Advertisement

Transfer learning of deep material network for seamless structure–property predictions

  • Zeliang LiuEmail author
  • C. T. Wu
  • M. Koishi
Original Paper
  • 38 Downloads

Abstract

Modern materials design requires reliable and consistent structure–property relationships. The paper addresses the need through transfer learning of deep material network (DMN). In the proposed learning strategy, we store the knowledge of a pre-trained network and reuse it to generate the initial structure for a new material via a naive approach. Significant improvements in the training accuracy and learning convergence are attained. Since all the databases share the same base network structure, their fitting parameters can be interpolated to seamlessly create intermediate databases. The new transferred models are shown to outperform the analytical micromechanics methods in predicting the volume fraction effects. We then apply the unified DMN databases to the design of failure properties, where the failure criteria are defined upon the distribution of microscale plastic strains. The Pareto frontier of toughness and ultimate tensile strength is extracted from a large-scale design space enabled by the efficiency of DMN extrapolation.

Keywords

Multiscale modeling Machine learning Micromechanics Nonlinear plasticity Failure analysis Materials design 

Notes

Acknowledgements

The authors give warmly thanks to Dr. John O. Hallquist of LSTC for his support to this research. The support from the Yokohama Rubber Co., LTD under the Yosemite project is also gratefully acknowledged.

