Transactions of Materials and Heat Treatment

Title：Application of artificial neural networks in metal plasticity constitutive modeling

Authors：

Unit：

KeyWords：

ClassificationCode：TG301

year,vol(issue):pagenumber：2024,49(7):1-18

Abstract：

The metal plasticity constitutive models were reviewed from macroscopic and microscopic perspectives, and the limitations of the model application were mainly focused on the acquisition of constitutive parameters and the numerical realization of mdel. Then, three widely used artificial neural networks, namely, back propagation neural networks, convolutional neural networks and recurrent neural networks were introduced, and the applications of artificial neural networks in plastic constitutive modeling were summarized from two aspects of calibration and calculation of the model. Furthermore, physics-informed neural networks were introduced, and the training efficiency and generalization ability were effectively improved by taking constraints into the artificial neural network based on the traditional physical theories. Finally, the challenges and future development directions of the application of artificial neural networks in metal plasticity constitutive modeling were indicated.

Funds：

国家自然科学基金资助项目（52075288）

作者简介：张韩旭（2000-），男，博士研究生 E-mail：hx-zhang22@mails.tsinghua.edu.cn 通信作者：方刚（1971-），男，博士，教授

Reference：

［1］Rezaei Ashtiani H R, Parsa M H, Bisadi H. Constitutive equations for elevated temperature flow behavior of commercial purity aluminum
［J］. Materials Science and Engineering: A, 2012, 545: 61-67.

［2］Xiao J, Li D S, Li X Q, et al. Constitutive modeling and microstructure change of Ti-6Al-4V during the hot tensile deformation
［J］. Journal of Alloys and Compounds, 2012, 541: 346-352.

［3］Chaboche J L. A review of some plasticity and viscoplasticity constitutive theories
［J］. International Journal of Plasticity, 2008, 24(10): 1642-1693.

［4］Westergaard H M. Theory of Elasticity and Plasticity
［M］. Harvard：Harvard University Press, 2013.

［5］赵辉, 彭艳, 石宝东. 金属材料各向异性本构模型研究进展
［J］. 塑性工程学报, 2022, 29(10): 32-42.

Zhao H, Peng Y, Shi B D. Research progress on anisotropic constitutive model of metal materials
［J］. Journal of Plasticity Engineering, 2022, 29(10): 32-42.

［6］Zeng P. Neural computing in mechanics
［J］. Applied Mechanics Reviews, 1998, 51(2): 173-197.

［7］Xia J, Won C, Kim H, et al. Artificial neural networks for predicting plastic anisotropy of sheet metals based on indentation test
［J］. Materials, 2022, 15(5): 1714.

［8］Ali U, Muhammad W, Brahme A, et al. Application of artificial neural networks in micromechanics for polycrystalline metals
［J］. International Journal of Plasticity, 2019, 120: 205-219.

［9］Mangal A, Holm E A. Applied machine learning to predict stress hotspots II: Hexagonal close packed materials
［J］. International Journal of Plasticity, 2019, 114: 1-14.

［10］李非凡, 雷丽萍, 方刚. 镁合金塑性变形及延性断裂预测研究进展(上)——宏观本构模型的开发及应用
［J］. 塑性工程学报, 2020, 27(1): 1-13.

Li F F, Lei L P, Fang G. Research advances of plastic deformation and ductile fracture prediction of magnesium alloys. Part I: Development and applications of macroscopic constitutive models
［J］. Journal of Plasticity Engineering, 2020, 27(1): 1-13.

［11］Li H, Hu X, Yang H, et al. Anisotropic and asymmetrical yielding and its distorted evolution: Modeling and applications
［J］. International Journal of Plasticity, 2016, 82: 127-158.

［12］Li F F, Fang G. Modeling of 3D plastic anisotropy and asymmetry of extruded magnesium alloy and its applications in three-point bending
［J］. International Journal of Plasticity, 2020, 130: 102704.

［13］Barlat F, Becker R C, Hayashida Y, et al. Yielding description for solution strengthened aluminum alloys
［J］. International Journal of Plasticity, 1997, 13(4): 385-401.

［14］Cazacu O, Plunkett B, Barlat F. Orthotropic yield criterion for hexagonal closed packed metals
［J］. International Journal of Plasticity, 2006, 22(7): 1171-1194.

［15］Soare S, Yoon J W, Cazacu O. On the use of homogeneous polynomials to develop anisotropic yield functions with applications to sheet forming
［J］. International Journal of Plasticity, 2008, 24(6): 915-944.

