Skip to main content
SpringerLink
Log in

Yield Loci of Reinforced Plates Made from Rigid-Plastic Unequiresistant Materials Considering the Two-Dimensional Stress State in Fibers II. Orthogonal Reinforcement1

  • Published:
Mechanics of Composite Materials Aims and scope

Structural models of hybrid fiber composites orthogonally reinforced in the plane are constructed. They allow one to calculate the yield loci taking into account the plane stress state in all composition components with different tensile and compressive yield stresses. Materials of the components are homogeneous and isotropic, and their mechanical behavior is described by the associated flow rule for a rigid-plastic body with the piecewise linear yield criteria of Johansen, Hu, and Tresca–Hu types. The fibers are located along the directions of principal stresses in the reinforced body. Analytical expressions for the equations of regimes on the yield loci of the composition are obtained, which can be used further in practical calculations. Different limit processes, from orthogonally reinforced composites to unidirectional reinforced ones and from fibrous media to homogeneous ones, are analyzed. It is proved that the plastic flow in a reinforced medium is associated with the yield loci constructed for it. The yield loci obtained for the composition are compared with those determined on the basis of the structural model with a one-dimensional stress state in fibers.

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
Fig. 4

Similar content being viewed by others

References

  1. T. P. Romanova and A. P. Jankovskii, “Yield loci of reinforced plates made from rigid-plastic unequiresistant materials considering the two-dimensional stress state in fibers. I. Unidirectional reinforcement,” Mech. Compos. Mater., 55, No. 6, 699−714 (2019). DOI: https://doi.org/https://doi.org/10.1007/s11029-020-09845-x

  2. A. Mishchenko and Yu. Nemirovsky, Structurally Ihomogeneous Profiled Rod Systems. Methods of Rational and Optimum Design, Palmarium Academic Publishing, Saarbrucken (2016).

  3. A. P. Jankovskii, “Modelling of the elastoplastic dynamics of longitudinally reinforced wall beams based on a timeexplicit central difference method,” J. Appl.Math and Mech., 81, No. 1, 36–51 (2017).

    Article  Google Scholar 

  4. Composite Materials. Handbook. Ed. D. M. Karpinos [in Russian], Naukova Dumka, Kiev (1985).

    Google Scholar 

  5. Handbook of Composites. Vol. 1., ed. J. Lubin, Van Nostrand Reinhold Company, N.Y. (1982).

  6. Composite Materials. Handbook, eds. V. V. Vasilyev and Yu. M. Tarnopol’skii [in Russian], Mashinostroenie, Moscow (1990).

  7. Yu. Nemirovsky, “On the condition of plasticity (strength) for a reinforced layer,” Prikl. Mekh. and Tekhn. Fiz., No. 5, 81–88 (1969).

  8. Yu. V. Nemirovsky and B. S. Resnikov, “On limit equilibrium of reinforced slabs and effectiveness of their reinforcemen,” Arch. Inż. Ląd., No. 1, 57–67 (1975).

  9. Z. Mróz and F. G. Shamiev, “Simplified yield condition for fiber-reinforced plates and shells,” Arch. Inż. Ląd., 25, No. 3, 463–476 (1979).

    Google Scholar 

  10. T. P. Romanova and A. P. Jankovskii, “Constructing yield loci for rigid-plastic reinforced plates considering the 2D stress state in fibers,” Mech. Compos. Mater., 54, No. 6, 697−718 (2018). DOI: https://doi.org/https://doi.org/10.1007/s11029-019-9777-5

  11. H. G. Hopkins, “Some remarks concerning of the solution of plastic plate problems upon the yield criterion,” Proc. 9th Inter. Cong. Appl. Mech., 6, 448–457 (1957).

  12. L. W. Hu, “Modified Tresks’s yield condition and associated flow rules for anisotropic materials and applications,” J. Franclin Inst., 265, No. 3, 187–204 (1958).

    Article  Google Scholar 

  13. Ya. Lellep, “Pulsed loading of circular plates, whose material has different yield limits in tension and compression,” Uch. Zap. Tartu Gos. Univ., No. 281, 261–269 (1971).

  14. Yu. P. Listratova and N. I. Mokashova, “On the limit equilibrium of structures made from materials with different yield stresses in tension and compression,” Izv. AN SSSR, Mekh. Tverd. Tela, No. 6, 81–85 (1967).

  15. Yu. P. Listratova, V. N. Potapov, and M. A. Rudis, “Limit equilibrium of shells of revolution made from material with different yield stresses in tension and compression,” Izv. AN SSSR, Mekh. Tverd. Tela, No. 1, 141–145 (1969).

  16. K. A. Matveev and N. V. Pustovoi, Variational Methods for Investigating the Stability of Anisotropic Plates at Thermal-Force Loading, Izd. NGTU, Novosibirsk (2005).

    Google Scholar 

  17. T. P. Romanova, “Modeling the dynamic bending of rigid-plastic hybrid composite elliptical plates with a rigid insert,” Mech. Compos. Mater., 53, No. 5, 564–578 (2017).

    Article  Google Scholar 

  18. D. Kolarov, A. Baltov, and N. Boncheva, Mechanics of Plastic Media [in Russian], Mir, Moscow, (1979).

    Google Scholar 

  19. G. I. Bykovtsev and D. D. Ivlev, Theory of Plasticity [in Russian], Dal’nauka, Vladivostok (1998).

    Google Scholar 

  20. N. V. Baninchuk, V. V. Kobelev, and R. B. Rikards, Optimization of Structural Members from Composite Materials [in Russian], Mashinostroenie, Moscow (1988).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. S. A. Khristianovich Institute of Theoretical and Applied Mechanics of the Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

    T. P. Romanova & A. P. Yankovskii

Authors
  1. T. P. Romanova
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. P. Yankovskii
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to T. P. Romanova.

Additional information

1For report 1, see [1]

Translated from Mekhanika Kompozitnykh Materialov, Vol. 56, No. 3, pp. 457-478, May-June, 2020.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Romanova, T.P., Yankovskii, A.P. Yield Loci of Reinforced Plates Made from Rigid-Plastic Unequiresistant Materials Considering the Two-Dimensional Stress State in Fibers II. Orthogonal Reinforcement1. Mech Compos Mater 56, 303–318 (2020). https://doi.org/10.1007/s11029-020-09882-6

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11029-020-09882-6

Keywords

Search

Navigation