Skip to main content
Log in

Reduced-Order Models for Ranking Damage Initiation in Dual-Phase Composites Using Bayesian Neural Networks

  • Augmenting Physics-based Models in ICME with Machine Learning and Uncertainty Quantification
  • Published:
JOM Aims and scope Submit manuscript

Abstract

The design and development of materials with increased damage resilience is often impeded by the difficulty in establishing the precise linkages, with quantified uncertainty, between the complex details of the internal structure of materials and their potential for damage initiation. We present herein a novel machine-learning-based approach for establishing reduced-order models (ROMs) that relate the microstructure of a material to its susceptibility to damage initiation. This is accomplished by combining the recently established materials knowledge system framework with toolsets such as feedforward neural networks and variational Bayesian inference. The overall approach is found to be versatile for training scalable and accurate ROMs with quantified prediction uncertainty for the propensity to damage initiation for a variety of microstructures. The approach is applicable to a large class of challenges encountered in multiscale materials design efforts.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. T.L. Anderson and T.L. Anderson, Fracture Mechanics: Fundamentals and Applications, 3rd ed. (Oxfordshire: Taylor & Francis, 2005), pp. 3–5.

    MATH  Google Scholar 

  2. D. Krajcinovic, Damage Mechanics (Amsterdam: Elsevier, 1996), pp. 3–5.

    Google Scholar 

  3. B. Anbarlooie, J. Kadkhodapour, H. Hosseini Toudeshky and S. Schmauder, Micromechanics of Dual-Phase Steels: Deformation, Damage, and Fatigue, in Handbook of Mechanics of Materials, S. Schmauder, C.-S. Chen, K.K. Chawla, N. Chawla, W. Chen and Y. Kagawa. (Singapore: Springer Singapore, 2018), pp. 1–30.

  4. T. De Geus, F. Maresca, R. Peerlings, and M. Geers, Mech. Mater. 101, 147 (2016).

    Google Scholar 

  5. T. de Geus, R. Peerlings, and M. Geers, Eng. Fract. Mech. 169, 354 (2017).

    Google Scholar 

  6. T.W.J. de Geus, R.H.J. Peerlings, and M.G.D. Geers, Eng. Fract. Mech. 147, 318 (2015).

    Google Scholar 

  7. S.K. Paul, Comput. Mater. Sci. 56, 34 (2012).

    Google Scholar 

  8. C.C. Tasan, J.P.M. Hoefnagels, M. Diehl, D. Yan, F. Roters, and D. Raabe, Int. J. Plast 63, 198 (2014).

    Google Scholar 

  9. T. de Geus, J. van Duuren, R. Peerlings, and M. Geers, Mater. Sci. Eng. A 673, 551 (2016).

    Google Scholar 

  10. T.W.J. de Geus, M. Cottura, B. Appolaire, R.H.J. Peerlings, and M.G.D. Geers, Mech. Mater. 97, 199 (2016).

    Google Scholar 

  11. T.W.J. de Geus, R.H.J. Peerlings, and M.G.D. Geers, Int. J. Solids Struct. 97–98, 687 (2016).

    Google Scholar 

  12. Y. Brechet, J. Embury, S. Tao, and L. Luo, Acta Metall. Mater. 39, 1781 (1991).

    Google Scholar 

  13. Y. Brechet, J. Newell, S. Tao, and J. Embury, Scr. Metall. Mater. 28, 47 (1993).

    Google Scholar 

  14. D. Wilkinson, E. Maire, and J. Embury, Mater. Sci. Eng. A 233, 145 (1997).

    Google Scholar 

  15. D. Wilkinson, E. Maire, and R. Fougeres, Mater. Sci. Eng. A 262, 264 (1999).

    Google Scholar 

  16. J. Llorca and J. Segurado, Mater. Sci. Eng. A 365, 267 (2004).

    Google Scholar 

  17. J. Segurado, C. Gonzalez, and J. Llorca, Acta Mater. 51, 2355 (2003).

    Google Scholar 

  18. J. Segurado and J. Llorca, Mech. Mater. 38, 873 (2006).

    Google Scholar 

  19. T.W.J. de Geus, R.H.J. Peerlings, and M.G.D. Geers, Int. J. Solids Struct. 67–68, 326 (2015).

    Google Scholar 

  20. D. Montes de Oca Zapiain, E. Popova, F. Abdeljawad, J.W. Foulk, S.R. Kalidindi, and H. Lim, Integr. Mater. Manuf. Innov. 7, 97 (2018).