［16］Nixon M E, Lebensohn R A, Cazacu O, et al. Experimental and finite-element analysis of the anisotropic response of high-purity α-titanium in bending
［J］. Acta Materialia, 2010, 58(17): 5759-5767.

［17］Cazacu O, Barlat F. A criterion for description of anisotropy and yield differential effects in pressure-insensitive metals
［J］. International Journal of Plasticity, 2004, 20(11): 2027-2045.

［18］Yoon J W, Lou Y, Yoon J, et al. Asymmetric yield function based on the stress invariants for pressure sensitive metals
［J］. International Journal of Plasticity, 2014, 56: 184-202.

［19］Hu Q, Li X, Han X, et al. A normalized stress invariant-based yield criterion: Modeling and validation
［J］. International Journal of Plasticity, 2017, 99: 248-273.

［20］Stoughton T B. A non-associated flow rule for sheet metal forming
［J］. International Journal of Plasticity, 2002, 18(5): 687-714.

［21］Bland D R. The associated flow rule of plasticity
［J］. Journal of the Mechanics and Physics of Solids, 1957, 6(1): 71-78.

［22］Hou Y, Myung D, Park J K, et al. A review of characterization and modelling approaches for sheet metal forming of lightweight metallic materials
［J］. Materials, 2023, 16(2): 836.

［23］Bruschi S, Altan T, Banabic D, et al. Testing and modelling of material behaviour and formability in sheet metal forming
［J］. CIRP Annals, 2014, 63(2): 727-749.

［24］Noman M, Clausmeyer T, Barthel C. A review of characterization and modelling approaches for sheet metal forming of lightweight metallic materials. Experimental characterization and modeling of the hardening behavior of the sheet steel LH800
［J］. Materials Science and Engineering: A, 2010, 527(10): 2515-2526.

［25］Stoughton T B, Yoon J W. Anisotropic hardening and non-associated flow in proportional loading of sheet metals
［J］. International Journal of Plasticity, 2009, 25(9): 1777-1817.

［26］Revil-Baudard B, Cazacu O, Flater P, et al. Plastic deformation of high-purity α-titanium: Model development and validation using the Taylor cylinder impact test
［J］. Mechanics of Materials, 2015, 80: 264-275.

［27］Plunkett B, Lebensohn R A, Cazacu O, et al. Anisotropic yield function of hexagonal materials taking into account texture development and anisotropic hardening
［J］. Acta Materialia, 2006, 54(16): 4159-4169.

［28］Segurado J, Lebensohn R A, Llorca J, et al. Multiscale modeling of plasticity based on embedding the viscoplastic self-consistent formulation in implicit finite elements
［J］. International Journal of Plasticity, 2012, 28(1): 124-140.

［29］Al-Hadi I, Kobaissy A, Ayoub G, et al. Modeling of the tension-compression asymmetry reduction of ECAPed Mg-3Al-1Zn through grain fragmentation
［J］. Computational Materials Science, 2022, 210: 111439.

［30］Walde T, Riedel H. Modeling texture evolution during hot rolling of magnesium alloy AZ31
［J］. Materials Science and Engineering: A, 2007, 443(1): 277-284.

［31］Peirce D, Asaro R J, Needleman A. An analysis of nonuniform and localized deformation in ductile single crystals
［J］. Acta Metallurgica, 1982, 30(6): 1087-1119.

［32］Kalidindi S R. Incorporation of deformation twinning in crystal plasticity models
［J］. Journal of the Mechanics and Physics of Solids, 1998, 46(2): 267-290.

［33］Tomé C N, Lebensohn R A, Kocks U F. A model for texture development dominated by deformation twinning: Application to zirconium alloys
［J］. Acta Metallurgica et Materialia, 1991, 39(11): 2667-2680.

［34］Wang H, Wu P D, Wang J, et al. A crystal plasticity model for hexagonal close packed (HCP) crystals including twinning and de-twinning mechanisms
［J］. International Journal of Plasticity, 2013, 49: 36-52.

［35］Weng G J. A micromechanical theory of grain-size dependence in metal plasticity
［J］. Journal of the Mechanics and Physics of Solids, 1983, 31(3): 193-203.

