Wu, Ling; Zulueta, Kepa; Major, Zoltan; Arriaga, Aitor; Noels, Ludovic Bayesian inference of non-linear multiscale model parameters accelerated by a deep neural network. (English) Zbl 1441.74192 Comput. Methods Appl. Mech. Eng. 360, Article ID 112693, 17 p. (2020). Summary: We develop a Bayesian Inference (BI) of the parameters of a non-linear multiscale model and of its material constitutive laws using experimental composite coupon tests as observation data. In particular, we consider non-aligned Short Fibers Reinforced Polymer (SFRP) as a composite material system and Mean-Field Homogenization (MFH) as a multiscale model. Although MFH is computationally efficient, when considering non-aligned inclusions, the evaluation cost of a non-linear response for a given set of model and material parameters remains too prohibitive to be coupled with the sampling process required by the BI. Therefore, a Neural-Network (NNW) is first trained using the MFH model, and is then used as a surrogate model during the BI process, making the identification process affordable. Cited in 13 Documents MSC: 74Q20 Bounds on effective properties in solid mechanics 62F15 Bayesian inference 62M45 Neural nets and related approaches to inference from stochastic processes 65Z05 Applications to the sciences Keywords:multiscale; composites; Bayesian inference; neural network; non-linear Software:PRMLT; Scikit PDFBibTeX XMLCite \textit{L. Wu} et al., Comput. Methods Appl. Mech. Eng. 360, Article ID 112693, 17 p. (2020; Zbl 1441.74192) Full Text: DOI Link References: [1] Matous, K.; Geers, M. G.; Kouznetsova, V. G.; Gillman, A., A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials, J. Comput. Phys., 330, Supplement C, 192-220 (2017) [2] Eshelby, J. D., The determination of the elastic field of an ellipsoidal inclusion, and related problems, Proc. R. Soc. A, 241, 1226, 376-396 (1957) · Zbl 0079.39606 [3] Mori, T.; Tanaka, K., Average stress in matrix and average elastic energy of materials with misfitting inclusions, Acta Metall., 21, 5, 571-574 (1973) [4] Hill, R., Continuum micro-mechanics of elastoplastic polycrystals, J. Mech. Phys. Solids, 13, 2, 89-101 (1965) · Zbl 0127.15302 [5] Talbot, D. R.S.; Willis, J. R., Variational principles for inhomogeneous non-linear media, IMA J. Appl. Math., 35, 1, 39-54 (1985) · Zbl 0588.73025 [6] Wu, L.; Noels, L.; Adam, L.; Doghri, I., A combined incremental-secant mean-field homogenization scheme with per-phase residual strains for elasto-plastic composites, Int. J. Plast., 51, 80-102 (2013) [7] Camacho, C. W.; Tucker, C. L.; Yalva c, S.; McGee, R. L., Stiffness and thermal expansion predictions for hybrid short fiber composites, Polym. Compos., 11, 4, 229-239 (1990) [8] Doghri, I.; Tinel, L., Micromechanics of inelastic composites with misaligned inclusions: numerical treatment of orientation, Comput. Methods Appl. Mech. Engrg., 195, 13, 1387-1406 (2006) · Zbl 1130.74036 [9] Vincent, M.; Giroud, T.; Clarke, A.; Eberhardt, C., Description and modeling of fiber orientation in injection molding of fiber reinforced thermoplastics, Polymer, 46, 17, 6719-6725 (2005) [10] Beck, J. L.; Katafygiotis, L. S., Updating models and their uncertainties. I: Bayesian statistical framework, J. Eng. Mech., 124, 455-461 (1998) [11] Most, T., Identification of the parameters of complex constitutive models: least squares minimization vs. Bayesian updating, (Straub, D., Reliability and Optimization of Structural Systems (2010)) [12] Madireddy, S.; Sista, B.; Vemaganti, K., A Bayesian approach to selecting hyperelastic constitutive models of soft tissue, Comput. Methods Appl. Mech. Engrg., 