基于机器学习的金属材料多尺度塑性力学研究进展
收稿日期: 2025-09-30
修回日期: 2025-11-13
网络出版日期: 2026-02-12
基金资助
国家自然科学基金项目(12192214);国家自然科学基金项目(12532004);国家自然科学基金项目(12222209)
Advances in Machine Learning-Based Multiscale Plasticity Mechanics of Metallic Materials
Received date: 2025-09-30
Revised date: 2025-11-13
Online published: 2026-02-12
Supported by
National Natural Science Foundation of China(12192214);National Natural Science Foundation of China(12532004);National Natural Science Foundation of China(12222209)
多尺度塑性力学研究旨在揭示材料塑性变形过程中的力学响应规律，建立微观结构、变形机制与宏观性能之间的物理联系，在材料设计与性能优化中具有重要意义。金属材料的塑性行为往往伴随位错、界面、相变等多种微观结构和变形机制的协同演化，构成高度复杂的时空耦合系统，传统建模方法在构型复杂性、尺度衔接及机理表征等方面面临诸多挑战。近年来，机器学习与多尺度数值模拟和本构模型构建的融合为多尺度塑性力学研究开辟了新路径。本文综述了基于机器学习的多尺度塑性力学研究进展，主要包括塑性变形行为的多尺度模拟和本构模型构建两方面，涵盖基于机器学习的分子动力学势函数构建与模拟、离散位错动力学模拟、晶体塑性有限元及本构模型构建等典型进展。最后，对未来机器学习赋能的多尺度塑性力学研究的发展方向进行了展望。
康国政 , 张旭 , 胡冰晖 , 双思垚 , 于峻石 , 熊宇凯 , 宋世杰 . 基于机器学习的金属材料多尺度塑性力学研究进展[J]. 金属学报, 2026 , 62(5) : 803 -821 . DOI: 10.11900/0412.1961.2025.00299
Multiscale plasticity mechanics aims to reveal the plastic deformation response of materials across length scales and to establish physical links among the microstructure, deformation mechanisms, and macroscopic properties, providing critical insights for materials design and performance optimization. Plasticity in metallic materials often involves the interplay of multiple microstructures and deformation mechanisms such as dislocations, interfaces, and phase transformations, which together form a highly complex spatiotemporal system. Traditional modeling approaches struggle to handle configurational complexity, bridge different scales, or represent the underlying mechanisms in such systems. Recently, machine learning has been integrated with multiscale simulations and constitutive modeling, opening new avenues in multiscale plasticity research. This review focuses on two primary aspects of machine learning-enabled multiscale plasticity studies: multiscale simulations of plastic deformation and the development of constitutive models. Representative examples include machine learning-based interatomic potential construction, dislocation dynamics simulations, finite element simulations of crystal plasticity, and data-driven constitutive modeling. Finally, the review envisages future directions for multiscale plasticity mechanics empowered by machine learning.
