Skip to main content
SpringerLink
Log in

Stress Concentration Near Stiff Cylindrical Inclusions under Anti-Plane Shear Loading

  • MECHANICS
  • Published:
Doklady Physics Aims and scope Submit manuscript

Abstract

Analytical solutions for the problems of stress concentration near cylindrical inclusion with circular or elliptical cross section under the anti-plane shear loading are presented. The solutions are obtained in the framework of the isotropic strain gradient elasticity theory with the assumption of high stiffness of the inclusions as compared to the matrix, which corresponds to the typical properties of the fiber-reinforced composite materials. It is shown that near the thin fibers, diameter of which is comparable to the characteristic size of the matrix microstructure, the stress concentration can decrease in comparison with conventional estimates known in the theory of elasticity. For circular cylindrical inclusions, the closed-form solutions are obtained for composites with low volume fraction of inclusions and can be used for the strength prediction of composites under the longitudinal shear and for the identification of additional parameters of the strain gradient theory of elasticity.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.

Similar content being viewed by others

REFERENCES

  1. V. V. Vasiliev and E. V. Morozov, Advanced Mechanics of Composite Materials and Structural Elements (Newnes, 2013).

    Google Scholar 

  2. S. S. Vel and R. C. Batra, J. Sound Vibr. 272, 703 (2004).

  3. J. Aboudi, Mechanics of Composite Materials: A Unified Micromechanical Approach (Elsevier, Amsterdam, 2013).

    MATH  Google Scholar 

  4. R. D. Mindlin, Arch. Ration. Mech. Anal. 16, 51 (1964).

    Article  Google Scholar 

  5. F. Dell’Isola, G. Sciarra, and S. Vidoli, Proc. R. Soc. A 465 (2107), 2177 (2009).

    Article  ADS  Google Scholar 

  6. S. Lurie et al., Comput. Mater. Sci. 116, 62 (2016).

    Article  Google Scholar 

  7. S. Lurie et al., J. Mater. Sci. 41, 6693 (2006).

    Article  ADS  Google Scholar 

  8. Y. Solyaev, S. Lurie, and V. Korolenko, Eur. J. Mech. A 78, 103853 (2019).

    Article  Google Scholar 

  9. E. V. Lomakin, S. A. Lurie, L. N. Rabinskiy, and Y. O. Solyaev, Dokl. Phys. 63, 161 (2018).

    Article  ADS  Google Scholar 

  10. Q. Zhang et al., RSC Adv. 5, 25208 (2015).

    Article  ADS  Google Scholar 

  11. H. M. Shodja and B. Alemi, Composites, Part B 117, 150 (2017). https://doi.org/10.1016/j.compositesb.2017.02.044

    Article  Google Scholar 

  12. S. Lurie, Y. Solyaev, and K. Shramko, Mech. Mater. 122, 133 (2018).

    Article  Google Scholar 

  13. Y. Solyaev, S. Lurie, and N. Semenov, J. Appl. Phys. 128, 035102 (2020). https://doi.org/10.1063/5.0014288

    Article  ADS  Google Scholar 

  14. S. Lurie et al., Int. J. Eng. Sci. 49, 1517 (2011).

    Article  Google Scholar 

  15. M. Abramowitz, I.A. Stegun, eds. Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables (Nation. Bureau of Standards, New York, 1964).

Download references

Funding

This study was supported by the Russian Foundation for Basic Research, project no. 18-31-20043.

Author information

Authors and Affiliations

  1. Moscow State University, 119899, Moscow, Russia

    E. V. Lomakin

  2. Moscow Aviation Institute (National Research University), 125080, Moscow, Russia

    E. V. Lomakin, S. A. Lurie, L. N. Rabinskiy & Y. O. Solyaev

  3. Institute of Applied Mechanics, Russian Academy of Sciences, 117312, Moscow, Russia

    S. A. Lurie & Y. O. Solyaev

Authors
  1. E. V. Lomakin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. A. Lurie
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. L. N. Rabinskiy
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Y. O. Solyaev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to E. V. Lomakin.

Additional information

Translated by V. Bukhanov

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lomakin, E.V., Lurie, S.A., Rabinskiy, L.N. et al. Stress Concentration Near Stiff Cylindrical Inclusions under Anti-Plane Shear Loading. Dokl. Phys. 65, 390–395 (2020). https://doi.org/10.1134/S1028335820110063

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1028335820110063

Keywords:

Search

Navigation