References

  1. 1.
    Olson GB (1997) Computational design of hierarchically structured materials. Science 277(5330):1237–1242CrossRefGoogle Scholar
  2. 2.
    Panchal JH, Kalidindi SR, McDowell DL (2013) Key computational modeling issues in integrated computational materials engineering. Comput Aided Des 45(1):4–25CrossRefGoogle Scholar
  3. 3.
    McVeigh C, Vernerey F, Liu WK, Brinson LC (2006) Multiresolution analysis for material design. Comput Methods Appl Mech Eng 195(37):5053–5076MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Buljac A, Jailin C, Mendoza A, Neggers J, Taillandier-Thomas T, Bouterf A, Smaniotto B, Hild F, Roux S (2018) Digital volume correlation: review of progress and challenges. Exp Mech 58(5):661–708CrossRefGoogle Scholar
  5. 5.
    Hill R (1963) Elastic properties of reinforced solids: some theoretical principles. J Mech Phys Solids 11(5):357–372MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Feyel F, Chaboche JL (2000) FE2 multiscale approach for modelling the elastoviscoplastic behaviour of long fibre SIC/TI composite materials. Comput Methods Appl Mech Eng 183(3):309–330CrossRefzbMATHGoogle Scholar
  7. 7.
    Wu CT, Koishi M (2012) Three-dimensional meshfree-enriched finite element formulation for micromechanical hyperelastic modeling of particulate rubber composites. Int J Numer Methods Eng 91(11):1137–1157MathSciNetCrossRefGoogle Scholar
  8. 8.
    Wu CT, Guo Y, Askari E (2013) Numerical modeling of composite solids using an immersed meshfree Galerkin method. Compos Part B Eng 45(1):1397–1413CrossRefGoogle Scholar
  9. 9.
    Moulinec H, Suquet P (1998) A numerical method for computing the overall response of nonlinear composites with complex microstructure. Comput Methods Appl Mech Eng 157(1–2):69–94MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    De Geus T, Vondřejc J, Zeman J, Peerlings R, Geers M (2017) Finite strain FFT-based non-linear solvers made simple. Comput Methods Appl Mech Eng 318:412–430MathSciNetCrossRefGoogle Scholar
  11. 11.
    Yvonnet J, Monteiro E, He QC (2013) Computational homogenization method and reduced database model for hyperelastic heterogeneous structures. Int J Multiscale Comput Eng 11(3):201–225CrossRefGoogle Scholar
  12. 12.
    Yang Z, Yabansu YC, Al-Bahrani R, Liao Wk, Choudhary AN, Kalidindi SR, Agrawal A (2018) Deep learning approaches for mining structure–property linkages in high contrast composites from simulation datasets. Comput Mater Sci 151:278–287CrossRefGoogle Scholar
  13. 13.
    Bessa M, Bostanabad R, Liu Z, Hu A, Apley D, Brinson C, Chen W, Liu W (2017) A framework for data-driven analysis of materials under uncertainty: countering the curse of dimensionality. Computer Methods Appl Mech Eng 320:633–667MathSciNetCrossRefGoogle Scholar
  14. 14.
    Raissi M, Karniadakis GE (2018) Hidden physics models: machine learning of nonlinear partial differential equations. J Comput Phys 357:125–141MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Chen Z, Huang T, Shao Y, Li Y, Xu H, Avery K, Zeng D, Chen W, Su X (2018) Multiscale finite element modeling of sheet molding compound (smc) composite structure based on stochastic mesostructure reconstruction. Compos Struct 188:25–38CrossRefGoogle Scholar
  16. 16.
    Oliver J, Caicedo M, Huespe A, Hernández J, Roubin E (2017) Reduced order modeling strategies for computational multiscale fracture. Computer Methods Appl Mech Eng 313:560–595MathSciNetCrossRefGoogle Scholar
  17. 17.
    Kalidindi SR (2015) Hierarchical materials informatics: novel analytics for materials data. Elsevier, AmsterdamGoogle Scholar
  18. 18.
    Latypov MI, Toth LS, Kalidindi SR (2019) Materials knowledge system for nonlinear composites. Computer Methods Appl Mech Eng 346:180–196MathSciNetCrossRefGoogle Scholar
  19. 19.
    Liu Z, Bessa M, Liu WK (2016) Self-consistent clustering analysis: an efficient multi-scale scheme for inelastic heterogeneous materials. Computer Methods Appl Mech Eng 306:319–341MathSciNetCrossRefGoogle Scholar
  20. 20.
    Liu Z, Fleming M, Liu WK (2018) Microstructural material database for self-consistent clustering analysis of elastoplastic strain softening materials. Computer Methods Appl Mech Eng 330:547–577MathSciNetCrossRefGoogle Scholar
  21. 21.
    Liu Z, Kafka OL, Yu C, Liu WK (2018) Data-driven self-consistent clustering analysis of heterogeneous materials with crystal plasticity. In: Advances in computational plasticity. Springer, pp 221–242Google Scholar
  22. 22.
    Yu C, Kafka OL, Liu WK (2019) Self-consistent clustering analysis for multiscale modeling at finite strains. Computer Methods Appl Mech Eng 349:339–359MathSciNetCrossRefGoogle Scholar
  23. 23.
    Liu Z, Wu C, Koishi M (2019) A deep material network for multiscale topology learning and accelerated nonlinear modeling of heterogeneous materials. Computer Methods Appl Mech Eng 345:1138–1168MathSciNetCrossRefGoogle Scholar
  24. 24.
    Liu Z, Wu C (2019) Exploring the 3d architectures of deep material network in data-driven multiscale mechanics. J Mech Phys Solids 127:20–46MathSciNetCrossRefGoogle Scholar
  25. 25.
    Thrun S (1996) Is learning the n-th thing any easier than learning the first? In: Advances in neural information processing systems, pp 640–646Google Scholar
  26. 26.
    Raina R, Ng AY, Koller D (2006) Constructing informative priors using transfer learning. In: Proceedings of the 23rd international conference on machine learning. ACM, pp 713–720Google Scholar
  27. 27.
    Lubbers N, Lookman T, Barros K (2017) Inferring low-dimensional microstructure representations using convolutional neural networks. Phys Rev E 96(5):052111CrossRefGoogle Scholar
  28. 28.
    Simonyan K, Zisserman A (2014) Very deep convolutional networks for large-scale image recognition. arXiv preprint arXiv:1409.1556
  29. 29.
    Li X, Zhang Y, Zhao H, Burkhart C, Brinson LC, Chen W (2018) A transfer learning approach for microstructure reconstruction and structure–property predictions. Sci Rep 8(1):13461CrossRefGoogle Scholar
  30. 30.
    Melro A, Camanho P, Pinho S (2008) Generation of random distribution of fibres in long-fibre reinforced composites. Compos Sci Technol 68(9):2092–2102CrossRefGoogle Scholar
  31. 31.
    Mori T, Tanaka K (1973) Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metall 21(5):571–574CrossRefGoogle Scholar
  32. 32.
    Hill R (1965) A self-consistent mechanics of composite materials. J Mech Phys Solids 13(4):213–222MathSciNetCrossRefGoogle Scholar
  33. 33.
    Eshelby JD (1957) The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proc R Soc Lond A 241(1226):376–396MathSciNetCrossRefzbMATHGoogle Scholar
  34. 34.
    Christensen R, Lo K (1979) Solutions for effective shear properties in three phase sphere and cylinder models. J Mech Phys Solids 27(4):315–330CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Livermore Software Technology Corporation (LSTC)LivermoreUSA
  2. 2.Koishi LaboratoryThe Yokohama Rubber Co., LTD.HiratsukaJapan

Personalised recommendations