| [1] | Wu W Y, Song C H, Zhang Z S, et al. Microstructure and properties of as-cast Co-28Cr alloy with aging treatment [J]. Chin. J. Rare Met., 2025, 49: 982 |
| 吴文源, 宋成浩, 张振山 等. 时效处理对铸态Co-28Cr合金组织和性能的影响 [J]. 稀有金属, 2025, 49: 982 | |
| [2] | Tong J B, Wang X D, Nie J J, et al. Diffusivities and atomic mobilities in the bcc phase of the Ti-Al-Fe system [J]. Foundry Technol., 2024, 45: 672 |
| 佟健博, 王向东, 聂晶晶 等. Ti-Al-Fe体系bcc相扩散系数及原子移动性 [J]. 铸造技术, 2024, 45: 672 | |
| [3] | Cheng J. Effect of deformation on microstructure and mechanical properties of (CoNiV)97Al3 medium entropy alloy [J]. Nonferrous Met. Mater. Eng., 2024, 45(3): 1 |
| 程 军. 变形量对(CoNiV)97Al3中熵合金组织和力学性能的影响 [J]. 有色金属材料与工程, 2024, 45(3): 1 | |
| [4] | Zhou R, Xiong Y K, Chu J L, et al. Parameter identification of nonlocal crystal plastic model based on machine learning and genetic algorithm [J]. Chin. J. Theor. Appl. Mech., 2024, 56: 751 |
| 周 瑞, 熊宇凯, 储节磊 等. 基于机器学习和遗传算法的非局部晶体塑性模型参数识别 [J]. 力学学报, 2024, 56: 751 | |
| [5] | Xie B B, Chen Y, Liu B, et al. Automatic intelligent multiscale simulation to predict mechanical properties and deformation mechanism of complex concentrated alloys [J]. Acta Mater., 2025, 297: 121359 |
| [6] | Behler J, Parrinello M. Generalized neural-network representation of high-dimensional potential-energy surfaces [J]. Phys. Rev. Lett., 2007, 98: 146401 |
| [7] | Behler J. Perspective: Machine learning potentials for atomistic simulations [J]. J. Chem. Phys., 2016, 145: 170901 |
| [8] | Salmenjoki H, Alava M J, Laurson L. Machine learning plastic deformation of crystals [J]. Nat. Commun., 2018, 9: 5307 |
| [9] | Hu Y W, Zhang H Y, Cheng J, et al. Machine learning for hot deformation flow stress prediction and dynamic recrystallization in Fe24.75Ni19.8Co9.9Cr14.85Al10.9Mn14.85Si4.95 high-entropy alloy [J]. Intermetallics, 2025, 185: 108914 |
| [10] | Daw M S, Baskes M I. Semiempirical, quantum mechanical calculation of hydrogen embrittlement in metals [J]. Phys. Rev. Lett., 1983, 50: 1285 |
| [11] | Baskes M I. Modified embedded-atom potentials for cubic materials and impurities [J]. Phys. Rev., 1992, 46B: 2727 |
| [12] | van Duin A C T, Dasgupta S, Lorant F, et al. ReaxFF: A reactive force field for hydrocarbons [J]. J. Phys. Chem., 2001, 105A: 9396 |
| [13] | Zuo Y X, Chen C, Li X G, et al. Performance and cost assessment of machine learning interatomic potentials [J]. J. Phys. Chem., 2020, 124A: 731 |
| [14] | Bartók A P, Payne M C, Kondor R, et al. Gaussian approximation potentials: The accuracy of quantum mechanics, without the electrons [J]. Phys. Rev. Lett., 2010, 104: 136403 |
| [15] | Novikov I S, Gubaev K, Podryabinkin E V, et al. The MLIP package: Moment tensor potentials with MPI and active learning [J]. Mach. Learn.: Sci. Technol., 2021, 2: 025002 |
| [16] | Fan Z Y, Wang Y Z, Ying P H, et al. GPUMD: A package for constructing accurate machine-learned potentials and performing highly efficient atomistic simulations [J]. J. Chem. Phys., 2022, 157: 114801 |
| [17] | Rowe P, Deringer V L, Gasparotto P, et al. An accurate and transferable machine learning potential for carbon [J]. J. Chem. Phys., 2020, 153: 034702 |
| [18] | Zhao R, Wang S C, Kong Z Z, et al. Development of a neuroevolution machine learning potential of Pd-Cu-Ni-P alloys [J]. Mater. Des., 2023, 231: 112012 |