［36］Lebensohn R A, Tomé C N. A self-consistent anisotropic approach for the simulation of plastic deformation and texture development of polycrystals: Application to zirconium alloys
［J］. Acta Metallurgica et Materialia, 1993, 41(9): 2611-2624.

［37］Sachs G. Plasticity problems in metals
［J］. Transactions of the Faraday Society, 1928, 24: 84-92.

［38］Taylor G I. Plastic strain in metals
［J］. J. Inst. Metals, 1938, 62: 307-324.

［39］Lebensohn R A, Tomé C N, Castaeda P P. Self-consistent modelling of the mechanical behaviour of viscoplastic polycrystals incorporating intragranular field fluctuations
［J］. Philosophical Magazine, 2007, 87(28): 4287-4322.

［40］Zhang H, Diehl M, Roters F, et al. A virtual laboratory using high resolution crystal plasticity simulations to determine the initial yield surface for sheet metal forming operations
［J］. International Journal of Plasticity, 2016, 80: 111-138.

［41］Roters F, Diehl M, Shanthraj P, et al. DAMASK-The Düsseldorf advanced material simulation kit for modeling multi-physics crystal plasticity, thermal, and damage phenomena from the single crystal up to the component scale
［J］. Computational Materials Science, 2019, 158: 420-478.

［42］Lou Y, Huh H, Yoon J W. Consideration of strength differential effect in sheet metals with symmetric yield functions
［J］. International Journal of Mechanical Sciences, 2013, 66: 214-223.

［43］Hosford W F, Allen T J. Twinning and directional slip as a cause for a strength differential effect
［J］. Metallurgical Transactions, 1973, 4(5): 1424-1425.

［44］Rodas E, Alejandro E. Microstructure-sensitive creep-fatigue interaction crystal-viscoplasticity model for single-crystal nickel-base superalloys
［J/OL］. 2017
［2024-04-27］. http://hdl.handle. net/1853/59788.

［45］隋天校, 石多奇, 杨秦政, 等. 晶体塑性本构模型材料参数识别方法研究
［J］. 推进技术, 2023, 44(3): 210593.

Sui T X, Shi D Q, Yang Q Z, et al. Material parameter identification method of crystal plastic constitutive models
［J］. Journal of Propulsion Technology, 2023, 44(3): 210593.

［46］Yang J, Meng C, Ling L. Prediction and simulation of wearable sensor devices for sports injury prevention based on BP neural network
［J］. Measurement: Sensors, 2024, 33: 101104.

［47］Wang Z, Chen Q, Wang Z, et al. The investigation into the failure criteria of concrete based on the BP neural network
［J］. Engineering Fracture Mechanics, 2022, 275: 108835.

［48］Li Y W, Cao K. Establishment and application of intelligent city building information model based on BP neural network model
［J］. Computer Communications, 2020, 153: 382-389.

［49］Glorot X, Bordes A, Bengio Y. Deep sparse rectifier neural networks
［A］. Proceedings of the Fourteenth International Conference on Artificial Intelligence and Statistics. JMLR Workshop and Conference Proceedings
［C］. 2011.

［50］Lecun Y, Boser B, Denker J S, et al. Backpropagation applied to handwritten zip code recognition
［J］. Neural Computation, 1989, 1(4): 541-551.

［51］Bacˇanin Dakula N. Convolutional neural network layers and architectures
［A］. Sinteza 2019-International Scientific Conference on Information Technology and Data Related Research
［C］. 2019.

［52］秦川, 高翔. 基于卷积神经网络的遥感图像目标识别仿真
［J］. 计算机仿真, 2024, 41(4): 274-278.

Qin C, Gao X. Simulation of remote sensing image target recognition based on convolutional neural network
［J］. Computer Simulation, 2024, 41(4): 274-278.

［53］Taye M M. Theoretical understanding of convolutional neural network: Concepts, architectures, applications, future directions
［J］. Computation, 2023, 11(3): 52.

［54］Jordan M I. Serial order: A parallel distributed processing approach
［J］. Advances in Psychology. North-Holland, 1997, 121: 471-495.

［55］Byeon W, Breuel T M, Raue F, et al. Scene labeling with LSTM recurrent neural networks
［A］. 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)
［C］. Boston: IEEE, 2015.

［56］张丽莉, 唐明冬. 循环神经网络模型下道路碳排放浓度预测
［J］. 交通科技与经济, 2024, 26(2): 23-30.

Zhang L L, Tang M D. Prediction of road carbon emission concentration based on recurrent neural network model
［J］. Technology & Economy in Areas of Communications, 2024, 26(2): 23-30.