    Google Scholar 

  21. N.H. Paulson, M.W. Priddy, D.L. McDowell, and S.R. Kalidindi, Int. J. Fatigue 119, 1 (2019).

    Google Scholar 

  22. D.T. Fullwood, S.R. Niezgoda, B.L. Adams, and S.R. Kalidindi, Prog. Mater Sci. 55, 477 (2010).

    Google Scholar 

  23. D.B. Brough, D. Wheeler, and S.R. Kalidindi, Integr. Mater. Manuf. Innov. 6, 36 (2017).

    Google Scholar 

  24. S.R. Kalidindi, Structure-Property linkages.Hierarchical Materials Informatics, ed. S.R. Kalidindi (Boston: Butterworth-Heinemann, 2015), pp. 145–189.

    Google Scholar 

  25. M.W. Priddy, N.H. Paulson, S.R. Kalidindi, and D.L. McDowell, Int. J. Fatigue 104, 231 (2017).

    Google Scholar 

  26. N.H. Paulson, M.W. Priddy, D.L. McDowell, and S.R. Kalidindi, Mater. Des. 154, 170 (2018).

    Google Scholar 

  27. T. Hastie, R. Tibshirani and J. Friedman, The Elements of Statistical Learning: Data Mining, Inference, and Prediction (Berlin: Springer, 2009), pp. 392–397, 534–538, 397–401.

  28. C.M. Bishop, Pattern Recognition and Machine Learning (Information Science and Statistics) (Berlin: Springer, 2006), pp. 225–246, 561–570, 21–23.

  29. A. Gelman, J.B. Carlin, H.S. Stern and D.B. Rubin, Bayesian Data Analysis. 2nd edn (Boca Raton: Chapman and Hall, 2004), pp. 6–8, 331.

  30. S.R. Kalidindi, MRS Commun. 9, 518 (2019).

    Google Scholar 

  31. S. Papanikolaou, Comput. Mech. 66, 141 (2020).

    MathSciNet  Google Scholar 

  32. H. Li, O.L. Kafka, J. Gao, C. Yu, Y. Nie, L. Zhang, M. Tajdari, S. Tang, X. Guo, G. Li, S. Tang, G. Cheng, and W.K. Liu, Comput. Mech. 64, 281 (2019).

    MathSciNet  Google Scholar 

  33. W.K. Liu, G. Karniadakis, S. Tang, and J. Yvonnet, Comput. Mech. 64, 275 (2019).

    MathSciNet  Google Scholar 

  34. X. Lu, D.G. Giovanis, J. Yvonnet, V. Papadopoulos, F. Detrez, and J. Bai, Comput. Mech. 64, 307 (2019).

    MathSciNet  Google Scholar 

  35. D.J.C. MacKay, Information Theory, Inference & Learning Algorithms (Cambridge: Cambridge University Press, 2002), pp. 422–424.

    Google Scholar 

  36. C. Blundell, J. Cornebise, K. Kavukcuoglu and D. Wierstra, Weight Uncertainty in Neural Network, in Proceedings of the 32nd International Conference on Machine Learning, B. Francis and B. David, Editors. 2015 (Proceedings of Machine Learning Research: PMLR), pp. 1613–1622.