| [19] | Zheng H, Fey L T W, Li X G, et al. Multi-scale investigation of short-range order and dislocation glide in MoNbTi and TaNbTi multi-principal element alloys [J]. npj Comput. Mater., 2023, 9: 89 |
| [20] | Han J Q, Zhang L F, Car R, et al. Deep potential: A general representation of a many-body potential energy surface [J]. Commun. Comput. Phys., 2018, 23: 629 |
| [21] | Zhang L F, Han J Q, Wang H, et al. Deep potential molecular dynamics: A scalable model with the accuracy of quantum mechanics [J]. Phys. Rev. Lett., 2018, 120: 143001 |
| [22] | Xu K, Bu H K, Pan S N, et al. GPUMD 4.0: A high-performance molecular dynamics package for versatile materials simulations with machine-learned potentials [J]. Mater. Genome Eng. Adv., 2025, 3: e70028 |
| [23] | Santos-Florez P A, Dai S C, Yao Y, et al. Short-range order and its impacts on the BCC MoNbTaW multi-principal element alloy by the machine-learning potential [J]. Acta Mater., 2023, 255: 119041 |
| [24] | Li X G, Chen C, Zheng H, et al. Complex strengthening mechanisms in the NbMoTaW multi-principal element alloy [J]. npj Comput. Mater., 2020, 6: 70 |
| [25] | Yin S, Zuo Y X, Abu-Odeh A, et al. Atomistic simulations of dislocation mobility in refractory high-entropy alloys and the effect of chemical short-range order [J]. Nat. Commun., 2021, 12: 4873 |
| [26] | Meng F S, Shinzato S, Zhang S H, et al. A highly transferable and efficient machine learning interatomic potentials study of α-Fe-C binary system [J]. Acta Mater., 2024, 281: 120408 |
| [27] | Gong X G, Li Z Y, Pattamatta A S L S, et al. An accurate and transferable machine learning interatomic potential for nickel [J]. Commun. Mater., 2024, 5: 157 |
| [28] | Takamoto S, Okanohara D, Li Q J, et al. Towards universal neural network interatomic potential [J]. J. Materiomics, 2023, 9: 447 |
| [29] | Song K K, Zhao R, Liu J H, et al. General-purpose machine-learned potential for 16 elemental metals and their alloys [J]. Nat. Commun., 2024, 15: 10208 |
| [30] | Bertin N, Sills R B, Cai W. Frontiers in the simulation of dislocations [J]. Annu. Rev. Mater. Res., 2020, 50: 437 |
| [31] | Steinberger D, Song H X, Sandfeld S. Machine learning-based classification of dislocation microstructures [J]. Front. Mater., 2019, 6: 141 |
| [32] | Zhou Z C, Zhu Y C, Luo J, et al. Characterisation of dislocation patterning behaviour with a continuum dislocation dynamics model on two parallel slip planes equipped with a deep neural network resolving local microstructures [J]. Int. J. Solids Struct., 2020, 198: 57 |
| [33] | Tao J, Wei D A, Yu J S, et al. Micropillar compression using discrete dislocation dynamics and machine learning [J]. Theor. Appl. Mech. Lett., 2024, 14: 100484 |
| [34] | Hiemer S, Fan H D, Zaiser M. Relating plasticity to dislocation properties by data analysis: Scaling vs. machine learning approaches [J]. Mater. Theory, 2023, 7: 1 |
| [35] | Salmenjoki H, Laurson L, Alava M J. Probing the transition from dislocation jamming to pinning by machine learning [J]. Mater. Theory, 2020, 4: 5 |
| [36] | Rafiei M H, Gu Y J, El-Awady J A. Machine learning of dislocation-induced stress fields and interaction forces [J]. JOM, 2020, 72: 4380 |
| [37] | Bertin N, Zhou F. Accelerating discrete dislocation dynamics simulations with graph neural networks [J]. J. Comput. Phys., 2023, 487: 112180 |
| [38] | Khan A S, Lopez-Pamies O, Kazmi R. Thermo-mechanical large deformation response and constitutive modeling of viscoelastic polymers over a wide range of strain rates and temperatures [J]. Int. J. Plast., 2006, 22: 581 |
