×

zbMATH — the first resource for mathematics

A machine learning based plasticity model using proper orthogonal decomposition. (English) Zbl 1442.74042
Summary: Data-driven material models have many advantages over classical numerical approaches, such as the direct utilization of experimental data and the possibility to improve performance of predictions when additional data is available. One approach to develop a data-driven material model is to use machine learning tools. These can be trained offline to fit an observed material behaviour and then be applied in online applications. However, learning and predicting history dependent material models, such as plasticity, is still challenging. In this work, a machine learning based material modelling framework is proposed for both elasticity and plasticity. The machine learning based hyperelasticity model is developed with the Feed forward Neural Network (FNN) directly whereas the machine learning based plasticity model is developed by using of a novel method called Proper Orthogonal Decomposition Feed forward Neural Network (PODFNN). In order to account for the loading history, the accumulated absolute strain is proposed to be the history variable of the plasticity model. Additionally, the strain-stress sequence data for plasticity is collected from different loading-unloading paths based on the concept of sequence for plasticity. By means of the POD, the multi-dimensional stress sequence is decoupled leading to independent one dimensional coefficient sequences. In this case, the neural network with multiple output is replaced by multiple independent neural networks each possessing a one-dimensional output, which leads to less training time and better training performance. To apply the machine learning based material model in finite element analysis, the tangent matrix is derived by the automatic symbolic differentiation tool AceGen. The effectiveness and generalization of the presented models are investigated by a series of numerical examples using both 2D and 3D finite element analysis.
MSC:
74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)
74S05 Finite element methods applied to problems in solid mechanics
74B20 Nonlinear elasticity
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Cao, Trong Son, Models for ductile damage and fracture prediction in cold bulk metal forming processes: a review, Int. J. Mater. Form., 10, 2, 139-171 (2017)
[2] Hassoun, Mohamad H., Fundamentals of Artificial Neural Networks (1995), MIT press · Zbl 0850.68271
[3] Rasmussen, Carl Edward, GaussIan processes in machine learning, (Summer School on Machine Learning (2003), Springer), 63-71 · Zbl 1120.68436
[4] Oishi, Atsuya; Yagawa, Genki, Computational mechanics enhanced by deep learning, Comput. Methods Appl. Mech. Engrg., 327, 327-351 (2017) · Zbl 1439.74458
[5] Kirchdoerfer, Trenton; Ortiz, Michael, Data-driven computational mechanics, Comput. Methods Appl. Mech. Engrg., 304, 81-101 (2016) · Zbl 1425.74503
[6] Kirchdoerfer, T.; Ortiz, M., Data-driven computing in dynamics, Internat. J. Numer. Methods Engrg., 113, 11, 1697-1710 (2018), URL https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.5716
[7] Eggersmann, R.; Kirchdoerfer, T.; Reese, S.; Stainier, L.; Ortiz, M., Model-free data-driven inelasticity, Comput. Methods Appl. Mech. Engrg., 350, 81-99 (2019), URL http://www.sciencedirect.com/science/article/pii/S0045782519300878 · Zbl 1441.74048
[8] Stainier, Laurent; Leygue, Adrien; Ortiz, Michael, Model-free data-driven methods in mechanics: material data identification and solvers, Comput. Mech., 1-13 (2019) · Zbl 07095670
[9] Ibañez, Ruben; Borzacchiello, Domenico; Aguado, Jose Vicente; Abisset-Chavanne, Emmanuelle; Cueto, Elias; Ladeveze, Pierre; Chinesta, Francisco, Data-driven non-linear elasticity: constitutive manifold construction and problem discretization, Comput. Mech., 60, 5, 813-826 (2017), URL https://doi.org/10.1007/s00466-017-1440-1 · Zbl 1387.74015
[10] Ibañez, Ruben; Abisset-Chavanne, Emmanuelle; Aguado, Jose Vicente; Gonzalez, David; Cueto, Elias; Chinesta, Francisco, A manifold learning approach to data-driven computational elasticity and inelasticity, Arch. Comput. Methods Eng., 25, 1, 47-57 (2018) · Zbl 1390.74195
[11] Ibañez, Ruben; Abisset-Chavanne, Emmanuelle; González, Jean-Louis; Cueto, Elias; Chinesta, Francisco, Hybrid constitutive modeling: data-driven learning of corrections to plasticity models, Int. J. Mater. Form., 12, 4, 717-725 (2019)
[12] Liu, Zeliang; Bessa, M. A.; Liu, Wing Kam, Self-consistent clustering analysis: an efficient multi-scale scheme for inelastic heterogeneous materials, Comput. Methods Appl. Mech. Engrg., 306, 319-341 (2016) · Zbl 1436.74070
[13] Shakoor, Modesar; Kafka, Orion L.; Yu, Cheng; Liu, Wing Kam, Data science for finite strain mechanical science of ductile materials, Comput. Mech., 64, 1, 33-45 (2019) · Zbl 07073965