  37. S.R. Kalidindi, S.R. Niezgoda, G. Landi, S. Vachhani, and T. Fast, Comput. Mater. Contin. 17, 103 (2010).

    Google Scholar 

  38. G. Landi, S.R. Niezgoda, and S.R. Kalidindi, Acta Mater. 58, 2716 (2010).

    Google Scholar 

  39. Y.C. Yabansu, D.K. Patel, and S.R. Kalidindi, Acta Mater. 81, 151 (2014).

    Google Scholar 

  40. Y.C. Yabansu and S.R. Kalidindi, Acta Mater. 94, 26 (2015).

    Google Scholar 

  41. M.A. Groeber and M.A. Jackson, Integrat. Mater. Manuf. Innov. 3, 56 (2014).

    Google Scholar 

  42. A. Cecen, H. Dai, Y.C. Yabansu, S.R. Kalidindi, and L. Song, Acta Mater. 146, 76 (2018).

    Google Scholar 

  43. R.A. Haddad and A.N. Akansu, Trans. Sig. Proc. 39, 723 (1991).

    Google Scholar 

  44. S.R. Kalidindi, Hierarchical Materials Informatics: Novel Analytics for Materials Data (Amsterdam: Elsevier, 2015).

    Google Scholar 

  45. S.R. Kalidindi, S.R. Niezgoda, and A.A. Salem, JOM 63, 34 (2011).

    Google Scholar 

  46. D. McDowell, S. Ghosh, and S. Kalidindi, JOM, 63, 45 (2011).

  47. S. Torquato, Random Heterogeneous Materials (Berlin: Springer, 2013).

    MATH  Google Scholar 

  48. D. Wheeler, D.B. Brough, T. Fast, S.R. Kalidindi and A. Reid, PyMKS: Materials Knowledge System in Python (2014).

  49. I. Jolliffe, Science 30, 487 (2002).

    Google Scholar 

  50. C. Suh, A. Rajagopalan, X. Li, and K. Rajan, Data Sci. J. 1, 19 (2002).

    Google Scholar 

  51. A. Mackenzie, J. Hancock, and D. Brown, Eng. Fract. Mech. 9, 167 (1977).

    Google Scholar 

  52. F.A. McClintock, Int. J. Fract. Mech. 4, 101 (1968).

    Google Scholar 

  53. G. Mirone, Eng. Fract. Mech. 74, 1203 (2007).

    Google Scholar 

  54. V. Tvergaard and A. Needleman, Acta Metall. 32, 157 (1984).

    Google Scholar 

  55. Y. Bao and T. Wierzbicki, Int. J. Mech. Sci. 46, 81 (2004).

    Google Scholar 

  56. P. Virtanen, R. Gommers, T.E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S.J. van der Walt, M. Brett, J. Wilson, K.J. Millman, N. Mayorov, A.R.J. Nelson, E. Jones, R. Kern, E. Larson, C.J. Carey, İ. Polat, Y. Feng, E.W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E.A. Quintero, C.R. Harris, A.M. Archibald, A.H. Ribeiro, F. Pedregosa, P. van Mulbregt, A. Vijaykumar, A.P. Bardelli, A. Rothberg, A. Hilboll, A. Kloeckner, A. Scopatz, A. Lee, A. Rokem, C.N. Woods, C. Fulton, C. Masson, C. Häggström, C. Fitzgerald, D.A. Nicholson, D.R. Hagen, D.V. Pasechnik, E. Olivetti, E. Martin, E. Wieser, F. Silva, F. Lenders, F. Wilhelm, G. Young, G.A. Price, G.-L. Ingold, G.E. Allen, G.R. Lee, H. Audren, I. Probst, J.P. Dietrich, J. Silterra, J.T. Webber, J. Slavič, J. Nothman, J. Buchner, J. Kulick, J.L. Schönberger, J.V. de Miranda Cardoso, J. Reimer, J. Harrington, J.L.C. Rodríguez, J. Nunez-Iglesias, J. Kuczynski, K. Tritz, M. Thoma, M. Newville, M. Kümmerer, M. Bolingbroke, M. Tartre, M. Pak, N.J. Smith, N. Nowaczyk, N. Shebanov, O. Pavlyk, P.A. Brodtkorb, P. Lee, R.T. McGibbon, R. Feldbauer, S. Lewis, S. Tygier, S. Sievert, S. Vigna, S. Peterson, S. More, T. Pudlik, T. Oshima, T.J. Pingel, T.P. Robitaille, T. Spura, T.R. Jones, T. Cera, T. Leslie, T. Zito, T. Krauss, U. Upadhyay, Y.O. Halchenko, Y. Vázquez-Baeza and C. SciPy, Nat. Methods 17(3), 261 (2020).

  57. I. Goodfellow, Y. Bengio, and A. Courville, Deep Learning (Cambridge: The MIT Press, 2016).

    MATH  Google Scholar 

  58. T.M. Mitchell, Machine Learning (New York: McGrawHill, 1997), pp. 96–97.

    MATH  Google Scholar 

  59. A. Paszke, S. Gross, F. Massa, A. Lerer, J. Bradbury, G. Chanan, T. Killeen, Z. Lin, N. Gimelshein, L. Antiga, A. Desmaison, A. Köpf, E. Yang, Z. DeVito, M. Raison, A. Tejani, S. Chilamkurthy, B. Steiner, L. Fang, J. Bai, and S. Chintala, PyTorch: An Imperative Style, High-Performance Deep Learning Library (2019), pp. 8024–8035.

  60. S. Kullback and R.A. Leibler, Ann. Math. Stat. 22, 79 (1951).

    Google Scholar 

  61. K. Hibbitt, ABAQUS/Standard User’s Manual (Hibbitt: Karlsson & Sorensen, 2001).

    Google Scholar 

  62. A. Castillo and S.R. Kalidindi, Front. Mater. 6, 169 (2019).

    Google Scholar 

  63. A.R. Castillo and S.R. Kalidindi, Meccanica (2020). https://doi.org/10.1007/s11012-020-01154-w.

  64. Y.C. Yabansu, A. Iskakov, A. Kapustina, S. Rajagopalan, and S.R. Kalidindi, Acta Mater. 178, 45 (2019).

Download references

Acknowledgements

The authors gratefully acknowledge support from ONR N00014-18-1-2879.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Surya R. Kalidindi.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Venkatraman, A., Montes de Oca Zapiain, D. & Kalidindi, S.R. Reduced-Order Models for Ranking Damage Initiation in Dual-Phase Composites Using Bayesian Neural Networks. JOM 72, 4359–4369 (2020). https://doi.org/10.1007/s11837-020-04387-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11837-020-04387-y

Navigation