291, 102-122 (2015) · Zbl 1423.74624 [13] H. Rappel, L. Beex, J. Hale, L. Noels, S. Bordas, A tutorial on Bayesian inference to identify material parameters in solid mechanics, Arch. Comput. Methods Eng. [14] Lai, T. C.; Ip, K., Parameter estimation of orthotropic plates by Bayesian sensitivity analysis, Compos. Struct., 34, 1, 29-42 (1996) [15] Daghia, F.; de Miranda, S.; Ubertini, F.; Viola, E., Estimation of elastic constants of thick laminated plates within a Bayesian framework, Compos. Struct., 80, 3, 461-473 (2007) [16] Mohamedou, M.; Uriondo, K. Z.; Chung, C. N.; Rappel, H.; Beex, L.; Adam, L.; Major, Z.; Wu, L.; Noels, L., Bayesian identification of mean-field homogenization model parameters and uncertain matrix behavior in non-aligned short fiber composites, Compos. Struct. (2019), (submitted for publication) [17] Le, B. A.; Yvonnet, J.; He, Q.-C., Computational homogenization of nonlinear elastic materials using neural networks, Internat. J. Numer. Methods Engrg., 104, 12, 1061-1084 (2015) · Zbl 1352.74266 [18] Bessa, M.; 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. Engrg., 320, 633-667 (2017) · Zbl 1439.74014 [19] Unger, J. F.; Könke, C., Coupling of scales in a multiscale simulation using neural networks, Comput. Struct., 86, 21, 1994-2003 (2008) [20] Fritzen, F.; Fernández, M.; Larsson, F., On-the-fly adaptivity for nonlinear twoscale simulations using artificial neural networks and reduced order modeling, Front. Mater., 6, 75 (2019) [21] Talbot, D. R.S.; Willis, J. R., Bounds and self-consistent estimates for the overall properties of nonlinear composites, IMA J. Appl. Math., 39, 3, 215-240 (1987) · Zbl 0649.73012 [22] Ponte Castañeda, P., A new variational principle and its application to nonlinear heterogeneous systems, SIAM J. Appl. Math., 52, 5, 1321-1341 (1992) · Zbl 0759.73064 [23] Weber, B.; Kenmeugne, B.; Clement, J.; Robert, J., Improvements of multiaxial fatigue criteria computation for a strong reduction of calculation duration, Comput. Mater. Sci., 15, 4, 381-399 (1999) [24] Pedregosa, F.; Varoquaux, G.; Gramfort, A.; Michel, V.; Thirion, B.; Grisel, O.; Blondel, M.; Prettenhofer, P.; Weiss, R.; Dubourg, V.; Vanderplas, J.; Passos, A.; Cournapeau, D.; Brucher, M.; Perrot, M.; Duchesnay, E., Scikit-learn: machine learning in python, J. Mach. Learn. Res., 12, 2825-2830 (2011) · Zbl 1280.68189 [25] Bishop, C. M., (Pattern Recognition and Machine Learning. Pattern Recognition and Machine Learning, Information Science and Statistics (2006), Springer-Verlag: Springer-Verlag New York, USA) · Zbl 1107.68072 [26] Haario, H.; Saksman, E.; Tamminen, J., Adaptive proposal distribution for random walk metropolis algorithm, Comput. Statist., 14, 3, 375-395 (1999) · Zbl 0941.62036 [27] Gilks, W.; Richardson, S.; Spiegelhalter, D., Markov chain Monte Carlo in practice, (Chapman & Hall/CRC Interdisciplinary Statistic (1995), Chapman and Hall: Chapman and Hall Weinheim, Germany) · Zbl 0832.00018 [28] Nouri, H., Modélisation et identification de lois de comportement avec endommagement en fatigue polycyclique de matériaux composite à matrice thermoplastique (2009), Arts et Métiers ParisTech: Arts et Métiers ParisTech Metz (France), (Ph.D. thesis) [29] Vigliotti, A.; Csányi, G.; Deshpande, V., Bayesian inference of the spatial distributions of material properties, J. Mech. Phys. Solids, 118, 74-97 (2018) [30] Rappel, H.; Beex, L., Estimating fibres’ material parameter distributions from limited data with the help of Bayesian inference, Eur. J. Mech. A Solids, 75, 169-196 (2019) · Zbl 1473.74005 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.