Mathematical Models and Computer Simulations

, Volume 8, Issue 5, pp 557–567 | Cite as

Numerical simulation of the failure of composite materials by using the grid-characteristic method

  • K. A. Beklemysheva
  • A. V. Vasyukov
  • A. S. Ermakov
  • I. B. Petrov
Article
  • 16 Downloads

Abstract

This is an overview of the existing criteria of the failure of the composite materials and of the results of the application of some of them to simulate a low-speed hit on the composition material for the three-dimensional statement of the problem. Simulation is made by means of the grid-characteristic method. Reasons are given for the selection of specific criteria and they are compared with each other.

Keywords

mathematical simulation parallel algorithms grid-characteristic method composition materials failure of composites 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    M. J. Hinton, A. S. Kaddour, and P. D. Soden, Failure Criteria in Fibre Reinforced Polymer Composites: The World-Wide Failure Exercise (Elsevier, Amsterdam, London, 2004).Google Scholar
  2. 2.
    M. J. Hinton and A. S. Kaddour, “Maturity of 3D failure criteria for fibre-reinforced composites: comparison between theories and experiments: Part B of WWFE-II,” J. Compos. Mater., No. 7, 925–966 (2013).Google Scholar
  3. 3.
    W. Nowacki, Theory of Elasticity (PWN, Warsaw, 1970; Mir, Moscow, 1970).MATHGoogle Scholar
  4. 4.
    L. I. Sedov, Mechanics of Continuous Media (Nauka, Moscow, 1970; World Scientific, Singapore, 1996), Vol. 1.Google Scholar
  5. 5.
    R. P. Fedorenko, Introduction to Computational Physics (Mosk. Fiz. Tekh. Inst., Moscow, 1994) [in Russian].Google Scholar
  6. 6.
    F. B. Chelnokov, “Explicit expression of grid-characteristic schemes for elasticity equations in 2D and 3D,” Mat. Model. 18 (6), 96–108 (2006).MathSciNetMATHGoogle Scholar
  7. 7.
    K. M. Magomedov and A. S. Kholodov, Grid-Characteristic Numerical Methods (Nauka, Moscow, 1988) [in Russian].MATHGoogle Scholar
  8. 8.
    I. B. Petrov and A. V. Favorskaya, “Library of high order interpolation methods on unstructured triangular and tetrahedral meshes,” Inform. Tekhnol., No. 9, 30–32 (2011).Google Scholar
  9. 9.
    P. I. Agapov, O. M. Belotserkovskii, and I. B. Petrov, “Numerical simulation of the consequences of a mechanical action on a human brain under a skull injury,” Comput. Math. Math. Phys. 46, 1629–1638 (2006).MathSciNetCrossRefGoogle Scholar
  10. 10.
    O. M. Belotserkovskii, Numerical Simulation in Continuous Media Mechanics (Nauka, Moscow, 1984) [in Russian].Google Scholar
  11. 11.
    K. A. Beklemysheva, I. B. Petrov, and A. V. Favorskaya, “Numerical simulation of processes in solid deformable media in the presence of dynamic contacts using the grid-characteristic method,” Math. Mod. Comput. Simul. 6, 294–304 (2014).CrossRefGoogle Scholar
  12. 12.
    A. A. Il’yushin, Plasticity (Gostekhizdat, Moscow, 1948) [in Russian].MATHGoogle Scholar
  13. 13.
    R. Hill, “A theory of the yielding and plastic flow of anisotropic metals,” Proc. R. Soc. London A 193, 281–297 (1948).MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    S. W. Tsai and E. M. Wu, “A general theory of strength for anisotropic materials,” J. Compos. Mater. 5, 58–80 (1971).CrossRefGoogle Scholar
  15. 15.
    R. Hill, “Theoretical plasticity of textured aggregates,” Math. Proc. Cambridge Philos. Soc., No. 85, 179–191 (1979).MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    S. Abrate, “Criteria for yielding or failure of cellular materials,” J. Sandwich Struct. Mater. 10, 5–51 (2008).CrossRefGoogle Scholar
  17. 17.
    F. Barlat and O. Cazacu, “Generalization of Drucker’s yield criterion to orthotropy,” Math. Mech. Solids 6, 613–630 (2001).CrossRefMATHGoogle Scholar
  18. 18.
    Y. Huang, C. Liu, and M. G. Stout, “On the asymmetric yield surface of plastically orthotropic materials: a phenomenological study,” Acta Mater. 45, 2397–2406 (1997).CrossRefGoogle Scholar
  19. 19.
    Z. Hashin and A. Rotem, “A fatigue failure criterion for fiber reinforced materials,” J. Compos. Mater. 7, 448–464 (1973).CrossRefGoogle Scholar
  20. 20.
    R. C. Batra, G. Gopinath, and J. Q. Zheng, “Damage and failure in low energy impact of fiber-reinforced polymeric composite laminates,” Compos. Struct. 94, 540–547 (2012).CrossRefGoogle Scholar
  21. 21.
    A. Puck and W. Schneider, “On failure mechanisms and failure criteria of filament-wound glass-fibre/resin composites,” Plast. Polym. 37, 33–42 (1969).Google Scholar
  22. 22.
    A. Puck and H. Schurmann, “Failure analysis of FRP laminates by means of physically based phenomenological models,” Compos. Sci. Technol. 62, 1633–1662 (2002).CrossRefGoogle Scholar
  23. 23.
    A. Elmarakbi, H. Fukunaga, H. Wang, and Y. Zemba, “Stable numerical simulations of propagations of complex damages in composite structures under transverse loads,” Compos. Sci. Technol. 67, 752–765 (2007).CrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  • K. A. Beklemysheva
    • 1
  • A. V. Vasyukov
    • 1
  • A. S. Ermakov
    • 1
  • I. B. Petrov
    • 1
  1. 1.Moscow Physical-Technical InstituteMoscowRussia

Personalised recommendations