[14] Tang, Shan; Zhang, Gang; Yang, Hang; Li, Ying; Liu, Wing Kam; Guo, Xu, Map123: A data-driven approach to use 1d data for 3d nonlinear elastic materials modeling, Comput. Methods Appl. Mech. Engrg., 357, Article 112587 pp. (2019)
[15] Ayensa-Jiménez, Jacobo; Doweidar, Mohamed H.; Sanz-Herrera, Jose A.; Doblaré, Manuel, A new reliability-based data-driven approach for noisy experimental data with physical constraints, Comput. Methods Appl. Mech. Engrg., 328, 752-774 (2018) · Zbl 1439.65217
[16] Ayensa-Jiménez, Jacobo; Doweidar, Mohamed H.; Sanz-Herrera, Jose A.; Doblaré, Manuel, An unsupervised data completion method for physically-based data-driven models, Comput. Methods Appl. Mech. Engrg., 344, 120-143 (2019), URL http://www.sciencedirect.com/science/article/pii/S0045782518304882 · Zbl 1440.62397
[17] González, David; Chinesta, Francisco; Cueto, Elías, Learning corrections for hyperelastic models from data (2019)
[18] González, David; Chinesta, Francisco; Cueto, Elías, Thermodynamically consistent data-driven computational mechanics, Contin. Mech. Thermodyn., 31, 1, 239-253 (2019)
[19] Ghaboussi, J.; Sidarta, D. E., New nested adaptive neural networks (nann) for constitutive modeling, Comput. Geotech., 22, 1, 29-52 (1998)
[20] Hashash, Y. M.A.; Jung, S.; Ghaboussi, J., Numerical implementation of a neural network based material model in finite element analysis, Internat. J. Numer. Methods Engrg., 59, 7, 989-1005 (2004) · Zbl 1065.74609
[21] Lefik, M.; Schrefler, B. A., Artificial neural network as an incremental non-linear constitutive model for a finite element code, Comput. Methods Appl. Mech. Engrg., 192, 28-30, 3265-3283 (2003) · Zbl 1054.74731
[22] Ghaboussi, Jamshid; Pecknold, David A.; Zhang, Mingfu; Haj-Ali, Rami M., Autoprogressive training of neural network constitutive models, Internat. J. Numer. Methods Engrg., 42, 1, 105-126 (1998) · Zbl 0915.73075
[23] Ali, Usman; Muhammad, Waqas; Brahme, Abhijit; Skiba, Oxana; Inal, Kaan, Application of artificial neural networks in micromechanics for polycrystalline metals, Int. J. Plast. (2019), URL http://www.sciencedirect.com/science/article/pii/S0749641918307290
[24] Pabisek, Ewa, Self-learning fem/nmm approach to identification of equivalent material models for plane stress problem, Comput. Assist. Mech. Eng. Sci., 15, 1, 67 (2008) · Zbl 1171.74045
[25] Le, B. A.; Yvonnet, Julien; 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
[26] Lu, Xiaoxin; Giovanis, Dimitris G.; Yvonnet, Julien; Papadopoulos, Vissarion; Detrez, Fabrice; Bai, Jinbo, A data-driven computational homogenization method based on neural networks for the nonlinear anisotropic electrical response of graphene/polymer nanocomposites, Comput. Mech., 64, 2, 307-321 (2019) · Zbl 07095666
[27] Li, Xiang; Liu, Zhanli; Cui, Shaoqing; Luo, Chengcheng; Li, Chenfeng; Zhuang, Zhuo, Predicting the effective mechanical property of heterogeneous materials by image based modeling and deep learning, Comput. Methods Appl. Mech. Engrg., 347, 735-753 (2019) · Zbl 1440.74258
[28] Liu, Zeliang; Wu, C. T.; Koishi, M., A deep material network for multiscale topology learning and accelerated nonlinear modeling of heterogeneous materials, Comput. Methods Appl. Mech. Engrg., 345, 1138-1168 (2019) · Zbl 1440.74340
[29] Yang, Hang; Guo, Xu; Tang, Shan; Liu, Wing Kam, Derivation of heterogeneous material laws via data-driven principal component expansions, Comput. Mech., 1-15 (2019) · Zbl 07095669
[30] Korelc, Joze; Wriggers, Peter, Automation OfFinite Element Methods (2016), Springer · Zbl 1367.74001
[31] Nguyen, Derrick; Widrow, Bernard, Improving the learning speed of 2-layer neural networks by choosing initial values of the adaptive weights, (1990 IJCNN International Joint Conference on Neural Networks (1990), IEEE), 21-26
[32] Hagan, Martin T., Training feed forward networks with the marquardt algorithm, IEEE Trans. Neural Netw., 5, 6, 989-993 (1994)
[33] Mohr, Dirk; Dunand, Matthieu; Kim, Keun-Hwan, Evaluation of associated and non-associated quadratic plasticity models for advanced high strength steel sheets under multi-axial loading, Int. J. Plast., 26, 7, 939-956 (2010) · Zbl 1454.74022
[34] Goel, A.; Sherafati, A.; Negahban, Mehrdad; Azizinamini, A.; Wang, Yenan, A finite deformation nonlinear thermo-elastic model that mimics plasticity during monotonic loading, Int. J. Solids Struct., 48, 20, 2977-2986 (2011)
[35] Xiao, Manyu; Breitkopf, Piotr; Coelho, Rajan Filomeno; Knopf-Lenoir, Catherine; Sidorkiewicz, Maryan; Villon, Pierre, Model reduction by cpod and kriging, Struct. Multidiscip. Optim., 41, 4, 555-574 (2010) · Zbl 1274.90365
[36] Mohan, Arvind T.; Gaitonde., Datta V., A deep learning based approach to reduced order modeling for turbulent flow control using lstm neural networks (2018), arXiv preprint arXiv:1804.09269
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.