［57］Greff K, Srivastava R K, Koutnik J, et al. LSTM: A search space odyssey
［J］. IEEE Transactions on Neural Networks and Learning Systems, 2017, 28(10): 2222-2232.

［58］Cho K, Van Merrinboer B, Gulcehre C, et al. Learning phrase representations using RNN encoder-decoder for statistical machine translation
［A］. Conference on Empirical Methods in Natural Language Processing (EMNLP)
［C］. 2014.

［59］Werbos P J. Backpropagation through time: What it does and how to do it
［J］. Proceedings of the IEEE, 1990, 78(10): 1550-1560.

［60］Li F F, Zhu J, Zhang W, et al. Investigation on the inhomogeneous deformation of magnesium alloy during bending using an advanced plasticity model
［J］. Journal of Materials Research and Technology, 2023, 25: 5064-5075.

［61］Palau T, Kuhn A, Nogales S, et al. A neural network based elasto-plasticity material model
［A］. CD-ROM Proceedings of the 6th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012)
［C］. TU Wien, 2012.

［62］Gorji M B, Mohr D. Towards neural network models for describing the large deformation behavior of sheet metal
［J］. IOP Conference Series: Materials Science and Engineering, 2019, 651(1): 012102.

［63］Linka K, Hillgrtner M, Abdolazizi K P, et al. Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning
［J］. Journal of Computational Physics, 2021, 429: 110010.

［64］Frankel A, Hamel C M, Bolintineanu D, et al. Machine learning constitutive models of elastomeric foams
［J］. Computer Methods in Applied Mechanics and Engineering, 2022, 391: 114492.

［65］Jang D P, Fazily P, Yoon J W. Machine learning-based constitutive model for J2-plasticity
［J］. International Journal of Plasticity, 2021, 138: 102919.

［66］Fazily P, Yoon J W. Machine learning-driven stress integration method for anisotropic plasticity in sheet metal forming
［J］. International Journal of Plasticity, 2023, 166: 103642.

［67］Souto N. Computational Design of a Technological Mechanical Test for Material Characterization by Inverse Analysis
［D］. Varna: Université de Bretagne Sud, 2015.

［68］Grediac M, Hild F. Full-Field Measurements and Identification in Solid Mechanics
［M］. John Wiley & Sons, 2012.

［69］Kavanagh K T, Clough R W. Finite element applications in the characterization of elastic solids
［J］. International Journal of Solids and Structures, 1971, 7(1): 11-23.

［70］Ladeveze P, Leguillon D. Error estimate procedure in the finite element method and applications
［J］. SIAM Journal on Numerical Analysis, 1983, 20(3): 485-509.

［71］Claire D, Hild F, Roux S. A finite element formulation to identify damage fields: The equilibrium gap method
［J］. International Journal for Numerical Methods in Engineering, 2004, 61(2): 189-208.

［72］Claire D, Hild F, Roux S. Identification of damage fields using kinematic measurements
［J］. Comptes Rendus. Mécanique, 2002, 330(11): 729-734.

［73］Grediac M. Principe des travaux virtuels et identification
［J］. Principe Des Travaux Virtuels et Identification, 1989, 309(1): 1-5.

［74］Martins J M P, Andrade-Campos A, Thuillier S. Comparison of inverse identification strategies for constitutive mechanical models using full-field measurements
［J］. International Journal of Mechanical Sciences, 2018, 145: 330-345.

［75］Martins J M P, Andrade-Campos A, Thuillier S. Calibration of anisotropic plasticity models using a biaxial test and the virtual fields method
［J］. International Journal of Solids and Structures, 2019, 172-173: 21-37.

［76］Bastos N, Prates P A, Andrade-Campos A. Material parameter identification of elastoplastic constitutive models using machine learning approaches
［J］. Key Engineering Materials, 2022, 926: 2193-2200.

［77］Cruz D J, Barbosa M R, Santos A D, et al. Application of machine learning to bending processes and material identification
［J］. Metals, 2021, 11(9): 1418.

［78］Jeong K, Lee K, Kwon D, et al. Parameter determination of anisotropic yield function using neural network-based indentation plastometry
［J］. International Journal of Mechanical Sciences, 2024, 263: 108776.

［79］Nascimento A, Roongta S, Diehl M, et al. A machine learning model to predict yield surfaces from crystal plasticity simulations
［J］. International Journal of Plasticity, 2023, 161: 103507.

