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A three-dimensional prediction method of stiffness properties of composites based on deep learning

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Abstract

It is significant to determine the macroscopic mechanical properties of composite materials with complex microstructure efficiently and accurately in many fields. We propose a deep learning method based on three-dimensional convolutional neural network (3D CNN) to predict the elastic coefficients of composite materials with inclusions of arbitrary sizes, shapes and material parameters. 3D datasets are generated, and a storage algorithm is proposed to reduce great storage costs in 3D. A general framework for 3D CNN models is constructed, and numerical experiments are carried out using 3D CNNs of various scales. Our results demonstrate that the scale of full connection part is the key factor of prediction ability of 3D CNNs in this task. We also demonstrate that our method can effectively save computational time compared with traditional numerical methods such as the finite element method in large-scale prediction tasks.

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References

  1. Tjong SC, Ma ZY (2000) Microstructural and mechanical characteristics of in situ metal matrix composites. Mater Sci Eng R Rep 29(3–4):49–113

    Article  Google Scholar 

  2. Sen O, Davis S, Jacobs G, Udaykumar HS (2015) Evaluation of convergence behavior of metamodeling techniques for bridging scales in multi-scale multimaterial simulation. J Comput Phys 294:585–604

    Article  MathSciNet  MATH  Google Scholar 

  3. Zhou XY, Gosling PD, Pearce CJ, Ullah Z, Kaczmarczyk L (2016) Perturbation-based stochastic multi-scale computational homogenization method for woven textile composites. Int J Solids Struct 80:368–380

    Article  Google Scholar 

  4. Gokhale AM, Singh H, Shan Z (2006) Microstructure representation and simulation tools for microstructure-based computational micro-mechanics of heterogeneous materials. In: Computational methods, dordrecht, pp 1629–1633

  5. Tagliavia G, Porfiri M, Gupta N (2009) Vinyl ester-glass hollow particle composites: dynamic mechanical properties at high inclusion volume fraction. J Compos Mater 43(5):561–582

    Article  Google Scholar 

  6. Smit RJM, Brekelmans WAM, Meijer HEH (1998) Prediction of the mechanical behavior of nonlinear heterogeneous systems by multi-level finite element modeling. Comput Methods Appl Mech Eng 155(1–2):181–192

    Article  MATH  Google Scholar 

  7. Hill R (1965) A self-consistent mechanics of composite materials. J Mech Phys Solids 13(4):213–222

    Article  MathSciNet  Google Scholar 

  8. Mori T, Tanaka K (1973) Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metall 21(5):571–574

    Article  Google Scholar 

  9. Xing YF, Du CY (2014) An improved multiscale eigenelement method of periodical composite structures. Compos Struct 118:200–207

    Article  Google Scholar 

  10. Omairey SL, Dunning PD, Sriramula S (2019) Development of an ABAQUS plugin tool for periodic RVE homogenisation. Eng Comput 35(2):567–577

    Article  Google Scholar 

  11. Cheng G-D, Cai Y-W, Xu L (2013) Novel implementation of homogenization method to predict effective properties of periodic materials. Acta Mech Sin 29(4):550–556

    Article  MathSciNet  MATH  Google Scholar 

  12. Ye S, Li B, Li Q, Zhao H-P, Feng X-Q (2019) Deep neural network method for predicting the mechanical properties of composites. Appl Phys Lett 115(16):161901

    Article  Google Scholar 

  13. Zhou K, Sun H, Enos R, Zhang D, Tang J (2021) Harnessing deep learning for physics-informed prediction of composite strength with microstructural uncertainties. Comput Mater Sci 197:110663

    Article  Google Scholar 

  14. Bargmann S, Klusemann B, Markmann J, Schnabel JE, Schneider K, Soyarslan C, Wilmers J (2018) Generation of 3D representative volume elements for heterogeneous materials: a review. Progress Mater Sci 96:322–384

    Article  Google Scholar 

  15. LeCun Y, Bengio Y, Hinton G (2015) Deep learning. Nature 521(7553):436–444

    Article  Google Scholar 

  16. Wang H, Zhang L, Han J, W E (2018) Deepmd-kit: a deep learning package for many-body potential energy representation and molecular dynamics. Comput Phys Commun 228:178–184

    Article  Google Scholar 

  17. Ryan K, Lengyel J, Shatruk M (2018) Crystal structure prediction via deep learning. J Am Chem Soc 140(32):10158–10168

    Article  Google Scholar 

  18. Moore BA, Rougier E, O’Malley D, Srinivasan G, Hunter A, Viswanathan H (2018) Predictive modeling of dynamic fracture growth in brittle materials with machine learning. Comput Mater Sci 148:46–53

