Mechanics of Composite Materials

, Volume 43, Issue 6, pp 521–534 | Cite as

Local near-surface buckling of a system consisting of an elastic (viscoelastic) substrate, a viscoelastic (elastic) bond layer, and an elastic (viscoelastic) covering layer

  • E. A. Aliyev


Within the framework of a piecewise homogenous body model and with the use of a three-dimensional linearized theory of stability (TLTS), the local near-surface buckling of a material system consisting of a viscoelastic (elastic) half-plane, an elastic (viscoelastic) bond layer, and a viscoelastic (elastic) covering layer is investigated. A plane-strain state is considered, and it is assumed that the near-surface buckling instability is caused by the evolution of a local initial curving (imperfection) of the elastic layer with time or with an external compressive force at fixed instants of time. The equations of TLTS are obtained from the three-dimensional geometrically nonlinear equations of the theory of viscoelasticity by using the boundary-form perturbation technique. A method for solving the problems considered by employing the Laplace and Fourier transformations is developed. It is supposed that the aforementioned elastic layer has an insignificant initial local imperfection, and the stability is lost if this imperfection starts to grow infinitely. Numerical results on the critical compressive force and the critical time are presented. The influence of rheological parameters of the viscoelastic materials on the critical time is investigated. The viscoelasticity of the materials is described by the Rabotnov fractional-exponential operator.


local near-surface buckling stability viscoelastic layer nanocomposite curved layer critical time initial local imperfection 


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  1. 1.
    K. Q. Xiao, L. C. Zhang, and I. Zarudi, “Mechanical and rheological properties of carbon nanotube-reinforced polyethylene composites,” Compos. Sci. Technol., 67, 77–182 (2007).CrossRefGoogle Scholar
  2. 2.
    A. N. Guz’, Fracture Mechanics of Composites in Compression [in Russian], Naukova Dumka, Kiev (1990).Google Scholar
  3. 3.
    S. D. Akbarov and A. N. Guz’, Mechanics of Curved Composites, Kluwer Academic Publisher, Dortrecht-Boston-London (2000).Google Scholar
  4. 4.
    S. D. Akbarov and A. N. Guz’, “Mechanics of curved composites and some related problems for structural members,” Mech. Adv. Mater. Struct., 11, No. 6, 445–515 (2004).CrossRefGoogle Scholar
  5. 5.
    S. D. Akbarov, T. Sismam, and N. Yahnioglu, “On the fracture of unidirectional composites in compression,” Int. J. Eng. Sci., 35, 1115–1135 (1997).CrossRefGoogle Scholar
  6. 6.
    S. D. Akbarov and R. Kosker, “Internal stability loss of two neighbouring fibers in a viscoelastic matrix,” Int. J. Eng. Sci., 42, 1847–1873 (2004).CrossRefGoogle Scholar
  7. 7.
    S. D. Akbarov and R. Tekercioglu, “Near-surface buckling instability of a system consisting of a moderately rigit substrate, a viscoelastic bond layer, and an elastic covering layer,” Mech. Compos. Mater., 42, No. 4, 363–372 (2006).CrossRefGoogle Scholar
  8. 8.
    S. D. Akbarov and R. Tekercioglu, “Surface undulation instability of the viscoelastic half-space covered with the stack of layer in bi-axial compression,” Int. J. Mech. Sci., 49, 778–789 (2007).CrossRefGoogle Scholar
  9. 9.
    S. D. Akbarov, A. Cilli, and A. N. Guz’, “The theorical strength limit in compression of viscoelastic layered composite materials,” Composites. Pt. B: Eng., 30, 365–472, (1999).CrossRefGoogle Scholar
  10. 10.
    M. A. Biot, Mechanics of Incremental Deformations, Wiley, New York (1965).Google Scholar
  11. 11.
    A. N. Guz’, Fundamentals of the Three-Dimensional Theory of Stability of Deformable Bodies, Springer-Verlag, Berlin (1999).Google Scholar
  12. 12.
    N. J. Hoff, “A surway of the theories of creep buckling,” in: Proc. Third US National Congress of the Applied Mechanics, ASME, New York (1958).Google Scholar
  13. 13.
    I. Yu. Babich, A. N. Guz’, and V. N. Chekov, “The three-dimentional theory of stability of fibrous and laminated materials,” Int. Appl. Mech., 37, No. 9, 1103–1141 (2001).CrossRefGoogle Scholar
  14. 14.
    R. A. Schapery, “Approximate method of transform inversion for viscoelastic stress analysis,” Proc. US Nat. Congr. Appl. Mech., ASME, 4, 1075–1085 (1966).Google Scholar
  15. 15.
    Yu. N. Rabotnov, Elements of Hereditary Mechanics of Solid Bodies [in Russian], Nauka, Moscow (1977)Google Scholar
  16. 16.
    A. Cilli, Fracture of the Uni-Directed Fiber-Layered Composites in Compression, PhD Thesis, The Yildiz Technical University, Istanbul (1998).Google Scholar
  17. 17.
    A. N. Guz’, “Three-dimensional theory of stability of carbon nanotube in a matrix II,” Int. Appl. Mech., 42, No. 1, 19–31 (2006).CrossRefGoogle Scholar
  18. 18.
    A. N. Guz’ and I. A. Guz’, “On models in the theory of stability of multiwalled carbon nanotubes in matrix,” Int. Appl. Mech., 42, No. 6, 617–628 (2006).CrossRefGoogle Scholar
  19. 19.
    Ya. A. Zhuk and I. A. Guz’, “Influence of prestress on the velocities of waves propagating normally to the layers of nanocomposites,” Int. Appl. Mech., 42, No. 7, 729–743 (2006).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • E. A. Aliyev
    • 1
  1. 1.Faculty of Arts and Sciences, Department of Physics, Esentepe CampusSakarya UniversitySakaryaTurkey

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