| [39] | Wei X L, van der Zwaag S, Jia Z X, et al. On the use of transfer modeling to design new steels with excellent rotating bending fatigue resistance even in the case of very small calibration datasets [J]. Acta Mater., 2022, 235: 118103 |
| [40] | Dai W, Wang H M, Guan Q, et al. Studying the micromechanical behaviors of a polycrystalline metal by artificial neural networks [J]. Acta Mater., 2021, 214: 117006 |
| [41] | Frydrych K, Tomczak M, Papanikolaou S. Crystal plasticity parameter optimization in cyclically deformed electrodeposited copper—A machine learning approach [J]. Materials, 2024, 17: 3397 |
| [42] | Bulgarevich D S, Watanabe M. Stress-strain curve predictions by crystal plasticity simulations and machine learning [J]. Sci. Rep., 2024, 14: 29492 |
| [43] | Veasna K, Feng Z X, Zhang Q, et al. Machine learning-based multi-objective optimization for efficient identification of crystal plasticity model parameters [J]. Comput. Methods Appl. Mech. Eng., 2023, 403: 115740 |
| [44] | Bishara D, Li S F. A machine-learning aided multiscale homogenization model for crystal plasticity: Application for face-centered cubic single crystals [J]. Comput. Mech., 2023, 72: 77 |
| [45] | Miyazawa Y, Briffod F, Shiraiwa T, et al. Prediction of cyclic stress-strain property of steels by crystal plasticity simulations and machine learning [J]. Materials, 2019, 12: 3668 |
| [46] | Sharma A S, Ahmad O, Bhowmick S, et al. Machine learning to accelerate full-field crystal plasticity simulations [J]. Procedia Struct. Integr., 2025, 71: 469 |
| [47] | Acar P. Machine learning reinforced crystal plasticity modeling under experimental uncertainty [J]. AIAA J., 2020, 58: 3569 |
| [48] | Weber G, Pinz M, Ghosh S. Machine learning-enabled self-consistent parametrically-upscaled crystal plasticity model for Ni-based superalloys [J]. Comput. Methods Appl. Mech. Eng., 2022, 402: 115384 |
| [49] | Saidi P, Pirgazi H, Sanjari M, et al. Deep learning and crystal plasticity: A preconditioning approach for accurate orientation evolution prediction [J]. Comput. Methods Appl. Mech. Eng., 2022, 389: 114392 |
| [50] | Ye W Y, Hohl J, Mushongera L T. Prediction of cyclic damage in metallic alloys with crystal plasticity modeling enhanced by machine learning [J]. Materialia, 2022, 22: 101388 |
| [51] | Ye W Y, Zhang X, Hohl J, et al. Life prediction for directed energy deposition-manufactured 316L stainless steel using a coupled crystal plasticity-machine learning framework [J]. Adv. Eng. Mater., 2023, 25: 2201429 |
| [52] | Lee J, Tasdemir B, Das S, et al. Productive automation of calibration processes for crystal plasticity model parameters via reinforcement learning [J]. Mater. Des., 2024, 248: 113470 |
| [53] | Lu S J, Zhang X, Hu Y N, et al. Machine learning-based constitutive parameter identification for crystal plasticity models [J]. Mech. Mater., 2025, 203: 105263 |
| [54] | Wang J, Chen J H, Li S X, et al. Prediction of white etching area damage based on machine learning model combined with crystal plasticity under rolling contact fatigue [J]. Int. J. Fatigue, 2025, 198: 108965 |
| [55] | Eghtesad A, Luo Q X, Shang S L, et al. Machine learning-enabled identification of micromechanical stress and strain hotspots predicted via dislocation density-based crystal plasticity simulations [J]. Int. J. Plast., 2023, 166: 103646 |
| [56] | Mao Y W, Keshavarz S, Kilic M N T, et al. A deep learning-based crystal plasticity finite element model [J]. Scr. Mater., 2025, 254: 116315 |
| [57] | Yuan M F, Paradiso S, Meredig B, et al. Machine learning-based reduce order crystal plasticity modeling for ICME applications [J]. Integr. Mater. Manuf. Innov., 2018, 7: 214 |
| [58] | Nascimento A, Roongta S, Diehl M, et al. A machine learning model to predict yield surfaces from crystal plasticity simulations [J]. Int. J. Plast., 2023, 161: 103507 |
| [59] | Ashby M F. The deformation of plastically non-homogeneous materials [J]. Philos. Mag., 1970, 21: 399 |
| [60] | Voyiadjis G Z, Song Y. Strain gradient continuum plasticity theories: Theoretical, numerical and experimental investigations [J]. Int. J. Plast., 2019, 121: 21 |
| [61] | Huang Y, Qu S, Hwang K C, et al. A conventional theory of mechanism-based strain gradient plasticity [J]. Int. J. Plast., 2004, 20: 753 |
| [62] | Fleck N A, Hutchinson J W. A phenomenological theory for strain gradient effects in plasticity [J]. J. Mech. Phys. Solids, 1993, 41: 1825 |
| [63] | Gao H, Huang Y, Nix W D, et al. Mechanism-based strain gradient plasticity— I. Theory [J]. J. Mech. Phys. Solids, 1999, 47: 1239 |
| [64] | Gurtin M E. A gradient theory of single-crystal viscoplasticity that accounts for geometrically necessary dislocations [J]. J. Mech. Phys. Solids, 2002, 50: 5 |
| [65] | Tan J Y, Maupin K, Shao S, et al. A Bayesian machine learning framework for selection of the strain gradient plasticity multiscale model [A]. ASME 2021 International Mechanical Engineering Congress and Exposition. Volume 12: Mechanics of Solids, Structures, and Fluids; Micro- and Nano-Systems Engineering and Packaging [C]. ASME, 2021: Virtual, Online, V012T12A009. |
| [66] | Gurtin M E, Reddy B D. Gradient single-crystal plasticity within a Mises-Hill framework based on a new formulation of self- and latent-hardening [J]. J. Mech. Phys. Solids, 2014, 68: 134 |
| [67] | Dao M, Chollacoop N, Van Vliet K J, et al. Computational modeling of the forward and reverse problems in instrumented sharp indentation [J]. Acta Mater., 2001, 49: 3899 |
| [68] | Lee J, Lee C, Kim B. Reverse analysis of nano-indentation using different representative strains and residual indentation profiles [J]. Mater. Des., 2009, 30: 3395 |
| [69] | Kang J J, Becker A A, Sun W. Determining elastic-plastic properties from indentation data obtained from finite element simulations and experimental results [J]. Int. J. Mech. Sci., 2012, 62: 34 |
| [70] | Chen H, Cai L X. Theoretical model for predicting uniaxial stress-strain relation by dual conical indentation based on equivalent energy principle [J]. Acta Mater., 2016, 121: 181 |
| [71] | Long X, Lu C H, Shen Z Y, et al. Identification of mechanical properties of thin-film elastoplastic materials by machine learning [J]. Acta Mech. Solida Sin., 2023, 36: 13 |
| [72] | Zhu D X, Zhao J F, Hu Y N, et al. Predicting tensile behavior from nanoindentation using gradient plasticity model with neural network and genetic algorithm [J]. Mech. Mater., 2025, 207: 105368 |
| [73] | Rajendran S. A technique to develop mesh-distortion immune finite elements [J]. Comput. Methods Appl. Mech. Eng., 2010, 199: 1044 |
| [74] | Reddy J N. On locking-free shear deformable beam finite elements [J]. Comput. Methods Appl. Mech. Eng., 1997, 149: 113 |