    Article  Google Scholar 

  19. Elapolu MSR, Shishir MIR, Tabarraei A (2022) A novel approach for studying crack propagation in polycrystalline graphene using machine learning algorithms. Comput Mater Sci 201:110878

    Article  Google Scholar 

  20. Liu X, Gasco F, Goodsell J, Yu W (2019) Initial failure strength prediction of woven composites using a new yarn failure criterion constructed by deep learning. Compos Struct 230:111505

    Article  Google Scholar 

  21. Zhang X, Garikipati K (2020) Machine learning materials physics: multi-resolution neural networks learn the free energy and nonlinear elastic response of evolving microstructures. Comput Methods Appl Mech Eng 372:113362

    Article  MathSciNet  MATH  Google Scholar 

  22. LeCun Y, Boser B, Denker J, Henderson D, Howard R, Hubbard W, Jackel LD (1990) Handwritten digit recognition with a back-propagation network. In: Advances in neural information processing systems (NIPS), vol 2

  23. LeCun Y, Kavukcuoglu K, Farabet C (2010) Convolutional networks and applications in vision. In: Proceedings of 2010 IEEE international symposium on circuits and systems, pp 253–256

  24. Wang Y, Zhang M, Lin A, Iyer A, Prasad AS, Li X, Zhang Y, Schadler LS, Chen W, Brinson LC (2020) Mining structure-property relationships in polymer nanocomposites using data driven finite element analysis and multi-task convolutional neural networks. Mol Syst Des Eng 5(5):962–975

    Article  Google Scholar 

  25. Wei A, Xiong J, Yang W, Guo F (2021) Deep learning-assisted elastic isotropy identification for architected materials. Extreme Mech Lett 43:101173

    Article  Google Scholar 

  26. Glorot X, Bengio Y (2010) Understanding the difficulty of training deep feedforward neural networks. In: In Proceedings of the international conference on artificial intelligence and statistics, pp 249–256

  27. Hara K, Kataoka H, Satoh Y (2018) Can spatiotemporal 3D CNNs retrace the history of 2D CNNs and ImageNet? In: 2018 IEEE/CVF conference on computer vision and pattern recognition, pp 6546–6555

  28. Zhang W, Lin J, Xu W, Fu H, Yang G (2017) SCStore: managing scientific computing packages for hybrid system with containers. Tsinghua Sci Technol 22(6):675–681

    Article  Google Scholar 

  29. Dassault Systèmes Simulia Corp: SIMULIA user assistance 2020 (2020)

  30. Ioffe S, Szegedy C (2015) Batch normalization: accelerating deep network training by reducing internal covariate shift. In: International conference on machine learning. Proceedings of machine learning research, vol 37, pp 448–456

  31. Nair V, Hinton GE (2010) Rectified linear units improve restricted boltzmann machines. In: Proceedings of the 27th international conference on international conference on machine learning, pp 807–814

  32. Srivastava N, Hinton G, Krizhevsky A, Sutskever I, Salakhutdinov R (2014) Dropout: a simple way to prevent neural networks from overfitting. J Mach Learn Res 15:1929–1958

    MathSciNet  MATH  Google Scholar 

  33. Abadi M, Barham P, Chen J, Chen Z, Davis A, Dean J, Devin M, Ghemawat S, Irving G, Isard M, Kudlur M, Levenberg J, Monga R, Moore S, Murray DG, Steiner B, Tucker P, Vasudevan V, Warden P, Wicke M, Yu Y, Zheng X (2016) TensorFlow: a system for large-scale machine learning. In: Proceedings of OSDI’16: 12th USENIX symposium on operating systems design and implementation, pp 265–283

  34. Kingma DP, Ba J (2015) Adam: a method for stochastic optimization. In: International conference on learning representations

  35. Wager S, Wang S, Liang P (2013) Dropout training as adaptive regularization. Adv Neural Inform Process Syst 26:351–359

    Google Scholar 

  36. Kay W, Carreira J, Simonyan K, Zhang B, Hillier C, Vijayanarasimhan S, Viola F, Green T, Back T, Natsev P, Suleyman M, Zisserman A (2017) The kinetics human action video dataset

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Acknowledgements

This work is supported by National Natural Science Foundation of China (Grant No. 12072172 and 11772171).

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Correspondence to Yan Liu.

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Su, H., Guan, T. & Liu, Y. A three-dimensional prediction method of stiffness properties of composites based on deep learning. Comput Mech 71, 583–597 (2023). https://doi.org/10.1007/s00466-022-02253-z

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