×

An enhanced data-driven constitutive model for predicting strain-rate and temperature dependent mechanical response of elastoplastic materials. (English) Zbl 1533.74008

The authors state that the novelty of their data-driven approach to elasto-plastic materials consists in the strain reconfiguration strategy, which is realized via Formula (3), to “enhance the strain rate and temperature effect.” Formula (3) is not mathematically comprehensible. Concerning the tension-compression asymmetry (see Sections 2.3 and 4), the stress triaxiality, \(\eta,\) which is introduced in terms of mean stress and second invariant of the stress-deviator, is misleading for 1D stress state. We notice that the presence of \(\eta\) inside the constitutive relation, see for instance [B. Erice and F. Gálvez, Int. J. Solids Struct. 51, No. 1, 93–110 (2014; doi:10.1016/j.ijsolstr.2013.09.015)], emphasizes the dependence of material behaviour on the mean stress. The basic formulation of data-driven constitutive model is declared to be Equation (1), which expresses the equivalent stress in terms of equivalent strain, i.e., an 1D-elastic type constitutive relation. Their modified forms, (5) and (14), compute the equivalent stress, but being defined in terms of sign of the triaxiality (i.e., the stress defined in terms of stress!). Formula (14) is derived from (5) by taking into account the composition with the re-configurated strain Expression (3), which involves also the so-called cumulative effective strain. The curves (1D-type) of true stress in terms of true strain (about 40 graphs), are plotted using the experimental database when different (but constant) tension-rate, compression-rate and temperature, respectively are imposed. In Figure 6 there are curves plotted for different triaxiality. To compare and validate their results the Johnson-Cook (J-C) model is considered but only one constitutive equation of (J-C) model, i.e., Equation (19), is written. Thus the formulae allowing the computation of the so-called effective cumulative plastic strain, or of the plastic strain, involved in Formulae (14) and (19), ought to be written. Formulae (12) are not correct. There are only verbal statements about the feasibility of “simulating history-dependent behaviors of elasto-plastic materials.” Concerning the numerical implementation of data-driven model (summarized the Box 1), the elastic trial solution, the trial stress factor, stress triaxiality, and \(C_{\mathrm{trial}}\) together with update the stress factor \(C_{\mathrm{uptrial}},\) involving a variable \(C_{\eta},\) are computed, without any reference to plastic behavior. \(C_{\eta},\) which denotes the “hydrostatic pressure effect on the plastic behavior,” is introduced with the mention that this coefficient can be iteratively determined based on the experimental curves, sending to the paper [Y. Bai and T. Wierzbicki, Int. J. Plast. 24, No. 6, 1071–1096 (2008; Zbl 1421.74016)], in which the plasticity and fracture with pressure and Lode dependence are considered (i.e., another type of constitutive framework). The numerical incremental-type algorithm ought to be developed within a well-defined constitutive framework (elasto-plasticity in this case) altogether with conservation laws.

MSC:

74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)
74A20 Theory of constitutive functions in solid mechanics
74F05 Thermal effects in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
68T05 Learning and adaptive systems in artificial intelligence

Citations:

Zbl 1421.74016

Software:

F3DAM; MAP123-EP
Full Text: DOI

References:

