Skip to main content
SpringerLink
Log in

Multiscale Statistical Model of Progressive Failure in Random Heterogeneous Media

  • Conference paper
  • First Online:
Proceedings of the 1st International Conference on Numerical Modelling in Engineering (NME 2018)

Part of the book series: Lecture Notes in Mechanical Engineering ((LNME))

Included in the following conference series:

  • 825 Accesses

Abstract

The analysis of mechanical behavior of structurally heterogeneous media keeps bringing up challenges due to development of new multiphase materials. Many theoretical and experimental studies had proven that microstructural features of heterogeneous materials significantly influence distributions of local stress and strain fields as well as processes of failure initiation and propagation. Thus, it is necessary to take into account multi-particle interactions of the components and contribution of each of them to the effective strength characteristics. One of the directions in the micromechanics of materials with random structure is related to the methods and tools of statistical analysis. They consider the representative volume element (RVE) of a material as a random system and allow to take into account interactions within the particles and to investigate distributions of stress and strain fields in each phase of material from the analytical point of view. Within such framework, the failure probability can be assessed on the basis of the statistical representation of the failure criteria. This work presents the approach for restoration of distribution of stress and strain fields in representative volume element of heterogeneous media and its constituents. The techniques for estimation of parameters of distribution laws are described. The statistical model of progressive failure is presented and illustrated with some numerical results and comparisons for particular case studies.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
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

References

  1. Sheidaei, A., Baniassadi, M., Banu, M., Askeland, P., Pahlavanpour, M., Kuuttila, N., Pourboghrat, F., Drzal, L.T., Garmestani, H.: 3-D microstructure reconstruction of polymer nano-composite using FIB-SEM and statistical correlation function. Compos. Sci. Technol. 80, 47–54 (2013). https://doi.org/10.1016/j.compscitech.2013.03.001

    Article  Google Scholar 

  2. Yeong, C., Torquato, S.: Reconstructing random media. II. Three-dimensional media from two-dimensional cuts. Phys. Rev. E 58, 224–233 (1998). https://doi.org/10.1103/PhysRevE.58.224

    Article  MathSciNet  Google Scholar 

  3. Baniassadi, M., Mortazavi, B., Hamedani, H.A., Garmestani, H., Ahzi, S., Fathi-Torbaghan, M., Ruch, D., Khaleel, M.: Three-dimensional reconstruction and homogenization of heterogeneous materials using statistical correlation functions and FEM. Comput. Mater. Sci. 51, 372–379 (2012). https://doi.org/10.1016/j.commatsci.2011.08.001

    Article  Google Scholar 

  4. Jiao, Y., Stillinger, F.H., Torquato, S.: Modeling heterogeneous materials via two-point correlation functions. II. Algorithmic details and applications. Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 77, 1–15 (2008). https://doi.org/10.1103/PhysRevE.77.031135

    Article  MathSciNet  Google Scholar 

  5. Liu, K.C., Ghoshal, A.: Validity of random microstructures simulation in fiber-reinforced composite materials. Compos. Part B Eng. 57, 56–70 (2014). https://doi.org/10.1016/j.compositesb.2013.08.006

    Article  Google Scholar 

  6. Hyun, S., Torquato, S.: Designing composite microstructures with targeted properties. J. Mater. Res. 16, 280–285 (2001). https://doi.org/10.1557/JMR.2001.0042

    Article  Google Scholar 

  7. Kpobie, W., Ben Khlifa, S., Bonfoh, N., Fendler, M., Lipinski, P.: Multi-site micromechanical modelling of thermo-elastic properties of heterogeneous materials. Compos. Struct. 94, 2068–2077 (2012). https://doi.org/10.1016/j.compstruct.2012.01.014

    Article  Google Scholar 

  8. Aboudi, J., Arnold, S.M., Bednarcyk, B.A.: The generalized method of cells micromechanics (2013)

    Chapter  Google Scholar 

  9. Torquato, S.: Optimal design of heterogeneous materials. Annu. Rev. Mater. Res. 40, 101–129 (2010). https://doi.org/10.1146/annurev-matsci-070909-104517

    Article  Google Scholar 

  10. Melro, A.R., Camanho, P.P., Pinho, S.T.: Influence of geometrical parameters on the elastic response of unidirectional composite materials. Compos. Struct. 94, 3223–3231 (2012). https://doi.org/10.1016/j.compstruct.2012.05.004