| [75] | Tyagi A, Suman U, Mamajiwala M, et al. Physics informed deep learning for strain gradient continuum plasticity [J]. 2024, arXiv: 2408. 06657 |
| [76] | Anand L, Gurtin M E, Lele S P, et al. A one-dimensional theory of strain-gradient plasticity: Formulation, analysis, numerical results [J]. J. Mech. Phys. Solids, 2005, 53: 1789 |
| [77] | Ghaboussi J, Garrett J H, Wu X. Knowledge‐based modeling of material behavior with neural networks [J]. J. Eng. Mech., 1991, 117: 132 |
| [78] | Liu Q B, Ji Z, Liu M B, et al. Acquiring the constitutive relationship for a thermal viscoplastic material using an artificial neural network [J]. J. Mater. Process. Technol., 1996, 62: 206 |
| [79] | Al-Haik M S, Hussaini M Y, Garmestani H. Prediction of nonlinear viscoelastic behavior of polymeric composites using an artificial neural network [J]. Int. J. Plast., 2006, 22: 1367 |
| [80] | Ghaboussi J, Sidarta D E. New nested adaptive neural networks (NANN) for constitutive modeling [J]. Comput. Geotech., 1998, 22: 29 |
| [81] | Mozaffar M, Bostanabad R, Chen W, et al. Deep learning predicts path-dependent plasticity [J]. Proc. Natl. Acad. Sci. USA, 2019, 116: 26414 |
| [82] | Gorji M B, Mozaffar M, Heidenreich J N, et al. On the potential of recurrent neural networks for modeling path dependent plasticity [J]. J. Mech. Phys. Solids, 2020, 143: 103972 |
| [83] | Versino D, Tonda A, Bronkhorst C A. Data driven modeling of plastic deformation [J]. Comput. Methods Appl. Mech. Eng., 2017, 318: 981 |
| [84] | Kabliman E, Kolody A H, Kronsteiner J, et al. Application of symbolic regression for constitutive modeling of plastic deformation [J]. Appl. Eng. Sci., 2021, 6: 100052 |
| [85] | Masi F, Stefanou I, Vannucci P, et al. Thermodynamics-based Artificial Neural Networks for constitutive modeling [J]. J. Mech. Phys. Solids, 2021, 147: 104277 |
| [86] | Deng X W, Hu Y N, Hu B H, et al. Machine learning based prediction models for uniaxial ratchetting of extruded AZ31 magnesium alloy [J]. Extreme Mech. Lett., 2024, 70: 102193 |
| [87] | Yu Z, Sun X Y, Xing R S, et al. Unified prediction of uniaxial ratcheting deformation at elevated temperatures with physics-informed multimodal network [J]. Int. J. Plast., 2025, 187: 104275 |
| [88] | Zhu J A, Xue Y H, Liu Z S. A transfer learning enhanced physics-informed neural network for parameter identification in soft materials [J]. Appl. Math. Mech., 2024, 45: 1685 |
| [89] | Su M M, Yu Y, Chen T H, et al. A thermodynamics-informed neural network for elastoplastic constitutive modeling of granular materials [J]. Comput. Methods Appl. Mech. Eng., 2024, 430: 117246 |
| [90] | Liu D P, Yang H, Elkhodary K I, et al. Mechanistically informed data-driven modeling of cyclic plasticity via artificial neural networks [J]. Comput. Methods Appl. Mech. Eng., 2022, 393: 114766 |
| [91] | Guo Z F, Bai R X, Lei Z K, et al. CPINet: Parameter identification of path-dependent constitutive model with automatic denoising based on CNN-LSTM [J]. Eur. J. Mech., 2021, 90A: 104327 |
| [92] | Du R, Song H X, Gao F H, et al. Machine learning informed visco-plastic model for the cyclic relaxation of 316H stainless steel at 550 °C [J]. Int. J. Plast., 2023, 170: 103743 |
| [93] | Messner M C, Rhee M, Arsenlis A, et al. A crystal plasticity model for slip in hexagonal close packed metals based on discrete dislocation simulations [J]. Modell. Simul. Mater. Sci. Eng., 2017, 25: 044001 |
/
| 〈 |
|
〉 |