[1] Ali, U.; Muhammad, W.; Brahme, A.; Skiba, O.; Inal, K., Application of artificial neural networks in micromechanics for polycrystalline metals, Int. J. Plast., 120, 205-219 (2019)
[2] Bai, Y.; Wierzbicki, T., A new model of metal plasticity and fracture with pressure and Lode dependence, Int. J. Plast., 24, 6, 1071-1096 (2008) · Zbl 1421.74016
[3] Balokas, G.; Czichon, S.; Rolfes, R., Neural network assisted multiscale analysis for the elastic properties prediction of 3D braided composites under uncertainty, Compos. Struct., 183, 550-562 (2018)
[4] Bessa, M. A.; Bostanabad, R.; Liu, Z.; Hu, A.; Apley, D. W.; Brinson, C.; Chen, W.; Liu, W. K., A framework for data-driven analysis of materials under uncertainty: countering the curse of dimensionality, Comput. Methods Appl. Mech. Eng., 320, 633-667 (2017) · Zbl 1439.74014
[5] Chakraverty, S.; Mall, S., Artificial Neural Networks for Engineers and Scientists: Solving Ordinary Differential Equations (2017), Boca Raton · Zbl 1375.00005
[6] Cheng, W.; Outeiro, J.; Costes, J. P.; M’Saoubi, R.; Karaouni, H.; Astakhov, V., A constitutive model for Ti6Al4V considering the state of stress and strain rate effects, Mech. Mater., 137, Article 103103 pp. (2019)
[7] Cheng, G.; Li, X.; Nie, Y.; Li, H., FEM-Cluster based reduction method for efficient numerical prediction of effective properties of heterogeneous material in nonlinear range, Comput. Methods Appl. Mech. Eng., 348, 157-184 (2019) · Zbl 1440.74383
[8] Chollet, F., Deep Learning with python (2017), Manning Publications Co.
[9] Doraiswamy, S.; Criscione, J. C.; Srinivasa, A. R., A technique for the classification of tissues by combining mechanics based models with Bayesian inference, Int. J. Eng. Sci., 106, 95-109 (2016)
[10] Eggersmann, R.; Kirchdoerfer, T.; Reese, S.; Stainier, L.; Ortiz, M., Model-free data-driven inelasticity, Comput. Methods Appl. Mech. Eng., 350, 81-99 (2019) · Zbl 1441.74048
[11] Feather, W. G.; Savage, D. J.; Knezevic, M., A crystal plasticity finite element model embedding strain-rate sensitivities inherent to deformation mechanisms: application to alloy AZ31, Int. J. Plast., 143, Article 103031 pp. (2021)
[12] Feng, Y.; Wang, Q.; Wu, D.; Luo, Z.; Chen, X.; Zhang, T.; Gao, W., Machine learning aided phase field method for fracture mechanics, Int. J. Eng. Sci., 169, Article 103587 pp. (2021) · Zbl 07444795
[13] Fuhg, J. N.; Böhm, C.; Bouklas, N.; Fau, A.; Wriggers, P.; Marino, M., Model-data-driven constitutive responses: application to a multiscale computational framework, Int. J. Eng. Sci., 167, Article 103522 pp. (2021) · Zbl 07411518
[14] Ghorbanpour, S.; Alam, M. E.; Ferreri, N. C.; Kumar, A.; McWilliams, B. A.; Vogel, S. C.; Bicknell, J.; Beyerlein, I. J.; Knezevic, M., Experimental characterization and crystal plasticity modeling of anisotropy, tension-compression asymmetry, and texture evolution of additively manufactured Inconel 718 at room and elevated temperatures, Int. J. Plast., 125, 63-79 (2020)
[15] Habib, S. A.; Khan, A. S.; Gnäupel-Herold, T.; Lloyd, J. T.; Schoenfeld, S. E., Anisotropy, tension-compression asymmetry and texture evolution of a rare-earth-containing magnesium alloy sheet, ZEK100, at different strain rates and temperatures: experiments and modeling, Int. J. Plast., 95, 163-190 (2017)
[16] Haight, S.; Wang, L.; Du, B. P., Development of a Titanium Alloy Ti-6Al-4V Material Model Used in LS-DYNA (Final Report). Report No. DOT/FAA/TC-15/23, United States, Department of Transportation, Federal Aviation Administration (2016), William J. Hughes Technical Center
[17] Hammer, J. T., Plastic Deformation and Ductile Fracture of Ti-6Al-4V under Various Loading Conditions (2012), The Ohio State University, The Degree of Master Dissertation
[18] Jenab, A.; Sarraf, S. I.; Green, D. E.; Rahmaan, T.; Worswick, M. J., The Use of genetic algorithm and neural network to predict rate-dependent tensile flow behaviour of AA5182-sheets, Mater. Des., 94, 262-273 (2016)
[19] Johnson, G. R.; Cook, W. H., Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures, Eng. Fract. Mech., 21, 1, 31-48 (1985)
[20] Jordan, B.; Gorji, M. B.; Mohr, D., Neural network model describing the temperature- and rate-dependent stress-strain response of polypropylene, Int. J. Plast., 135, Article 102811 pp. (2020)
[21] Karapiperis, K.; Stainier, L.; Ortiz, M.; Andrade, J. E., Data-driven multiscale modeling in mechanics, J. Mech. Phys. Solid., 147, Article 104239 pp. (2021)
[22] Khan, A. S.; Yu, S.; Liu, H., Deformation induced anisotropic responses of Ti-6Al-4V alloy Part II: a strain rate and temperature dependent anisotropic yield criterion, Int. J. Plast., 38, 14-26 (2012)
[23] Kirchdoerfer, T.; Ortiz, M., Data-driven computational mechanics, Comput. Methods Appl. Mech. Eng., 304, 81-101 (2016) · Zbl 1425.74503
[24] Kirchdoerfer, T.; Ortiz, M., Data-driven computing in dynamics, Int. J. Numer. Methods Eng., 113, 1697-1710 (2018) · Zbl 07868547
[25] Korkmaz, M. E.; Günay, M.; Verleysen, P., Investigation of tensile Johnson-Cook model parameters for Nimonic 80A superalloy, J. Alloys Compd., 801, 542-549 (2019)
[26] Li, X.; Roth, C. C.; Mohr, D., Machine-learning based temperature- and rate-dependent plasticity model: application to analysis of fracture experiments on DP steel, Int. J. Plast., 118, 320-344 (2019)
[27] Li, X.; Zhang, C.; Wu, Z., An inverse determination method for strain rate and temperature dependent constitutive model of elastoplastic materials, Struct. Eng. Mech., 80, 5, 539-551 (2021)
[28] Li, X.; Roth, C. C.; Bonatti, C.; Mohr, D., Counterexample-trained neural network model of rate and temperature dependent hardening with dynamic strain aging, Int. J. Plast., 151, Article 103218 pp. (2022)
[29] Liu, Z. L.; Moore, J. A.; Aldousari, S. M.; Hedia, H. S.; Asiri, S. A.; Liu, W. K., A statistical descriptor based volume-integral micromechanics model of heterogeneous material with arbitrary inclusion shape, Comput. Mech., 55, 963-981 (2015) · Zbl 1329.74026
[30] Liu, Z. L.; Bessa, M. A.; Liu, W. K., Self-consistent clustering analysis: an efficient multi-scale scheme for inelastic heterogeneous materials, Comput. Methods Appl. Mech. Eng., 306, 319-341 (2016) · Zbl 1436.74070
[31] Liu, Z. L.; Fleming, M.; Liu, W. K., Microstructural material database for self-consistent clustering analysis of elastoplastic strain softening materials, Comput. Methods Appl. Mech. Eng., 330, 547-577 (2018) · Zbl 1439.74063
[32] Liu, X.; Gasco, F.; Goodsell, J.; Yu, W., Initial failure strength prediction of woven composites using a new yarn failure criterion constructed by deep learning, Compos. Struct., 230, Article 111505 pp. (2019)
[33] Mozaffar, M.; Bostanabad, R.; Chen, W.; Ehmann, K.; Cao, J.; Bessa, M. A., Deep learning predicts path-dependent plasticity, Proc. Natl. Acad. Sci. USA, 116, 52, 26414-26420 (2019)
[34] Muhammad, W.; Brahme, A. P.; Ibragimova, O.; Kang, J.; Inal, K., A machine learning framework to predict local strain distribution and the evolution of plastic anisotropy & fracture in additively manufactured alloys, Int. J. Plast., 136, Article 102867 pp. (2020)
[35] Pandya, K. S.; Roth, C. C.; Mohr, D., Strain rate and temperature dependent fracture of aluminum alloy 7075: experiments and neural network modeling, Int. J. Plast., 135, 5, Article 102788 pp. (2020)
[36] Qiu, H.; Yang, H.; Elkhodary, K. I.; Tang, S.; Guo, X., A data-driven approach for modeling tension-compression asymmetric material behavior: numerical simulation and experiment, Comput. Mech., 69, 299-313 (2022) · Zbl 07492670
[37] Rahmanpanah, H.; Mouloodi, S.; Burvill, C.; Gohari, S.; Davies, M. S., Prediction of load-displacement curve in a complex structure using artificial neural networks: a study on a long bone, Int. J. Eng. Sci., 154, Article 103319 pp. (2020) · Zbl 07228663
[38] Shang, H.; Wu, P.; Lou, Y.; Wang, J.; Chen, Q., Machine learning-based modeling of the coupling effect of strain rate and temperature on strain hardening for 5182-O aluminum alloy, J. Mater. Process. Technol., 302, Article 117501 pp. (2022)
[39] Tang, S.; Zhang, G.; Yang, H.; Li, Y.; Liu, W. K.; Guo, X., MAP123: a data-driven approach to use 1D data for 3D nonlinear elastic materials modeling, Comput. Methods Appl. Mech. Eng., 357, Article 112587 pp. (2019) · Zbl 1442.65417
[40] Tang, S.; Li, Y.; Qiu, H.; Yang, H.; Saha, S.; Mojumder, S.; Liu, W. K.; Guo, X., MAP123-EP: a mechanistic-based data-driven approach for numerical elastoplastic analysis, Comput. Methods Appl. Mech. Eng., 364, Article 112955 pp. (2020) · Zbl 1442.74044
[41] Tran-Ngoc, H.; Khatir, S.; Le-Xuan, T.; Roeck, G. D.; Bui-Tien, T.; Wahab, M. A., A novel machine-learning based on the global search techniques using vectorized data for damage detection in structures, Int. J. Eng. Sci., 157, Article 103376 pp. (2020), 2020 · Zbl 07278778
[42] Wang, Y.; Zhao, G.; Xu, X.; Chen, X.; Zhang, C., Constitutive modeling, processing map establishment and microstructure analysis of spray deposited Al-Cu-Li alloy 2195, J. Alloys Compd., 779, 735-751 (2019)
[43] Wen, J.; Zou, Q.; Wei, Y., Physics-driven machine learning model on temperature and time-dependent deformation in lithium metal and its finite element implementation, J. Mech. Phys. Solid., 153, Article 104481 pp. (2021)
[44] Wu, L.; Nguyen, V. D.; Kilingar, N. G.; Noels, L., A recurrent neural network-accelerated multi-scale model for elasto-plastic heterogeneous materials subjected to random cyclic and non-proportional loading paths, Comput. Methods Appl. Mech. Eng., 369, Article 113234 pp. (2020) · Zbl 1506.74453
[45] Zhang, A.; Mohr, D., Using neural networks to represent von Mises plasticity with isotropic hardening, Int. J. Plast., 132, Article 102732 pp. (2020)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.