    Article  Google Scholar 

  11. Yu, M., Zhu, P., Ma, Y.: Effects of particle clustering on the tensile properties and failure mechanisms of hollow spheres filled syntactic foams: a numerical investigation by microstructure based modeling. Mater. Des. 47, 80–89 (2013). https://doi.org/10.1016/j.matdes.2012.12.004

    Article  Google Scholar 

  12. Matveeva, A.Y., Pyrlin, S.V., Ramos, M.M.D., Böhm, H.J., Van Hattum, F.W.J.: Influence of waviness and curliness of fibres on mechanical properties of composites. Comput. Mater. Sci. 87, 1–11 (2014). https://doi.org/10.1016/j.commatsci.2014.01.061

    Article  Google Scholar 

  13. Rasool, A., Böhm, H.J.: Effects of particle shape on the macroscopic and microscopic linear behaviors of particle reinforced composites. Int. J. Eng. Sci. 58, 21–34 (2012). https://doi.org/10.1016/j.ijengsci.2012.03.022

    Article  MATH  Google Scholar 

  14. Le Cam, L., Lo Yang, G.: Asymptotics in Statistics: Some Basic Concepts (2000)

    Google Scholar 

  15. Kroener, E.: Statistical modelling. In: Modelling Small Deformations of Polycrystals, pp. 229–291. Springer, Dordrecht (1986)

    Google Scholar 

  16. Fullwood, D.T., Niezgoda, S.R., Adams, B.L., Kalidindi, S.R.: Microstructure sensitive design for performance optimization. Prog. Mater. Sci. 55, 477–562 (2010). https://doi.org/10.1016/j.pmatsci.2009.08.002

    Article  Google Scholar 

  17. Tashkinov, M.: Micro-scale modeling of phase-level elastic fields of SiC reinforced metal matrix multiphase composites using statistical approach. Comput. Mater. Sci. 116, 113–121 (2016). https://doi.org/10.1016/j.commatsci.2015.10.047

    Article  Google Scholar 

  18. Buryachenko, V.A.: Micromehcanics of Heterogenous Materials. Springer, Boston (2007)

    Book  Google Scholar 

  19. Xu, X.F., Chen, X., Shen, L.: A Green-function-based multiscale method for uncertainty quantification of finite body random heterogeneous materials. Comput. Struct. 87, 1416–1426 (2009). https://doi.org/10.1016/j.compstruc.2009.05.009

    Article  Google Scholar 

  20. Chen, E.L., Ang, W.T.: Green’s functions and boundary element analysis for bimaterials with soft and stiff planar interfaces under plane elastostatic deformations. Eng. Anal. Bound. Elem. 40, 50–61 (2014). https://doi.org/10.1016/j.enganabound.2013.11.014

    Article  MathSciNet  MATH  Google Scholar 

  21. Beran, M.J., McCoy, J.J.: Mean field variations in a statistical sample of heterogeneous linearly elastic solids. Int. J. Solids Struct. 6, 1035–1054 (1970). https://doi.org/10.1016/0020-7683(70)90046-6

    Article  MATH  Google Scholar 

  22. Kanouté, P., Boso, D.P., Chaboche, J.L., Schrefler, B.A.: Multiscale methods for composites: a review. Arch. Comput. Methods Eng. 16, 31–75 (2009). https://doi.org/10.1007/s11831-008-9028-8

    Article  MATH  Google Scholar 

Download references

Acknowledgements

This work was supported by the Grant of the President of Russian Federation for state support of young Russian scientists (MK-2395.2017.1) and by the Russian Foundation for Basic Research (project 16-01-00327_a).

Author information

Authors and Affiliations

  1. Perm National Research Polytechnic University, Komsomolsky Avenue 29, 614990, Perm, Russia

    Mikhail Tashkinov

Authors
  1. Mikhail Tashkinov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mikhail Tashkinov .

Editor information

Editors and Affiliations

  1. Faculty of Engineering and Architecture, Ghent University, Laboratory Soete, Ghent, Belgium

    Magd Abdel Wahab

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Tashkinov, M. (2019). Multiscale Statistical Model of Progressive Failure in Random Heterogeneous Media. In: Abdel Wahab, M. (eds) Proceedings of the 1st International Conference on Numerical Modelling in Engineering . NME 2018. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-13-2273-0_10

Download citation

  • DOI: https://doi.org/10.1007/978-981-13-2273-0_10

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-13-2272-3

  • Online ISBN: 978-981-13-2273-0

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation