.ijplas.2007.07.003
[3] P.A. Prates, A.F.G. Pereira, N.A. Sakharova, M.C. Oliveira, J.V. Fernandes, Inverse Strategies for Identifying the Parameters of Constitutive Laws of Metal Sheets, Advances in Materials Science and Engineering 2016 (2016) 4152963. https://doi.org/10.1155/2016/4152963
[4] D. Banabic, Sheet Metal Forming Processes, Springer, Berlin, Heidelberg, 2010. https://doi.org/10.1007/978-3-540-88113-1
[5] F. Barlat, J.C. Brem, J.W. Yoon, K. Chung, R.E. Dick, D.J. Lege, F. Pourboghrat, S.-H. Choi, E. Chu, Plane stress yield function for aluminum alloy sheets—part 1: theory, International Journal of Plasticity 19 (2003) 1297–1319. https://doi.org/10.1016/S0749-6419(02)00019-0
[6] F. Barlat, H. Aretz, J.W. Yoon, M.E. Karabin, J.C. Brem, R.E. Dick, Linear transfomation-based anisotropic yield functions, International Journal of Plasticity 21 (2005) 1009–1039. https://doi.org/10.1016/j.ijplas.2004.06.004
[7] E.M. Mamros, S.M. Mayer, D.K. Banerjee, M.A. Iadicola, B.L. Kinsey, J. Ha, Plastic anisotropy evolution of SS316L and modeling for novel cruciform specimen, International Journal of Mechanical Sciences 234 (2022) 107663. https://doi.org/10.1016/j.ijmecsci.2022.107663
[8] Q.T. Pham, M.G. Lee, Y.S. Kim, Characterization of the isotropic-distortional hardening model and its application to commercially pure titanium sheets, International Journal of Mechanical Sciences 160 (2019) 90–102. https://doi.org/10.1016/j.ijmecsci.2019.06.023
[9] B. Revil-Baudard, O. Cazacu, E. Massoni, Room-temperature plastic behavior and formability of a commercially pure titanium: Mechanical characterization, modeling, and validation, International Journal of Solids and Structures 228 (2021) 111121. https://doi.org/10.1016/j.ijsolstr.2021.111121
[10] A.S. Ebrahim, Q. Zhang, J. Ha, Artificial neural network enhanced plasticity modeling and ductile fracture characterization of grade-1 commercial pure titanium, International Journal of Plasticity 179 (2024) 104044. https://doi.org/10.1016/j.ijplas.2024.104044
[11] J. Kim, Q.T. Pham, Y. Kim, Thinning prediction of hole-expansion test for DP980 sheet based on a non-associated flow rule, International Journal of Mechanical Sciences 191 (2021) 106067. https://doi.org/10.1016/j.ijmecsci.2020.106067
[12] J. Ha, J. Fones, B.L. Kinsey, Y.P. Korkolis, Plasticity and Formability of Annealed, Commercially-Pure Aluminum: Experiments and Modeling, Materials 13 (2020) 4285. https://doi.org/10.3390/ma13194285
[13] S. Avril, M. Bonnet, A.S. Bretelle, M. Grediac, F. Hild, P. Ienny, F. Latourte, D. Lemosse, S. Pagano, E. Pagnacco, F. Pierron, Overview of identification methods of mechanical parameters based on full-field measurements, Experimental Mechanics 48 (2008) 381–402. https://doi.org/10.1007/s11340-008-9148-y
[14] A. Güner, C. Soyarslan, A. Brosius, A.E. Tekkaya, Characterization of anisotropy of sheet metals employing inhomogeneous strain fields for Yld2000-2D yield function, International Journal of Solids and Structures 49 (2012) 3517–3527. https://doi.org/10.1016/j.ijsolstr.2012.05.001
[15] S. Cooreman, D. Lecompte, H. Sol, J. Vantomme, D. Debruyne, Identification of Mechanical Material Behavior Through Inverse Modeling and DIC, Exp Mech 48 (2008) 421–433. https://doi.org/10.1007/s11340-007-9094-0
[16] S. Coppieters, T. Hakoyama, D. Debruyne, S. Takahashi, T. Kuwabara, Inverse Yield Locus Identification using a biaxial tension apparatus with link mechanism and displacement fields, J. Phys.: Conf. Ser. 1063 (2018) 012039. https://doi.org/10.1088/1742-6596/1063/1/012039
[17] J.-H. Kim, F. Barlat, F. Pierron, M.-G. Lee, Determination of Anisotropic Plastic Constitutive Parameters Using the Virtual Fields Method, Exp Mech 54 (2014) 1189–1204. https://doi.org/10.1007/s11340-014-9879-x
[18] S. Zhang, L. Leotoing, D. Guines, S. Thuillier, S. Zang, Calibration of anisotropic yield criterion with conventional tests or biaxial test, International Journal of Mechanical Sciences 85 (2014) 142–151. https://doi.org/10.1016/j.ijmecsci.2014.05.020
[19] Y. Zhang, A. Yamanaka, S. Cooreman, T. Kuwabara, S. Coppieters, Inverse identification of plastic anisotropy through multiple non-conventional mechanical experiments, International Journal of Solids and Structures 285 (2023) 112534. https://doi.org/10.1016/j.ijsolstr.2023.112534
[20] M. Grédiac, F. Pierron, Applying the Virtual Fields Method to the identification of elasto-plastic constitutive parameters, International Journal of Plasticity 22 (2006) 602–627. https://doi.org/10.1016/j.ijplas.2005.04.007
[21] M. Rossi, F. Pierron, M. Štamborská, Application of the virtual fields method to large strain anisotropic plasticity, International Journal of Solids and Structures 97–98 (2016) 322–335. https://doi.org/10.1016/j.ijsolstr.2016.07.015
[22] A. Marek, F.M. Davis, F. Pierron, Sensitivity-based virtual fields for the non-linear virtual fields method, Comput Mech 60 (2017) 409–431. https://doi.org/10.1007/s00466-017-1411-6
[23] J. Kim, A.S. Ebrahim, B.L. Kinsey, J. Ha, Identification of Yld2000–2d anisotropic yield function parameters from single hole expansion test using machine learning, CIRP Annals (2024) S0007850624000349. https://doi.org/10.1016/j.cirp.2024.04.026
[24] K. Prasad, A.S. Ebrahim, H. Krishnaswamy, U. Chakkingal, D.K. Banerjee, Evaluation of hole expansion formability of high strength AA7075 alloy under varying temper conditions, IOP Conf. Ser.: Mater. Sci. Eng. 1238 (2022) 012038. https://doi.org/10.1088/1757-899X/1238/1/012038
[25] A.S. Ebrahim, U. Aravind, U. Chakkingal, Comparison of hole expansion ratios in a dual phase steel for holes prepared by conventional punching and fine piercing, IOP Conf. Ser.: Mater. Sci. Eng. 1307 (2024) 012016. https://doi.org/10.1088/1757-899X/1307/1/012016
[26] J. Ha, S. Coppieters, Y.P. Korkolis, On the expansion of a circular hole in an orthotropic elastoplastic thin sheet, International Journal of Mechanical Sciences 182 (2020) 105706. https://doi.org/10.1016/j.ijmecsci.2020.105706
[27] J. Ha, Y.P. Korkolis, Hole-Expansion: Sensitivity of Failure Prediction on Plastic Anisotropy Modeling, JMMP 5 (2021) 28. https://doi.org/10.3390/jmmp5020028
[28] H. Tian, B. Brownell, M. Baral, Y.P. Korkolis, Earing in cup-drawing of anisotropic Al-6022-T4 sheets, Int J Mater Form 10 (2017) 329–343. https://doi.org/10.1007/s12289-016-1282-y
[29] F. Grytten, B. Holmedal, O.S. Hopperstad, T. Børvik, Evaluation of identification methods for YLD2004-18p, International Journal of Plasticity 24 (2008) 2248–2277. https://doi.org/10.1016/j.ijplas.2007.11.005
[30] H.-S. Park, F. Barlat, S.-Y. Lee, Comparison of anisotropic yield functions and calibrations for accurate thickness prediction in hole expansion test, Journal of Materials Processing Technology 319 (2023) 118070. https://doi.org/10.1016/j.jmatprotec.2023.118070
[31] M. Halilovič, B. Starman, S. Coppieters, Computationally efficient stress reconstruction from full-field strain measurements, Comput Mech 74 (2024) 849–872. https://doi.org/10.1007/s00466-024-02458-4.