［80］Logarzo H J, Capuano G, Rimoli J J. Smart constitutive laws: Inelastic homogenization through machine learning
［J］. Computer Methods in Applied Mechanics and Engineering, 2021, 373: 113482.

［81］Tancogne-Dejean T, Gorji M B, Zhu J, et al. Recurrent neural network modeling of the large deformation of lithium-ion battery cells
［J］. International Journal of Plasticity, 2021, 146: 103072.

［82］Abueidda D W, Koric S, Sobh N A, et al. Deep learning for plasticity and thermo-viscoplasticity
［J］. International Journal of Plasticity, 2021, 136: 102852.

［83］Mozaffar M, Bostanabad R, Chen W, et al. Deep learning predicts path-dependent plasticity
［J］. Proceedings of the National Academy of Sciences, 2019, 116(52): 26414-26420.

［84］Acar P. Machine learning reinforced crystal plasticity modeling under experimental uncertainty
［J］. AIAA Journal, 2020, 58(8): 3569-3576.

［85］Bock F E, Aydin R C, Cyron C J, et al. A review of the application of machine learning and data mining approaches in continuum materials mechanics
［J］. Frontiers in Materials, 2019, 6: 00110.

［86］Muhammad W, Brahme A P, Ibragimova O, et al. A machine learning framework to predict local strain distribution and the evolution of plastic anisotropy & fracture in additively manufactured alloys
［J］. International Journal of Plasticity, 2021, 136: 102867.

［87］Mianroodi J R, H Siboni N, Raabe D. Teaching solid mechanics to artificial intelligence-A fast solver for heterogeneous materials
［J］. NPJ Computational Materials, 2021, 7(1): 99.

［88］Heidenreich J N, Gorji M B, Mohr D. Modeling structure-property relationships with convolutional neural networks: Yield surface prediction based on microstructure images
［J］. International Journal of Plasticity, 2023, 163: 103506.

［89］Frankel A, Tachida K, Jones R. Prediction of the evolution of the stress field of polycrystals undergoing elastic-plastic deformation with a hybrid neural network model
［J］. Machine Learning: Science and Technology, 2020, 1(3): 035005.

［90］Pandey A, Pokharel R. Machine learning enabled surrogate crystal plasticity model for spatially resolved 3D orientation evolution under uniaxial tension
［J］. arXiv preprint arXiv:2005.00951, 2020.

［91］Montes de Oca Zapiain D, Lim H, Park T, et al. Predicting plastic anisotropy using crystal plasticity and Bayesian neural network surrogate models
［J］. Materials Science and Engineering: A, 2022, 833: 142472.

［92］何宽. 基于BP神经网络的晶体塑性本构参数预测方法研究
［D］. 秦皇岛：燕山大学, 2023.

He K. Study on Prediction Method of Crystal Plastic Constitutive Parameters Based on BP Neural Network Algorithm
［D］. Qinhuangdao: Yanshan University, 2023.

［93］王帅帅. 基于优化算法耦合神经网络的镁合金晶体塑性本构参数识别方法
［D］. 长春：吉林大学, 2023.

Wang S S. Identification Method of Magnesium Alloy Crystal Plasticity Constitutive Parameters Based on Optimization Algorithm Coupled with Neural Network
［D］. Changchun: Jilin University, 2023.

［94］Yang S, Tang X, Deng L, et al. Interpretable calibration of crystal plasticity model using a Bayesian surrogate-assisted genetic algorithm
［J］. Metals, 2023, 13(1): 166.

［95］Masi F, Stefanou I, Vannucci P, et al. Material modeling via thermodynamics-based artificial neural networks
［A］. Barbaresco F, Nielsen F. Geometric Structures of Statistical Physics, Information Geometry, and Learning
［C］. Cham: Springer International Publishing, 2021.

［96］Masi F, Stefanou I, Vannucci P, et al. Thermodynamics-based artificial neural networks for constitutive modeling
［J］. Journal of the Mechanics and Physics of Solids, 2021, 147: 104277.

［97］Vlassis N N, Sun W. Sobolev training of thermodynamic-informed neural networks for interpretable elasto-plasticity models with level set hardening
［J］. Computer Methods in Applied Mechanics and Engineering, 2021, 377: 113695.

Service：

【This site has not yet opened Download Service】【Add Favorite】