Skip to main content

A Data-Driven Multiscale Theory for Modeling Damage and Fracture of Composite Materials

  • Chapter
  • First Online:
Meshfree Methods for Partial Differential Equations IX (IWMMPDE 2017)

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 129))

Abstract

The advent of advanced processing and manufacturing techniques has led to new material classes with complex microstructures across scales from nanometers to meters. In this paper, a data-driven computational framework for the analysis of these complex material systems is presented. A mechanistic concurrent multiscale method called Self-consistent Clustering Analysis (SCA) is developed for general inelastic heterogeneous material systems. The efficiency of SCA is achieved via data compression algorithms which group local microstructures into clusters during the training stage, thereby reducing required computational expense. Its accuracy is guaranteed by introducing a self-consistent method for solving the Lippmann–Schwinger integral equation in the prediction stage. The proposed framework is illustrated for a composite cutting process where fracture can be analyzed simultaneously at the microstructure and part scales.

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

Access this chapter

eBook
USD 19.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 29.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 29.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Z.P. Bažant, M. Jirásek, Nonlocal integral formulations of plasticity and damage: survey of progress. J. Eng. Mech. 128(11), 1119–1149 (2002)

    Article  Google Scholar 

  2. M.A. Bessa, R. Bostanabad, Z. Liu, A. Hu, D.W. Apley, C. Brinson, W. Chen, W.K. Liu, A framework for data-driven analysis of materials under uncertainty: countering the curse of dimensionality. Comput. Methods Appl. Mech. Eng. 320, 633–667 (2017)

    Article  MathSciNet  Google Scholar 

  3. H. Cheng, J. Gao, O.L. Kafka, K. Zhang, B. Luo, W.K. Liu, A micro-scale cutting model for ud cfrp composites with thermo-mechanical coupling. Compos. Sci. Technol. 153, 18–31 (2017)

    Article  Google Scholar 

  4. F. Chinesta, A. Leygue, F. Bordeu, J.V. Aguado, E. Cueto, D. Gonzalez, I. Alfaro, A. Ammar, A. Huerta, PGD-based computational vademecum for efficient design, optimization and control. Arch. Comput. Methods Eng. 20(1), 31–59 (2013)

    Article  MathSciNet  Google Scholar 

  5. O. Goury, D. Amsallem, S.P.A. Bordas, W.K. Liu, P. Kerfriden, Automatised selection of load paths to construct reduced-order models in computational damage micromechanics: from dissipation-driven random selection to Bayesian optimization. Comput. Mech. 58(2), 213–234 (2016)

    Article  MathSciNet  Google Scholar 

  6. J.A. Hernández, J. Oliver, A.E. Huespe, M.A. Caicedo, J.C. Cante, High-performance model reduction techniques in computational multiscale homogenization. Comput. Methods Appl. Mech. Eng. 276, 149–189 (2014)

    Article  MathSciNet  Google Scholar 

  7. D. Iliescu, D. Gehin, I. Iordanoff, F. Girot, M.E. Gutiérrez, A discrete element method for the simulation of CFRP cutting. Compos. Sci. Technol. 70(1), 73–80 (2010)

    Article  Google Scholar 

  8. W.J. Joost, Reducing vehicle weight and improving U.S. energy efficiency using integrated computational materials engineering. JOM 64(9), 1032–1038 (2012)

    Article  Google Scholar 

  9. M. Kabel, T. Böhlke, M. Schneider, Efficient fixed point and Newton–Krylov solvers for FFT-based homogenization of elasticity at large deformations. Comput. Mech. 54(6), 1497–1514 (2014)

    Article  MathSciNet  Google Scholar 

  10. Z. Liu, M.A. Bessa, W.K. Liu, Self-consistent clustering analysis: an efficient multi-scale scheme for inelastic heterogeneous materials. Comput. Methods Appl. Mech. Eng. 306, 319–341 (2016)

    Article  MathSciNet  Google Scholar 

  11. Z. Liu, M. Fleming, W.K. Liu, Microstructural material database for self-consistent clustering analysis of elastoplastic strain softening materials. Comput. Methods Appl. Mech. Eng. 330, 547–577 (2018)

    Article  MathSciNet  Google Scholar 

  12. J. Macqueen, Some methods for classification and analysis of multivariate observations, in Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, vol. 1 (University of California Press, Berkeley, 1967), pp. 281–297

    Google Scholar 

  13. K. Matouš, M.G.D. Geers, V.G. Kouznetsova, A. Gillman, A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials. J. Comput. Phys. 330, 192–220 (2017)

    Article  MathSciNet  Google Scholar 

  14. A.R. Melro, P.P. Camanho, F.M.A. Pires, S.T. Pinho, Micromechanical analysis of polymer composites reinforced by unidirectional fibres: Part I–constitutive modelling. Int. J. Solids Struct. 50(11), 1897–1905 (2013)

    Article  Google Scholar 

  15. H. Moulinec, P. Suquet, A numerical method for computing the overall response of nonlinear composites with complex microstructure. Comput. Methods Appl. Mech. Eng. 157(1–2), 69–94 (1998)

    Article  MathSciNet  Google Scholar 

  16. J.H. Panchal, S.R. Kalidindi, D.L. McDowell, Key computational modeling issues in integrated computational materials engineering. Comput. Aided Des. 45(1), 4–25 (2013)

    Article  Google Scholar 

  17. J. Smith, W. Xiong, W. Yan, S. Lin, P. Cheng, O.L. Kafka, G.J. Wagner, J. Cao, W.K. Liu, Linking process, structure, property, and performance for metal-based additive manufacturing: computational approaches with experimental support. Comput. Mech. 57(4), 583–610 (2016)

    Article  Google Scholar 

Download references

Acknowledgements

Modesar Shakoor and Wing Kam Liu warmly thank the support from National Institute of Standards and Technology and Center for Hierarchical Materials Design (CHiMaD) under grant No. 70NANB13Hl94 and 70NANB14H012. Jiaying Gao and Wing Kam Liu warmly thank the support from DOECF-ICME project under grant No. DE-EE0006867. Zeliang Liu would like to thank Dr. John O. Hallquist of LSTC for his support.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Wing Kam Liu .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Shakoor, M., Gao, J., Liu, Z., Liu, W.K. (2019). A Data-Driven Multiscale Theory for Modeling Damage and Fracture of Composite Materials. In: Griebel, M., Schweitzer, M. (eds) Meshfree Methods for Partial Differential Equations IX. IWMMPDE 2017. Lecture Notes in Computational Science and Engineering, vol 129. Springer, Cham. https://doi.org/10.1007/978-3-030-15119-5_8

Download citation

Publish with us

Policies and ethics